steam - its generation and use - 41st edition
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The document is the 41st edition of 'Steam: Its Generation and Use', published by the Babcock & Wilcox Company, providing comprehensive information on steam generation, including technology advancements and applications in various industries. It includes technical details on steam fundamentals, combustion principles, environmental protections, and operational practices, reflecting a long-standing engineering tradition. The document serves as a key resource for professionals in the field, underscoring the importance of efficiency and environmental considerations in power generation.
![1-4 Steam 41 / Steam Generation – An Overview
The Babcock & Wilcox Company
cause the steam-water mixture (B-C) to move upward
into the steam drum. The rate of water flow or circula-
tion depends upon the difference in average density be-
tween the unheated water and the heated steam-wa-
ter mixture.
The total circulation rate in a natural circulation
systemdependsprimarilyuponfourfactors:1)theheight
of the boiler, 2) the operating pressure, 3) the heat in-
put rate, and 4) the free flow areas of the components.
Taller boilers result in a larger total pressure difference
betweentheheatedandunheatedlegsandthereforecan
produce larger total flow rates. Higher operating pres-
sures provide higher density steam and higher density
steam-watermixtures.Thisreducesthetotalweightdif-
ferencebetweentheheatedandunheatedsegmentsand
tends to reduce flow rate. Higher heat input typically
increases the amount of steam in the heated segments
and reduces the average density of the steam-water
mixture, increasing total flow rate. An increase in the
cross-sectional (free flow) areas for the water or steam-
water mixtures may increase the circulation rate. For
each unit of steam produced, the amount of water en-
tering the tube can vary from 3 to 25 units.
Forced or pumped circulation is illustrated in Fig.
8b.Amechanical pump is added to the simple flow loop
and the pressure difference created by the pump con-
trols the water flow rate.
The steam-water separation in the drum requires
careful consideration. In small, low pressure boilers,
steam-water separation can be easily accomplished
with a large drum approximately half full of water.
Natural gravity steam-water separation (similar to a
kettle) can be sufficient. However, in today’s high ca-
pacity, high pressure units, mechanical steam-water
separators are needed to economically provide mois-
ture-free steam from the drum. With such devices in-
stalled in the drum, the vessel diameter and cost can
be significantly reduced.
At very high pressures, a point is reached where
water no longer exhibits boiling behavior. Above this
critical pressure [3200.11 psi (22.1 MPa)], the water
temperature continuously increases with heat addi-
tion. Steam generators can be designed to operate at
pressures above this critical pressure. Drums and
steam-water separation are no longer required and
the steam generator operates effectively on the once-
through principle.
There are a large number of design methods used to
evaluate the expected flow rate for a specific steam
generator design and set of operating conditions. In
addition, there are several criteria which establish the
minimum required flow rate and maximum allowable
steam content or quality in individual tubes, as well as
the maximum allowable flow rates for the steam drum.
System arrangement and key components
Most applications of steam generators involve the
production of electricity or the supply of process steam.
In some cases, a combination of the two applications,
called cogeneration, is used. In each application, the
steam generator is a major part of a larger system that
has many subsystems and components. Fig. 9 shows a
modern coal-fired power generating facility; Fig. 10
identifies the major subsystems. Key subsystems in-
clude fuel receiving and preparation, steam generator
Fig. 8 Simple circulation systems.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-44-320.jpg)
![Steam 41 / Steam Generation – An Overview 1-11
The Babcock & Wilcox Company
safely generate steam. The system is based upon the
energy released when atoms within certain materials,
such as uranium, break apart or fission. Fission oc-
curs when a fissionable atom nucleus captures a free
subatomic particle – a neutron. This upsets the inter-
nal forces which hold the atom nucleus together. The
nucleus splits apart producing new atoms as well as
an average of two to three neutrons, gamma radia-
tion and energy.
The nuclear steam supply system (NSSS) is de-
signed to serve a number of functions: 1) house the
nuclear fuel, 2) stimulate the controlled fission of the
fuel, 3) control the nuclear reaction rate to produce
the required amount of thermal energy, 4) collect the
heat and generate steam, 5) safely contain the reac-
tion products, and 6) provide backup systems to pre-
vent release of radioactive material to the environ-
ment. Various systems have been developed to accom-
plish these functions. The main power producing sys-
tem in commercial operation today is the pressurized
water reactor (PWR).
A key difference between the nuclear and chemi-
cal energy driven systems is the quantity of fuel. The
energy released per unit mass of nuclear fuel is many
orders of magnitude greater than that for chemical
based fuels. For example, 1 lb (0.454 kg) of 3% en-
riched uranium fuel produces about the same amount
of thermal energy in a commercial nuclear system as
100,000 lb (45,360 kg) of coal in a fossil-fired steam
system. While a 500 MW power plant must handle ap-
proximately one million tons of coal per year, the
nuclear plant will handle only 10 tons of fuel. The fossil
fuel plant must be designed for a continuous fuel sup-
ply process, while most nuclear plants use a batch fuel
process, where about one third of the fuel is replaced
during periodic outages. However, once the steam is
generated, the balance of the power producing sys-
tem (turbine, condenser, cooling system, etc.) is simi-
lar to that used in the fossil fuel plant.
Nuclear steam system components
A typical nuclear steam system from The Babcock
& Wilcox Company (B&W) is shown in Fig. 3 and a
simplified schematic is shown in Fig. 18. This nuclear
system consists of two coolant loops. The primary loop
cools the reactor, transports heat to two or more steam
generators (only one shown), and returns coolant to
the reactor by four or more primary coolant pumps
(only one shown). The coolant is high purity, subcooled,
single-phase water flowing at very high rates [350,000
to 450,000 GPM (22,100 to 28,400 l/s)] at around 2200
psi(15.17MPa)andanaveragetemperatureofapproxi-
mately 580F (304C). The primary loop also contains a
pressurizer to maintain the loop pressure at design op-
erating levels.
The secondary loop includes the steam generation
and interface with the balance of the power plant.
High purity water from the last feedwater heater
passes through the steam generator and is converted
into steam. From the steam generator outlet, the satu-
rated or superheated steam flows out of the contain-
ment building to the high pressure turbine. The op-
erating pressure is typically around 1000 psi (6.9
MPa). The balance of the secondary loop resembles
fossil fuel-fired systems. (See Figs. 10 and 11.)
The center of the NSSS is the reactor vessel and re-
actor core (Fig. 19). The fuel consists of compressed pel-
lets [for example, 0.37 in. (9.4 mm) diameter by 0.7 in.
(18 mm) long] of 2.5 to 5% enriched uranium oxide.
These pellets are placed in zircaloy tubes which are
sealed at both ends to protect the fuel and to contain
thenuclearreactionproducts.Thetubesareassembled
into bundles with spacer and closure devices. These
bundles are then assembled into the nuclear fuel core.
The reactor enclosure (Fig. 19) is a low alloy steel
pressure vessel lined with stainless steel for corrosion
protection. The rest of the reactor includes flow distri-
bution devices, control rods, core support structures,
Table 1
Typical 500 MW Subcritical Coal-Fired Steam Generator Emissions and Byproducts*
Power System Characteristics
• 500 MW net
• 196 t/h (49.4 kg/s) bituminous coal
− 2.5% sulfur
− 16% ash
− 12,360 Btu/lb (28,749 kJ/kg)
• 65% capacity factor
Discharge Rate t/h (tm/h)
Emission Typical Control Equipment Uncontrolled Controlled
SOx as SO2 Wet limestone scrubber 9.3 (8.4) 0.3 (0.3)
NOx as NO2 Low NOx burners and SCR 2.9 (2.6) 0.1 (0.1)
CO2 Not applicable 485 (440)
Flyash to air** Electrostatic precipitator or baghouse 22.9 (20.8) 0.05 (0.04)
Thermal discharge to water sources Natural draft cooling tower 2.8 x 109
Btu/h (821 MWt) ∼0 (0)
Ash to landfill** Controlled landfill 9.1 (8.3) 32 (29)
Scrubber sludge: gypsum plus water Controlled landfill or wallboard quality gypsum 0 (0) 27.7 (25)
* See Chapter 32, Table 1, for a modern 615 MW supercritical coal-fired steam generator.
** As flyash emissions to the air decline, ash to landfill increases.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-51-320.jpg)
![1-12 Steam 41 / Steam Generation – An Overview
The Babcock & Wilcox Company
thermal shielding and moderator. The moderator in
this case is water which serves a dual purpose. It re-
duces the velocity of the neutrons thereby making the
nuclear reactions more likely. It also serves as the cool-
ant to maintain the core materials within acceptable
temperature limits and transports thermal energy to
the steam generators. The control rods contain neutron
absorbing material and are moved into and out of the
nuclear core to control the energy output.
The steam generators can be of two types, once-
through (Fig. 20) and recirculating (Fig. 21). In both
types, the pressure vessel is a large heat exchanger
designed to generate steam for the secondary loop from
heat contained in the primary coolant. The primary
coolant enters a plenum and passes through several
thousand small diameter [approximately 0.625 in.
(15.9 mm)] Inconel®
tubes. The steam generator is a
large, carbon steel pressure vessel. Specially designed
tubesheets, support plates, shrouds, and baffles pro-
vide effective heat transfer, avoid thermal expansion
problems, and avoid flow-induced vibration.
In the once-through steam generator (OTSG), Fig.
20, the secondary loop water flows from the bottom to
the top of the shell side of the tube bundle and is con-
tinuously converted from water to superheated steam.
The superheated steam then passes to the high pres-
sure turbine.
In the recirculating steam generator (RSG), Fig. 21,
water moves from the bottom to the top of the shell side
ofthetubebundlebeingconvertedpartiallyintosteam.
The steam-water mixture passes into the upper shell
where steam-water separators supply saturated dry
steam to the steam generator outlet. The steam is sent
to the high pressure turbine. The water leaving the
steam generator upper shell is mixed with feedwater
and is returned to the bottom of the tube bundle.
The pressurizer is a simple cylindrical pressure ves-
sel which contains both water and steam at equilib-
rium. Electrical heaters and spray systems maintain
the pressure in the pressurizer vessel and the primary
loop within set limits. The primary loop circulating
pumps maintain high flow rates to the reactor core to
control its temperature and transfer heat to the steam
generators.
A number of support systems are also provided.
These include reactor coolant charging systems,
makeup water addition, spent fuel storage cooling, and
decay heat removal systems for when the reactor is
shut down. Other specialized systems protect the re-
actor system in the case of a loss of coolant event. The
key function of these systems is to keep the fuel bundle
temperature within safe limits if the primary coolant
flow is interrupted.
Nuclear steam system classifications
A variety of reactor systems have been developed
to recover thermal energy from nuclear fuel and to
generate steam for power generation. These are usu-
ally identified by their coolant and moderator types.
The principal systems for power generation include:
1. Pressurized water reactor (PWR) This is the sys-
tem discussed above, using water as both reactor
coolant and moderator, and enriched uranium
oxide as the fuel.
2. Boiling water reactor (BWR) The steam genera-
tor is eliminated and steam is generated directly
in the reactor core. A steam-water mixture cools
and moderates the reactor core. Enriched uranium
oxide fuel is used.
Fig. 19 Reactor vessel and internals.
Fig. 18 Nuclear steam system schematic.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-52-320.jpg)
![1-16 Steam 41 / Steam Generation – An Overview
The Babcock & Wilcox Company
unit area of surface are very high and relatively inde-
pendent of the tubewall temperatures. Boiling water
provides an effective means to cool the tubes and keep
the tube metal temperatures within acceptable limits
as long as the boiling conditions are maintained.
Fig. 26 shows the effect of the furnace on gas tem-
perature. The gas temperature is reduced from 3600
at point A to 2400F at point B (1982 to 1316C), while
boiling takes place in the water walls (points 1 to 2).A
large amount of heat transfer takes place on a small
amount of surface. From the furnace, the gases pass
through the furnace screen tubes shown in Fig. 23.
The temperature drops a small amount [50F (28C)]
from points B to C in Fig. 26, but more importantly,
the superheater surface is partially shielded from the
furnace thermal radiation. The furnace screen tubes
are connected to the drum and contain boiling water.
Next, the gas passes through the superheater where
the gas temperature drops from 2350 at point C to
1750F at point D (1288 to 954C). Saturated steam
from the drum is passed through the superheater tub-
ing to raise its temperature from 490F (254C) satura-
tiontemperaturetothe850F(454C)desiredoutlettem-
perature (points 5 to 4).
The location of the superheater and its configura-
tion are critical in order to keep the steam outlet tem-
perature constant under all load conditions. This in-
volves radiation heat transfer from the furnace with
convection heat transfer from the gas passing across
the surface. In addition, where dirty gases such as
combustion products from coal are used, the spacing
of the superheater tubes is also adjusted to accommo-
date the accumulation of fouling ash deposits and the
use of cleaning equipment.
After the superheater, almost half of the energy in
the gas stream has been recovered with only a small
amount of heat transfer surface [approximately 6400
ft2
(595 m2
)]. This is possible because of the large tem-
perature difference between the gas and the boiling
water or steam. The gas temperature has now been dra-
matically reduced, requiring much larger heat transfer
surfaces to recover incremental amounts of energy.
The balance of the steam is generated by passing
the gas through the boiler bank. (See Figs. 22 and 23.)
This bank is composed of a large number of water-
containing tubes that connect the steam drum to a
lower (mud) drum. The temperature of the boiling
water is effectively constant (points 5 to 6 in Fig. 26),
while the gas temperature drops by almost 1000F
(556C) to an outlet temperature of 760F (404C), be-
tween points D and E. The tubes are spaced as closely
as possible to increase the gas flow heat transfer rate.
If a particulate-laden gas stream were present, the
spacing would be set to limit erosion of the tubes, re-
duce the heat transfer degradation due to ash depos-
its, and permit removal of the ash. Spacing is also
controlled by the allowable pressure drop across the
bank. In addition, a baffle can be used in the boiler
bank bundle to force the gas to travel at higher veloc-
ity through the bundle, increase the heat transfer rate,
and thereby reduce the bundle size and cost. To re-
cover this additional percentage of the supplied en-
ergy, the boiler bank contains more than 32,000 ft2
(3000 m2
) of surface, or approximately nine times more
surface per unit of energy than in the high tempera-
ture furnace and superheater. At this point in the
process, the temperature difference between the satu-
rated water and gas is only 270F (150C), between
points 6 and E in Fig. 26.
Economics and technical limits dictate the type and
arrangement of additional heat transfer surfaces. An
economizer or water-cooled heat exchanger could be
used to heat the makeup or feedwater and cool the gas.
The lowest gas exit temperature possible is the inlet
temperature of the feedwater [280F (138C)]. However,
the economizer would have to be infinitely large to
accomplish this goal. Even if the exit gas temperature
is 310F (154C), the temperature difference at this
point in the heat exchanger would only be 30F (17C),
still making the heat exchanger relatively large. In-
stead of incorporating an economizer, an air preheater
could be used to recover the remaining gas energy and
preheat the combustion air. This would reduce the
Fig. 24 Industrial boiler – temperature versus heat transfer surface.
Fig. 25 Steam-water temperature profile.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-56-320.jpg)
![Steam 41 / Thermodynamics of Steam 2-7
The Babcock & Wilcox Company
where ms is the mass of steam and mw is the mass of
water. The quality is frequently recorded as a percent
steam by weight (% SBW) after multiplying by 100%.
The mixture enthalpy (H ) (see Note below), entropy
(s) and specific volume (v) of a steam-water mixture
can then be simply defined as:
H H x H Hf g f= + −( ) (2a)
s s x s sf g f= + −( ) (2b)
v v x v vf g f= + −( ) (2c)
where the subscripts f and g refer to properties at satu-
rated liquid and vapor conditions, respectively. The
difference in a property between saturated liquid and
vapor conditions is frequently denoted by the subscript
fg; for example, Hfg = Hg – Hf. With these definitions,
if the pressure or temperature of a steam-water mix-
ture is known along with one of the mixture proper-
ties, the quality can then be calculated. For example,
if the mixture enthalpy is known, then:
x H H Hf fg= −( ) / (3)
Engineering problems deal mainly with changes or
differences in enthalpy and entropy. It is not neces-
sary to establish an absolute zero for these properties,
although this may be done for entropy. The Steam
Tables indicate an arbitrary zero internal energy and
entropy for the liquid state of water at the triple point
corresponding to a temperature of 32.018F (0.01C) and
a vapor pressure of 0.08865 psi (0.6112 kPa). The
triple point is a unique condition where the three states
of water (solid, liquid and vapor) coexist at equilibrium.
Properties of gases
In addition to steam, air is a common working fluid
for some thermodynamic cycles.As with steam, well de-
fined properties are important in cycle analysis.Air and
many common gases used in power cycle applications
can usually be treated as ideal gases. An ideal gas is
defined as a substance that obeys the ideal gas law:
Pv RT= (4)
where R is a constant which varies with gas species;
P and T are the pressure and temperature, respec-
tively. R is equal to the universal gas constant, R [1545
ft lb/lb-mole R (8.3143 kJ/kg mole K)], divided by the
molecular weight of the gas. For dry air, R is equal to
53.34 lbf ft/lbm R (0.287 kJ/kg K). Values for other
gases are summarized in Reference 3. The ideal gas
law is commonly used in a first analysis of a process
or cycle because it simplifies calculations. Final calcu-
lations often rely on tabulated gas properties for
greater accuracy.
Tabulated gas properties are available from numer-
ous sources. (See References 4 and 5 for examples.)
Unfortunately, there is less agreement on gas proper-
ties than on those for steam. The United States (U.S.)
boiler industry customarily uses 80F (27C) and 14.7
psia (101.35 kPa) as the zero enthalpy of air and com-
bustion products. A more general reference is one at-
mosphere pressure, 14.696 psia (101.35 kPa), and 77F
(25C). This is the standard reference point for heats
of formation of compounds from elements in their
standard states, latent heats of phase changes and free
energy changes. Because of different engineering con-
ventions, considerable care must be exercised when
using tabulated properties. Selected properties for air
and other gases are provided in Chapter 3, Table 3.
Conservation of mass and energy
Thermodynamic processes are governed by the laws
of conservation of mass and conservation of energy ex-
cept for the special case of nuclear reactions discussed
in Chapter 47. These conservation laws basically state
that the total mass and total energy (in any of its forms)
can neither be created nor destroyed in a process. In an
open flowing power system, where mass continually
enters and exits a system such as Fig. 2, these laws can
take the forms:
Conservation of mass
m m m1 2− = ∆ (5)
Conservation of energy
E E E Q W2 1− + = −∆ (6)
Note: To avoid confusion with the symbol for heat trans-
fer coefficient, enthalpy (Btu/lb or kJ/kg) is denoted by H
in this chapter and the balance of Steam unless specially
noted. Enthalpy is frequently denoted by h in thermody-
namic texts. Fig. 2 Diagram illustrating thermodynamic processes.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-67-320.jpg)
![Steam 41 / Thermodynamics of Steam 2-19
The Babcock & Wilcox Company
double reheat, and turbine steam extraction for regen-
erative feedwater heating, among others. This evalu-
ation is based upon a steam turbine heat balance or
steam cycle diagram such as that shown in Fig. 8 for
a 3500 psig (24.13 MPa) supercritical pressure fossil
fuel-fired unit, or Fig. 10 for a 2400 psig (16.55 MPa)
subcritical pressure unit. The subcritical pressure unit
shown has a single reheat, six closed feedwater heat-
ers and one open feedwater heater.
Rankine cycle heat rate
Heat rate is a term frequently used to define vari-
ous power plant efficiencies. If the electrical genera-
tion used is the net output after subtracting all auxil-
iary electrical power needs, then Equation 42 defines
the net heat rate using English units. If the auxiliary
electrical usage is not deducted, Equation 42 defines
the gross heat rate.
Heat rate
Total fuel heat input (Btu/h)
Electrical generati
=
oon (kW)
(42)
Heat rate is directly related to plant efficiency, η,
by the following relationships:
Net heat rate
Btu/kWh
net
=
3412 14.
η (43a)
Gross heat rate
Btu/kWh
gross
=
3412 14.
η (43b)
Steam cycle in a nuclear plant
Fig. 11 illustrates a Rankine cycle whose thermal
energy source is a pressurized water nuclear steam
system. High pressure cooling water is circulated from
a pressurized water reactor to a steam generator.
Therefore, heat produced by the fission of enriched
uranium in the reactor core is transferred to
feedwater supplied to the steam generator which, in
turn, supplies steam for the turbine. The steam gen-
erators of a nuclear plant are shell and tube heat ex-
changers in which the high pressure reactor coolant
flows inside the tubes and lower pressure feedwater
is boiled outside of the tubes. For the pressurized wa-
ter reactor system, the Rankine cycle for power genera-
tiontakesplaceentirelyinthenonradioactivewaterside
(secondary side) that is boiling and circulating in the
steam system; the reactor coolant system is simply the
heat source for the power producing Rankine cycle.
The steam pressure at the outlet of the steam gen-
erator varies among plants due to design differences
and ranges from 700 to 1000 psi (4.83 to 6.90 MPa).
Nominally, a nuclear steam system by The Babcock &
Wilcox Company (B&W) with a once-through steam
generator provides slightly superheated steam at 570F
(299C) and 925 psi (6.38 MPa). Steam flow from the
once-through generator reaches the high pressure
turbine at about 900 psi (6.21 MPa) and 566F (297C).
More prevalent are nuclear steam systems that use a
recirculating steam generator. In this design,
feedwater is mixed with saturated water coming from
the steam generator’s separators before entering the
tube bundle and boiling to generate steam. This boil-
ing steam-water mixture reaches a quality of 25 to 33%
at the end of the heat exchanger and enters the steam
generator’s internal separators. The separators return
the liquid flow to mix with incoming feedwater and
direct the saturated steam flow to the outlet of the
steam generator. Inevitably, a small amount of mois-
ture is formed by the time the steam flow reaches the
high pressure turbine.
Even though the once-through steam generator is
capable of providing superheated steam to the turbine,
the pressure and temperature limitations of nuclear
plant components must be observed. As a result, the
expansion lines of the power cycle lie largely in the
wet steam region. This is essentially a saturated or
nearly saturated steam cycle. The expansion lines for
the nuclear steam system shown in Fig. 11 (featuring
a once-through steam generator) are plotted on an
enthalpy-entropy or H-s diagram in Fig. 12.
The superheated steam is delivered to the turbine
at a temperature only 34F (19C) above saturation.Al-
though this superheat improves cycle efficiency, large
quantities of condensed moisture still exist in the tur-
bine. For example, if expansion from the initial con-
ditions shown in Fig. 12 proceed down one step to the
back pressure of 2.0 in. Hg [approximately 1.0 psi (6.9
kPa)] the moisture formed would exceed 20%.At best,
steam turbines can accommodate about 15% moisture
content. High moisture promotes erosion, especially in
the turbine blades, and reduces expansion efficiency.
In addition to mechanical losses from momentum
exchanges between slow moving condensate particles,
high velocity steam and rotating turbine blades, there
is also a thermodynamic loss resulting from the con-
densate in the turbine. The expansion of the steam is
too rapid to permit equilibrium conditions to exist when
condensation is occurring. Under this condition, the
steam becomes subcooled, retaining a part of the avail-
able energy which would be released by condensation.
Fig. 11 indicates two methods of moisture removal
used in this cycle and Fig. 12 shows the effect of this
moisture removal on the cycle. After expansion in the
high pressure turbine, the steam passes through a
moisture separator, which is a low pressure drop sepa-
rator external to the turbine. After passing through
this separator, the steam is reheated in two stages, first
by bleed steam and then by high pressure steam to
503F (262C), before entering the low pressure turbine.
Here a second method of moisture removal, in which
grooves on the back of the turbine blades drain the
moisture from several stages of the low pressure tur-
bine, is used. The separated moisture is carried off with
the bleed steam.
Internal moisture separation reduces erosion and
affords a thermodynamic advantage due to the diver-
gence of the constant pressure lines with increasing
enthalpy and entropy. This can be shown by the use
of available energy, e, as follows. Consider the mois-
ture removal stage at 10.8 psi in Fig. 12. After expan-
sion to 10.8 psi, the steam moisture content is 8.9%.
Internal separation reduces this to approximately
8.2%. Other properties are as follows:](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-79-320.jpg)
![Steam 41 / Thermodynamics of Steam 2-25
The Babcock & Wilcox Company
heat source and then expanded in a turbine to pro-
duce work or to generate electricity. Steam is fre-
quently used in the bottoming cycle because of its
ability to condense at low temperatures in the closed
Rankine cycle. The bottoming cycle is shown in Fig.
20. The steam Rankine cycle used as a bottoming cycle
has been illustrated previously in the descriptions of
combined cycle plants.
Combustion processes
To this point, cycles have been compared based on
the thermodynamic efficiency achieved, i.e., the net
work produced divided by the total heat input to the
cycle. To complete the evaluation of a combustion-
based cycle, however, the performance must be ex-
pressed in terms of fuel consumption. In addition, the
ability of the different machines to make full use of
the combustion energy varies with temperatures
reached in the combustion chamber and with disso-
ciation of the combustion products.
The energy release during combustion is illustrated
by considering the combustion of carbon (C) and oxy-
gen (O2) to form carbon dioxide (CO2):
C O CO+ →2 2
If heat is removed from the combustion chamber
and the reactants and products are maintained at 25C
and 0.1 MPa (77F and 14.5 psi) during the process,
the heat transfer from the combustion chamber would
be 393,522 kJ per kmole of CO2 formed. From the first
law applied to the process, the heat transfer is equal
to the difference in enthalpy between the reactants
and products:
q w H HP R− = − (62)
The subscripts R and P refer to reactants and prod-
ucts, respectively.Assuming that no work is done in the
combustion chamber and expressing the enthalpy of
reactantsandproductsonapermolebasis,thisbecomes:
Q n H n HP P R R= − ∑∑ (63)
The number of moles of each element or molecular
species entering or leaving the chamber, nR or nP re-
spectively, is obtained from the chemical reaction equa-
tion. By convention, the enthalpy of elements at 25C
and 0.1 MPa (77F and 14.5 psi) are assigned the value
of zero. Consequently, the enthalpy of CO2 at these
conditions is –393,522 kJ/kmole (the negative sign is
due to the convention of denoting heat transferred
from a control volume as negative). This is referred to
as the enthalpy of formation and is designated by the
symbol Hf
o
. The enthalpy of CO2 (and other molecular
species) at other conditions is found by adding the
change in enthalpy between the desired condition and
the standard state to the enthalpy of formation. [Note
that some tables may not use 25C and 0.1 MPa (77F
and 14.5 psi) as the standard state when listing the
enthalpy of formation.] Ideal gas behavior or tabu-
lated properties are used to determine enthalpy
changes from the standard state.
The stoichiometrically balanced chemical reaction
equationprovidestherelativequantitiesofreactantsand
products entering and leaving the combustion chamber.
Thefirstlawanalysisisusuallyperformedonapermole
or unit mass of fuel basis. The heat transfer from a com-
bustion process is obtained from a first law analysis of
thecombustionprocess,giventhepressureandtempera-
ture of the reactants and products. Unfortunately, even
in the case of complete combustion as assumed in the
previous example, the temperature of the combustion
products must be determined by additional calculations
discussed later in this section.
The combustion of fossil or carbon based fuel is com-
monly accompanied by the formation of steam or water
(H2O) as in the reaction:
CH 2O CO 2H O2 2 24 + → +
Again, the difference in enthalpy between the reac-
tants and products is equal to the heat transfer from
the combustion process. The heat transfer per unit
mass of fuel (methane in this example) is referred to
as the heating value of the fuel. If the H2O is present
as liquid in the products, the heat transferred is re-
ferred to as the higher heating value (HHV). The term
lower heating value (LHV) is used when the H2O is
present as a vapor. The difference between these two
values is frequently small (about 4% for most hydro-
carbon fuels) but still significant. When the efficiency
Fig. 19 Topping cycle. Fig. 20 Bottoming cycle.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-85-320.jpg)
![3-6 Steam 41 / Fluid Dynamics
The Babcock & Wilcox Company
ible pressure losses resulting from fluid flow. (See
Equation 29 and explanation, Chapter 2.) Therefore:
Tds dQ dQF= + (30)
where dQF is the heat equivalent of fluid friction and
any local irrecoverable pressure losses such as those
from pipe fittings, bends, expansions or contractions.
Substituting Equation 30 into Equation 29, cancel-
ing dQ on both sides of the equation, setting dWk equal
to 0 (no shaft work), and rearranging Equation 29
results in:
dP
VdV
vg
dQ
vc
F
= − − (31)
Three significant facts should be noted from Equa-
tion 31 and its derivation. First, the general energy
equation does not accommodate pressure losses due
to fluid friction or geometry changes. To accommodate
these losses Equation 31 must be altered based on the
first and second laws of thermodynamics (Chapter 2).
Second, Equation 31 does not account for heat trans-
fer except as it may change the specific volume, υ,
along the length of the flow channel. Third, there is
also a pressure loss as the result of a velocity change.
This loss is independent of any flow area change but
is dependent on specific volume changes. The pressure
loss is due to acceleration which is always present in
compressible fluids. It is generally negligible in incom-
pressible flow without heat transfer because friction
heating has little effect on fluid temperature and the
accompanying specific volume change.
Equation 27 contains no acceleration term and
applies only to friction and local pressure losses. There-
fore, dQF/υ in Equation 31 is equivalent to dP of
Equation 27, or:
dQ
v
f
dx
D
V
v g
F
c
=
2
2 (32)
Substitution of Equation 32 into Equation 31 yields:
dP
VdV
vg
f
D
V
v g
dx
c c
= − −
2
2 (33)
From Equation 5, the continuity equation permits
definition of the mass flux, G, or mass velocity or mass
flow rate per unit area [lb/h ft2
(kg/m2
s)] as:
V
v
G= = constant (34)
Substituting Equation 34 into Equation 33 for a flow
channel of constant area:
dP
G
g
dv f
G
g
v
D
dx
c c
= − −2
2 2
2 2
(35)
Integrating Equation 35 between points 1 and 2, lo-
cated at x = 0 and x = L, respectively:
P P
G
g
v v f
G
g D
vdx
c c
L
1 2
2
2 1
2
0
2
2 2
1
− = −( ) + ∫ (36)
The second term on the right side of Equation 36 may
be integrated provided a functional relationship be-
tween υ and x can be established. For example, where
the heat absorption rate over the length of the flow
channel is constant, temperature T is approximately
linear in x, or:
dx
L
T T
dT=
−2 1
(37)
and
vdx
L
T T
vdT Lv
L
av0
2 1
1
2
∫ ∫=
−
= (38)
The term υaυ is an average specific volume with re-
spect to temperature, T.
v v v v vav R= +( ) = +( )φ φ2 1 1 1 (39)
where
υR = υ2/υ1
φ = averaging factor
In most engineering evaluations, υ is almost lin-
ear in T and φ ≈ l/2. Combining Equations 36 and
37, and rewriting υ 2 – υ 1 as υ 1 (υ R – 1):
P P
G
g
v v
f
L
D
G
g
v v
c
R
c
R
1 2
2
1
2
1
2
2
1
2
1
− = −( )
+ +( )φ
(40)
Equation 40 is completely general. It is valid for com-
pressible and incompressible flow in pipes of constant
cross-section as long as the function T = F(x) can be as-
signed. The only limitation is that dP/dx is negative at
every point along the pipe. Equation 33 can be solved
for dP/dx making use of Equation 34 and the fact that
P1υ1 can be considered equal to P2υ2 for adiabatic flow
over a short section of tube length. The result is:
dP
dx
Pf D
g Pv
V
c
=
−
/2
1 2
(41)
At any point where V 2
= gcPυ, the flow becomes choked
because the pressure gradient is positive for velocities
greater than (gcPυ)0.5
. The flow is essentially choked
by excessive stream expansion due to the drop in pres-
sure. The minimum downstream pressure that is ef-
fective in producing flow in a channel is:
P V v g v G gc c2
2
2 2
2
= =/ / (42)
Dividing both sides of Equation 40 by G2
υ l / 2gc,
the pressure loss is expressed in terms of velocity
heads. One velocity head equals:
∆P
V
g Cv
V
g Cc c
(one velocity head) =
2 2
2 2
=
ρ
(43)](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-94-320.jpg)
![Steam 41 / Fluid Dynamics 3-9
The Babcock & Wilcox Company
excessive friction loss. Consequently, it is customary
to design for Reynolds numbers above 4000 in steam
generating units.
Turbulence fluctuations in the instantaneous ve-
locity introduce additional terms to the momentum
conservation equation called Reynolds stresses. These
fluctuations influence the mean motion and increase
the flow resistance in a manner producing an increase
in the apparent viscosity. Analysis of turbulent flow
must consider the impact of the fluctuating velocity
component along with the mean flow velocity or re-
sort to empirical methods that account for the addi-
tional momentum dissipation.4, 6, 8
Velocity ranges
Table 1 lists the velocity ranges generally encoun-
tered in the heat transfer equipment as well as in duct
and piping systems of steam generating units. These
values, plus the specific volumes from the ASME
Steam Tables (see Chapter 2) and the densities listed
in Tables 2 and 3 in this chapter, are used to establish
mass velocities for calculating Reynolds numbers and
fluid friction pressure drops. In addition, values of
viscosity, also required in calculating the Reynolds
number, are given in Figs. 3, 4 and 5 for selected liq-
uids and gases. Table 4 lists the relationship between
various units of viscosity.
Resistance to flow in valves and fittings
Pipelines and duct systems contain many valves and
fittings. Unless the lines are used to transport fluids
over long distances, as in the distribution of process
steam at a factory or the cross country transmission
of oil or gas, the straight runs of pipe or duct are rela-
tively short. Water, steam, air and gas lines in a power
plant have relatively short runs of straight pipe and
many valves and fittings. Consequently, the flow re-
sistance due to valves and fittings is a substantial part
of the total resistance.
Methods for estimating the flow resistance in valves
and fittings are less exact than those used in estab-
lishing the friction factor for straight pipes and ducts.
In the latter, pressure drop is considered to be the re-
sult of the fluid shear stress at the boundary walls of
the flow channel; this leads to relatively simple bound-
ary value evaluations. On the other hand, pressure
losses associated with valves, fittings and bends are
mainly the result of impacts and inelastic exchanges
Fig. 2 Relative roughness of various conduit surfaces. (SI conver-
sion: mm = 25.4 X in.)
Table 1
Velocities Common in Steam Generating Systems
Velocity
Nature of Service ft/min m/s
Air:
Air heater 1000 to 5000 5.1 to 25.4
Coal and air lines,
pulverized coal 3000 to 4500 15.2 to 22.9
Compressed air lines 1500 to 2000 7.6 to 10.2
Forced draft air ducts 1500 to 3600 7.6 to 18.3
Forced draft air ducts,
entrance to burners 1500 to 2000 7.6 to 10.2
Ventilating ducts 1000 to 3000 5.1 to 15.2
Crude oil lines [6 to 30
in. (152 to 762 mm)] 60 to 3600 0.3 to 18.3
Flue gas:
Air heater 1000 to 5000 5.1 to 25.4
Boiler gas passes 3000 to 6000 15.2 to 30.5
Induced draft flues
and breaching 2000 to 3500 10.2 to 17.8
Stacks and chimneys 2000 to 5000 10.2 to 25.4
Natural gas lines (large
interstate) 1000 to 1500 5.1 to 7.6
Steam:
Steam lines
High pressure 8000 to 12,000 40.6 to 61.0
Low pressure 12,000 to 15,000 61.0 to 76.2
Vacuum 20,000 to 40,000 101.6 to 203.2
Superheater tubes 2000 to 5000 10.2 to 25.4
Water:
Boiler circulation 70 to 700 0.4 to 3.6
Economizer tubes 150 to 300 0.8 to 1.5
Pressurized water
reactors
Fuel assembly channels 400 to 1300 2.0 to 6.6
Reactor coolant piping 2400 to 3600 12.2 to 18.3
Water lines, general 500 to 750 2.5 to 3.8](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-97-320.jpg)
![3-12 Steam 41 / Fluid Dynamics
The Babcock & Wilcox Company
When the elevation change (Z2 – Z1) is zero, the
mechanical energy balance for converging boundaries
becomes:
P v
V
g
P v
V
g
N
V
gc c
c
c
1
1
2
2
2
2
2
2
2 2 2
+ = + + (53)
Subscripts 1 and 2 identify the upstream and down-
stream sections. Nc, the contraction loss factor, is the
number of velocity heads lost by friction and local non-
recoverable pressure loss in contraction. Fig. 6 shows
values of this factor.
When there is an enlargement of the conduit sec-
tion in the direction of flow, the expansion of the flow
stream is proportional to the kinetic energy of the
flowing fluid and is subject to a pressure loss depend-
ing on the geometry. Just as in the case of the con-
traction loss, this is an irreversible energy conversion
to heat resulting from inelastic momentum ex-
changes. Because it is customary to show these losses
as coefficients of the higher kinetic energy term, the
mechanical energy balance for enlargement loss is:
P v
V
g
P v
V
g
N
V
gc c
e
c
1
1
2
2
2
2
1
2
2 2 2
+ = + + (54)
The case of sudden enlargement [angle of divergence
β = 180 deg (π rad)] yields an energy loss of (V1 - V2)2
/
2gc. This can also be expressed as:
N
A
A
e = −
1 1
2
2
(55)
where A1 and A2 are the upstream and downstream
cross-sectional flow areas, respectively and (A1 < A2).
Even this solution, based on the conservation laws,
depends on qualifying assumptions regarding static
Fig. 6 Contraction loss factor for β>30 deg (Nc = 0.05 for β≤30 deg).
Table 5
Resistance to Flow of Fluids Through
Commercial Fittings*
Fitting Loss in Velocity Heads
L-shaped, 90 deg (1.57 rad)
standard sweep elbow 0.3 to 0.7
L-shaped, 90 deg (1.57 rad)
long sweep elbow 0.2 to 0.5
T-shaped, flow through run 0.15 to 0.5
T-shaped, flow through 90 deg
(1.57 rad) branch 0.6 to 1.6
Return bend, close 0.6 to 1.7
Gate valve, open 0.1 to 0.2
Check valve, open 2.0 to 10.0
Globe valve, open 5.0 to 16.0
Angle valve, 90 deg (1.57 rad) open 3.0 to 7.0
Boiler nonreturn valve, open 1.0 to 3.0
* See Fig. 9 for loss in velocity heads for flow of fluids
through pipe bends.
Fig. 5 Absolute viscosities of saturated and superheated steam.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-100-320.jpg)
![Steam 41 / Heat Transfer 4-11
The Babcock & Wilcox Company
literature claim emittances between 0.5 and 0.9 for
most ash and slag deposits.
The effect of coal ash composition, structure, and
temperature on deposit emittance5,7
is shown in Fig.
8.Afriable particulate material has low emittance be-
cause radiation is scattered (and reflected) from indi-
vidual particles and does not penetrate beyond a thin
layer (~1 mm) near the surface. Emittance of friable
ash deposits decreases with increasing surface tem-
perature, until sintering and fusion changes the struc-
ture of the deposit. A sharp increase in emittance is
associated with ash fusion as particles grow together
(pores close) and there are fewer internal surfaces to
scatter radiation. Completely molten ash or slag is
partially transparent to radiation, and emittance may
depend upon substrate conditions. The emittance of
completely fused deposits (molten or frozen slag) on
oxidized carbon steel is about 0.9. Emittance increases
Table 8a
Properties of Selected Gases
at 14.696 psi (101.33 kPa) (see Note 1)
cp k µ
T ρ Btu/ Btu/ lbm/
F lb/ft3
lb F h ft F ft h Pr
Air
0 0.0860 0.239 0.0133 0.0400 0.719
100 0.0709 0.240 0.0154 0.0463 0.721
300 0.0522 0.243 0.0193 0.0580 0.730
500 0.0413 0.247 0.0231 0.0680 0.728
1000 0.0272 0.262 0.0319 0.0889 0.730
1500 0.0202 0.276 0.0400 0.1080 0.745
2000 0.0161 0.286 0.0471 0.1242 0.754
2500 0.0134 0.292 0.0510 0.1328 0.760
3000 0.0115 0.297 0.0540 0.1390 0.765
Carbon Dioxide (CO2)
0 0.1311 0.184 0.0076 0.0317 0.767
100 0.1077 0.203 0.0100 0.0378 0.767
300 0.0793 0.226 0.0149 0.0493 0.748
500 0.0628 0.247 0.0198 0.0601 0.750
1000 0.0413 0.280 0.0318 0.0828 0.729
1500 0.0308 0.298 0.0420 0.1030 0.731
2000 0.0245 0.309 0.0500 0.1188 0.734
2500 0.0204 0.316 0.0555 0.1300 0.739
3000 0.0174 0.322 0.0610 0.1411 0.745
Water Vapor (H2O)
212 0.0372 0.451 0.0145 0.0313 0.974
300 0.0328 0.456 0.0171 0.0360 0.960
500 0.0258 0.470 0.0228 0.0455 0.938
1000 0.0169 0.510 0.0388 0.0691 0.908
1500 0.0127 0.555 0.0570 0.0889 0.866
2000 0.0100 0.600 0.0760 0.1091 0.861
2500 0.0083 0.640 0.0960 0.1289 0.859
3000 0.0071 0.670 0.1140 0.1440 0.846
Oxygen (O2)
0 0.0953 0.219 0.0131 0.0437 0.730
100 0.0783 0.220 0.0159 0.0511 0.707
300 0.0577 0.227 0.0204 0.0642 0.715
500 0.0457 0.235 0.0253 0.0759 0.705
1000 0.0300 0.253 0.0366 0.1001 0.691
1500 0.0224 0.264 0.0465 0.1195 0.677
2000 0.0178 0.269 0.0542 0.1414 0.701
2500 0.0148 0.275 0.0624 0.1594 0.703
3000 0.0127 0.281 0.0703 0.1764 0.703
Nitrogen (N2)
0 0.0835 0.248 0.0132 0.0380 0.713
100 0.0686 0.248 0.0154 0.0440 0.710
300 0.0505 0.250 0.0193 0.0547 0.710
500 0.0400 0.254 0.0232 0.0644 0.704
1000 0.0263 0.269 0.0330 0.0848 0.691
1500 0.0196 0.284 0.0423 0.1008 0.676
2000 0.0156 0.292 0.0489 0.1170 0.699
2500 0.0130 0.300 0.0565 0.1319 0.700
3000 0.0111 0.305 0.0636 0.1460 0.701
Note:
1. SI conversions: T(C) = [T(F) − 32]/1.8; ρ, 1 lb/ft3
= 16.018
kg/m3
; cp, 1 Btu/lb F = 4.1869 kJ/kg K; k, 1 Btu/h ft F =
1.7307 W/m K; µ, 1 lbm/ft h = 0.0004134 kg/m s.
Table 8b
Properties of Selected Gases
at 14.696 psi (101.33 kPa) (see Note 1)
cp k µ
T ρ Btu/ Btu/ lbm/
F lb/ft3
lb F h ft F ft h Pr
Flue gas − natural gas (see Note 2)
300 0.0498 0.271 0.0194 0.0498 0.694
500 0.0394 0.278 0.0237 0.0593 0.694
1000 0.0259 0.298 0.0345 0.0803 0.694
1500 0.0193 0.317 0.0452 0.0989 0.693
2000 0.0154 0.331 0.0555 0.1160 0.692
2500 0.0128 0.342 0.0651 0.1313 0.691
3000 0.0109 0.351 0.0742 0.1456 0.689
Flue gas − fuel oil (see Note 3)
300 0.0524 0.259 0.0192 0.0513 0.692
500 0.0415 0.266 0.0233 0.0608 0.694
1000 0.0273 0.287 0.0336 0.0817 0.696
1500 0.0203 0.304 0.0436 0.1001 0.697
2000 0.0162 0.316 0.0531 0.1169 0.697
2500 0.0134 0.326 0.0618 0.1318 0.696
3000 0.0115 0.334 0.0700 0.1459 0.695
Flue gas − coal (see Note 4)
300 0.0537 0.254 0.0191 0.0519 0.691
500 0.0425 0.261 0.0232 0.0615 0.693
1000 0.0279 0.282 0.0333 0.0824 0.697
1500 0.0208 0.299 0.0430 0.1007 0.699
2000 0.0166 0.311 0.0521 0.1173 0.700
2500 0.0138 0.320 0.0605 0.1322 0.701
3000 0.0118 0.328 0.0684 0.1462 0.701
Notes:
1. SI conversions: T(C) = [T(F) − 32]/1.8; ρ, 1 lb/ft3
= 16.018
kg/m3
; cp, 1 Btu/lb F = 4.1869 kJ/kg K; k, 1 Btu/h ft F =
1.7307 W/m K; µ, 1 lbm/ft h = 0.0004134 kg/m s.
2. Flue gas composition by volume (natural gas, 15% excess air):
71.44% N2, 2.44% O2, 8.22% CO2, 17.9% H2O.
3. Flue gas composition by volume (fuel oil, 15% excess air):
74.15% N2, 2.54% O2, 12.53% CO2, 0.06% SO2, 10.72% H2O.
4. Flue gas composition by volume (coal, 20% excess air):
74.86% N2, 3.28% O2, 13.97% CO2, 0.08% SO2, 7.81% H2O.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-117-320.jpg)
![4-12 Steam 41 / Heat Transfer
The Babcock & Wilcox Company
with increasing particle size of friable particulate de-
posits (Fig. 8a), because larger particles have less ca-
pacity to back-scatter incident radiation. Emittance
increases with increasing iron oxide (Fe2O3) and un-
burned carbon content of the ash (Fig. 8b) because
these components have a greater capacity to absorb
radiation. Low emittance of some lignitic ash depos-
its, known as reflective ash, may be attributed to low
Fe2O3 content, although this alone is not a reliable
indicator of a reflective ash. Emittance is also indi-
rectly dependent upon oxidizing and reducing envi-
ronment of the flue gas, due to the effect on the melt-
ing characteristics and unburned carbon content in
the ash. The thermal and radiative effects of coal-ash
deposits are further described by Wall et al.5
Combustion gases Although many gases, such as
oxygen and nitrogen, absorb or emit only insignificant
amounts of radiation, others, such as water vapor,
carbon dioxide, sulfur dioxide and carbon monoxide,
substantially absorb and emit. Water vapor and car-
bon dioxide are important in boiler calculations be-
cause of their presence in the combustion products of
hydrocarbon fuels. These gases are selective radiators.
They emit and absorb radiation only in certain bands
(wavelengths) of the spectrum that lie outside of the
visible range and are consequently identified as
nonluminous radiators. Whereas the radiation from
a furnace wall is a surface phenomenon, a gas radi-
ates and absorbs (within its absorption bands) at ev-
ery point throughout the furnace. Furthermore, the
emissivity of a gas changes with temperature, and the
presence of one radiating gas may have characteris-
tics that overlap with the radiating characteristics of
another gas when they are mixed. The energy emit-
ted by a radiating gaseous mixture depends on gas
temperature, the partial pressures, p, of the constitu-
ents and a beam length, L, that depends on the shape
and dimensions of the gas volume. An estimate of the
mean beam length is L = 3.6 V/A for radiative trans-
fer from the gas to the surface of the enclosure, where
V is the enclosure volume and A is the enclosure sur-
face area. The factor 3.6 is approximate, and values
between 3.4 to 3.8 have been recommended depend-
ing on the actual geometry.4
Figs. 9 and 10 show the emissivity for water vapor
and carbon dioxide.8
The accuracy of these charts has
gainedgreateracceptancethanthemorewidelyknown
chartsofHottel,4
particularlyathightemperaturesand
short path lengths. The effective emissivity of a water
vapor-carbon dioxide mixture is calculated as follows:
ε ε ε ε= + −H O CO2 2
∆ (41)
where ∆ε is a correction factor that accounts for the
effect of overlapping spectral bands. This equation
neglects pressure corrections and considers boilers op-
erating at approximately 1 atm. The factors shown in
Fig. 11 depend on temperature, the partial pressures,
p, of the constituents and the beam length, L. The pres-
ence of carbon monoxide and sulfur dioxide can typi-
cally be neglected in combustion products, because CO
and SO2 are weakly participating and overlap with the
infrared spectrum of H2O and CO2.
When using Figs. 9 to 11 to evaluate absorptivity,
α, of a gas, Hottel4
recommends modification of the pL
product by a surface to gas temperature ratio. This is
illustrated in Example 6 at the end of this chapter.
Table 9
Normal Emissivities, ε, for
Various Surfaces13
(see Note 1)
Material Emissivity, ε Temp., F Description
Aluminum 0.09 212 Commercial sheet
Aluminum
oxide 0.63 to 0.42 530 to 930
Aluminum Varying age and Al
paint 0.27 to 0.67 212 content
Brass 0.22 120 to 660 Dull plate
Copper 0.16 to 0.13 1970 to 2330 Molten
Copper 0.023 242 Polished
Cuprous
oxide 0.66 to 0.54 1470 to 2012
Iron 0.21 392 Polished, cast
Iron 0.55 to 0.60 1650 to 1900 Smooth sheet
Iron 0.24 68 Fresh emeried
Iron oxide 0.85 to 0.89 930 to 2190
Steel 0.79 390 to 1110 Oxidized at 1100F
Steel 0.66 70 Rolled sheet
Steel 0.28 2910 to 3270 Molten
Steel (Cr-Ni) 0.44 to 0.36 420 to 914 18-8 rough, after
heating
Steel (Cr-Ni) 0.90 to 0.97 420 to 980 25-20 oxidized in
service
Brick, red 0.93 70 Rough
Brick, fireclay 0.75 1832
Carbon, lamp-
black 0.945 100 to 700 0.003 in. or thicker
Water 0.95 to 0.963 32 to 212
Note:
1. SI conversion: T(C) = [T(F) − 32]/1.8; 1 in. = 25.4 mm.
Fig. 8 Effect of coal ash composition, structure and temperature on
deposit emittance.5,7
0.9
1100900
Increasing
Absorption
700500300100
0.4
0.5
0.6
0.7
0.8
0.9
(b)
Surface Temperature, T , C
With Carbon
With Fe O
Colorless
Increasing
Particle
Size
1.0
0.8
0.7
0.6
0.5
0.4
(a)
211-422 µm
211 µm
104-
<44 µm
53-104 µm
Cooling
Particulates
Heating
Fused
Sintering
Fusion
1.0
TotalEmissivityorEmittance,](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-118-320.jpg)
![Steam 41 / Heat Transfer 4-13
The Babcock & Wilcox Company
Radiation properties of gases can be calculated more
accurately based on fundamental models for spectral
gas radiation. The exponential wide band model9
pre-
dicts spectral absorption and emission properties of
single and multi-component gases including H2O,
CO2, CO, CH4, NO, and SO2 as a function of tempera-
ture and pressure. Diatomic gases N2, O2 and H2 may
contribute to the total gas volume and pressure of the
mixture, but are considered transparent to infrared
radiation. Radiation properties are conveniently ex-
pressed as emission and absorption coefficients that
dependonlocalvariationsingascomposition,tempera-
ture, and pressure. This approach is suitable for nu-
mericalmodelingofradiationwithparticipatingmedia,
which requires frequent evaluation of gas properties
at a large number of control volumes.
Entrained particles Combustion usually involves
some form of particulate that is entrained in combus-
tion gases. Particles are introduced as the fuel which
undergo transformations of combustion and/or are
formed by the processes of condensation and agglom-
eration of aerosol particles. Entrained particles have
asignificantroleinradiationheattransferbecausethey
absorb, emit, and scatter radiation. Scattering effec-
tively extends the beam length of radiation in an en-
closure,becausethebeamchangesdirectionmanytimes
before it reaches a wall. Radiation from entrained par-
ticles depends on the particle shape, size distribution,
chemicalcomposition,concentration,temperature,and
the wavelength of incident radiation.
Particulates in boilers are comprised of unreacted
fuel (coal, oil, black liquor), char, ash, soot, and other
aerosols. Soot is an example of an aerosol that con-
0.05
1.0
0.06
0.07
0.04
0.03
0.02
0.01
0.00
0.0 0.2 0.4 0.6 0.8
90 bar cm
30 bar cm
60 bar cm
90 bar cm
1700F (925C) and Above
p L + p L = 120 bar cm
p
p + p
Fig. 11 Radiation heat transfer correction factor associated with
mixtures of water vapor and carbon dioxide.8
(1 bar-cm = 0.0324 ft-atm)
Fig.10 Emissivity of carbon dioxide at one atmosphere total pressure:
pcL= partial pressure in atmospheres x mean beam length in feet.8
(1 bar-cm = 0.0324 ft-atm; T(F) = [T(C) x 1.8] + 32)
EmissivityofCarbonDioxide
0.005
0.05
0.10
0.20
0.30
0.01
2200200016001200800200 1000 1400 1800400 600
Carbon Dioxide
Total Pressure 1 bar
Partial Pressure 0 bar
0.3 bar cm
0.15
bar cm
2 bar cm
4 bar cm
15 bar cm
40 bar cm
8 bar cm
1 bar cm
0.6 bar cm
100 bar cm
Temperature, C
(T)F = (T(C) x 1.8) + 32
0.04
0.03
0.02
p
c L
=
0.5
bar cm
Fig. 9 Emissivity of water vapor at one atmosphere total pressure:
pwL= partial pressure in atmospheres x mean beam length in feet.8
(1 bar-cm = 0.0324 ft-atm; T(F) = [T(C) x 1.8] + 32)
EmissivityofWaterVapor
0.70
0.50
0.10
0.05
0.01
2200200016001200800200
Temperature, C
T(F) = (T(C) x 1.8) + 32
1000 1400 1800400 600
Water Vapor
Total Pressure 1 bar
Partial Pressure 0 bar
40 bar cm
80 bar cm
150 bar cm
400 bar cm
10 bar cm
20 bar cm
3 bar cm
0.5
bar cm
1.5 bar cm
6 bar cm0.08
0.04
0.03
0.02
0.20
p
w L
=
0.2
bar cm](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-119-320.jpg)
![4-18 Steam 41 / Heat Transfer
The Babcock & Wilcox Company
have any physical significance and are dependent
upon the choice of engineering units. The physical
properties factor, Fpp, similar to the one previously
defined, is evaluated at the gas film temperature for
a particular fluid (gas or air). The mass flux or mass
flow per unit area, G, and the Reynolds numbers used
in Equations 59 and 60 and Figs. 18, 21 and 22 are
calculated based on flow conditions at the minimum
free area (maximum velocity) between tubes.
The arrangement factor, Fa, depends on the geomet-
ric configuration of tubes, the ratio of tube spacing to
diameter, Reynolds number, and the presence of ash
in the flue gas. Values of Fa for clean tube conditions
with air or flue gas without ash are given in Fig. 21.
Values of Fa for commercially clean tube conditions
with ash-laden flue gas are given in Fig. 22.
The depth factor, Fd, accounts for entrance effects
for banks of tubes which are less than ten rows deep
in the direction of gas flow. For undisturbed flow [flow
that is straight and uninterrupted for at least 4 ft (1.2
m) before entering a tube bank] approaching a bank
of less than ten rows, the film conductance must in-
clude the correction factor, Fd, shown in Fig. 23. Fd is
unity when the tube bank is preceded by a bend, screen,
damper or another tube bank in close proximity.
Turbulent longitudinal flow around tubes Correla-
tions that were developed based on turbulent flow in
tubes (Equations 56 and 57, and Figs. 13 to 17) can
also be applied for external flow parallel to tubes. In
this case, the equivalent diameter De (defined by
Equation 46) is used in the evaluation of Reynolds
number. For flow parallel to a bank of circular tubes
arranged on rectangular spacing, the equivalent di-
ameter becomes:
D
D
De
o
o= −
4 1 2
π (62)
where Do is the tube outside diameter and 1 and 2 are
the centerline spacing between tubes. The mass flux
or mass flow per unit area, G, in Equations 56 and
57, and Fig. 13 is calculated based on the free area
between tubes.
Fig. 19 Effect of film temperature, Tf, and moisture on the physical
properties factor, Fpp, for gas in turbulent crossflow over tubes
(English units only).
Fig. 20 Effect of film temperature, Tf, and moisture on the physical
properties factor, Fpp, for air in crossflow over tubes (English units only).
Fig. 17 Temperature factor, FT, for converting mass velocity from
bulk to film basis for air, gas or steam; turbulent flow inside tubes or
longitudinal flow over tubes.
100
1000
0.1 1 10
D
= Outside Tube Diameter, in.
5
4
3
2
1
0.5
G = Mass Flux of Gas or Air, 1000 lb/h ft
200
100
300
500
10
50
20
30
1
2
3
5
h = 0.321 G /D
Crossflow
h=BasicConvectionVelocityandGeometryFactor
forCrossflow
Fig. 18 Basic crossflow convection velocity and geometry factor,
h′c, for gas or air (English units only).](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-124-320.jpg)
![4-22 Steam 41 / Heat Transfer
The Babcock & Wilcox Company
previously tested. The outlet temperatures can only be
found by trial and error using the methods previously
presented. These applications are best handled by the
net transfer unit (NTU) method that uses the heat
exchanger effectiveness (see Reference 16).
Heat transfer in porous materials
Porosity is an important factor in evaluating the ef-
fectiveness of insulation materials. In boiler applica-
tions, porous materials are backed up by solid walls or
casings,sothatthereisminimalflowthroughthepores.
Heat flow in porous insulating materials occurs by
conduction through the material and by a combina-
tion of conduction and radiation through the gas-filled
voids. In most refractory materials, the Grashof-
Prandtl (Raleigh) number is small enough that neg-
ligible convection exists although this is not the case
in low density insulations [< 2 lb/ft3
(32 kg/m3
)]. The
relative magnitudes of the heat transfer mechanisms
depend, however, on various factors including poros-
ity of the material, gas density and composition fill-
ing the voids, temperature gradient across the mate-
rial, and absolute temperature of the material.
Analytical evaluation of the separate mechanisms
is complex, but recent experimental studies at B&W
have shown that the effective conductivity can be
approximated by:
k a bT cTeff = + + 3
(75)
Experimental data can be correlated through this
form, where a, b and c are correlation coefficients. The
heat flow is calculated using Equation 1; k is replaced
by keff and T is the local temperature in the insulation.
Fig. 28 Coefficient Y as a function of ratio R/r for fin efficiency.
In high temperature applications, heat transfer
across the voids occurs mainly by radiation and the
third term of Equation 75 dominates. In low tempera-
ture applications, heat flow by conduction dominates
and the first two terms of Equation 75 are controlling.
Film condensation
When a pure saturated vapor strikes a surface of
lower temperature, the vapor condenses and a liquid
film is formed on the surface. If the film flows along
the surface because of gravity alone and a condition
of laminar flow exists throughout the film thickness,
then heat transfer through this film is by conduction
only. As a result, the thickness of the condensate film
has a direct effect on the quantity of heat transferred.
The film thickness, in turn, depends on the flow rate
of the condensate. On a vertical surface, because of
drainage, the thickness of the film at the bottom will
be greater than at the top. Film thickness increases
as a plate surface is inclined from the vertical position.
As the film temperature increases, its thickness
decreases primarily due to increased drainage veloc-
ity. In addition, the film thickness decreases with in-
creasing vapor velocity in the direction of drainage.
Mass diffusion and transfer
Heat transfer can also occur by diffusion and mass
transfer. When a mixture of a condensable vapor and
a noncondensable gas is in contact with a surface that
is below the dew point of the mixture, some conden-
sation occurs and a film of liquid is formed on the sur-
face. An example of this phenomenon is the conden-
sation of water vapor on the outside of a metal con-
tainer. As vapor from the main body of the mixture
diffuses through the vapor-lean layer, it is condensed
on the cold surface as shown in Fig. 29. The rate of
condensation is therefore governed by the laws of gas
diffusion. The heat transfer is controlled by the laws
of conduction and convection.
The heat transferred across the liquid layer must
equal the heat transferred across the gas film plus the
latent heat given up at the gas-liquid interface due
to condensation of the mass transferred across the gas
film. An equation relating the mass transfer is:
h T T h T T K H Y Yi g g i y fg g iδ δ−( ) = −( ) + −( ) (76)
where T and Y define the temperatures and concen-
trations respectively identified in Fig. 29, hδ is the
heat transfer coefficient across the liquid film, hg is
the heat transfer coefficient across the gas film, and
Ky is the mass transfer coefficient. Hfg is the latent
heat of vaporization.
Heat transfer due to mass transfer is important in de-
signing cooling towers and humidifiers, where mixtures
of vapors and noncondensable gases are encountered.
Evaporation or boiling
The phenomenon of boiling is discussed in Chap-
ters 1 and 5, where the heat transfer advantages of
nucleate boiling are noted. Natural-circulation fossil
fuel boilers are designed to operate in the boiling
range. In this range, the heat transfer coefficient var-
Fig. 27 Fin efficiency as a function of parameter X.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-128-320.jpg)
![4-28 Steam 41 / Heat Transfer
The Babcock & Wilcox Company
an arrangement that is expensive to fabricate, diffi-
cult to install, or costly to maintain. A compromise
between heat transfer effectiveness and manufactur-
ing, erection, and service limitations is therefore nec-
essary in selecting tube diameter.
Penetration of radiation A convection bank of tubes
bordering a furnace or a cavity acts as a blackbody
radiant heat absorber. Some of the impinging heat,
however, radiates through the spaces between the
tubes of the first row and may penetrate as far as the
fourth row. The quantity of heat penetration can be
established by geometric or analytical methods. The
effect of this penetration is especially important in
establishing tube temperatures for superheaters lo-
cated close to a furnace or high temperature cavity.
Consider 2.0 in. (50.8 mm) OD tubes placed in an ar-
ray of tubes on a 6.0 in. (152.4 mm) pitch. Fig. 33,
curve 1 can be used to estimate the remaining radia-
tion. For a given radiant heat flux, 45% is absorbed
in the first tube row, and 55% passes to the second
row. 45% of this reduced amount is again absorbed in
the second tube row. After the fourth row, less than
10% of the initial radiation remains.
Effect of lanes Lanes in tube banks, formed by the
omission of rows of tubes, may decrease the heat ab-
sorption considerably. These passages act as bypasses
for flowing hot gases and radiation losses. Although
the overall efficiency decreases, the high mass flow
through the lanes increases the absorption rate of the
adjacent tubes. Critical tube temperatures in super-
heaters or steaming conditions in economizers may
develop. Whenever possible, lanes should be avoided
within tube banks and between tube banks and walls;
however, this is not always possible. A calculation ac-
counting for the lanes is necessary in such cases.
Heat transfer to water
Water heat transfer coefficient The heat transfer co-
efficient for water in economizers is so much higher
than the gas-side heat transfer coefficient that it can
be neglected in determining economizer surface.
Boiling water heat transfer coefficient The combined
gas-side heat transfer coefficient (convection plus
intertube radiation) seldom exceeds 30 Btu/h ft2
F (170
W/m2
K) in boiler design practice. The heat transfer
coefficient for boiling water [l0,000 Btu/h ft2
F (56,784
W/m2
K)] is so much larger that it is generally ne-
glected in calculating the resistance to heat flow, al-
though Equation 4 in Chapter 5 can be used to calcu-
late this value.
Effect of scale Water-side and steam-side scale de-
posits provide high resistance to heat flow. As scale
thickness increases, additional heat is required to
maintain a given temperature inside a furnace tube.
This leads to high metal temperatures and can cause
tube failure. Deposition of scale and other contami-
nants is prevented by good feedwater treatment and
proper operating practices.
Heat transfer to steam In superheaters, the steam-
side convection constitutes a significant resistance to
heat flow.Although this resistance is much lower than
the gas-side resistance, it can not be neglected in com-
puting the overall heat flow resistance or the heat
transfer rate. It is particularly significant in calculat-
ing superheater tube temperatures, because the mean
tube wall temperature is equal to the steam tempera-
ture plus the temperature drop through the steam film
plus half of the metal temperature drop.
Thesteam-sideheattransfercoefficientiscalculated
from Equation 58 using information from Figs. 13, 16
and 17. If the steam heat transfer coefficient is desig-
nated as h, the film temperature drop, ∆Tf, is q/(hA),
using the outside surface area of the tube as the base
in each expression.
It is imperative to prevent scale deposits in super-
heater tubes. Because of its high resistance to heat flow
and due to the elevated temperatures, even a thin layer
of scale may be sufficient to overheat and fail a tube.
Cavities
Cavities are necessary between tube banks of steam
generating units for access, for sootblowers, and for
possible surface addition. Hot flue gas radiates heat
to the boundary surfaces while passing through the
cavity. The factors involved in calculating heat trans-
fer in cavities are as follows.
Temperature level Radiation from nonluminous
gases to boundary surfaces and radiation to the gas
by the surroundings increase approximately by the
fourth power of their respective absolute tempera-
tures. Remembering that Eb = σ T4
, Equations 39 and
40 illustrate this relationship.
Gas composition Carbon dioxide and water vapor
are the normal constituents of flue gases which emit
nonluminous radiation in steam generating units.
The concentrations of these constituents depend on the
fuel burned and the amount of excess air.
Particles in the gas The particles carried by flue
gases receive heat from the gas by radiation, convec-
tion, and conduction, and emit heat by radiation to
the furnace enclosure.
Size of cavity The heat transfer rate increases with
cavity size. Thick layers of gas radiate more vigorously
than thin layers. The shape of the cavity can also com-
plicate heat transfer calculations.
Fig. 39 Comparison of radiative and convective heat transfer
contributions to absorption in various locations within a large utility
boiler (SH = superheater; RH = reheater; 1 in. = 2.54 cm).
Surfaces in Zone
60
(189.3)
50
(157.7)
40
(126.1)
30
(94.6)
20
(63.1)
10
(31.5)
0
HeatFlux,1000Btu/hft2(kW/m2)
1 2 3 4 5 6 7 8 9 10
Convective
Radiative
1
6 8
97
10
2
3
5
24in.SHPlatens
Cavity
12in.SH
9in.RH
Cavity
9in.RH
Cavity
48-54in.Platens+Enclosure
4](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-134-320.jpg)
![Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-1
The Babcock & Wilcox Company
Chapter 5
Boiling Heat Transfer,
Two-Phase Flow and Circulation
A case of heat transfer and flow of particular inter-
est in steam generation is the process of boiling and
steam-water flow. The boiling or evaporation of wa-
ter is a familiar phenomenon. In general terms, boil-
ing is the heat transfer process where heat addition
to a liquid no longer raises its temperature under con-
stant pressure conditions; the heat is absorbed as the
liquid becomes a gas. The heat transfer rates are high,
making this an ideal cooling method for surfaces ex-
posed to the high heat input rates found in fossil fuel
boilers, concentrated solar energy collectors and the
nuclear reactor fuel bundles. However, the boiling
phenomenon poses special challenges such as: 1) the
sudden breakdown of the boiling behavior at very high
heat input rates, 2) the potential flow rate fluctuations
which may occur in steam-water flows, and 3) the ef-
ficient separation of steam from water. An additional
feature of boiling and two-phase flow is the creation
of significant density differences between heated and
unheated tubes. These density differences result in
water flowing to the heated tubes in a well designed
boiler natural circulation loop.
Most fossil fuel steam generators and all commer-
cial nuclear steam supply systems operate in the pres-
sure range where boiling is a key element of the heat
transfer process. Therefore, a comprehensive under-
standing of boiling and its various related phenom-
ena is essential in the design of these units. Even at
operating conditions above the critical pressure, where
water no longer boils but experiences a continuous
transition from a liquid-like to a gas-like fluid, boil-
ing type behavior and special heat transfer charac-
teristics occur.
Boiling process and fundamentals
Boiling point and thermophysical properties
The boiling point, or saturation temperature, of a
liquid can be defined as the temperature at which its
vapor pressure is equal to the total local pressure. The
saturation temperature for water at atmospheric pres-
sure is 212F (100C). This is the point at which net
vapor generation occurs and free steam bubbles are
formed from a liquid undergoing continuous heating.
As discussed in Chapter 2, this saturation tempera-
ture (Tsat) is a unique function of pressure. TheAmeri-
can Society of Mechanical Engineers (ASME) and the
International Association for the Properties of Steam
(IAPS) have compiled extensive correlations of thermo-
physical characteristics of water. These characteristics
include the enthalpy (or heat content) of water, the
enthalpy of evaporation (also referred to as the latent
heat of vaporization), and the enthalpy of steam. As
the pressure is increased to the critical pressure [3200
psi (22.1 MPa)], the latent heat of vaporization declines
to zero and the bubble formation associated with boil-
ing no longer occurs. Instead, a smooth transition from
liquid to gaseous behavior occurs with a continuous in-
crease in temperature as energy is applied.
Two other definitions are also helpful in discussing
boiling heat transfer:
1. Subcooling For water below the local saturation
temperature, this is the difference between the
saturation temperature and the local water tem-
perature (Tsat – T ).
2. Quality This is the flowing mass fraction of steam
(frequently stated as percent steam by weight or
%SBW after multiplying by 100%):
x
m
m m
=
+
steam
water steam
(1)
where
msteam
= steam flow rate, lb/h (kg/s)
mwater
= water flow rate, lb/h (kg/s)
Thermodynamically, this can also be defined as:
x
H H
H
or
H H
H H
f
fg
f
g f
=
− −
− (2)
where
H = local average fluid enthalpy, Btu/lb (J/kg)
Hf = enthalpy of water at saturation, Btu/lb (J/kg)
Hg = enthalpy of steam at saturation, Btu/lb (J/kg)
Hfg = latent heat of vaporization, Btu/lb (J/kg)
When boiling is occurring at saturated, thermal
equilibrium conditions, Equation 2 provides the frac-
tional steam flow rate by mass. For subcooled condi-](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-141-320.jpg)
![Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-9
The Babcock & Wilcox Company
uid is flowing in the annular film. At lower steam
qualities, the liquid film may have larger ampli-
tude waves adding to the liquid droplet entrain-
ment and transport in the continuous steam core.
At high qualities, the annular film becomes very
thin, bubble generation is suppressed and the
large amplitude waves disappear.
4. Mist flow A continuous steam core transports en-
trained water droplets which slowly evaporate
until a single-phase steam flow occurs. This is also
referred to as droplet or dispersed flow.
In the case of inclined and horizontal co-current
steam-water flow in heated tubes, the flow patterns
arefurthercomplicatedbystratificationeffects.Athigh
flow rates, the flow patterns approach those of verti-
cal tubes. At lower rates, additional distinct flow pat-
terns (wavy, stratified and modified plug) emerge as
gravity stratifies the flow with steam concentrated in
the upper portion of the tube. This can be a problem
where inclined tubes are heated from the top. CHF or
dryout conditions occur at much lower steam quali-
ties and lower heat input rates in such inclined or
horizontal tubes.
Additional complexity in patterns is observed when
two-phase flow occurs in parallel or crossflow tube
bundles. The tubes, baffles, support plates and mix-
ing devices further disrupt the flow pattern formation.
Flow maps The transitions from one flow regime to
another are quite complex, with each transition rep-
resenting a combination of factors. However, two di-
mensional flow maps provide at least a general indi-
cation of which flow pattern is likely under given op-
erating conditions. The maps generally are functions
of superficial gas and liquid velocities.An example for
vertical, upward, steam-water co-current flow is pro-
vided in Fig. 13.11
The axes in this figure represent
the superficial momentum fluxes of the steam (y-axis)
and water (x-axis). A sample flow line is shown begin-
ning at nearly saturated water conditions and end-
ing with saturated steam conditions. The tube expe-
riences bubbly flow only near its inlet. This is followed
by a brief change to intermediate flow before annu-
lar flow dominates the heated length.
Other flow maps are available for arrangements
such as downflow tubes, inclined tubes and bundles.
Flow maps, however, are only approximations provid-
ing guidance in determining the relevant flow struc-
ture for a given situation.
Pressure loss
The local pressure loss, ∆P [lb/ft2
(Pa)] or gradient
δP/δl [lb/ft2
/ft (Pa/m)] in a two-phase steam-water
system may be represented by:
∆ ∆ ∆ ∆ ∆P P P P Pf a g l= + + + (6a)
or
− = −
−
−
+
δ
δ
δ
δ
δ
δ
δ
δ
P
l
P
l
P
l
P
l
P
f a g
l∆ (6b)
The ∆Pf and –(δ P/δ l)f terms account for local wall
friction losses. The ∆Pa and –(δ P/δ l)a terms address
the momentum or acceleration loss incurred as the
volume increases due to evaporation. The hydraulic
or static head loss is accounted for by ∆Pg and –(δ P/
δ l)g. Finally, all of the local losses due to fittings, con-
tractions, expansions, bends, or orifices are included
in ∆Pl. The evaluation of these parameters is usually
made using one of two models: homogeneous flow or
separated flow.
A parameter of particular importance when evalu-
ating the pressure loss in steam-water flows is void
fraction. The void fraction can be defined by time-av-
eraged flow area ratios or local-volume ratios of steam
to the total flow. The area-based void fraction, α, can
be defined as the ratio of the time-averaged steam flow
cross-sectional area (Asteam) to the total flow area (Asteam
+ Awater):
α =
+
A
A A
steam
steam water
(7)
Using the simple continuity equation, the relation-
ship between quality, x, and void fraction is:
α
ρ
ρ
=
+ −( )
x
x x Sg
f
1 (8)
where
S = ratio of the average cross-sectional velocities
of steam and water (referred to as slip)
ρg = saturated steam density, lb/ft3
(kg/m3
)
ρf = saturated water density, lb/ft3
(kg/m3
)
Fig. 13 Flow pattern map for vertical upward flow of water.11](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-149-320.jpg)
![Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-15
The Babcock & Wilcox Company
bution of the steam-water mixture, 3) added flow re-
sistance, and 4) the maximum steam flow travel length
to enhance the gravity-driven separation process.
Various combinations of perforated plates have also
been used. The performance of these devices must be
determined by experimental evaluations and they are
typically limited to smaller, low capacity boilers.
Mechanical primary separators
Centrifugal force or radial acceleration is used al-
most universally for modern steam-water separators.
Three types of separators are shown in Fig. 23: the
conical cyclone, the curved arm and the horizontal
cyclone. The B&W vertical cyclone steam separator is
shown in more detail in Fig. 24. Vertical cyclones are
arranged internally in rows along the length of the
drum and the steam-water mixture is admitted tan-
gentially as shown in Fig. 19. The water forms a layer
against the cylinder walls and the steam moves to the
core of the cylinder then upward. The water flows
downward in the cylinder and is discharged through
an annulus at the bottom, below the drum water level.
With the water returning from drum storage to the
Fig. 20 Effect of rate of steam generation on steam separation in a
boiler drum without separation devices.
Fig. 21 Effect of location of discharge from risers on steam
separation in a boiler drum without separation devices.
downcomers virtually free of steam bubbles, the maxi-
mum net pumping head is available for producing flow
in the circuits. The steam moving upward from the
cylinder passes through a small primary corrugated
scrubber at the top of the cyclone (see Fig. 24) for ad-
ditional separation. Under many operating conditions,
no further separation is required.
When wide load fluctuations and water analysis
variations are expected, large corrugated secondary
scrubbers may be installed at the top of the drum (see
Fig. 19) to provide very high steam separation. These
scrubbers are also termed secondary separators. They
provide a large surface which intercepts water drop-
lets as the steam flows sinuously between closely fit-
ted plates. Steam velocity through the corrugated plate
assembly is very low, so that water re-entrainment is
avoided. The collected water is drained from the bot-
tom of the assembly to the water below.
One to four rows of cyclone separators are installed
in boiler drums, with ample room for access. For
smaller boilers at lower pressures [100 psig (0.7 MPa
gauge)], the separation rate of clean steam by single
and double rows of cyclone separators is approximately
Fig. 22 Simple types of primary steam separators in boiler drums: a) deflector baffle, b) alternate deflector baffle, and c) compartment baffle.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-155-320.jpg)
![Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-19
The Babcock & Wilcox Company
changes in heating surface cleanliness and changes
in burner operation.
Natural circulation is most effective where there is
a considerable difference in density between steam
and water phases. As shown in Fig. 29, the potential
for natural circulation flow remains very high even
at pressures of 3100 psi (21.4 MPa).
Forced circulation
In recirculating or once-through forced circulation
systems, mechanical pumps provide the driving head
to overcome the pressure losses in the flow circuitry.
Unlike natural circulation, forced circulation does not
enjoy an inherent flow-compensating effect when
heat input changes, i.e., flow does not increase signifi-
cantly with increasing heat input. This is because a
large portion of the total flow resistance in the boiler
tubes arises from the flow distribution devices (usually
orifices) used to balance flow at the circuit inlets. The
large resistance of the flow distributors prevents signifi-
cant increases in flow when heat absorption is increased.
Forced circulation is, however, used where the boil-
ers are designed to operate near or above the critical
pressure [3200 psi (22.1 MPa)]. There are instances
in the process and waste heat fields and in some spe-
cialized boiler designs where the use of circulating
pumps and forced circulation can be economically at-
tractive. Atpressuresabove3100psi(21.4MPa)anatu-
ral circulation system becomes increasingly large and
costly and a pump can be more economical. In addition,
the forced circulation principle can work effectively in
both the supercritical and subcritical pressure ranges.
In forced recirculation there is a net thermal loss
because of the separate circulating pump. While prac-
tically all the energy required to drive the pumps re-
appears in the water as added enthalpy, this energy
originally came from the fuel at a conversion to use-
ful energy factor of less than 1.0. If an electric motor
drive is used, the net energy lost is about twice the
energy supplied to the pump motor for typical fossil
fuel systems.
Circulation design and evaluation
The furnace wall enclosure circuits are very impor-
tant areas in a boiler. High constant heat flux condi-
tions make uninterrupted cooling of furnace tubes
essential. Inadequate cooling can result in rapid over-
heating, cycling thermal stress failure, or material
failures from differential tube expansion. Sufficient
conservatism must be engineered into the system to
provide adequate cooling even during transient up-
set conditions. Simultaneously, the rated steam flow
conditions must be maintained at the drum outlet.Any
of the circulation methods discussed may be used to
cool the furnace waterwall tubes. In evaluating the
circulation method selected for a particular situation,
the following general procedure can be used:
1. The furnace geometry is set by the fuel and combus-
tion system selected. (SeeChapters11,14,19and21.)
2. Standardized components (furnace walls, headers,
drums, etc.) are selected to enclose the furnace ar-
rangement as needed. (See Chapters 19 and 21.)
3. The local heat absorption is evaluated based upon
the furnace geometry, fuel and firing method. Lo-
cal upset factors are evaluated based upon past
field experience. (See Chapter 4.)
4. Circulation calculations are performed using the
pressure drop relationships.
5. Thecalculatedcirculationresults(velocities,steam
qualities, etc.) are compared to the design criteria.
6. The flow circuitry is modified and the circulation
re-evaluated until all of the design criteria are met.
Some of the design criteria include:
1. Critical heat flux limits For recirculating systems,
CHF conditions are generally avoided. For once-
through systems, the temperature excursions at
CHF are accommodated as part of the design.
2. Stability limits These limits generally indicate
acceptablepressuredropversusmassflowrelation-
ships to ensure positive flow in all circuits and to
avoid oscillating flow behavior.
3. Steam separator and steam drum limits These
indicate maximum steam and water flow rates to
individual steam-water separators and maximum
water flow to the drum downcomer locations to
ensure that steam carryunder and water carryover
will not be problems.
4. Minimum velocity limits Minimum circuit satu-
rated velocities assure that solids deposition, po-
tentially detrimental chemistry interactions, and
selected operating problems are minimized.
5. Sensitivity The system flow characteristic is
checked to ensure that flow increases with heat
input for all expected operating conditions.
Circulation is analyzed by dividing the boiler into
individual simple circuits – groups of tubes or circuits
with common end points and similar geometry and
heat absorption characteristics. The balanced flow
condition is the simultaneous solution of the flow char-
acteristics of all boiler circuits.
At the heart of a B&W circulation evaluation is a
circulation computer program that incorporates tech-Fig. 29 Effect of pressure on pumping head.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-159-320.jpg)
![The Babcock & Wilcox Company
Steam 41 / Metallurgy, Materials and Mechanical Properties 7-7
low alloy ferritic steels. It reduces the coefficient of
thermal expansion and diminishes the electrical and
thermal conductivities. It is attacked by sulfur com-
pounds at elevated temperatures.
Cobalt(Co) suppresses hardenability in steels. How-
ever, when added to austenite, it is a strong solution
strengthener and a carbide former. It also significantly
improves creep strength. Binary Fe-Co alloys have the
highest magnetic saturation induction of any known
materials. Therefore, such alloys are often used in
permanent magnets.
Tungsten (W) acts similarly to molybdenum. It is a
very strong carbide former and solid solution
strengthener. It forms hard, abrasion resisting car-
bides in tool steels, develops high temperature hard-
ness in quenched and tempered steels, and contrib-
utes to creep strength in some high temperature alloys.5
Vanadium (V) is a degasifying and deoxidizing
agent, but it is seldom used in that capacity because
of high cost. It is applied chiefly as an alloying ele-
ment in steel to increase strength, toughness and
hardness. It is essentially a carbide forming element
which stabilizes the structure, especially at high tem-
peratures. Vanadium minimizes grain growth tenden-
cies,therebypermittingmuchhigherheattreatingtem-
peratures. It also intensifies the properties of other ele-
ments in alloy steels. Small additions of vanadium (0.1
to 0.5%), accompanied by proper heat treatment, give
steels containing 0.5 to 1.0% molybdenum pronounced
improvement in high temperature creep properties.
Titanium (Ti) and columbium (Cb) (also known as
niobium) are the most potent carbide forming ele-
ments. Ti is also a good deoxidizer and denitrider.
These elements are most effective in the Cr-Ni auste-
nitic alloys, where they react more readily with car-
bon than does Cr. This allows the Cr to remain in solid
solution and in the concentrations necessary to main-
tain corrosion resistance. Ti and Cb [or Cb plus tan-
talum (Ta)] are used to reduce air hardening tenden-
cies and to increase oxidation resistance in steel
containing up to 14% Cr. These elements have a ben-
eficial effect on the long term, high temperature proper-
ties of Cr-Ni stainless steels because of the stability of
theircarbides,nitridesandcarbonitrides.CbandTihave
also been used in some of the super alloys to improve
high temperature properties. Ti forms an intermetallic
compound with Ni in these alloys, Ni3Ti, called gamma
prime ′( )γ , which is a potent strengthening phase.
Copper (Cu), when added to steel in small amounts,
improves its resistance to atmospheric corrosion and
lowers the attack rate in reducing acids. Cu, like Ni,
is not resistant to sulfur compounds at elevated tem-
peratures. Consequently, it is not ordinarily used in
low alloy steels intended for high temperature service
where sulfur is a major component of the environ-
ment, as in combustion gases. Cu is added (up to 1%)
in low alloy constructional steels to improve yield
strength and resistance to atmospheric corrosion. Its
presence in some of the high alloy steels increases
corrosion resistance to sulfuric acid.
Boron (B) is usually added to steel to improve
hardenability, that is, to increase the depth of hard-
ening during quenching of alloy steels. When com-
bined with Mo, it is a strong bainite stabilizer. Small
amounts of boron in the presence of Mo suppress the
formation of martensite, leading to the complete trans-
formation to bainite before the Ms temperature is
reached. This substantially improves the strength and
stability of Cr-Mo pressure vessel steels. The B-10 iso-
tope of boron has a very high neutron-capture cross-
section,soitisaddedtosteelsusedforcontainmentand
storage vessels of nuclear fuels and waste products.
Nitrogen (N) has two primary functions as an al-
loying agent in steels. In carbon and low alloy steels,
it is used in case hardening, in which nascent nitro-
gen is diffused into the steel surface. Nitrogen and car-
bon are interstitial solid solution strengtheners. In the
presence of Al or Ti, additional strengthening results
by precipitate formations of the respective nitrides or
carbonitrides. In austenitic stainless steels, nitrogen
provides the same interstitial strengthening as car-
bon, but does not deplete the austenite of chromium
as does carbon by the formation of carbides. The
strength of nitrogen-containing stainless steels is
therefore equivalent to that of the carbon-containing
stainlesses. This strength is achieved without the sus-
ceptibility to corrosive attack that results from local
carbide formation at grain boundaries of these steels.
Oxygen (O) is not normally considered to be an al-
loying element. It is present in steel as a residual of
the steel making process.6,7
However, a few oxides are
so hard and stable, notably those ofAl, Ti and thorium
(Th),thattheyarepotentstrengthenerswhendispersed
as fine particles throughout an alloy. This can be accom-
plished by internal oxidation in an oxygen-containing
atmosphere or by powder metallurgical techniques.
Aluminum (Al) is an important minor constituent
of low alloy steels. It is an efficient deoxidizer and
grain refiner, and is widely used in producing killed
steel. When added to steel in appreciable quantities,
Al forms tightly adhering refractory oxide scales and
therefore, increases resistance to scaling. It is difficult,
however, to add appreciable amounts of this element
without producing undesirable effects. In the amounts
customarily added (0.015 to 0.080%), Al does not in-
crease resistance to ordinary forms of corrosion. Be-
cause of their affinity for oxygen, high-aluminum
steels generally contain numerous alumina inclusions
which can promote pitting corrosion. The refined grain
size does improve room temperature toughness and
ductility of carbon steels.
An excessive quantity of aluminum has a detrimen-
tal effect on creep properties, particularly in plain
carbon steel. This is attributable to its grain refining
effect and to its acceleration of graphitization of the
carbide phase.
Silicon (Si) greatly contributes to steel quality be-
cause of its deoxidizing and degasifying properties.
When added in amounts up to 2.5%, the ultimate
strength of steel is increased without loss in ductility.
Si in excess of 2.5% causes brittleness and amounts
higher than 5% make the steel nonmalleable.
Resistance to oxidation of steel is increased by add-
ing silicon. Si increases the electrical conductivity of
steel and decreases hysteresis losses. Si steels are,
therefore, widely used in electrical apparatus.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-195-320.jpg)
![The Babcock & Wilcox Company
Steam 41 / Metallurgy, Materials and Mechanical Properties 7-23
and flow balancing among circuits); mechanical fac-
tors (internal pressure, design temperature, support
systems and relative thermal expansion stresses);
environmental factors (resistance to steam oxidation
and out of service pitting corrosion on the ID, and oxi-
dation, fuel ash corrosion, and erosion on the outside
diameter/OD); and manufacturing process and equip-
mentlimitationsandconsiderations,suchasweldability.
Cost
Material cost is usually the single largest factor
affecting material selection when more than one ma-
terial candidate exists for a given set of boiler appli-
cation conditions. Raw material cost is established by
taking into account each material’s allowable design
stress, at design temperature and pressure, and re-
quired mass flow requirements for the water or steam.
Pressure part sizes are established, average weight
determined, and material cost is estimated when
knowing the raw material cost offered by the selected
raw material supplier. Other factors are also consid-
ered such as required corrosion allowance, if any, and
unique manufacturing costs and risks. Once this
evaluationisaccomplishedandcomparisonofmaterials
is completed, it is quite common to find that stronger,
higher alloys become economically attractive over lower
strength, less costly steels at operating conditions usu-
ally acceptable and appropriate for the lower alloy steel.
Headers and piping
Specifications for most of the commonly used pipe
materials are listed in Table 1. As these components
are usually not in the gas stream and are unheated,
the major design factor, other than strength at tem-
perature, is steam oxidation resistance. Carbon steels
are not used above 800F (427C) outside the boiler set-
ting, and C-Mo is limited to applications of small sizes
[less than 10.75 in. (273 mm) OD] and below 875F
(468C) to avoid graphitization.
9Cr-1Mo-V has replaced 2-1/4Cr-1Mo for many
superheater outlet header applications (see Fig. 25).
This material is not operating in the creep range even
at the 1000 to 1050F (538 to 566C) design tempera-
tures of most such components. This factor and its very
high strength allow thinner components which are
much less susceptible to the creep-fatigue failures
observed in older 1-1/4Cr-1/2Mo-Si and 2-1/4Cr-1Mo
headers. The use of forged outlet nozzle tee sections
in place of welded nozzles has also reduced the poten-
tial for failure of these large piping connections.
Drums
Carbon steel plate is the primary material used in
drums. SA-299, a 75,000 psi (517.1 MPa) tensile
strength material, ordered to fine grain melting prac-
tice for improved toughness, is used for heavy section
Fig. 25 The 9Cr-1Mo-V superheater outlet header features high strength and thin material less susceptible to creep-fatigue failure.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-211-320.jpg)
![The Babcock & Wilcox Company
8-8 Steam 41 / Structural Analysis and Design
βδM1 = radial displacement of Element (1) due to unit
moment load
βγV1 = rotation of Element (1) due to unit shear load
βγM1 = rotation of Element (1) due to unit moment
load
Because δFINAL 1 = δFINAL 2 and γFINAL 1 = γFINAL 2 from com-
patibility requirements, Equations 28 through 31 can
be reduced to two equations for two unknowns, Vo and
Mo, which are solved simultaneously. Note that the
number of equations reduces to the number of redun-
dant loadings and that the force F can be determined
by static equilibrium requirements.
Once Vo and Mo have been calculated, handbook
solutions can be applied to determine the resulting
membrane and bending stresses. The discontinuity
stress must then be added to the free body stress to
obtain the total stress at the intersection.
Although the example demonstrates internal pres-
sure loading, the same method applies to determin-
ing thermally induced discontinuity stress. For more
complicated geometries involving four or more un-
known redundant loadings, commercially available
computer programs should be considered for solution.
Finite element analysis Whenthegeometryofacom-
ponent or vessel is too complex for classical formulas
or closed form solutions, finite element analysis (FEA)
can often provide the required results. FEA is a pow-
erful numerical technique that can evaluate structural
deformations and stresses, heat flows and tempera-
tures, and dynamic responses of a structure. Because
FEA is usually more economical than experimental
stress analysis, scale modeling, or other numerical
methods, it has become the dominant sophisticated
stress analysis method.
During product development, FEA is used to pre-
dict performance of a new product or concept before
building an expensive prototype. For example, a de-
sign idea to protect the inside of a burner could be ana-
lyzed to find out if it will have adequate cooling and fa-
tigue life. FEA is also used to investigate field problems.
To apply FEA, the structure is modeled as an as-
sembly of discrete building blocks called elements. The
elements canbelinear(onedimensionaltrussorbeam),
plane (representing two dimensional behavior), or solid
(three dimensional bricks). Elements are connected at
their boundaries by nodes as illustrated in Fig. 8.
Except for analyses using truss or beam elements,
the accuracy of FEA is dependent on the mesh den-
sity. This refers to the number of nodes per modeled
volume. As mesh density increases, the result accu-
racy also increases. Alternatively, in p-method analy-
sis, the mesh density remains constant while increased
accuracy is attained through mathematical changes
to the solution process.
Acomputersolutionisessentialbecauseofthenumer-
ous calculations involved. A medium sized FEA may re-
quire the simultaneous solution of thousands of equa-
tions, but taking merely seconds of computer time. FEA
is one of the most demanding computer applications.
FEA theory is illustrated by considering a simple
structural analysis with applied loads and specified
node displacements. The mathematical theory is es-
sentially as follows.
For each element, a stiffness matrix satisfying the
following relationship is found:
k d r { } = { } (34)
where
[k] = an element stiffness matrix. It is square and
defines the element stiffness in each direction
(degree of freedom)
{d} = a column of nodal displacements for one element
{r} = a column of nodal loads for one element
The determination of [k] can be very complex and its
theory is not outlined here. Modeling the whole struc-
ture requires that:
K D R { } = { } (35)
where
[K] = structure stiffness matrix; each member of [K]
is an assembly of the individual stiffness
contributions surrounding a given node
{D} = column of nodal displacements for the struc-
ture
{R} = column of nodal loads on the structure
In general, neither {D} nor {R} is completely known.
Therefore, Equation 35 must be partitioned (rear-
ranged) to separate known and unknown quantities.
Equation 35 then becomes:
K K
K K
D
D
R
R
s
o
o
s
11 12
21 22
=
(36)
where
Ds = unknown displacements
Do = known displacements
Rs = unknown loads
Ro = known loads
Equation 36 represents the two following equations:
K D K D Rs o o11 12 { } + { } = { } (37)
K D K D Rs o s21 22 { } + { } = { } (38)
Equation 37 can be solved for Ds and Equation 38 can
then be solved for Rs.
Using the calculated displacements {D}, {d} can be
Fig. 8 Finite element model composed of brick elements.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-222-320.jpg)
![The Babcock & Wilcox Company
Steam 41 / Structural Analysis and Design 8-9
found for each element and the stress can be calcu-
lated by:
σ{ } = { }E B d (39)
where
{σ} are element stresses
[E] and [B] relate stresses to strains and strains to
displacements respectively
FEA theory may also be used to determine tempera-
tures throughout complex geometric components. (See
also Chapter 4.) Considering conduction alone, the
governing relationship for thermal analysis is:
C T K T Q { }+ { } = { } (40)
where
[C] = system heat capacity matrix
{T } = column of rate of change of nodal
temperatures
[K ] = system thermal conductivity matrix
{T} = column of nodal temperatures
{Q} = column of nodal rates of heat transfer
In many respects, the solution for thermal analy-
sis is similar to that of the structural analysis. One im-
portant difference, however, is that the thermal solu-
tion is iterative and nonlinear. Three aspects of a ther-
mal analysis require an iterative solution.
First, thermal material properties are temperature
dependent. Because they are primary unknowns, tem-
perature assumptions must be made to establish the
initial material properties. Each node is first given an
assumed temperature. The first thermal distribution
is then obtained, and the calculated temperatures are
used in a second iteration. Convergence is attained
when the calculated temperature distributions from
two successive iterations are nearly the same.
Second, when convective heat transfer is accounted
for, heat transfer at a fluid boundary is dependent on
the material surface temperature. Again, because tem-
peratures are the primary unknowns, the solution must
be iterative.
Third, in a transient analysis, the input parameters,
including boundary conditions, may change with time,
and the analysis must be broken into discrete steps.
Within each time step, the input parameters are held
constant. For this reason, transient thermal analysis
is sometimes termed quasi-static.
FEA applied to dynamic problems is based upon the
differential equation of motion:
M D C D K D R { }+ { }+ { } = { } (41)
where
[M ] = structure lumped mass matrix
[C] = structure damping matrix
[K ] = structure stiffness matrix
{R} = column of nodal forcing functions
{ }, { } { }D D Dand are columns of nodal displacements,
velocities, and accelerations, respectively.
Variations on Equation 41 can be used to solve for
the natural frequencies, mode shapes, and responses
due to a forcing function (periodic or nonperiodic), or
to do a dynamic seismic analysis.
Limitations of FEA involve computer and human
resources. The user must have substantial experience
and, among other abilities, he must be skilled in se-
lecting element types and in geometry modeling.
In FEA, result accuracy increases with the num-
ber of nodes and elements. However, computation
time also increases and handling the mass of data can
be cumbersome.
In most finite element analyses, large scale yield-
ing (plastic strain) and deformations (including buck-
ling instability), and creep are not accounted for; the
material is considered to be linear elastic. In a linear
structural analysis, the response (stress, strain, etc.)
is proportional to the load. For example, if the applied
load is doubled, the stress response would also double.
For nonlinear analysis, FEA can also be beneficial.
Recent advancements in computer hardware and soft-
ware have enabled increased use of nonlinear analy-
sis techniques.
AlthoughmostFEAsoftwarehaswelldevelopedthree
dimensionalcapabilities,somepressurevesselanalyses
are imprecise due to a lack of acceptance criteria.
Computer software consists of commercially avail-
able and proprietary FEA programs. This software can
be categorized into three groups: 1) preprocessors, 2)
finite element solvers, and 3) postprocessors.
A preprocessor builds a model geometry and applies
boundary conditions, then verifies and optimizes the
model. The output of a finite element solver consists
of displacements, stresses, temperatures, or dynamic
response data.
Postprocessors manipulate the output from the fi-
nite element solver for comparison to acceptance cri-
teria or to make contour map plots.
Application of FEA Because classical formulas and
shell analysis solutions are limited to simple shapes,
FEA fills a technical void and is applied in response
to ASME Code requirements. A large portion of The
Babcock & Wilcox Company’s (B&W) FEA supports
pressure vessel design. Stresses can be calculated near
nozzles and other abrupt geometry changes. In addi-
tion, temperature changes and the resulting thermal
stresses can be predicted using FEA.
The raw output from a finite element solver can not
be directly applied to the ASME Code criteria. The
stressesorstrainsmustfirstbeclassifiedasmembrane,
bending, or peak (Fig. 9). B&W pioneered the classi-
fication of finite element stresses and these procedures
are now used throughout the industry.
Piping flexibility, for example, is an ideal FEA ap-
plication. In addition, structural steel designers rely
on FEA to analyze complex frame systems that sup-
portsteamgenerationandemissionscontrolequipment.
Finite element analysis is often used for preliminary
review of new product designs. For example, Fig. 10
shows the deflected shape of two economizer fin con-
figurations modeled using FEA.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-223-320.jpg)
![The Babcock & Wilcox Company
Steam 41 / Structural Analysis and Design 8-13
By using the energy rate definition, Ct can be de-
terminedexperimentallyfromtestspecimens.Thecon-
stants b and q are determined by a curve fit technique.
Under steady-state creep where the crack tip stresses
no longer change with time, the crack growth can be
characterized solely by the path independent energy
rate line integral C*, analogous to the J-integral.
C* and Ct can both be interpreted as the difference
in energy rates (power) between two bodies with in-
crementally differing crack lengths. Furthermore, C*
characterizes the strength of the crack tip stress sin-
gularity in the same manner as the J-integral char-
acterizes the elastic-plastic stress singularity.
The fully plastic deformation solutions from the
EPRI Elastic-Plastic Fracture Handbook can then be
used to estimate the creep crack tip steady-state pa-
rameter, C*.
Significant data support Ct as a parameter for corre-
latingcreepcrackgrowthbehaviorrepresentedbyEqua-
tion 47. An approximate expression8
for Ct is as follows:
C C t tt T
n
n
= ( ) +
−
−
* /
3
1
1 (48)
where tT is the transition time given by:
t
K
n EC
T
I
=
−( )
+( )
1
1
2 2
µ
*
(49)
and µ is Poisson’s ratio, and n is the secondary creep
rate exponent.
For continuous operation, Equation 48 is integrated
over the time covering crack growth from the initial
flaw size to the final flaw size. The limiting final flaw
size is chosen based on fracture toughness or insta-
bility considerations, possibly governed by cold startup
conditions. For this calculation, fracture toughness
data such as KIC, JIC or the JR curve would be used in
a failure assessment diagram approach to determine
the limiting final flaw size.
Construction features
All pressure vessels require construction features
such as fluid inlets and outlets, access openings, and
structural attachments at support locations. These
shell areas must have adequate reinforcement and
gradualgeometrictransitionswhichlimitlocalstresses
to acceptable levels.
Openings Openings are the most prevalent con-
struction features on a vessel. They can become ar-
eas of weakness and may lead to unacceptable local
distortion, known as bell mouthing, when the vessel
is pressurized. Such distortions are associated with
high local membrane stresses around the opening.
Analytical studies have shown that these high stresses
are confined to a distance of approximately one hole
diameter, d, along the shell from the axis of the open-
ing and are limited to a distance of 0.37 (dtnozzle)1/2
nor-
mal to the shell.
Reinforcement to reduce the membrane stress near
an opening can be provided by increasing the vessel
wall thickness. An alternate, more economical stress
reduction method is to thicken the vessel locally
around the nozzle axis of symmetry. The reinforcing
material must be within the area of high local stress
to be effective.
The ASME Code provides guidelines for reinforc-
ing openings. The reinforcement must meet require-
ments for the amount and distribution of the added
material. A relatively small opening [approximately
d<0.2 (Rts)1/2
where R is mean radius of shell and ts is
thickness of shell] remote from other locally stressed
areas does not require reinforcement.
Larger openings are normally reinforced as illus-
trated in Figs. 14a and 14b. It is important to avoid
excessive reinforcement that may result in high sec-
ondary stresses. Fig. 14c shows an opening with over
reinforcement and Fig. 14a shows one with well pro-
portionedreinforcement.Fig.14balsoshowsabalanced
design that minimizes secondary stresses at the nozzle/
shell juncture. Designs a and b, combined with gener-
ous radii r, are most suitable for cyclic load applications.
The ligament efficiency method is also used to com-
pensate for metal removed at shell openings. This
method considers the load carrying ability of an area
between two points in relation to the load carrying
ability of the remaining ligament when the two points
become the centers of two openings. The ASME Code
guidelines used in this method only apply to cylindri-
Fig. 13 Relationship between da/dN and ∆K as plotted on logarithmic
coordinates.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-227-320.jpg)
![9-6 Steam 41 / Sources of Chemical Energy
The Babcock & Wilcox Company
Dry, mineral-free
Dry, mineral-free
VM
FC
=
−100 , %
(2)
Moist, mineral-free Btu
Btu S
S
, per l
=
−
− +( )
×
50
100 1 08 0 55
100
. .A
bb (3)
Approximation Formulas
Dry, mineral-free
S
FC
FC
M A
=
− + +( )
×
100 1 1 0 1
100
. .
, % (4)
Dry, mineral-free
Dry, mineral-free
VM
FC
=
−100 , %
(5)
Moist, mineral-free Btu
Btu
S
, per lb
=
− +( )
×
100 1 1 0 1
100
. .A
(6)
where
Btu = heating value per lb (kJ/kg = 2.326 × Btu/lb)
FC = fixed carbon, %
VM = volatile matter, %
M = bed moisture,
A = ash, %
S = sulfur, %
all for coal on a moist basis.
Table 5 lists 16 selected U.S. coals, arranged in order
ofASTMclassification.Thefollowingdescriptionsbriefly
summarize the characteristics of each coal rank.
Peat Peat, the first product in the formation of coal,
is a heterogeneous material consisting of partially de-
composed plant and mineral matter. Its color ranges
from yellow to brownish-black, depending on its geo-
logic age. Peat has a moisture content up to 70% and
a heating value as low as 3000 Btu/lb (6978 kJ/kg).
Lignite Lignite is the lowest rank coal. Lignites are
relatively soft and brown to black in color with heat-
ing values of less than 8300 Btu/lb (19,306 kJ/kg). The
deposits are geologically young and can contain rec-
ognizable remains of plant debris. The moisture con-
tent of lignites is as high as 30% but the volatile con-
tent is also high; consequently, they ignite easily. Lig-
nite coal dries when exposed to air and spontaneous
combustion during storage is a concern. Long distance
shipment of these coals is usually not economical be-
cause of their high moisture and low Btu content. The
largest lignite deposit in the world spreads over the
regions of North and South Dakota, Wyoming, and
Montana in the U.S. and parts of Saskatchewan and
Manitoba in Canada.
Subbituminous Subbituminous coals are black,
having little of the plant-like texture and none of the
brown color associated with the lower rank lignite
coal. Subbituminous coals are non-coking (undergo
little swelling upon heating) and have a relatively high
moisture content which averages from 15 to 30%. They
also display a tendency toward spontaneous combus-
tion when drying.
Although they are high in VM content and ignite
easily, subbituminous coals generally have less ash
and are cleaner burning than lignite coals. Subbitu-
minous coals in the U.S. in general have a very low
sulfur content, often less than 1%. Because they have
reasonably high heating values [8300 to 11,500 Btu/
lb (19,306 to 26,749 kJ/kg)] and low sulfur content,
switching to subbituminous coal has become an attrac-
tiveoptionformanypowerplantstolimitSO2 emissions.
Bituminous Bituminous coal is the rank most com-
monly burned in electric utility boilers. In general, it
appears black with banded layers of glossy and dull
black. Typical bituminous coals have heating values
of 10,500 to 14,000 Btu/lb (24,423 to 32,564 kJ/kg)
and a fixed carbon content of 69 to 86%. The heating
value is higher, but moisture and volatile content are
lower than the subbituminous and lignite coals. Bi-
tuminous coals rarely experience spontaneous com-
bustion in storage. Furthermore, the high heating
value and fairly high volatile content enable bitumi-
nous coals to burn easily when pulverized to a fine
powder. Some types of bituminous coal, when heated
in the absence of air, soften and release volatiles to
form the porous, hard, black product known as coke.
Coke is used as fuel in blast furnaces to make iron.
Anthracite Anthracite, the highest rank of coal, is
shiny black, hard and brittle, with little appearance
of layers. It has the highest content of fixed carbon,
86 to 98%. However, its low volatile content makes it
a slow burning fuel. Most anthracites have a very low
moisture content of about 3%; heating values of
15,000 Btu/lb (34,890 kJ/kg) are slightly lower than
the best quality bituminous coals.Anthracite is low in
sulfur and volatiles and burns with a hot, clean flame.
These qualities make it a premium fuel used mostly
for domestic heating.
Other classification systems
There are other classifications of coal that are cur-
rently in limited use in Europe. These are the Inter-
national Classification of Hard Coals by Type and the
Table 4
Coal Analyses on As-Received Basis
(Pittsburgh Seam Coal, West Virginia)
Proximate Analysis Ultimate Analysis
Component % by wt Component % by wt
Moisture 2.5 Moisture 2.5
Volatile matter 37.6 Carbon 75.0
Fixed carbon 52.9 Hydrogen 5.0
Ash 7.0 Sulfur 2.3
Total 100.0 Nitrogen 1.5
Oxygen 6.7
Heating value, Ash 7.0
Btu/lb 13,000 Total 100.0
(kJ/kg) (30,238)](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-239-320.jpg)
![9-14 Steam 41 / Sources of Chemical Energy
The Babcock & Wilcox Company
Fuel analyses
A typical analysis of a fuel oil or waste liquid con-
tains the following information:
1. ultimate analysis
2. API gravity
3. heating value
4. viscosity
5. pour point
6. flash point
7. water and sediment
Ultimate analysis The ultimate analysis for an oil is
similar to that for a coal. The results indicate the quan-
tities of sulfur, hydrogen, carbon, nitrogen, oxygen
and ash. Ultimate analyses for various fuel oils are
given in Table 11.
The sulfur content of the oil is an indicator of its
corrosiveness and is oxidized to sulfur oxides during
combustion. These oxides can react with water vapor
or ash constituents to form corrosive acids, salts, or
boiler fouling potassium sulfate. When molten, these
ash deposits are corrosive. Furthermore, vanadium
can combine with the sulfur oxides to form a corro-
sive product. (See Chapter 21.)
API gravity The petroleum industry uses the API
gravity scale to determine the relative density of oil.
The scale was devised jointly by the American Petro-
leum Institute (API) and the National Bureau of Stan-
dards. The relationship between the API gravity and
the specific gravity is given by the following formula:
Deg API Gravity
Specific gravity at 60/60F
=
−
141 5
131 5
.
.
Given this relationship, heavier liquid fuels are de-
noted by lower API gravity values.
Heating value The heating value of a liquid fuel in-
dicates the heat released by the complete combustion
of one unit of fuel [lb (kg)]. As for coal, there are two
calculated heating values, higher (HHV) and lower
(LHV). In computing the HHV, it is assumed that any
water vapor formed by burning the hydrogen constitu-
ent is condensed and cooled to its initial temperature.
Therefore, the heat of vaporization of the water formed
is included in the HHV. For the LHV, it is assumed that
none of the water vapor condenses. Both heating values
are determined by using an oxygen bomb calorimeter.
Viscosity The viscosity of a liquid is the measure of
its internal resistance to flow. Although there are nu-
merous viscosity scales, those most commonly used in
the U.S. are:
1. Saybolt Universal Seconds (SUS),
2. Saybolt Furol Seconds (SFS),
3. absolute viscosity (centipoise), and
4. kinematic viscosity (centistokes).
The kinematic viscosity of oil is related to the abso-
lute viscosity by the following formula:
Kinematic viscosity (centistokes)
Absolute viscosity (cen
=
ttipoise)
Specific gravity
Pour point The pour point is the lowest tempera-
ture at which a liquid fuel flows under standardized
conditions.
Flash point The flash point is the temperature to
which a liquid must be heated to produce vapors that
flash but do not burn continuously when ignited.
There are two instruments used to determine the flash
point: the Pensky-Martens or closed cup flash tester,
and the Cleveland or open cup tester. The closed cup
tester indicates a lower flash point because it retains
light vapors which are lost by the open cup unit.
Water and sediment The water and sediment level,
also called bottom sediment and water (BSW), is a
measure of the contaminants in a liquid fuel. The sedi-
mentnormallyconsistsofcalcium,sodium,magnesium
and iron compounds. For heavy fuels, the sediment
may also contain carbon.
The basic analyses described are important in de-
signing oil-fired boilers. The HHV determines the
quantity of fuel required to reach a given heat input.
The ultimate analysis determines the theoretical air
required for complete combustion and therefore indi-
cates the size of the burner throat.Also available from
the ultimate analysis is the carbon/hydrogen ratio,
which shows the ease with which a fuel burns. This
ratio also indicates the expected level of carbon par-
ticulate emissions. A carbon/hydrogen ratio in excess
of 7.5 is usually indicative of troublesome burning.
Considering the percentages of nitrogen and sul-
fur in conjunction with the HHV, an estimate of NOx
and SO2 emissions can be made. The ash percentage
has a similar bearing on particulate emissions. The ash
constituent analysis and ash content indicate fouling
and corrosion tendencies.
Additional information, which is often required
when designing a boiler, includes:
1. carbon residue,
2. asphaltenes,
3. elemental ash analysis,
4. burning profile, and
5. distillation curve.
ThousandBarrelsperDay 30,000
25,000
20,000
15,000
10,000
5,000
0
North
America
Central
andSouth
America
Western
Europe
Eastern
Europe
andFSU
Middle
East
Africa
FarEast
andOceania
1980
1989
2000
20,204
20,750
23,775
13,947
12,880
14,672
3,573
3,612
5,131
11,082
10,567
4,773
4,456
3,117
2,058
1,474
2,004
2,440
10,733
12,868
20,773
Fig. 13 Major petroleum consumption.](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-247-320.jpg)
![10-8 Steam 41 / Principles of Combustion
The Babcock & Wilcox Company
Table 7
Combustion Calculations Molar Basis
INPUTS (see also lightly shaded blocks) FUEL − Bituminous coal, Virginia
1 Excess air: at burner/at boiler/econ, % 20/20 4 Fuel input, 1,000,000 Btu/h 330.0
2 Moisture in air, lb/lb dry air 0.013 5 Unburned carbon loss, % efficiency 0.40
3 Fuel heating value, Btu/lb 14,100 6 Unburned carbon (UBC), [5] x [3] / 14,500 0.39
COMBUSTION PRODUCTS CALCULATIONS
7 Ultimate Analysis, % mass 8 Molecular 9 Moles 10 Moles O2
11 Moles Theo. 12
Fuel As- Carbon Weight /100 lb Fuel /Mole Fuel O2/100 lb Fuel Combustion
Constituent Fired Burned(CB) lb/mole [7] / [8] Constituent [9] x [10] Product
A C 80.31 80.31
B UBC [6] 0.39
C CB [A] − [B] 79.92 12.011 6.654 1.0 6.654 CO2
D S 1.54 32.066 0.048 1.0 0.048 SO2
E H2 4.47 2.016 2.217 0.5 1.109 H2O
F H2O 2.90 18.015 0.161 H2O
G N2 1.38 28.013 0.049 N2 (fuel)
H O2 2.85 31.999 0.089 −1.0 −0.089
I Ash 6.55
K Total 100.00 9.218 7.722
AIR CONSTITUENTS, Moles/100 lb Fuel At Burner At Blr/Econ
13 O2 − excess [11K] x [1] / 100 1.544 1.544
14 O2 − total [13] + [11K] 9.266 9.266
15 N2a − air [14] x 3.77 34.933 34.933
16 Air (dry) [14] + [15] 44.199 44.199
17 H2O − air [16] x [2] x 1.608 0.924 0.924
18 Air (wet) [16] + [17] 45.123 45.123
19 20 Vol % Dry 21 Vol % Wet 22 Molecular 23 Flue Gas
Moles 100 x 100 x Weight lb/100 lb Fuel
FLUE GAS CONSTITUENTS /100 lb Fuel [19] / [19G] [19] / [19H] lb/mole [19] x [22]
A CO2 [9C] 6.654 15.39 14.30 44.010 292.8
B SO2 [9D] 0.048 0.11 0.10 64.065 3.1
C O2 [13] 1.544 3.57 3.32 31.999 49.4
D N2 (fuel) [9G] 0.049 0.11 0.11 28.013 1.4
E N2a (air) [15] 34.933 80.82 75.07 28.158 983.6
F H2O [9E] + [9F] + [17] 3.302 7.10 18.015 59.5
G Total dry Sum [A] through [E] 43.228 100.00 1330.3
H Total wet Sum [A] through [F] 46.530 100.00 1389.8
KEY PERFORMANCE PARAMETERS At Burner At Blr/Econ
24 Molecular weight wet flue gas, lb/mole [23H] / [19H] 29.869
25 H2O in wet gas, % by wt 100 x [23F] / [23H] 4.28
26 Dry gas weight, lb/10,000 Btu 100 x [23G] / [3] 9.435
27 Wet gas weight, lb/10,000 Btu 100 x [23H] / [3] 9.857
28 Wet gas weight, 1000 lb/h [27] x [4] / 10 325.3
29 Air flow (wet), lb/100 lb fuel [16] x 28.966 + [17] x 18.015 1296.9
30 Air flow (wet), lb/10,000 Btu 100 x [29] / [3] 9.198
31 Air flow (wet), 1000 lb/h [30] x [4] / 10 303.5](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-261-320.jpg)
![Steam 41 / Principles of Combustion 10-11
The Babcock & Wilcox Company
Adiabatic flame temperature
The adiabatic flame temperature is the maximum
theoretical temperature that can be reached by the
products of combustion of a specific fuel and air (or
oxygen) combination, assuming no loss of heat to the
surroundings and no dissociation. The fuel’s heat of
combustion is the major factor in the flame tempera-
ture, but increasing the temperature of the air or the
fuel also raises the flame temperature. This adiabatic
temperature is a maximum with zero excess air (only
enough air chemically required to combine with the
fuel). Excess air is not involved in the combustion
process; it only acts as a dilutant and reduces the av-
erage temperature of the products of combustion.
The adiabatic temperature is determined from the
adiabatic enthalpy of the flue gas:
H
HHV
g =
− +Latent heat H O Sensible heat in air
Wet gas weight
2 (14)
where
Hg = adiabatic enthalpy, Btu/lb
Knowing the moisture content and enthalpy of the
products of combustion, the theoretical flame or gas
temperature can be obtained from Fig. 3 (see pages
12 and 13).
Theadiabatictemperatureisafictitiouslyhighvalue
that can not exist. Actual flame temperatures are
lower for two main reasons:
1. Combustion is not instantaneous. Some heat is lost
to the surroundings as combustion takes place.
Faster combustion reduces heat loss. However, if
combustion is slow enough, the gases may be cooled
sufficiently and incomplete combustion may occur,
i.e., some of the fuel may remain unburned.
2. At temperatures above 3000F, some of the CO2 and
H2O in the flue gases dissociates, absorbing heat
in the process. At 3500F, about 10% of the CO2 in
a typical flue gas dissociates to CO and O2. Heat
absorption occurs at 4342 Btu/lb of CO formed,
and about 3% of the H2O dissociates to H2 and O2,
with a heat absorption of 61,029 Btu/lb of H2
formed. As the gas cools, the dissociated CO and
H2 recombine with the O2 and liberate the heat
absorbed in dissociation, so the heat is not lost.
However, the overall effect is to lower the maxi-
mum actual flame temperature.
The term heat available (Btu/h) is used through-
out this text to define the heat available to the fur-
nace. This term is analogous to the energy term (nu-
merator) in the adiabatic sensible heat equation above
except that one half of the radiation heat loss and the
manufacturer’s margin portion are not considered
available to the furnace.
Practical combustion application issues
In addition to the theoretical combustion evalua-
tion methodologies addressed above, several applica-
tion issues are very important in accurate combustion
calculations of actual applications. These include the
impact of the injection of SO2 sorbents and other
chemicals into the combustion process, solid ash or
residue, unburned carbon and excess air.
Sorbents and other chemical additives
In some combustion systems, chemical compounds
are added to the gas side of the steam generator to
reduce emissions. For example, limestone is used uni-
versally in fluidized-bed steam generators to reduce
SO2 emissions. (See Chapter 17.)
Limestone impacts the combustion and efficiency
calculations by: 1) altering the mass of flue gas by
reducing SO2 and increasing CO2 levels, 2) increas-
ing the mass of solid waste material (ash residue), 3)
increasing the air required in forming SO3 to produce
calcium sulfate, CaSO4, 4) absorbing energy (heat)
from the fuel to calcine the calcium and magnesium
carbonates, and 5) adding energy to the system in the
sulfation reaction (SO2 + ½ O2 + CaO → CaSO4). The
impact of sorbent/limestone is shown as a correction
to the normal combustion calculations presented later.
The limestone constituents that are required in the
combustion and efficiency calculations are:
Reactive constituents:
Calcium carbonate (CaCO3)
Magnesium carbonate (MgCO3)
Water
Inerts
Some processes may use sorbents derived from lime-
stone. These sorbents contain reactive constituents
such as calcium hydroxide [Ca(OH)2] and magnesium
hydroxide [Mg(OH)2].
For design purposes, the amount of sorbent is de-
termined from the design calcium to sulfur molar ra-
tio, MOFCAS. The sorbent to fuel ratio, MFSBF, is a
Table 10
Ignition Temperatures of Fuels in Air
(Approximate Values or Ranges
at Atmospheric Pressure)
Combustible Formula Temperature, F
Sulfur S 470
Charcoal C 650
Fixed carbon
(bituminous coal) C 765
Fixed carbon
(semi-anthracite) C 870
Fixed carbon
(anthracite) C 840 to 1115
Acetylene C2H2 580 to 825
Ethane C2H6 880 to 1165
Ethylene C2H4 900 to 1020
Hydrogen H2 1065 to 1095
Methane CH4 1170 to 1380
Carbon monoxide CO 1130 to 1215
Kerosene 490 to 560
Gasoline 500 to 800](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-264-320.jpg)
![10-26 Steam 41 / Principles of Combustion
The Babcock & Wilcox Company
Table 13A
Combustion Calculations (Efficiency per PTC 4.1) Btu Method
INPUT CONDITIONS − BY TEST OR SPECIFICATION FUEL − Bituminous coal, Virginia: no sorbent
1 Excess air: at burners; leaving boiler/econ/entering AH, % by wt. 20/20 15 Ultimate Analysis 16 Theo Air, lb/100 lb fuel 17 H2O, lb/100 lb fuel
2 Entering air temperature, F 80 Constituent % by weight K1 [15] x K1 K2 [15] x K2
3 Reference temperature, F (tRA = 77 for PTC 4) 80 A C 80.31 11.51 924.4
4 Fuel temperature, F 80 B S 1.54 4.31 6.6
5 Air temperature leaving air heater, F 350 C H2 4.47 34.29 153.3 8.94 39.96
6 Flue gas temperature leaving (excluding leakage), F 390 D H2O 2.90 1.00 2.90
7 Moisture in air, lb/lb dry air 0.013 E N2 1.38
8 Additional moisture, lb/100 lb fuel 0 F O2 2.85 −4.32 −12.3
9 Residue leaving boiler/econ/entering AH, % Total 85 G Ash 6.55
10 Output, 1,000,000 Btu/h 285.5 H Total 100.00 Air 1072.0 H2O 42.86
Corrections for sorbent (if used)
11 Sulfur capture, lbm/lbm sulfur Table 16, Item [24] 0 18 Higher heating value (HHV), Btu/lb 14,100
12 CO2 from sorbent, lb/10,000 Btu Table 14, Item [19] 0 19 Unburned carbon loss, % fuel input 0.40
13 H2O from sorbent, lb/10,000 Btu Table 14, Item [20] 0 20 Theoretical air, lb/10,000 Btu [16H] x 100 / [18] 7.603
14 Spent sorbent, lb/10,000 Btu Table 14, Item [24] 0 21 Unburned carbon, % of fuel [19] x [18] / 14,500 0.39
COMBUSTION GAS CALCULATIONS, Quantity per 10,000 Btu Fuel Input
22 Theoretical air (corrected), lb/10,000 Btu [20] − [21] x 1151 / [18] + [11] x [15B] x 216 / [18] 7.571
23 Residue from fuel, lb/10,000 Btu ([15G] + [21]) x 100 / [18] 0.049
24 Total residue, lb/10,000 Btu [23] + [14] 0.049
A At Burners B Infiltration C Leaving Furnace D Leaving Blr/Econ/Entering AH
25 Excess air, % weight 20.0 0.0 20.0 20.0
26 Dry air, lb/10,000 Btu (1 + [25] / 100) x [22] 9.085 9.085
27 H2O from air, lb/10,000 Btu [26] x [7] 0.118 0.118 0.118 0.118
28 Additional moisture, lb/10,000 Btu [8] x 100 / [18] 0.000 0.000 0.000 0.000
29 H2O from fuel, lb/10,000 Btu [17H] x 100 / [18] 0.304 0.304
30 Wet gas from fuel, lb/10,000 Btu (100 − [15G] − [21] − [11] x [15B]) x 100 / [18] 0.660 0.660
31 CO2 from sorbent, lb/10,000 Btu [12] 0.000 0.000
32 H2O from sorbent, lb/10,000 Btu [13] 0.000 0.000 0.000 0.000
33 Total wet gas, lb/10,000 Btu Summation [26] through [32] 9.863 9.863
34 Water in wet gas, lb/10,000 Btu Summation [27] + [28] + [29] + [32] 0.422 0.422 0.422 0.422
35 Dry gas, lb/10,000 Btu [33] − [34] 9.441 9.441
36 H2O in gas, % by weight 100 x [34] / [33] 4.28 4.28
37 Residue, % by weight (zero if < 0.15 lbm/10KB) [9] x [24] / [33] 0.00 0.00
EFFICIENCY CALCULATIONS, % Input from Fuel
Losses
38 Dry gas, % [35D] x (HFg[6] − HFg[3]) / 100 9.441 x (75.3 − 0.7) / 100 7.04
39 Water from Enthalpy of steam at 1 psia, T = [6] H1 = (3.958E − 5 x T + 0.4329) x T + 1062.2 1237.1
40 fuel, as fired Enthalpy of water at T = [3] H2 = [3] − 32 48.0
41 % [29] x ([39] − [40]) / 100 0.304 x 1189.1 / 100 3.61
42 Moisture in air, % [27D] x (HWv[6] − HWv[3]) / 100 0.118 x (142.0 − 1.3) / 100 0.17
43 Unburned carbon, % [19] or [21] x 14,500 / [18] 0.39 x 14,500 / 14,100 0.40
44 Surface radiation and convection See surface radiation and convection loss 0.40
45 Other, % (include manufacturers margin if applicable) 1.50
46 Sensible heat of residue, % (PTC 4) [24] x (100 − [9]) x 516 + [9] x HRs[6] / 10,000 HRs[6] = 0 (or Table 14, Item [40]) 0.00
47 Sorbent net losses, % if sorbent used From Table 14, Items ([30] − [31] + [37]) 0.00
48 Summation of losses, % Summation [38] through [46] 13.12
Credits
49 Entering dry air, % [26D] x (HDA[2] − HDA[3]) / 100 9.085 x (0.7 − 0.7) / 100 0.00
50 Moisture in entering air, % [27D] x (HWv[2] − HWv[3]) / 100 0.118 x (1.3 − 1.3) / 100 0.00
51 Sensible heat in fuel, % 100 x (HF[4] − HF[3]) / [18] 100 x (1.0 − 1.0) / 14,100 0.00
52 Other, % 0.00
53 Summation of credits, % Summation [48] through [51] 0.00
54 Efficiency, % 100 − [48] + [53] 86.88
KEY PERFORMANCE PARAMETERS Leaving Furnace Leaving Blr/Econ/Entering AH
55 Input from fuel, 1,000,000 Btu/h 100 x [10] / [54] 328.6
56 Fuel rate, 1000 lb/h 1000 x [55] / [18] 23.3
57 Wet gas weight, 1000 lb/h [55] x [33] / 10 324.1 324.1
58 Air to burners (wet), lb/10,000 Btu (1 + [7]) x (1 + [25A] / 100) x [22] 9.203
59 Air to burners (wet), 1000 lb/h [55] x [58] / 10 302.4
60 Heat available, 1,000,000 Btu/h [55] x {([18] − 10.30 x [17H]) / [18] − 0.005
Ha = 66.0 Btu/lb x ([44] + [45]) + Ha[5] x [58] / 10,000} 335.2
61 Heat available/lb wet gas, Btu/lb 1000 x [60] / [57] 1034.2
62 Adiabatic flame temperature, F From Fig. 3 at H = [61], % H2O = [36C] 3560](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-279-320.jpg)
![Steam 41 / Principles of Combustion 10-27
The Babcock & Wilcox Company
Table 13B
Combustion Calculations (Efficiency per PTC 4) Btu Method (with Sorbent)
INPUT CONDITIONS − BY TEST OR SPECIFICATION FUEL − Bituminous coal, Virginia: with sorbent
1 Excess air: at burners; leaving boiler/econ/entering AH, % by wt. 18/20 15 Ultimate Analysis 16 Theo Air, lb/100 lb fuel 17 H2O, lb/100 lb fuel
2 Entering air temperature, F 80 Constituent % by weight K1 [15] x K1 K2 [15] x K2
3 Reference temperature, F (tRA = 77 for PTC 4) 77 A C 80.31 11.51 924.4
4 Fuel temperature, F 80 B S 1.54 4.31 6.6
5 Air temperature leaving air heater, F 350 C H2 4.47 34.29 153.3 8.94 39.96
6 Flue gas temperature leaving (excluding leakage), F 390 D H2O 2.90 1.00 2.90
7 Moisture in air, lb/lb dry air 0.013 E N2 1.38
8 Additional moisture, lb/100 lb fuel 0 F O2 2.85 −4.32 −12.3
9 Residue leaving boiler/econ/entering AH, % Total 90 G Ash 6.55
10 Output, 1,000,000 Btu/h 285.5 H Total 100.00 Air 1072.0 H2O 42.86
Corrections for sorbent (if used)
11 Sulfur capture, lbm/lbm sulfur Table 16, Item [24] 0.9000 18 Higher heating value (HHV), Btu/lb 14,100
12 CO2 from sorbent, lb/10,000 Btu Table 14, Item [19] 0.0362 19 Unburned carbon loss, % fuel input 2.50
13 H2O from sorbent, lb/10,000 Btu Table 14, Item [20] 0.0015 20 Theoretical air, lb/10,000 Btu [16H] x 100 / [18] 7.603
14 Spent sorbent, lb/10,000 Btu Table 14, Item [24] 0.0819 21 Unburned carbon, % of fuel [19] x [18] / 14,500 2.43
COMBUSTION GAS CALCULATIONS, Quantity per 10,000 Btu Fuel Input
22 Theoretical air (corrected), lb/10,000 Btu [20] − [21] x 1151 / [18] + [11] x [15B] x 216 / [18] 7.426
23 Residue from fuel, lb/10,000 Btu ([15G] + [21]) x 100 / [18] 0.064
24 Total residue, lb/10,000 Btu [23] + [14] 0.146
A At Burners B Infiltration C Leaving Furnace D Leaving Blr/Econ/Entering AH
25 Excess air, % weight 18.0 1.0 19.0 20.0
26 Dry air, lb/10,000 Btu (1 + [25] / 100) x [22] 8.837 8.911
27 H2O from air, lb/10,000 Btu [26] x [7] 0.115 0.115 0.116 0.116
28 Additional moisture, lb/10,000 Btu [8] x 100 / [18] 0.000 0.000 0.000 0.000
29 H2O from fuel, lb/10,000 Btu [17H] x 100 / [18] 0.304 0.304
30 Wet gas from fuel, lb/10,000 Btu (100 − [15G] − [21] − [11] x [15B]) x 100 / [18] 0.636 0.636
31 CO2 from sorbent, lb/10,000 Btu [12] 0.036 0.036
32 H2O from sorbent, lb/10,000 Btu [13] 0.002 0.002 0.002 0.002
33 Total wet gas, lb/10,000 Btu Summation [26] through [32] 9.626 9.701
34 Water in wet gas, lb/10,000 Btu Summation [27] + [28] + [29] + [32] 0.421 0.421 0.422 0.422
35 Dry gas, lb/10,000 Btu [33] − [34] 9.205 9.279
36 H2O in gas, % by weight 100 x [34] / [33] 4.37 4.35
37 Residue, % by weight (zero if < 0.15 lbm/10KB) [9] x [24] / [33] 1.37 1.35
EFFICIENCY CALCULATIONS, % Input from Fuel
Losses
38 Dry gas, % [35D] x (HFg[6] − HFg[3]) / 100 9.279 x (75.3 − 0.0) / 100 6.99
39 Water from Enthalpy of steam at psia, T = [6] H1 = (3.958E − 5 x T + 0.4329) x T + 1062.2 1237.1
40 fuel, as fired Enthalpy of water at T = [3] H2 = [3] − 32 45.0
41 % [29] x ([39] − [40]) / 100 0.304 x 1192.1 / 100 3.62
42 Moisture in air, % [27D] x (HWv[6] − HWv[3]) / 100 0.116 x (142.0 − 0.0) / 100 0.16
43 Unburned carbon, % [19] or [21] x 14,500 / [18] 2.43 x 14,500 / 14,100 2.50
44 Surface radiation and convection See surface radiation and convection loss 0.40
45 Other, % (include manufacturers margin if applicable) 1.50
46 Sensible heat of residue, % (PTC 4) [24] x (100 − [9]) x 516 + [9] x HRs[6] / 10,000 HRs[6] = 65.1 (or Table 14, Item [40]) 0.15
47 Sorbent net losses, % if sorbent used From Table 14, Items ([30] − [31] + [37]) −0.03
48 Summation of losses, % Summation [38] through [46] 15.45
Credits
49 Entering dry air, % [26D] x (HDA[2] − HDA[3]) / 100 8.911 x (0.7 − 0.0) / 100 0.06
50 Moisture in entering air, % [27D] x (HWv[2] − HWv[3]) / 100 0.116 x (1.3 − 0.0) / 100 0.00
51 Sensible heat in fuel, % 100 x (HF[4] − HF[3]) / [18] 100 x (1.0 − 0.0) / 14,100 0.01
52 Other, % 0.00
53 Summation of credits, % Summation [49] through [51] 0.07
54 Efficiency, % 100 − [48] + [53] 84.78
KEY PERFORMANCE PARAMETERS Leaving Furnace Leaving Blr/Econ/Entering AH
55 Input from fuel, 1,000,000 Btu/h 100 x [10] / [54] 336.8
56 Fuel rate, 1000 lb/h 1000 x [55] / [18] 23.9
57 Wet gas weight, 1000 lb/h [55] x [33] / 10 324.2 326.7
58 Air to burners (wet), lb/10,000 Btu (1 + [7]) x (1 + [25A] / 100) x [22] 8.877
59 Air to burners (wet), 1000 lb/h [55] x [58] / 10 299.0
60 Heat available, 1,000,000 Btu/h [55] x {([18] − 10.30 x [17H]) / [18] − 0.005
Ha = 66.0 Btu/lb x ([44] + [45]) + Ha[5] x [58] / 10,000} 342.8
61 Heat available/lb wet gas, Btu/lb 1000 x [60] / [57] 1057.4
62 Adiabatic flame temperature, F From Fig. 3 at H = [61], % H2O = [36C] 3627](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-280-320.jpg)
![10-28 Steam 41 / Principles of Combustion
The Babcock & Wilcox Company
H2O from
sorbent, %
INPUTS (see also lightly shaded blocks) FUEL − Bituminous coal, Virginia
1 Sulfur in fuel, % by weight 1.54 6 Sulfur capture, lb/lb sulfur 0.90
2 Ash in fuel, % by weight 6.55 7 Reference temperature, F 80.0
3 HHV of fuel, Btu/lb 14,100 8 Exit gas temperature (excluding leakage), F 390.0
4 Unburned carbon loss, % fuel input 2.5 9 Sorbent temperature, F 80.0
5 Calcium to sulfur molar ratio 2.5
SORBENT PRODUCTS
10 Chemical 11 Molecular 12 Ca 13 14 Molecular 15 CO2 16 H2O
Analysis Weight mole/100 lb sorb Calcination Weight lb/100 lb sorb lb/100 lb sorb
% Mass lb/mole [10] / [11] Fraction lb/mole [10]x[13]x[14]/[11] [10]x[13]x[14]/[11]
A CaCO3 89.80 100.089 0.897 0.90 44.010 35.529
B MgCO3 5.00 84.321 1.00 44.010 2.610
C Ca(OH)2 0.00 74.096 0.000 1.00 18.015 0.000
D Mg(OH)2 0.00 58.328 1.00 18.015 0.000
E H2O 1.60 18.015 1.00 18.015 1.600
F Inert 3.60
G Total Ca, mole/100 lb sorbent 0.897 Total 38.139 1.600
SORBENT/GAS CALCULATIONS, lb/10,000 Btu Except as Noted
17 Sorbent, lb/lb fuel [1] x [5] / [12G] / 32.066 0.1339
18 Sorbent, lb/10,000 Btu 10,000 x [17] / [3] 0.0950
19 CO2 from sorbent, lb/10,000 Btu [15G] x [18] / 100 0.0362
20 H2O from sorbent, lb/10,000 Btu [16G] x [18] / 100 0.0015
21 Additional theoretical air, lb/10,000 Btu 216 x [1] x [6] / [3] 0.0212
22 SO2 reduction, lb/10,000 Btu 200 x [1] x [6] / [3] 0.0197
23 SO3 formed, lb/10,000 Btu 0.2314 x [21] + [22] 0.0246
24 Spent sorbent, lb/10,000 Btu [18] − [19] − [20] + [23] 0.0819
25 Unburned carbon, lb/10,000 Btu [4] x 100 / 14,500 0.0172
26 Residue from fuel, lb/10,000 Btu [2] x 100 / [3] + [25] 0.0637
27 Total residue, lb/10,000 Btu [24] + [26] 0.1456
LOSSES DUE TO SORBENT, % Input from Fuel
28 H of steam at 1 psi, T = [8] H1 = (3.958E − 5 x [8] + 0.4329) x [8] + 1062.2 1237.1
29 H of water H2 = [9] − 32 48.0
30 0.01 x [20] x ([28] − [29]) 0.018
31 Sensible heat sorbent (dry), % [18] x (1.0 − [10E] / 100) x (H at T = [9] − H at T = [7]) / 100
H of limestone (dry) = (0.1128E − 3 x T + 0.179) x T − 14.45 0.000
Calcination/Dehydration, %
32 CaCO3, % [10A] x [13A] x [18] x 766 / 10,000 0.588
33 MgCO3, % [10B] x 1.0 x [18] x 652 / 10,000 0.031
34 Ca(OH)2, % [10C] x 1.0 x [18] x 636 / 10,000 0.000
35 Mg(OH)2, % [10D] x 1.0 x [18] x 625 / 10,000 0.000
36 Heat gain due to sulfation, % [6] x [1] x 6733 / [3] 0.662
37 Total of losses due to chemical reactions, % [32] + [33] + [34] + [35] − [36] −0.043
Sensible Heat of Residue Loss, %
38 Temp 39 Loss
Location Residue, F %
A Bed drain 1500 0.055
B Economizer 600 0.017
C Flyash 390 0.074
H Residue = (( −2.843E − 8 x T + 1.09E − 4) x T + 0.16) x T − 12.95 40 Total 0.146
41 Summation losses due to sorbent, % [30] − [31] + [37] + [40] 0.121
Table 14
Combustion Calculations Sorbent
Mass Flow x [27] x ( H at T = [38] − H at T = [7] ) / 10,000 =
Rate, % Total x lb/10,000 Btu x ( Btu/lb − Btu/lb ) / 10,000 =
10 x 0.1456 x ( 376.3 − 0.5 ) / 10,000 =
10 x 0.1456 x ( 116.2 − 0.5 ) / 10,000 =
80 x 0.1456 x ( 64.3 − 0.5 ) / 10,000 =](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-281-320.jpg)
![Steam 41 / Principles of Combustion 10-29
The Babcock & Wilcox Company
Table 15A
Excess Air Calculations from Measured O2
Bituminous coal, Virginia − O2 on wet basis
INPUTS (see also lightly shaded blocks) SORBENT DATA (if applicable)
1 Moisture in air, lb/lb dry air 0.013 6 CO2 from sorbent, moles/100 lb fuel, Table 16 [17] 0
2 Additional moisture, lb/100 lb fuel 0.00 7 H2O from sorbent, moles/100 lb fuel, Table 16 [16] 0
3 HHV fuel, Btu/lb 14,100 8 Sulfur capture, lb/lb sulfur fuel, Table 16 [24] 0
4 Unburned carbon loss, % fuel input 0.40
5 Unburned carbon (UBC), [3] x [4] / 14,500 0.39
COMBUSTION PRODUCTS
9 Ultimate Analysis, % Mass 10 Theoretical Air 11 Dry Products from Fuel 12 Wet Products from Fuel
Fuel As- Carbon lb/100 lb Fuel mole/100lb Fuel mole/100 lb Fuel
Constituent Fired Burned (CB) K1 [9] x K1 K2 [9] / K2 K3 [9] / K3
A C 80.31 80.31
B UBC [5] 0.39
C CB [A] − [B] 79.92 11.51 919.9 12.011 6.654
D S 1.54 4.31 6.6 32.066 0.048
E H2 4.47 34.29 153.3 2.016 2.217
F H2O 2.90 18.015 0.161
G N2 1.38 28.013 0.049
H O2 2.85 −4.32 −12.3
I Ash 6.55
K Total 100.00 1067.5 6.751 2.378
13 Dry products of combustion, mole/100 lb fuel [11K] − [11D] x [8] + [6] 6.751
14 Wet products of combustion, mole/100 lb fuel [12K] + [13] + [7] 9.129
15 Theoretical air (corrected), mole/100 lb fuel ([10K] + [8] x [9D] x 2.16) / 28.963 36.857
EXCESS AIR WHEN O2 KNOWN
16 O2, % volume (input) 3.315
17 O2 measurement basis 0 = Dry 1 = Wet 1 Dry Wet
18 Moisture in air, mole/mole dry air 0.0 [1] x 1.608 0.021
19 Dry/wet products of combustion, mole/100 lb fuel [13] [14] 9.129
20 Additional moisture, mole/100 lb fuel 0.0 [2] / 18.016 0.000
21 Intermediate calculation, step 1 [15] x (0.7905 + [18]) 29.909
22 Intermediate calculation, step 2 [19] + [20] + [21] 39.038
23 Intermediate calculation, step 3 20.95 − [16] x (1 + [18]) 17.565
24 Excess air, % by weight 100 x [16] x [22] / [15] / [23] 20.0
O2, CO2, SO2 WHEN EXCESS AIR KNOWN
25 Excess air, % by weight 20.0
26 Dry gas, mole/100 lb fuel [13] + [15] x (0.7905 + [25] / 100) 43.258
27 Wet gas, mole/100 lb fuel [14] + [15] x (0.7905 + [18] + (1 + [18]) x [25] / 100) + [20] 46.565
Dry Wet
28 O2, % by volume [25] x [15] x 0.2095 / ([26] or [27]) [26] [27] 3.32
29 CO2, % by volume 100 x ([11C] + [6]) / ([26] or [27]) [26] [27] 14.29
30 SO2, % by volume 100 x (1 − [8]) x [11D] / ([26] or [27]) [26] [27] 0.1031
31 H2O, % by volume H2O = 0.0 if dry or 100 x ([27] − [26]) / [27] NA [27] 7.10
32 N2 (fuel), % by volume 100 x [11G] / ([26] or [27]) [26] [27] 0.11
33 N2a (air), % by volume 100 − [28] − [29] − [30] − [31] − [32] 75.08
34 MW wet flue gas, lbm/mole 0.32 x [28] + 0.4401 x [29] + 0.64064 x [30] + 0.18015 x [31] + 0.28013 x [32] + 0.28158 x [55] 29.868
35 Density flue gas, lbm/ft3
at 60F and 29.92 in. Hg 0.0026356 x [34] Wet basis 0.07872](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-282-320.jpg)
![10-30 Steam 41 / Principles of Combustion
The Babcock & Wilcox Company
Table 15B
Excess Air Calculations from Measured O2
Bituminous coal, Virginia: with sorbent − O2 on wet basis
INPUTS (see also lightly shaded blocks) SORBENT DATA (if applicable)
1 Moisture in air, lb/lb dry air 0.013 6 CO2 from sorbent, moles/100 lb fuel, Table 16 [17] 0.116
2 Additional moisture, lb/100 lb fuel 0.00 7 H2O from sorbent, moles/100 lb fuel, Table 16 [16] 0.012
3 HHV fuel, Btu/lb 14,100 8 Sulfur capture, lb/lb sulfur fuel, Table 16 [24] 0.90
4 Unburned carbon loss, % fuel input 2.50
5 Unburned carbon (UBC), [3] x [4] / 14,500 2.43
COMBUSTION PRODUCTS
9 Ultimate Analysis, % Mass 10 Theoretical Air 11 Dry Products from Fuel 12 Wet Products from Fuel
Fuel As- Carbon lb/100 lb Fuel mole/100lb Fuel mole/100 lb Fuel
Constituent Fired Burned (CB) K1 [9] x K1 K2 [9] / K2 K3 [9] / K3
A C 80.31 80.31
B UBC [5] 2.43
C CB [A] − [B] 77.88 11.51 896.4 12.011 6.484
D S 1.54 4.31 6.6 32.066 0.048
E H2 4.47 34.29 153.3 2.016 2.217
F H2O 2.90 18.015 0.161
G N2 1.38 28.013 0.049
H O2 2.85 −4.32 −12.3
I Ash 6.55
K Total 100.00 1044.0 6.581 2.378
13 Dry products of combustion, mole/100 lb fuel [11K] − [11D] x [8] + [6] 6.654
14 Wet products of combustion, mole/100 lb fuel [12K] + [13] + [7] 9.044
15 Theoretical air (corrected), mole/100 lb fuel ([10K] + [8] x [9D] x 2.16) / 28.963 36.149
EXCESS AIR WHEN O2 KNOWN
16 O2, % volume (input) 3.315
17 O2 measurement basis 0 = Dry 1 = Wet 1 Dry Wet
18 Moisture in air, mole/mole dry air 0.0 [1] x 1.608 0.021
19 Dry/wet products of combustion, mole/100 lb fuel [13] [14] 9.044
20 Additional moisture, mole/100 lb fuel 0.0 [2] / 18.016 0.000
21 Intermediate calculation, step 1 [15] x (0.7905 + [18]) 29.335
22 Intermediate calculation, step 2 [19] + [20] + [21] 38.379
23 Intermediate calculation, step 3 20.95 − [16] x (1 + [18]) 17.565
24 Excess air, % by weight 100 x [16] x [22] / [15] / [23] 20.0
O2, CO2, SO2 WHEN EXCESS AIR KNOWN
25 Excess air, % by weight 20.0
26 Dry gas, mole/100 lb fuel [13] + [15] x (0.7905 + [25] / 100) 42.460
27 Wet gas, mole/100 lb fuel [14] + [15] x (0.7905 + [18] + (1 + [18]) x [25] / 100) + [20] 45.761
Dry Wet
28 O2, % by volume [25] x [15] x 0.2095 / ([26] or [27]) [26] [27] 3.31
29 CO2, % by volume 100 x ([11C] + [6]) / ([26] or [27]) [26] [27] 14.42
30 SO2, % by volume 100 x (1 − [8]) x [11D] / ([26] or [27]) [26] [27] 0.0105
31 H2O, % by volume H2O = 0.0 if dry or 100 x ([27] − [26]) / [27] NA [27] 7.21
32 N2 (fuel), % by volume 100 x [11G] / ([26] or [27]) [26] [27] 0.11
33 N2a (air), % by volume 100 − [28] − [29] − [30] − [31] − [32] 74.94
34 MW wet flue gas, lbm/mole 0.32 x [28] + 0.4401 x [29] + 0.64064 x [30] + 0.18015 x [31] + 0.28013 x [32] + 0.28158 x [55] 29.843
35 Density flue gas, lbm/ft3
at 60F and 29.92 in. Hg 0.0026356 x [34] Wet basis 0.07866](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-283-320.jpg)
![Steam 41 / Principles of Combustion 10-31
The Babcock & Wilcox Company
INPUTS
1 SO2, ppm 105 / 10,000 = % 0.0105 2 O2 Flue gas at location SO2 measured, % 3.31
Data from Table 15, Excess Air Calculations from Measured O2
3 Moisture in air, lb/lb dry air [1] 0.013 7 Theoretical air, lb/100 lb fuel [10K] 1044.0
4 Additional moisture, lb/100 lb fuel [2] 0 8 Dry products of fuel, mole/100 lb fuel [11K] 6.581
5 Sulfur in fuel, % by weight [9D] 1.54 9 Wet products of fuel, mole/100 lb fuel [12K] 2.378
6 HHV fuel, Btu/lb fuel [3] 14,100
Data from Table 14, Combustion Calculations - Sorbent
10 CO2 from sorbent, lb/100 lb sorbent [15G] 38.139 12 Sorbent, lb sorbent/lb fuel [17] 0.134
11 H2O from sorbent, lb/100 lb sorbent [16G] 1.600
CALCULATIONS, Moles/100 lb Fuel Except As Noted
SO2 / O2 Measurement basis 0 = Dry 1 = Wet 1 Dry Wet
13 Moisture in air, mole/mole dry air 0.0 [3] x 1.608 0.0209
14 Additional moisture 0.0 [4] / 18.015 0.000
15 Products of combustion from fuel [8] [8] + [9] 8.959
16 H2O from sorbent [11] x [12] / 18.015 0.0 Calculate 0.012
17 CO2 from sorbent [10] x [12] / 44.01 0.116
18 Intermediate calculation, step 1 (0.7905 + [13]) x [7] / 28.963 29.245
19 Intermediate calculation, step 2 Summation [14] through [18] 38.332
20 Intermediate calculation, step 3 1.0 − (1.0 + [13]) x [2] / 20.95 0.8387
21 Intermediate calculation, step 4 (0.7905 + [13]) x 2.387 − 1.0 0.9368
22 Intermediate calculation, step 5 [1] x [19] x 32.066 / [5] / [20] 9.992
23 Intermediate calculation, step 6 [21] x [1] / [20] 0.0117
24 Sulfur capture, lb/lb sulfur (100 − [22]) / (100 + [23]) 0.90
25 SO2 released, lb/1,000,000 Btu 20,000 x (1.0 − [24]) x [5] / [6] 0.22
Table 16
Sulfur Capture Based on Gas Analysis
Bituminous coal, Virginia
INPUTS
A Wet Analysis B Dry
(not required) Analysis
1 O2, % volume 9.28 Measured dry or 100 / (100 − [3A]) x [1A] 10.55
2 CO2, % volume 8.56 Measured dry or 100 / (100 − [3A]) x [2A] 9.73
3 H2O, % volume 12.00
4 Mass flow wet gas, 1000 lb/h 539.2
5 Moisture in wet gas, lb/lb wet gas 0.0754
6 Moisture in air, lb/lb dry air 0.0130
7 Additional moisture (sources other than fuel and air), 1000 lb/h 0
CALCULATIONS
8 Water in wet gas, 1000 lb/h [4] x [5] 40.7
9 Dry gas weight, 1000 lb/h [4] − [8] 498.5
10 N2a in dry gas, % dry volume 100 − [1B] − [2B] 79.72
11 Molecular weight of dry gas, lb/mole 0.32 x [1B] + 0.4401 x [2B] + 0.28158 x [10] 30.11
12 Dry gas, 1000 moles/h [9] / [11] 16.56
13 Dry air weight, 1000 lb/h 0.28161 x [10] x [12] / 0.7685 483.8
14 Water in dry air, 1000 lb/h [13] x [6] 6.3
15 Water evaporated, 1000 lb/h [8] − [7] − [14] 34.4
16 Excess air, 1000 lb/h [1B] x [9] x 0.32 / 0.2314 / [11] 241.5
17 Theoretical air, 1000 lb/h [13] − [16] 242.3
18 Excess air, % by weight 100 x [16] / [17] 99.7
Table 17
Combustion Calculations Measured Gas Weight](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-284-320.jpg)
![The Babcock & Wilcox Company
11-2 Steam 41 / Oil and Gas Utilization
transportation and handling of fuel oil. Storage tanks,
piping and heaters for heavy oils must be cleaned pe-
riodically because of fouling or sludge accumulation.
Fuel properties
Safe and efficient transportation, handling and com-
bustion of fuel oil requires a knowledge of fuel charac-
teristics.Principalphysicalpropertiesoffueloils,impor-
tant to boiler applications, are summarized below (see
Chapter 9 for typical fuel oil physical property values):
Viscosity The viscosity of an oil is the measure of
its resistance to internal movement, or flow. Viscosity
is important because of its effect on the rate at which
oil flows through pipelines and on the degree of at-
omization obtained by oil firing equipment.
Ultimate analysis An ultimate analysis is used to
determine theoretical air requirements for combustion
of the fuel and also to identify potential environmen-
tal emission characteristics.
Heating value The heating value of a liquid fuel is
the energy produced by the complete combustion of
one unit of fuel [Btu/lb (J/kg)]. Heating value can be
reported either as the gross or higher heating value
(HHV) or the net or lower heating value (LHV). To
determine HHV, it is assumed that any water vapor
formed during combustion is condensed and cooled to
the initial temperature (i.e., all of the chemical energy
is available). The heat of vaporization of the water
formed is included in the HHV. For LHV, it is assumed
that the water vapor does not condense and is not
available. The heating value determines the quantity
of fuel necessary to achieve a specified heat input.
Specific gravity Specific gravity (sp gr) is the ratio
of the density of oil to the density of water. It is im-
portant because fuel is purchased by volume, in gal-
lons (l) or barrels (m3
). The most widely used fuel oil
gravity scale is degree API devised by the American
Petroleum Institute; its use is recommended by the
U.S. Bureau of Standards and the U.S. Bureau of
Mines. The scale is based on the following formula:
degreesAPI =
141 5.
sp gr at 60/60F (16/16C)
– 131.5
[sp gr at 60/60F (16/16C) means when both oil and
water are at 60F (16C)]
Flash and fire point Flash point is the lowest tem-
perature at which a volatile oil will give off explosive
or ignitable vapors. It is important in determining oil
handling and storage requirements. The fire point is
the temperature to which a liquid must be heated to
produce vapors sufficient for continuous burning
when ignited by an external flame.
Pourpoint Thepourpointisthetemperatureatwhich
aliquidfuelwillfirstflowunderstandardizedconditions.
Distillation Distillation determines the quantity
and number of fractions which make up the liquid fuel.
Water and sediment Water and sediment are a mea-
sure of the contaminates in a liquid fuel. The sediment
normally consists of calcium, sodium, magnesium, and
iron compounds. Impurities in the fuel provide an
indication of the potential for plugging of fuel han-
dling and combustion equipment.
Carbon residue Residue that remains after a liquid
fuel is heated in the absence of air is termed carbon resi-
due. The tests commonly used to determine carbon resi-
duearetheConradsonCarbonTestandtheRamsbottom
Carbon Test. Carbon residue gives an indication of the
coking tendency of a particular fuel (i.e. the tendency of
oil, when heated, to form solid compounds).
Asphaltene content Asphaltenes are long chain,
high molecular weight hydrocarbon compounds. The
asphaltene content of a petroleum product is the per-
centage by weight of wax free material insoluble in
n-heptane but soluble in hot benzene. Their structure
requires high temperatures and high atomization
energy for the fuel to burn completely. Higher
asphaltene content indicates a higher potential to
produce particulate emissions.
Burning profile Burning profile is a plot of the rate
at which a sample of fuel burns under standard con-
ditions as temperature is increased at a fixed rate. The
burning profile is a characteristic fingerprint of the
fuel oxidized under standard conditions and is not in-
tended to provide absolute kinetic and thermodynamic
data. It helps evaluate combustion characteristics of
various fuels on a relative basis to determine excess air
and residence time necessary for complete combustion.
Natural gas
Preparation
Natural gas, found in crude oil reservoirs, either dis-
solved in the oil or as a gas cap above the oil, is called
associated gas. Natural gas is also found in reservoirs
that contain no oil and is termed non-associated gas.
Natural gas, directly from the well, must be treated
to produce commercially marketable fuels. Initially,
natural gas undergoes a process to remove conden-
sate which is distilled to produce butane, propane and
stabilized gasoline. Propane and butane are widely
used as bottle gas. They are distributed and stored
liquefied under pressure. When the pressure is re-
leased, the liquid boils, producing a gaseous fuel.
Natural gas may contain enough sand or gaseous
sulfur compounds to be troublesome. The sand is usu-
ally removed at the source. Natural gas containing
excessive amounts of hydrogen sulfide, commonly
known as sour gas, can be treated by a process known
as sweetening. Sweetening removes hydrogen sulfide
as well as carbon dioxide. Additional treatments in-
clude the removal of mercaptan by soda fixation and
the extraction of long chain hydrocarbons.
Where natural gas is used to replace or supplement
manufactured gas, it is sometimes reformed to bring its
heating value in line with the manufactured gas. Natu-
ral gas may also be mixed directly with manufactured
gas to increase the heating value of the final product.
Transportation, storage and handling
Pipelines are an economical means of transporting
natural gas in its gaseous form. The rapid increase in
consumption of natural gas in areas far from the
source has resulted in an extensive system of long
distance pipelines. Natural gas can also be transported](https://image.slidesharecdn.com/172049386-steam-its-generation-and-use-41st-ed-150925172316-lva1-app6891/85/steam-its-generation-and-use-41st-edition-287-320.jpg)
steam - its generation and use - 41st edition
- 2. Edited by J.B. Kitto and S.C. Stultz
- 3. The Babcock & Wilcox Company Steam 41 Copyright © 2005 by The Babcock & Wilcox Company a McDermott company Forty-first edition First printing All rights reserved. Reproduction or translation of any part of this work in any form or by any means beyond that permitted by the 1976 United States Copyright Act without the permission of the copyright holder is unlawful. Requests for permission or further information should be addressed to: STEAM, The Babcock & Wilcox Company, 20 S. Van Buren Avenue, P.O. Box 351, Barberton, Ohio, U.S.A. 44203-0351. Disclaimer The information contained within this book has been obtained by The Babcock & Wilcox Company from sources believed to be reliable. However, neither The Babcock & Wilcox Company nor its authors make any guarantee or warranty, expressed or implied, about the accuracy, completeness or usefulness of the information, product, process or apparatus discussed within this book, nor shall The Babcock & Wilcox Company or any of its authors be liable for error, omission, losses or damages of any kind or nature. This book is published with the understanding that The Babcock & Wilcox Company and its authors are supplying general information and neither attempting to render engineering or professional services nor offering a product for sale. If services are desired, an appropriate professional should be consulted. Steam/its generation and use. 41st edition. Editors: John B. Kitto and Steven C. Stultz. The Babcock & Wilcox Company, Barberton, Ohio, U.S.A. 2005 Includes bibliographic references and index. Subject areas: 1. Steam boilers. 2. Combustion – Fossil fuels. 3. Nuclear power. The editors welcome any technical comments, notes on inaccuracies, or thoughts on important omissions. Please direct these to the editors at SteamBook@babcock.com. © 1955, 1960, 1963, 1972, 1975, 1978, 1992, The Babcock & Wilcox Company. All rights reserved. ISBN 0-9634570-1-2 Library of Congress Catalog Number: 92-74123 ISSN 1556-5173 Printed in the United States of America. ii
- 4. The Babcock & Wilcox Company Steam 41 iii Steam/its generation and use is the longest continuously published engineer- ing text of its kind in the world. It has always been, and continues to be, writ- ten and published by The Babcock & Wilcox Company, the Original, head- quartered in Barberton, Ohio, and incorporated in Delaware, The United States of America. Steam, Edition: 41
- 5. The Babcock & Wilcox Company Steam 41iv The Babcock & Wilcox Company
- 6. The Babcock & Wilcox Company Steam 41 v Preface Dear Reader: The founders of our company, George Babcock and Stephen Wilcox, invented the safety water tube boiler. This invention resulted in the commercialization of large-scale utility generating stations. Rapid increases in generation of safe, dependable and economic electricity literally fueled the Industrial Revolution and dramatically increased the standard of living in the United States and industrialized economies worldwide throughout the twentieth century. Advancements in technology to improve efficiency and reduce environmen- tal emissions have continued for nearly 140 years, creating a unique and valu- able body of applied engineering that represents the individual and collective contributions of several generations of employees. As in other areas of science and engineering, our field has continued to evolve, resulting in an extensive amount of new material that has been incorporated into our 41st edition of Steam/its generation and use. This edition required an extensive amount of personal time and energy from hundreds of employees and reflects our com- mitment to both our industry and our future. Today it is clear that the challenge to generate power more efficiently from fossil fuels, while minimizing impacts to our environment and global climate, will require significant technological advancements. These advances will re- quire creativity, perseverance and ingenuity on the part of our employees and our customers. For inspiration, we can recall the relentless drive and imagi- nation of one of our first customers, Mr. Thomas Alva Edison. For strength, we will continue to embrace our Core Values of Quality, Integrity, Service and People which have served us well over our long history as a company. I thank our shareholders, our employees, our customers, our partners and our suppliers for their continued dedication,cooperationandsupportaswemove forward into what will prove to be a challenging and rewarding century. To help guide us all along the way, I am very pleased to present Edition: 41. David L. Keller President and Chief Operating Officer The Babcock & Wilcox Company
- 7. The Babcock & Wilcox Company Steam 41vi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii to ix System of Units: English and Système International . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Editors’ Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Introduction to Steam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intro-1 to 17 Selected Color Plates, Edition: 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plates 1 to 8 Section I – Steam Fundamentals Chapter 1 Steam Generation – An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1 to 1-17 2 Thermodynamics of Steam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 to 2-27 3 Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1 to 3-17 4 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1 to 4-33 5 Boiling Heat Transfer, Two-Phase Flow and Circulation . . . . . . . . . . . . . . 5-1 to 5-21 6 Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion . . . . 6-1 to 6-25 7 Metallurgy, Materials and Mechanical Properties . . . . . . . . . . . . . . . . . . . . 7-1 to 7-25 8 Structural Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1 to 8-17 Section II – Steam Generation from Chemical Energy Chapter 9 Sources of Chemical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1 to 9-19 10 Principles of Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1 to 10-31 11 Oil and Gas Utilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1 to 11-17 12 Solid Fuel Processing and Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-1 to 12-19 13 Coal Pulverization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1 to 13-15 14 Burners and Combustion Systems for Pulverized Coal . . . . . . . . . . . . . . . 14-1 to 14-21 15 Cyclone Furnaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 to 15-13 16 Stokers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1 to 16-11 17 Fluidized-Bed Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1 to 17-15 18 Coal Gasification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1 to 18-17 19 Boilers, Superheaters and Reheaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-1 to 19-21 20 Economizers and Air Heaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-1 to 20-17 21 Fuel Ash Effects on Boiler Design and Operation . . . . . . . . . . . . . . . . . . . . 21-1 to 21-27 22 Performance Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-1 to 22-21 23 Boiler Enclosures, Casing and Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . 23-1 to 23-9 24 Boiler Cleaning and Ash Handling Systems . . . . . . . . . . . . . . . . . . . . . . . . 24-1 to 24-21 25 Boiler Auxiliaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-1 to 25-23 Section Ill – Applications of Steam Chapter 26 Fossil Fuel Boilers for Electric Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26-1 to 26-17 27 Boilers for Industry and Small Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27-1 to 27-21 28 Chemical and Heat Recovery in the Paper Industry . . . . . . . . . . . . . . . . . 28-1 to 28-29 29 Waste-to-Energy Installations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29-1 to 29-23 30 Wood and Biomass Installations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30-1 to 30-11 31 Marine Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-1 to 31-13 Table of Contents
- 8. The Babcock & Wilcox Company Steam 41 vii Section IV – Environmental Protection Chapter 32 Environmental Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32-1 to 32-17 33 Particulate Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33-1 to 33-13 34 Nitrogen Oxides Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34-1 to 34-15 35 Sulfur Dioxide Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35-1 to 35-19 36 Environmental Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36-1 to 36-15 Section V – Specification, Manufacturing and Construction Chapter 37 Equipment Specification, Economics and Evaluation . . . . . . . . . . . . . . . . . 37-1 to 37-17 38 Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38-1 to 38-13 39 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39-1 to 39-19 Section VI – Operations Chapter 40 Pressure, Temperature, Quality and Flow Measurement . . . . . . . . . . . . . . 40-1 to 40-25 41 Controls for Fossil Fuel-Fired Steam Generating Plants . . . . . . . . . . . . . . 41-1 to 41-21 42 Water and Steam Chemistry, Deposits and Corrosion . . . . . . . . . . . . . . . . . 42-1 to 42-29 43 Boiler Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43-1 to 43-17 Section VII – Service and Maintenance Chapter 44 Maintaining Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44-1 to 44-21 45 Condition Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45-1 to 45-21 Section VIII – Steam Generation from Nuclear Energy Chapter 46 Steam Generation from Nuclear Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 46-1 to 46-25 47 Fundamentals of Nuclear Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47-1 to 47-15 48 Nuclear Steam Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48-1 to 48-15 49 Nuclear Services and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49-1 to 49-21 50 Nuclear Equipment Manufacture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50-1 to 50-13 Appendices Appendix 1 Conversion Factors, SI Steam Properties and Useful Tables . . . . . . . . . . . T-1 to T-16 2 Codes and Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-1 to C-6 Symbols, Acronyms and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-1 to S-10 B&W Trademarks in Edition: 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TM-1 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-1 to I-22
- 9. The Babcock & Wilcox Company Steam 41 Steam/its generation and use is the culmination of the work of hundreds of B&W employees who have con- tributed directly and indirectly to this edition and to the technology upon which it is based. Particular recogni- tion goes to individuals who formally committed to preparing and completing this expanded 41st edition. * The editors offer special acknowledgment to authors J.E. Granger and E.H. Mayer who passed away during the preparation of Edition: 41. Acknowledgments viii Editor-in-Chief/Project Manager S.C. Stultz Technical Editor/Technical Advisor J.B. Kitto Art Director/Assistant Editor G.L. Tomei Assistant Technical Editors J.J. Gaidos M.A. Miklic Lead Authors M.J. Albrecht G.T. Bielawski K.P. Brolly P.A. Campanizzi P.L. Cioffi R.A. Clocker P.L. Daniel R.A. Detzel J.A. Dickinson W. Downs D.D. Dueck S.J. Elmiger J.S. Gittinger J.E. Granger* G.R. Grant G.H. Harth T.C. Heil D.A. Huston B.J. Jankura C.S. Jones K.L. Jorgensen J.B. Kitto D.L. Kraft A.D. LaRue M.P. Lefebvre P. Li G.J. Maringo W.N. Martin E.H. Mayer* D.K. McDonald R.M. McNertney Jr. J.E. Monacelli T.E. Moskal N.C. Polosky E.F. Radke K.E. Redinger J.D. Riggs D.E. Ryan D.P. Scavuzzo S.A. Scavuzzo W.G. Schneider T.D. Shovlin T.A. Silva B.C. Sisler J.W. Smith R.E. Snyder W.R. Stirgwolt J.R. Strempek S.C. Stultz J.M. Tanzosh G.L. Tomei D.P. Tonn S.J. Vecci P.S. Weitzel R.A. Wessel L.C. Westfall P.J. Williams
- 10. The Babcock & Wilcox Company Steam 41 ix Primary Support Authors S.A. Bryk D.E. Burnham D.S. Fedock J.T. Griffin B.L. Johnson N. Kettenbauer T.P. Kors G.J. Lance R.C. Lenzer E.P.B. Mogensen G.M. Pifer K.J. Rogers B.J. Youmans Executive Steering Committee B.C. Bethards E.M. Competti J.S. Kulig D.C. Langley J.W. Malone M.G. Morash R.E. Reimels Production Group J.L. Basar L.A. Brower P.L. Fox L.M. Shepherd Outside Support P.C. Lutjen (Art) J.R. Grizer (Tables)
- 11. The Babcock & Wilcox Company Steam 41 To recognize the globalization of the power industry, the 41st edition of Steam incorporates the Système International d’Unitès (SI) along with the contin- ued use of English or U.S. Customary System (USCS) units. English units continue to be the primary system of units with SI provided as secondary units in parentheses. In some instances, SI units alone have been provided where these units are common usage. In selected figures and tables where dual units could detract from clarity (logarithmic scales, for example) SI conversions are provided within the figure titles or as a table footnote. Extensive English-SI conversion tables are provided in Appendix 1. This appendix also contains a complete SI set of the Steam Tables, Mollier diagram, pressure-enthalpy diagram and psychrometric chart. The decision was made to provide exact conversions rounded to an appro- priate number of figures. This was done to avoid confusion about the original source values. Absolute pressure is denoted by psi or kPa/MPa and gauge pressure by psig or kPa/MPa gauge. The difference between absolute pressure and pressure difference is identified by the context. Finally, in Chapters 10 and 22, as well as selected other areas of Steam which provide extensive numerical examples, only English units have been provided for clarity. For reference and clarity, power in British thermal units per hour (Btu/h) has typically been converted to megawatts-thermal and is denoted by MWt while megawatts-electric in both systems of units has been denoted by MW. TheeditorshopethattheseconversionpracticeswillmakeSteameasilyusable by the broadest possible audience. System of Units English and Système International x
- 12. The Babcock & Wilcox Company Steam 41 When we completed the 40th edition of Steam in 1992, we had a sense that perhaps our industry was stabilizing. But activity has again accelerated. To- day, efficiencies are being driven even higher. Emissions are being driven even lower. Many current technologies are being stretched, and new technologies are being developed, tested and installed. We have once again changed much of Steam to reflect our industry’s activity and anticipated developments. Recognizing the rich history of this publication, we previously drew words from an 1883 edition’s preface to say that “we have revised the whole, and added much new and valuable matter.” For this new 41st edition we can draw from the 1885 edition to say “Having again revised Steam, and enlarged it by the addition of new and useful information, not published heretofore, we shall feel repaid for the labor if it shall prove of value to our customers.” We hope this new edition is of equal value to our partners and suppliers, government personnel, students and educators, and all present and future em- ployees of The Babcock & Wilcox Company. Editors’ Foreword xi
- 13. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-1 Introduction to Steam Throughout history, mankind has reached beyond the acceptable to pursue a challenge, achieving sig- nificant accomplishments and developing new tech- nology. This process is both scientific and creative. En- tire civilizations, organizations, and most notably, in- dividuals have succeeded by simply doing what has never been done before. A prime example is the safe and efficient use of steam. One of the most significant series of events shap- ing today’s world is the industrial revolution that be- gan in the late seventeenth century. The desire to gen- erate steam on demand sparked this revolution, and technical advances in steam generation allowed it to continue. Without these developments, the industrial revolution as we know it would not have taken place. It is therefore appropriate to say that few technolo- gies developed through human ingenuity have done so much to advance mankind as the safe and depend- able generation of steam. Steam as a resource In 200 B.C., a Greek named Hero designed a simple machine that used steam as a power source (Fig. 1). He began with a cauldron of water, placed above an open fire. As the fire heated the cauldron, the caul- dron shell transferred the heat to the water. When the water reached the boiling point of 212F (100C), it changed form and turned into steam. The steam passed through two pipes into a hollow sphere, which was pivoted at both sides. As the steam escaped through two tubes attached to the sphere, each bent at an angle, the sphere moved, rotating on its axis. Hero, a mathematician and scientist, labeled the device aeolipile, meaning rotary steam engine. Al- though the invention was only a novelty, and Hero made no suggestion for its use, the idea of generating steam to do useful work was born. Even today, the basic idea has remained the same – generate heat, trans- fer the heat to water, and produce steam. Intimately related to steam generation is the steam turbine, a device that changes the energy of steam into mechanical work. In the early 1600s, an Italian named Giovanni Branca produced a unique invention (Fig. 2). He first produced steam, based on Hero’s aeolipile. By channeling the steam to a wheel that rotated, the steam pressure caused the wheel to turn. Thus began the development of the steam turbine. The primary use of steam turbines today is for elec- tric power production. In one of the most complex sys- tems ever designed by mankind, superheated high- pressure steam is produced in a boiler and channeled to turbine-generators to produce electricity. Fig. 1 Hero’s aeolipile.
- 14. The Babcock & Wilcox Company Intro-2 Steam 41 / Introduction to Steam Today’s steam plants are a complex and highly so- phisticated combination of engineered elements. Heat is obtained either from primary fossil fuels like coal, oil or natural gas, or from nuclear fuel in the form of uranium. Other sources of heat-producing energy in- clude waste heat and exhaust gases, bagasse and bio- mass, spent chemicals and municipal waste, and geo- thermal and solar energy. Each fuel contains potential energy, or a heating value measured in Btu/lb (J/kg). The goal is to release this energy, most often by a controlled combustion process or, with uranium, through fission. The heat is then transferred to water through tube walls and other components or liquids. The heated water then changes form, turning into steam. The steam is normally heated further to specific temperatures and pressures. Steam is also a vital resource in industry. It drives pumps and valves, helps produce paper and wood products, prepares foods, and heats and cools large buildings and institutions. Steam also propels much of the world’s naval fleets and a high percentage of commercial marine transport. Insomecountries,steam plays a continuing role in railway transportation. Steam generators, commonly referred to as boilers, range in size from those needed to heat a small build- ing to those used individually to produce 1300 mega- watts of electricity in a power generating station – enough power for more than one million people. These larger units deliver more than ten million pounds of superheated steam per hour (1260 kg/s) with steam temperatures exceeding 1000F (538C) and pressures exceeding 3800 psi (26.2 MPa). Today’s steam generating systems owe their de- pendability and safety to the design, fabrication and operation of safe water tube boilers, first patented by George Babcock and Stephen Wilcox in 1867 (Fig. 3). Because the production of steam power is a tremen- dous resource, it is our challenge and responsibility to further develop and use this resource safely, efficiently, dependably, and in an environmentally-friendly manner. The early use of steam Steam generation as an industry began almost two thousand years after Hero’s invention, in the seven- teenth century. Many conditions began to stimulate the development of steam use in a power cycle. Min- ing for ores and minerals had expanded greatly and large quantities of fuel were needed for ore refining. Fuels were needed for space heating and cooking and forgeneralindustrialandmilitarygrowth.Forestswere being stripped and coal was becoming an important fuel. Coal mining was emerging as a major industry. As mines became deeper, they were often flooded with underground water. The English in particular were faced with a very serious curtailment of their industrial growth if they could not find some economi- cal way to pump water from the mines. Many people began working on the problem and numerous patents were issued for machines to pump water from the mines using the expansive power of steam. The early machines used wood and charcoal for fuel, but coal eventually became the dominant fuel. The most common source of steam at the time was a shell boiler, little more than a large kettle filled with water and heated at the bottom (Fig. 4). Not all early developments in steam were directed toward pumps and engines. In 1680, Dr. Denis Papin, a Frenchman, invented a steam digester for food pro- Fig. 3 First Babcock & Wilcox boiler, patented in 1867. Fig. 4 Haycock shell boiler, 1720.Fig. 2 Branca’s steam turbine.
- 15. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-3 cessing, using a boiler under heavy pressure. To avoid explosion,Papinaddedadevicewhichisthefirstsafety valve on record. Papin also invented a boiler with an internal firebox, the earliest record of such construction. Many experiments concentrated on using steam pressure or atmospheric pressure combined with a vacuum. The result was the first commercially suc- cessful steam engine, patented by Thomas Savery in 1698, to pump water by direct displacement (Fig. 5). The patent credits Savery with an engine for raising water by the impellant force of fire, meaning steam. The mining industry needed the invention, but the engine had a limited pumping height set by the pres- sure the boiler and other vessels could withstand. Before its replacement by Thomas Newcomen’s engine (described below), John Desaguliers improved the Savery engine, adding the Papin safety valve and us- ing an internal jet for the condensing part of the cycle. Steam engine developments continued and the ear- liest cylinder-and-piston unit was based on Papin’s suggestion, in 1690, that the condensation of steam should be used to make a vacuum beneath a piston, after the piston had been raised by expanding steam. Newcomen’s atmospheric pressure engine made prac- tical use of this principle. While Papin neglected his own ideas of a steam en- gine to develop Savery’s invention, Thomas Newcomen and his assistant John Cawley adapted Papin’s suggestions in a practical engine. Years of ex- perimentation ended with success in 1711 (Fig. 6). Steam admitted from the boiler to a cylinder raised a piston by expansion and assistance from a counter- weight on the other end of a beam, actuated by the piston. The steam valve was then closed and the steam in the cylinder was condensed by a spray of cold wa- ter. The vacuum which formed caused the piston to be forced downward by atmospheric pressure, doing work on a pump. Condensed water in the cylinder was expelled through a valve by the entry of steam which was at a pressure slightly above atmospheric. A 25 ft (7.6 m) oak beam, used to transmit power from the cylinder to the water pump, was a dominant feature of what came to be called the beam engine. The boiler used by Newcomen, a plain copper brewer’s kettle, was known as the Haycock type. (See Fig. 4.) The key technical challenge remained the need for higher pressures, which meant a more reliable and stronger boiler. Basically, evolution of the steam boiler paralleled evolution of the steam engine. During the late 1700s, the inventor James Watt pursued developments of the steam engine, now physically separated from the boiler. Evidence indi- cates that he helped introduce the first waggon boiler, so named because of its shape (Fig. 7). Watt concen- trated on the engine and developed the separate steam condenser to create the vacuum and also replaced atmospheric pressure with steam pressure, improving the engine’s efficiency. He also established the mea- surement of horsepower, calculating that one horse could raise 550 lb (249 kg) of weight a distance of 1 ft (0.3 m) in one second, the equivalent of 33,000 lb (14,969 kg) a distance of one foot in one minute. Fig. 6 Newcomen’s beam engine, 1711. Fig. 7 Waggon boiler, 1769.Fig. 5 Savery’s engine, circa 1700.
- 16. The Babcock & Wilcox Company Intro-4 Steam 41 / Introduction to Steam Fire tube boilers The next outstanding inventor and builder was Ri- chard Trevithick, who had observed many pumping stations at his father’s mines. He realized that the problem with many pumping systems was the boiler capacity. Whereas copper was the only material previ- ously available, hammered wrought iron plates could now be used, although the maximum length was 2 ft (0.6 m). Rolled iron plates became available in 1875. In 1804, Trevithick designed a higher pressure en- gine, made possible by the successful construction of a high pressure boiler (Fig. 8). Trevithick’s boiler design featured a cast iron cylindrical shell and dished end. As demand grew further, it became necessary to ei- ther build larger boilers with more capacity or put up with the inconveniences of operating many smaller units. Engineersknewthatthelongerthehotgaseswere in contact with the shell and the greater the exposed sur- face area, the greater the capacity and efficiency. While a significant advance, Newcomen’s engine and boiler were so thermally inefficient that they were frequently only practical at coal mine sites. To make thesystemmorewidelyapplicable,developersofsteam engines began to think in terms of fuel economy. Not- ing that nearly half the heat from the fire was lost because of short contact time between the hot gases and the boiler heating surface, Dr. John Allen may have made the first calculation of boiler efficiency in 1730. To reduce heat loss, Allen developed an inter- nal furnace with a smoke flue winding through the water, like a coil in a still. To prevent a deficiency of combustion air, he suggested the use of bellows to force the gases through the flue. This probably represents the first use of forced draft. Laterdevelopmentssawthesinglepipefluereplaced by many gas tubes, which increased the amount of heating surface. These fire tube boilers were essen- tially the design of about 1870. However, they were limited in capacity and pressure and could not meet the needs that were developing for higher pressures and larger unit sizes. Also, there was the ominous record of explosions and personal injury because of direct heating of the pressure shell, which contained large volumes of water and steam at high tempera- ture and pressure. The following appeared in the 1898 edition of Steam: That the ordinary forms of boilers (fire tube boilers) are liable to explode with disastrous effect is conceded. That they do so explode is witnessed by the sad list of casualties from this cause every year, and almost every day. In the year 1880, there were 170 explosions reported in the United States, with a loss of 259 lives, and 555 persons injured. In 1887 the number of explosions recorded was 198, with 652 per- sons either killed or badly wounded. The average re- ported for ten years past has been about the same as the two years given, while doubtless many occur which are not recorded. Inventors recognized the need for a new design, one that could increase capacity and limit the conse- quences of pressure part rupture at high pressure and temperature. Water tube boiler development began. Early water tube design A patent granted to William Blakey in 1766, cover- ing an improvement in Savery’s steam engine, includes a form of steam generator (Fig. 9). This probably was the first step in the development of the water tube boiler. However, the first successful use of a water tube design was by James Rumsey, an American in- ventor who patented several types of boilers in 1788. Some of these boilers used water tube designs. At about this time John Stevens, also anAmerican, invented a water tube boiler consisting of a group of small tubes closed at one end and connected at the Fig. 8 Trevithick boiler, 1804. Fig. 9 William Blakey boiler, 1766.
- 17. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-5 other to a central reservoir (Fig. 10). Patented in the United States (U.S.) in 1803, this boiler was used on a Hudson River steam boat. The design was short lived, however, due to basic engineering problems in construction and operation. Blakey had gone to England to obtain his patents, as there were no similar laws in North America. Stevens, a lawyer, petitioned the U.S. Congress for a patent law to protect his invention and such a law was enacted in 1790. It may be said that part of the basis of present U.S. patent laws grew out of the need to protect a water tube boiler design. Fig. 11 shows an- other form of water tube boiler, this one patented by John Cox Stevens in 1805. In 1822, Jacob Perkins built a water tube boiler that is the predecessor of the once-through steam genera- tor.Anumber of cast iron bars with longitudinal holes were arranged over the fire in three tiers by connect- ing the ends outside of the furnace with a series of bent pipes. Water was fed to the top tier by a feed pump and superheated steam was discharged from the lower tier to a collecting chamber. The Babcock & Wilcox Company It was not until 1856, however, that a truly success- ful water tube boiler emerged. In that year, Stephen Wilcox, Jr. introduced his version of the water tube design with improved water circulation and increased heating surface (Fig. 12). Wilcox had designed a boiler with inclined water tubes that connected water spaces at the front and rear, with a steam chamber above. Most important, as a water tube boiler, his unit was in- herently safe. His design revolutionized the boiler in- dustry. In 1866, Wilcox partnered with his long-time friend, George H. Babcock. The following year, U.S. Patent No. 65,042 was granted to George H. Babcock and Steven Wilcox, Jr., and the partnership of Babcock, Wilcox and Company was formed. In 1870 or 1871, Babcock and Wilcox became the sole proprietors, drop- ping Company from the name, and the firm was known as Babcock & Wilcox until its incorporation in 1881, when it changed its name to The Babcock & Wilcox Company (B&W). (see Fig. 3). Industrial progress continued. In 1876, a giant- sized Corliss steam engine, a device invented in Rhode Island in 1849, went on display at the Centennial Ex- Fig. 10 John Stevens water tube boiler, 1803. Fig. 11 Water tube boiler with tubes connecting water chamber below and steam chamber above. John Cox Stevens, 1805. Fig. 12 Inclined water tubes connecting front and rear water spaces, complete with steam space above. Stephen Wilcox, 1856. Fig. 13 Babcock & Wilcox Centennial boiler, 1876.
- 18. The Babcock & Wilcox Company Intro-6 Steam 41 / Introduction to Steam hibition in Philadelphia, Pennsylvania, as a symbol of worldwide industrial development. Also on promi- nent display was a 150 horsepower water tube boiler (Fig. 13) by George Babcock and Stephen Wilcox, who were by then recognized as engineers of unusual abil- ity. Their professional reputation was high and their names carried prestige. By 1877, theBabcock&Wilcox boiler had been modified and improved by the partners several times (Fig. 14). At the exhibition, the public was awed by the size of the Corliss engine. It weighed 600 tons and had cyl- inders 3 ft (0.9 m) in diameter. But this giant size was to also mark the end of the steam engine, in favor of more efficient prime movers, such as the steam tur- bine. This transition would add momentum to further development of the Babcock & Wilcox water tube boiler. By 1900, the steam turbine gained importance as the major steam powered source of rotary motion, dueprimarilytoitslowermaintenancecosts,greaterover- loading tolerance, fewer number of moving parts, and smallersize. Perhaps the most visible technical accomplishments of the time were in Philadelphia and New York City. In 1881 in Philadelphia, the Brush Electric Light Com- pany began operations with four boilers totaling 292 horsepower. In New York the following year, Thomas Alva Edison threw the switch to open the Pearl Street Central station, ushering in the age of the cities. The boilers in Philadelphia and the four used by Thomas Edison in New York were built by B&W, now incorpo- rated. The boilers were heralded as sturdy, safe and reliable. When asked in 1888 to comment on one of the units, Edison wrote: It is the best boiler God has permitted man yet to make. (Fig. 15). ThehistoricPearlStreetCentralstationopenedwith 59 customers using about 1300 lamps. The B&W boil- ers consumed 5 tons of coal and 11,500 gal (43,532 l) of water per day. The B&W boiler of 1881 was a safe and efficient steam generator, ready for the part it would play in worldwide industrial development. Water tube marine boilers The first water tube marine boiler built by B&W was for the Monroe of the U.S. Army’s Quartermaster Fig. 14 Babcock & Wilcox boiler developed in 1877. George Herman Babcock GeorgeHermanBabcockwasbornJune17,1832 near Otsego, New York. His father was a well known inventor and mechanic. When George was 12 years old, his parents moved to Westerly, Rhode Island, where he met Stephen Wilcox, Jr. At age 19, Babcock started the Literary Echo, editingthepaperandrunningaprintingbusiness. With his father, he invented the first polychro- matic printing press, and he also patented a job press which won a prize at the London Crystal Palace International Exposition in 1855. Intheearly1860s,hewasmadechiefdraftsman of the Hope Iron Works at Providence, Rhode Is- land, where he renewed his acquaintance with Stephen Wilcox and worked with him in develop- ing the first B&W boiler. In 1886, Babcock became the sixth president of the American Society of Me- chanical Engineers. He was the first president of The Babcock & Wilcox Company, a position he held until his death in 1893.
- 19. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-7 department. A major step in water tube marine boiler design came in 1889, with a unit for the steam yacht Reverie. The U.S. Navy then ordered three ships fea- turing a more improved design that saved about 30% in weight from previous designs. This design was again improved in 1899, for a unit installed in the U.S. cruiser Alert, establishing the superiority of the wa- ter tube boiler for marine propulsion. In this installa- tion, the firing end of the boiler was reversed, placing the firing door in what had been the rear wall of the boiler. The furnace was thereby enlarged in the di- rection in which combustion took place, greatly im- proving combustion conditions. The development of marine boilers for naval and merchant ship propulsion has paralleled that for land use (see Fig. 16). Throughout the twentieth century and into the twenty-first, dependable water tube ma- rineboilershavecontributedgreatlytotheexcellentper- formance of naval and commercial ships worldwide. Bent tube design The success and widespread use of the inclined straight tube B&W boiler stimulated other inventors to explore new ideas. In 1880,Allan Stirling developed a design connecting the steam generating tubes di- rectly to a steam separating drum and featuring low headroom above the furnace. The Stirling Boiler Com- pany was formed to manufacture and market an im- proved Stirling® design, essentially the same as shown in Fig. 17. The merits of bent tubes for certain applications Stephen Wilcox, Jr. Stephen Wilcox was born February 12, 1830 at Westerly, Rhode Island. Thefirstdefiniteinformationconcerninghisen- gineering activities locates him in Providence, Rhode Island, about 1849, trying to introduce a caloric engine. In 1853, in association with Amos Taylor of Mystic, Connecticut, he patented a letoff motion for looms. In 1856, a patent for a steam boiler was issued to Stephen Wilcox and O.M. Stillman. While this boiler differed materially from later designs, it is notable as his first re- corded step into the field of steam generation. In 1866 with George Babcock, Wilcox developed the first B&W boiler, which was patented the fol- lowing year. In 1869 he went to New York as selling agent for the Hope Iron Works and took an active part in improving the boiler and the building of the business. He was vice president of The Babcock & Wilcox Company from its incorporation in 1881 until his death in 1893. were soon recognized by George Babcock and Stephen Wilcox, and what had become the Stirling Consoli- dated Boiler Company in Barberton, Ohio, was pur- chased by B&W in 1906. After the problems of internal tube cleaning were solved, the bent tube boiler replaced the straight tube design. The continuous and economi- calproductionofclean,drysteam,evenwhenusingpoor quality feedwater, and the ability to meet sudden load swings were features of the new B&W design. Electric power Until the late 1800s, steam was used primarily for heat and as a tool for industry. Then, with the advent of practical electric power generation and distribution, utility companies were formed to serve industrial and residential users across wide areas. The pioneer sta- tions in the U.S. were the Brush Electric Light Com- pany and the Commonwealth Edison Company. Both used B&W boilers exclusively. During the first two decades of the twentieth cen- tury, there was an increase in steam pressures and temperatures to 275 psi (1.9 MPa) and 560F (293C), with 146F (81C) superheat. In 1921, the North Tess station of the Newcastle Electric Supply Company in northern England went into operation with steam at 450 psi (3.1 MPa) and a temperature of 650F (343C). The steam was reheated to 500F (260C) and regen- erative feedwater heating was used to attain a boiler feedwater temperature of 300F (149C). Three years later, the Crawford Avenue station of the Common- wealth Edison Company and the Philo and Twin
- 20. The Babcock & Wilcox Company Intro-8 Steam 41 / Introduction to Steam Fig. 15 Thomas Edison’s endorsement, 1888.
- 21. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-9 Branch stations of the present American Electric Power system were placed in service with steam at 550 psi (38 MPa) and 725F (385C) at the turbine throttle. The steam was reheated to 700F (371C). A station designed for much higher steam pressure, the Weymouth (later named Edgar) station of the Bos- ton Edison Company in Massachusetts, began opera- tion in 1925. The 3150 kW high pressure unit used steam at 1200 psi (8.3 MPa) and 700F (371C), re- heated to 700F (371C) for the main turbines (Fig. 18). Pulverized coal and water-cooled furnaces Other major changes in boiler design and fabrica- tion occurred in the 1920s. Previously, as power gen- erating stations increased capacity, they increased the number of boilers, but attempts were being made to increase the size of the boilers as well. Soon the size requirement became such that existing furnace de- signs and methods of burning coal, primarily stokers, were no longer adequate. Pulverized coal was the answer in achieving higher volumetric combustion rates and increased boiler ca- pacity. This could not have been fully exploited with- out the use of water-cooled furnaces. Such furnaces eliminated the problem of rapid deterioration of the refractory walls due to slag (molten ash). Also, these designs lowered the temperature of the gases leaving the furnace and thereby reduced fouling (accumula- tion of ash) of convection pass heating surfaces to manageable levels. The first use of pulverized coal in furnaces of stationary steam boilers had been dem- onstrated at the Oneida Street plant in Milwaukee, Wisconsin, in 1918. Integral Furnace boiler Water cooling was applied to existing boiler designs, with its circulatory system essentially independent of the boiler steam-water circulation. In the early 1930s, however, a new concept was developed that arranged Fig. 16 Two drum Integral Furnace marine boiler. Requirements of a Perfect Steam Boiler – 1875 the different sections to equalize the water line and pres- sure in all. 7th. A great excess of strength over any legitimate strain, the boiler being so constructed as to be free from strains due to unequal expansion, and, if possible, to avoid joints exposed to the direct action of the fire. 8th. A combustion chamber so arranged that the com- bustion of the gases started in the furnace may be com- pleted before the gases escape to the chimney. 9th. The heating surface as nearly as possible at right angles to the currents of heated gases, so as to break up the currents and extract the entire available heat from the gases. 10th. All parts readily accessible for cleaning and re- pairs. This is a point of the greatest importance as re- gards safety and economy. 11th. Proportioned for the work to be done, and capable of working to its full rated capacity with the highest economy. 12th. Equipped with the very best gauges, safety valves and other fixtures. In 1875, George Babcock and Stephen Wilcox pub- lished their conception of the perfect boiler, listing twelve principles that even today generally represent good de- sign practice: 1st. Proper workmanship and simple construction, us- ing materials which experience has shown to be best, thus avoiding the necessity of early repairs. 2nd. A mud-drum to receive all impurities deposited from the water, and so placed as to be removed from the action of the fire. 3rd. A steam and water capacity sufficient to prevent any fluctuation in steam pressure or water level. 4th. A water surface for the disengagement of the steam from the water, of sufficient extent to prevent foaming. 5th. A constant and thorough circulation of water throughout the boiler, so as to maintain all parts at the same temperature. 6th. The water space divided into sections so arranged that, should any section fail, no general explosion can occur and the destructive effects will be confined to the escape of the contents. Large and free passages between
- 22. The Babcock & Wilcox Company Intro-10 Steam 41 / Introduction to Steam the furnace water-cooled surface and the boiler surface together, each as an integral part of the unit (Fig. 19). Shop-assembled water tube boilers In the late 1940s, the increasing need for industrial andheatingboilers,combinedwiththeincreasingcosts of field-assembled equipment, led to development of the shop-assembled package boiler. These units are now designed in capacities up to 600,000 lb/h (75.6 kg/s) at pressures up to 1800 psi (12.4 MPa) and tem- peratures to 1000F (538C). Further developments In addition to reducing furnace maintenance and the fouling of convection heating surfaces, water cool- ing also helped to generate more steam. Boiler tube bank surface was reduced because additional steam generating surface was available in the furnace. In- creased feedwater and steam temperatures and in- creased steam pressures, for greater cycle efficiency, further reduced boiler tube bank surface and permit- ted the use of additional superheater surface. Asaresult,Radiantboilersforsteampressuresabove 1800 psi (12.4 MPa) generally consist of furnace water wall tubes, superheaters, and such heat recovery acces- soriesaseconomizersandairheaters(Fig.20).Unitsfor lowerpressures,however,haveconsiderablesteamgen- erating surface in tube banks (boiler banks) in addition to the water-cooled furnace (Fig. 21). Universal Pressure boilers An important milestone in producing electricity at the lowest possible cost took place in 1957. The first Fig. 19 Integral Furnace boiler, 1933. Fig. 17 Early Stirling® boiler arranged for hand firing. Fig. 18 High pressure reheat boiler, 1925.
- 23. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-11 boiler with steam pressure above the critical value of 3200 psi (22.1 MPa) began commercial operation. This 125 MW B&W Universal Pressure (UP ) steam gen- erator(Fig.22),locatedatOhioPowerCompany’sPhilo plant, delivered 675,000 lb/h (85 kg/s) steam at 4550 psi (31.4 MPa); the steam was superheated to 1150F (621C) with two reheats to 1050 and 1000F (566 and 538C). B&Wbuiltandtesteditsfirstonce-throughsteamgen- erator for 600 psi (4.1 MPa) in 1916, and built an experi- mental 5000 psi (34.5 MPa) unit in the late 1920s. The UP boiler, so named because it can be designed for subcritical or supercritical operation, is capable of rapid load pickup. Increases in load rates up to 5% per minute can be attained. Fig. 23 shows a typical 1300 MW UP boiler rated at 9,775,000 lb/h (1232 kg/s) steam at 3845 psi (26.5 MPa) and 1010F (543C) with reheat to 1000F (538C). In 1987, one of these B&W units, located in West Vir- ginia, achieved 607 days of continuous operation. Most recently, UP boilers with spiral wound fur- naces (SWUP steam generators) have gained wider acceptance for their on/off cycling capabilities and their ability to operate at variable pressure with higher low load power cycle efficiency (see Fig. 24). Subcritical units, however, remain the dominant design in the existing worldwide boiler fleet. Coal has remained the dominant fuel because of its abundant supply in many countries. Other fuels and systems B&W has continued to develop steam generators that can produce power from an ever widening array of fuels in an increasingly clean and environmentally acceptable manner. Landmark developments by B&W include atmospheric fluidized-bed combustion instal- Air Heater Catalyst Economizer SCR Primary Superheater Final Reheat Superheater Furnace Steam Drum Platen Secondary Superheater Secondary Superheater Pulverizer Forced Draft Fan Primary Air Fan Primary Reheater Fig. 20 Typical B&W® Radiant utility boiler. lations, both bubbling and circulating bed, for reduced emissions. Waste-to-energy systems also became a major effort worldwide. B&W has installed both mass burn and refuse-derived fuel units to meet this growing demand for waste disposal and electric power generation. B&W installedtheworld’sfirstwaste-to-energyboilerin1972. In 2000, an acquisition by Babcock & Wilcox expanded the company’s capabilities in design and construction of waste-to-energy and biomass boilers and other multi- fuel burning plants. For the paper industry, B&W installed the first chemical recovery boiler in the U.S. in 1940. Since that time,B&Whasdevelopedalongtraditionoffirstsinthis industryandhasinstalledoneofthelargestblackliquor chemical recovery units operating in the world today. Modified steam cycles High efficiency cycles involve combinations of gas turbines and steam power in cogeneration, and direct thermal to electrical energy conversion. One direct conversion system includes using conventional fuel or char byproduct from coal gasification or liquefaction. Despite many complex cycles devised to increase overall plant efficiency, the conventional steam cycle Fig. 21 Lower pressure Stirling® boiler design.
- 24. The Babcock & Wilcox Company Intro-12 Steam 41 / Introduction to Steam remains the most economical. The increasing use of high steam pressures and temperatures, reheat super- heaters, economizers, and air heaters has led to im- proved efficiency in the modern steam power cycle. Nuclear power Since 1942, when Enrico Fermi demonstrated a con- trolled self-sustaining reaction, nuclear fission has been recognized as an important source of heat for producing steam for power generation. The first sig- nificant application of this new source was the land- based prototype reactor for the U.S.S. Nautilus sub- marine (Fig. 25), operated at the National Reactor Testing Station in Idaho in the early 1950s. This pro- totype reactor, designed by B&W, was also the basis for land-based pressurized water reactors now being used for electric power generation worldwide. B&W and its affiliates have continued their active involve- ment in both naval and land-based programs. The first nuclear electric utility installation was the 90 MW unit at the Shippingport atomic power station in Pennsylvania. This plant, built partly by Duquesne Light Company and partly by the U.S.Atomic Energy Commission, began operations in 1957. Spurred by the trend toward larger unit capacity, developments in the use of nuclear energy for electric power reached a milestone in 1967 when, in the U.S., nuclear units constituted almost 50% of the 54,000 MW of new capacity ordered that year. Single unit ca- pacity designs have reached 1300 MW. Activity re- garding nuclear power was also strong outside the Fig. 22 125 MW B&W® Universal Pressure (UP® ) boiler, 1957. Fig. 23 1300 MW B&W® Universal Pressure (UP® ) boiler. Fig. 25 U.S.S. Nautilus – world’s first nuclear-powered ship. Fig. 24 Boiler with spiral wound universal pressure (SWUP™) furnace. Low NOX Burners Overfire Air Ports Flue Gas Outlet Primary Air Fan Air Heater Steam Coil Air Heater Forced Draft Fan B&W Roll Wheel Pulverizers Ammonia Injection Grid Steam Separator Water Collection Tank Primary Superheater Economizer Platen Superheater Final Superheater Final Reheater Circulation Pump Primary Reheater Catalyst Intermediate Superheater Spiral Transition Headers Furnace SCR
- 25. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-13 U.S., especially in Europe. By 2004, there were 103 reactors licensed to operate in the U.S. Fifty of the oper- ating units had net capacities greater than 1000 MW. Throughout this period, the nuclear power program in Canada continued to develop based on a design called the Canada Deuterium Uranium (CANDU) reactor system. This system is rated high in both avail- ability and dependability. By 2003, there were 21 units in Canada, all with B&W nuclear steam gen- erators, an additional 11 units operating outside of Canada, and 18 units operating, under construction or planned that are based on CANDU technology. The B&W recirculating steam generators in these units have continually held excellent performance records and are being ordered to replace aging equip- ment. (See Fig. 26.) While the use of nuclear power has remained some- what steady in the U.S., the future of nuclear power is uncertainasissuesofplantoperatingsafetyandlong- term waste disposal are still being resolved. However, nuclear power continues to offer one of the least pollut- ing forms of large-scale power generation available and may eventually see a resurgence in new construction. Materials and fabrication Pressure parts for water tube boilers were originally made of iron and later of steel. Now, steam drums and nuclear pressure vessels are fabricated from heavy steel plates and steel forgings joined by welding. The development of the steam boiler has been necessarily concurrent with advances in metallurgy and progres- sive improvements in the fabrication and welding of steel and steel alloys. The cast iron generating tubes used in the first B&W boilers were later superseded by steel tubes. Shortly after 1900, B&W developed a commercial process for the manufacture of hot finished seamless steel boiler tubes, combining strength and reliability with reason- able cost. In the midst of World War II, B&W completed a mill to manufacture tubes by the electric resistance welding (ERW) process. This tubing has now been used in thousands of steam generating units throughout the world. The cast iron tubes used for steam and water stor- age in the original B&W boilers were soon replaced by drums. By 1888, drum construction was improved by changing from wrought iron to steel plates rolled into cylinders. Before 1930, riveting was the standard method of joining boiler drum plates. Drum plate thickness was limited to about 2.75 in. (70 mm) because no satisfac- tory method was known to secure a tight joint in thicker plates. The only alternative available was to forge and machine a solid ingot of steel into a drum, which was an extremely expensive process. This method was only used on boilers operatingatwhatwas then considered high pressure, above 700 psi (4.8 MPa). The story behind the development of fusion weld- ing was one of intensive research activity beginning in 1926. Welding techniques had to be improved in many respects. Equally, if not more important, an ac- ceptable test procedure had to be found and instituted that would examine the drum without destroying it in the test. After extensive investigation of various testing methods, the medical radiography (x-ray) ma- chine was adapted in 1929 to production examination of welds. By utilizing both x-ray examination and physical tests of samples of the weld material, the soundness of the welds could be determined without affecting the drum. In 1930, the U.S. Navy adopted a specification for construction of welded boiler drums for naval vessels. In that same year, the first welded drums ever ac- cepted by an engineering authority were part of the B&W boilers installed in several naval cruisers. Also in 1930, the Boiler Code Committee of the American Society of Mechanical Engineers (ASME) issued com- plete rules and specifications for the fusion welding of drums for power boilers. In 1931, B&W shipped the first welded power boiler drum built under this code. The x-ray examination of welded drums, the rules declared for the qualification of welders, and the con- trol of welding operations were major first steps in the development of modern methods of quality control in the boiler industry. Quality assurance has received additional stimulus from the naval nuclear propulsion program and from the U.S. Nuclear Regulatory Com- mission in connection with the licensing of nuclear plants for power generation. Research and development Since the founding of the partnership of Babcock, Wilcox and Company in 1867 and continuing to the present day, research and development have played im- portant roles in B&W’s continuing service to the power industry.FromtheinitialimprovementsofWilcox’sorigi- nalsafetywatertubeboilertothefirstsupercriticalpres- sure boilers, and from the first privately operated nuclear research reactor to today’s advanced environ- mental systems, innovation and the new ideas of its em- ployees have placed B&W at the forefront of safe, effi- cient and clean steam generation and energy conver- siontechnology.Today,researchanddevelopmentactivi- tiesremainanintegralpartofB&W’sfocusontomorrow’s product and process requirements. Fig. 26 B&W replacement recirculating steam generators.
- 26. The Babcock & Wilcox Company Intro-14 Steam 41 / Introduction to Steam A key to the continued success of B&W is the abil- ity to bring together cross-disciplinary research teams of experts from the many technical specialties in the steam generation field. These are combined with state- of-the-art test facilities and computer systems. Expert scientists and engineers use equipment de- signed specifically for research programs in all aspects of fossil power development, nuclear steam systems, materials development and evaluation, and manufac- turing technology. Research focuses upon areas of cen- tral importance to B&W and steam power generation. However, partners in these research programs have grown to include the U.S. Departments of Energy and Defense, the Environmental Protection Agency, pub- lic and private research institutes, state governments, and electric utilities. Key areas of current research include environmen- tal protection, fuels and combustion technology, heat transfer and fluid mechanics, materials and manufac- turing technologies, structural analysis and design, fuels and water chemistry, and measurement and monitoring technology. Environmental protection Environmental protection is a key element in all modern steam producing systems where low cost steam and electricity must be produced with minimum impact on the environment. Air pollution control is a key issue for all combustion processes, and B&W has been a leader in this area. Several generations of low nitrogen oxides (NOx) burners and combustion tech- nology for coal-, oil- and gas-fired systems have been developed, tested and patented by B&W. Post-combus- tion NOx reduction has focused on both selective cata- lytic and non-catalytic reduction systems. Combined with low NOx burners, these technologies have reduced NOx levels by up to 95% from historical uncontrolled levels. Ongoing research and testing are being com- bined with fundamental studies and computer numeri- cal modeling to produce the ultra-low NOx steam gen- erating systems of tomorrow. Since the early 1970s, extensive research efforts have been underway to reduce sulfur dioxide (SO2) emissions. These efforts have included combustion modifications and post-combustion removal. Research during this time aided in the development of B&W’s wet SO2 scrubbing system. This system has helped con- trol emissions from more than 32,000 MW of boiler ca- pacity. Current research focuses on improved removal and operational efficiency, and multi-pollution control technology. B&W has installed more than 9000 MW of boiler capacity using various dry scrubbing tech- nologies. Major pilot facilities have permitted the test- ing of in-furnace injection, in-duct injection, and dry scrubber systems, as well as atomization, gas condi- tioning and combined SO2, NOx and particulate con- trol. (See Fig. 27.) Since 1975, B&W has been a leader in fluidized- bed combustion (FBC) technology which offers the ability to simultaneously control SO2 and NOx forma- tion as an integral part of the combustion process, as well as burn a variety of waste and other difficult to combust fuels. This work led to the first large scale (20 MW) bubbling-bed system installation in the U.S. B&W’s research and development work has focused on process optimization, limestone utilization, and per- formance characteristics of various fuels and sorbents. Additional areas of ongoing environmental research include air toxic emissions characterization, efficient removal of mercury, multi-pollutant emissions control, and sulfur trioxide (SO3) capture, among others (Fig. 28). B&W also continues to review and evaluate pro- cesses to characterize, reuse, and if needed, safely dispose of solid waste products. Fuels and combustion technology A large number of fuels have been used to gener- ate steam. This is even true today as an ever-widen- ing and varied supply of waste and byproduct fuels such as municipal refuse, coal mine tailings and bio- mass wastes, join coal, oil and natural gas to meet steam production needs. These fuels must be burned and their combustion products successfully handled while addressing two key trends: 1) declining fuel quality (lower heating value and poorer combustion), and 2) more restrictive emissions limits. Major strengths of B&W and its work in research and development have been: 1) the characterization of fuels and their ashes, 2) combustion of difficult fu- els, and 3) effective heat recovery from the products of combustion. (See Fig. 29.) B&W has earned inter- Fig. 27 B&W boiler with SO2, NOx, and particulate control systems.
- 27. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-15 national recognition for its fuels analysis capabilities that are based upon generally accepted procedures, as well as specialized B&W procedures. Detailed analyses include, but are not limited to: heating value, chemical constituents, grindability, abrasion resis- tance, erosiveness, ignition, combustion characteris- tics,ashcomposition/viscosity/fusiontemperature,and particle size. The results of these tests assist in pul- verizer specification and design, internal boiler dimen- sion selection, efficiency calculations, predicted unit availability, ash removal system design, sootblower placement, and precipitator performance evaluation. Thousands of coal and ash samples have been ana- lyzed and catalogued, forming part of the basis for B&W’s design methods. Combustion and fuel preparation facilities are maintained that can test a broad range of fuels at large scale. The 6 × 106 Btu/h (1.8 MWt) small boiler simulator (Fig. 30) permits a simulation of the time- temperature history of the entire combustion process. The subsystems include a vertical test furnace; fuel subsystem for pulverizing, collecting and firing solid fuels; fuel storage and feeding; emission control mod- ules; gas and stack particulate analyzers for O2, CO, CO2 and NOx; and instrumentation for solids grind- ing characterization. Research continues in the areas of gas-side corro- sion, boiler fouling and cleaning characteristics, ad- vanced pulp and paper black liquor combustion, oxy- gen and oxygen enhanced firing systems, and coal gas- ification, among others. Heat transfer and fluid dynamics Heat transfer is a critical technology in the design of steam generation equipment. For many years, B&W has been conducting heat transfer research from hot gases to tube walls and from the tube walls to enclosed water, steam and air. Early in the 1950s, research in heat transfer and fluid mechanics was initiated in the supercritical pressure region above 3200 psi (22.1 MPa). This work was the technical foundation for the large number of supercritical pressure once-through steam generators currently in service in the electric power industry. A key advancement in steam-water flow was the invention of the ribbed tube, patented by B&W in 1960. By preventing deterioration of heat transfer under many flow conditions (called critical heat flux or departure from nucleate boiling), the internally ribbed tube made possible the use of natural circula- tion boilers at virtually all pressures up to the critical point. Extensive experimental studies have provided the critical heat flux data necessary for the design of boilers with both ribbed and smooth bore tubes. Fig. 28 Tests for multi-pollutant emissions control. Fig. 29 Atomic absorption test for ash composition. Fig. 30 B&W’s small boiler simulator.
- 28. The Babcock & Wilcox Company Intro-16 Steam 41 / Introduction to Steam Closely related to heat transfer, and of equal im- portance in steam generating equipment, is fluid me- chanics. Both low pressure fluids (air and gas in ducts and flues) and high pressure fluids (water, steam- water mixtures, steam and fuel oil) must be investi- gated. The theories of single-phase fluid flow are well understood, but the application of theory to the com- plex, irregular and multiple parallel path geometry of practical situations is often difficult and sometimes impossible. In these cases, analytical procedures must be supplemented or replaced by experimental meth- ods. If reliable extrapolations are possible, economi- cal modeling techniques can be used. Where extrapo- lation is not feasible, large-scale testing at full pres- sure, temperature and flow rate is needed. Advances in numerical modeling technology have made possible the evaluation of the complex three-di- mensional flow, heat transfer and combustion pro- cesses in coal-fired boiler furnaces. B&W is a leader in the development of numerical computational mod- els to evaluate the combustion of coal, biomass, black liquor and other fuels that have a discrete phase, and the application of these models to full boiler and sys- tem analysis (Fig. 31). Continuing development and validation of these models will enhance new boiler designs and expand applications. These models are also valuable tools in the design and evaluation of com- bustion processes, pollutant formation, and environ- mental control equipment. Research, analytical and field test studies in boil- ing heat transfer, two-phase flow, and stability, among other key areas, continue today by B&W alone and incooperationwitharangeofworldclassorganizations. Materials and manufacturing technologies Because advanced steam producing and energy conversion systems require the application and fabri- cation of a wide variety of carbon, alloy and stainless steels, nonferrous metals, and nonmetallic materials, it is essential that experienced metallurgical and ma- terials science personnel are equipped with the finest investigative tools. Areas of primary interest in the metallurgical field are fabrication processes such as welding, room temperature and high temperature ma- terial properties, resistance to corrosion properties, wear resistance properties, robotic welding, and changes in such material properties under various operating conditions. Development of oxidation-resis- tant alloys that retain strength at high temperature, and determination of short-term and long-term high temperature properties permitted the increase in steam temperature that has been and continues to be of critical importance in increasing power plant effi- ciency and reducing the cost of producing electricity. Advancements in manufacturing have included a process to manufacture large pressure components entirely from weld wire, designing a unique manu- facturing process for bi-metallic tubing, using pressure forming to produce metallic heat exchangers, devel- oping air blown ultra-high temperature fibrous insu- lation, and combining sensor and control capabilities to improve quality and productivity of manufactur- ing processes. Research and development activities also include the study of materials processing, joining processes, process metallurgy, analytical and physical metallur- gical examination, and mechanical testing. The results are subsequently applied to product improvement. Structural analysis and design The complex geometries and high stresses under which metals must serve in many products require careful study to allow prediction of stress distribution and intensity. Applied mechanics, a discipline with highly sophisticated analytical and experimental tech- niques, can provide designers with calculation meth- ods and other information to assure the safety of struc- tures and reduce costs by eliminating unnecessarily conservativedesignpractices.Theanalyticaltechniques involve advanced mathematical procedures and compu- tational tools as well as the use of advanced computers. An array of experimental tools and techniques are used to supplement these powerful analytical techniques. Computational finite element analysis has largely displaced experimental measurement for establishing detailed local stress relationships. B&W has developed and applied some of the most advanced computer pro- grams in the design of components for the power in- dustry.Advanced techniques permit the evaluation of stresses resulting from component response to ther- mal and mechanical (including vibratory) loading. Fracture mechanics, the evaluation of crack forma- tion and growth, is an important area where analyti- cal techniques and new experimental methods permit a better understanding of failure modes and the pre- Fig. 31 B&W has developed advanced computational numerical models to evaluate complex flow, heat transfer and combustion processes.
- 29. The Babcock & Wilcox Company Steam 41 / Introduction to Steam Intro-17 diction of remaining component life. This branch of technology has contributed to the feasibility and safety of advanced designs in many types of equipment. To provide part of the basis for these models, exten- sivecomputer-controlledexperimentalfacilitiesallowthe assessment of mechanical properties for materials un- der environments similar to those in which they will operate. Some of the evaluations include tensile and impact testing, fatigue and corrosion fatigue, fracture toughness,aswellasenvironmentallyassistedcracking. Fuel and water chemistry Chemistry plays an important role in supporting the effective operation of steam generating systems. Therefore, diversified chemistry capabilities are essen- tial to support research, development and engineer- ing. The design and operation of fuel burning equip- ment must be supported by expert analysis of a wide variety of solid, liquid and gaseous fuels and their products of combustion, and characterization of their behavior under various conditions. Long-term opera- tion of steam generating equipment requires exten- sive water programs including high purity water analysis, water treatment and water purification. Equipment must also be chemically cleaned at inter- vals to remove water-side deposits. To develop customized programs to meet specific needs, B&W maintains a leadership position in these areas through an expert staff for fuels characteriza- tion, water chemistry and chemical cleaning. Studies focusonwatertreatment,productionandmeasurement ofultra-highpuritywater(partsperbillion),water-side deposit analysis, and corrosion product transport. B&W was involved in the introduction of oxygen water treatment for U.S. utility applications. Special- ized chemical cleaning evaluations are conducted to prepare cleaning programs for utility boilers, indus- trial boilers and nuclear steam generators. Special analyses are frequently required to develop boiler-spe- cific cleaning solvent solutions that will remove the desired deposits without damaging the equipment. Measurements and monitoring technology Development, evaluation and accurate assessment of modern power systems require increasingly precise measurements in difficult to reach locations, often in hostile environments. To meet these demanding needs, B&W continues the investigation of specialized sensors, measurement and nondestructive examina- tion. B&W continues to develop diagnostic methods that lead to advanced systems for burner and combus- tion systems as well as boiler condition assessment. These techniques have been used to aid in labora- tory research such as void fraction measurements for steam-water flows. They have also been applied to operating steam generating systems. New methods have been introduced by B&W to nondestructively measure oxide thicknesses on the inside of boiler tubes, detect hydrogen damage, and detect and mea- sure corrosion fatigue cracks.Acoustic pyrometry sys- tems have been introduced by B&W to nonintrusively measure high temperature gases in boiler furnaces. Steam/its generation and use This updated and expanded edition provides a broad, in-depth look at steam generating technology and equip- ment, including related auxiliaries that are of interest to engineersandstudentsinthesteampowerindustry.The reader will find discussions of the fundamental technolo- giessuchasthermodynamics,fluidmechanics,heattrans- fer,solidmechanics,numericalandcomputationalmeth- ods,materialsscienceandfuelsscience.Thevariouscom- ponents of the steam generating equipment, plus their integration and performance evaluation, are covered in depth. Extensive additions and updates have been made to the chapters covering environmental control technolo- gies and numerical modeling. Key elements of the bal- anceofthesteamgeneratingsystemlifeincludingopera- tion,conditionassessment,maintenance,andretrofitsare alsodiscussed.
- 30. The Babcock & Wilcox Company Intro-18 Steam 41 / Introduction to Steam
- 31. The Babcock & Wilcox Company Steam 41 Selected Color Plates — Edition: 41
- 32. The Babcock & Wilcox Company Steam 41 / Selected Color Plates Plate 1 Low NOX Burners Overfire Air Ports Primary Air Fan Trisector Air Heater Axial Forced Draft Fan Vertical Steam Separators Primary Superheater Primary Reheater Intermediate Superheater Furnace SCR Economizer Platen Superheater Final Superheater Final Reheater Circulation Pump B&W Roll Wheel Pulverizers B&W supercritical boiler with spiral wound Universal Pressure (SWUP™) furnace.
- 33. The Babcock & Wilcox Company Plate 2 Steam 41 / Selected Color Plates Steam Drum Primary Air Fans Low NOx Burners Overfire Air Ports Furnace SCR Trisector Air Heater B&W Roll Wheel Pulverizers Platen Secondary Superheater Secondary Superheater Reheat Superheater Primary Superheater Forced Draft Fans Economizer Wing Walls Carolina-type 550 MW Radiant boiler for pulverized coal.
- 34. The Babcock & Wilcox Company Steam 41 / Selected Color Plates Plate 3 Large coal- and oil-fired two-drum Stirling® power boiler for industry, 885,000 lb/h (112 kg/s) steam flow.
- 35. The Babcock & Wilcox Company Plate 4 Steam 41 / Selected Color Plates Single-drum chemical recovery boiler for the pulp and paper industry.
- 36. The Babcock & Wilcox Company Steam 41 / Selected Color Plates Plate 5 Steam Drum Wing Wall Coal Silo Economizer Internal Evaporative Circuit Superheater U-Beams Primary Air Secondary Air Forced Draft Fan Startup Burner Bottom Ash Cooler Dust Collector Furnace Tubular Air Heater Coal-fired circulating fluidized-bed combustion steam generator.
- 37. The Babcock & Wilcox Company Plate 6 Steam 41 / Selected Color Plates Wet flue gas desulfurization scrubber module for sulfur dioxide control.
- 38. The Babcock & Wilcox Company Steam 41 / Selected Color Plates Plate 7 Tubesheet Outlet Poppet Damper Rotary Atomizer Central Gas Disperser Inlet Flue Gas (Lower) Inlet Flue Gas (Upper) To Particulate Collection Pulse Air Header Filter Bag with Internal Cage Outlet Manifold Inlet Louver Damper Inlet Manifold Pulse Air Blowpipe Dry flue gas desulfurization spray dryer absorber for sulfur dioxide control (upper left) and fabric filter baghouse for particulate control (lower right).
- 39. The Babcock & Wilcox Company Plate 8 Steam 41 / Selected Color Plates SCR Induced DraftFan Forced DraftFan Air HeaterPrecipitator Stack Absorber Furnace Primary AirFan Steam Drum Platen Secondary Superheater Intermediate Secondary Superheater FinalSecondary Superheater Reheat Superheater Primary Superheater Economizer B&WRollWheel Pulverizers Modern 660 MW coal-fired utility boiler system with environmental control equipment.
- 40. The Babcock & Wilcox Company Steam 41 Section I Steam Fundamentals Steam is uniquely adapted, by its availability and advantageous properties, for use in industrial and heating processes and in power cycles. The funda- mentals of the steam generating process and the core technologies upon which performance and equipment design are based are described in this section of eight chapters. Chapter 1 provides an initial overview of the process, equip- ment and design of steam generating systems, and how they interface with other processes that produce power and use steam. This is followed by funda- mental discussions of thermodynamics, fluid dynamics, heat transfer, and the complexities of boiling and steam-water flow in Chapters 2 through 5. New Chapter 6 is dedicated to exploring the dramatic increase in the use of advanced computational numerical analysis in the design of modern steam generators. The section concludes with Chapters 7 and 8 discussing key elements of mate- rial science and structural analysis that permit the safe and efficient design of the steam generating units and components.
- 41. Steam 41 / Steam Generation – An Overview 1-1 The Babcock & Wilcox Company Chapter 1 Steam Generation – An Overview Steam generators, or boilers, use heat to convert water into steam for a variety of applications. Primary among these are electric power generation and indus- trial process heating. Steam is a key resource because of its wide availability, advantageous properties and nontoxic nature. Steam flow rates and operating con- ditions are the principal design considerations for any steam generator and can vary dramatically: from 1000 lb/h (0.1 kg/s) in one process use to more than 10 mil- lion lb/h (1260 kg/s) in large electric power plants; from about 14.7 psi (0.1013 MPa) and 212F (100C) in some heatingapplicationstomorethan4500psi(31.03MPa) and 1100F (593C) in advanced cycle power plants. Fuel use and handling add to the complexity and variety of steam generating systems. The fuels used in most steam generators are coal, natural gas and oil. However, nuclear energy also plays a major role in at least the electric power generation area. Also, an in- creasing variety of biomass materials and process byproducts have become heat sources for steam gen- eration. These include peat, wood and wood wastes, bagasse, straw, coffee grounds, corn husks, coal mine wastes (culm), and waste heat from steelmaking fur- naces. Even renewable energy sources, e.g., solar, are being used to generate steam. The steam generating process has also been adapted to incorporate functions such as chemical recovery from paper pulping pro- cesses, volume reduction for municipal solid waste or trash, and hazardous waste destruction. Steam generators designed to accomplish these tasks range from a small package boiler (Fig. 1) to large, high capacity utility boilers used to generate 1300 MW of electricity (Fig. 2). The former is a fac- tory-assembled, fully-automated, gas-fired boiler, which can supply saturated steam for a large build- ing, perhaps for a hospital. It arrives at the site with all controls and equipment assembled. The large field- erected utility boiler will produce more than 10 mil- lion lb/h (1260 kg/s) steam at 3860 psi (26.62 MPa) and 1010F (543C). Such a unit, or its companion nuclear option (Fig. 3), is part of some of the most com- plex and demanding engineering systems in opera- tion today. Other examples, illustrating the range of combustion systems, are shown by the 750 t/d (680 tm/d) mass-fired refuse power boiler in Fig. 4 and the circulating fluidized-bed combustion boiler in Fig. 5. The central job of the boiler designer in any of these applications is to combine fundamental science, tech- nology, empirical data, and practical experience to produce a steam generating system that meets the steam supply requirements in the most economical package. Other factors in the design process include fuelcharacteristics,environmentalprotection,thermal efficiency, operations, maintenance and operating costs, regulatory requirements, and local geographic and weather conditions, among others. The design process involves balancing these complex and some- times competing factors. For example, the reduction of pollutants such as nitrogen oxides (NOx) may re- quire a larger boiler volume, increasing capital costs and potentially increasing maintenance costs. Such a design activity is firmly based upon the physical and thermal sciences such as solid mechanics, thermody- namics, heat transfer, fluid mechanics and materials science. However, the real world is so complex and variable, and so interrelated, that it is only by apply- ing the art of boiler design to combine science and practice that the most economical and dependable design can be achieved. Steam generator design must also strive to address in advance the many changes occurring in the world to provide the best possible option. Fuel prices are expected to escalate while fuel supplies become less certain, thereby enforcing the need for continued ef- ficiency improvement and fuel flexibility. Increased environmental protection will drive improvements in combustion to reduce NOx and in efficiency to reduce carbon dioxide (CO2) emissions. Demand growth con- tinues in many areas where steam generator load Fig. 1 Small shop-assembled package boiler.
- 42. 1-2 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company may have to cycle up and down more frequently and at a faster rate. There are technologies such as pressurized fluid- ized-bed combustion and integrated gasification com- bined cycle systems, plus others, which actually inte- grate the environmental control with the entire steam generation process to reduce emissions and increase power plant thermal efficiency. Also, modularization and further standardization will help reduce fabrica- tion and erection schedules to meet more dynamic capacity addition needs. Steam generation fundamentals Boiling The process of boiling water to make steam is a fa- miliar phenomenon. Thermodynamically, instead of increasing the water temperature, the energy used results in a change of phase from a liquid to a gaseous state, i.e., water to steam. A steam generating system shouldprovideacontinuousprocessforthisconversion. The simplest case for such a device is a kettle boiler where a fixed quantity of water is heated (Fig. 6). The applied heat raises the water temperature. Eventu- ally, for the given pressure, the boiling (saturation) temperature is reached and bubbles begin to form. As heat continues to be applied, the temperature remains constant, and steam escapes from the water surface. If the steam is continuously removed from the vessel, the temperature will remain constant until all of the water is evaporated.At this point, heat addition would increase the temperature of the kettle and of any steam remaining in the vessel. To provide a continu- ous process, all that is needed is a regulated supply of water to the vessel to equal the steam being gener- ated and removed. Technicalandeconomicfactorsindicatethatthemost effective way to produce high pressure steam is to heat relativelysmalldiametertubescontainingacontinuous flow of water. Regardless of whether the energy source is nuclear or fossil fuel, two distinct boiling systems are Fig. 2 1300 MW coal-fired utility steam generator. Fig. 3 900 MW nuclear power system. Fig. 4 Babcock & Wilcox 750 ton per day mass-fired refuse power boiler.
- 43. Steam 41 / Steam Generation – An Overview 1-3 The Babcock & Wilcox Company used to accomplish this task: those that include a steam drum(seeFig.7a),orfixedsteam-waterseparationpoint, and those that do not (see Fig. 7b), termed once-through steam generators (OTSG). The most common and simplest to control is the steam drum system. In this system, the drum serves as the point of separation of steam from water throughout its boiler’s load range. Subcooled water (less than boiling temperature) enters the tube to which heat is applied. As the water flows through the tube, it is heated to the boiling point, bubbles are formed, and wet steam is generated. In most boilers, a steam-water mixture leaves the tube and enters the steam drum, where steam is separated from water. The remaining water is then mixed with the replacement water and returned to the heated tube. Without a steam drum, i.e., for an OTSG system, subcooled water also enters the tube to which heat is applied, but the flowing water turns into steam some- where along the flow path (length of tube), dependent upon water flow rate (boiler load) and heat input rates. Shown in Fig. 7b, the flow rate and heat input are closely controlled and coordinated so that all of the water is evaporated and only steam leaves the tube. There is no need for the steam drum (fixed steam- water separation point). Circulation For both types of boiling systems described above, water must continuously pass through, or circulate through, the tubes for the system to generate steam continuously. For an OTSG, water makes one pass through the boiler’s tubes before becoming steam to be sent to the turbine-generator. However, for those boilers with a fixed steam-water separation point or steam drum, a molecule of water can make many passes through a circulation loop before it leaves as steam to the turbine-generator. Options for this lat- ter system are shown in Fig. 8. Twodifferentapproachestocirculationarecommonly used: natural or thermal circulation, and forced or pumped circulation. Natural circulation is illustrated in Fig. 8a. In the downcomer, unheated tube segment A-B, no steam is present. Heat addition generates a steam-water mixture in segment B-C. Because the steamandsteam-watermixtureinsegmentB-Careless dense than the water segment A-B, gravity will cause the water to flow downward in segment A-B and will Fig. 6 Simple kettle boiler. Fig. 7 Boiling process in tubular geometries.Fig. 5 Coal-fired circulating fluidized-bed combustion steam generator. Refractory Line Air Heater Steam Coil Air Heater Flue Gas Multi-Cyclone Dust Collector Economizer Superheater Feedwater to Drum Secondary Air Duct Primary Air Duct Air Duct to Fluid Bed Cooler Ash Recycle System Gravimetric Feeder Fuel Chute Fluid Bed Cooler Steam Drum Internal Evaporative Circuit In-Furnace U-Beams Wing Wall Fuel Bunker Downcomer External U-Beams
- 44. 1-4 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company cause the steam-water mixture (B-C) to move upward into the steam drum. The rate of water flow or circula- tion depends upon the difference in average density be- tween the unheated water and the heated steam-wa- ter mixture. The total circulation rate in a natural circulation systemdependsprimarilyuponfourfactors:1)theheight of the boiler, 2) the operating pressure, 3) the heat in- put rate, and 4) the free flow areas of the components. Taller boilers result in a larger total pressure difference betweentheheatedandunheatedlegsandthereforecan produce larger total flow rates. Higher operating pres- sures provide higher density steam and higher density steam-watermixtures.Thisreducesthetotalweightdif- ferencebetweentheheatedandunheatedsegmentsand tends to reduce flow rate. Higher heat input typically increases the amount of steam in the heated segments and reduces the average density of the steam-water mixture, increasing total flow rate. An increase in the cross-sectional (free flow) areas for the water or steam- water mixtures may increase the circulation rate. For each unit of steam produced, the amount of water en- tering the tube can vary from 3 to 25 units. Forced or pumped circulation is illustrated in Fig. 8b.Amechanical pump is added to the simple flow loop and the pressure difference created by the pump con- trols the water flow rate. The steam-water separation in the drum requires careful consideration. In small, low pressure boilers, steam-water separation can be easily accomplished with a large drum approximately half full of water. Natural gravity steam-water separation (similar to a kettle) can be sufficient. However, in today’s high ca- pacity, high pressure units, mechanical steam-water separators are needed to economically provide mois- ture-free steam from the drum. With such devices in- stalled in the drum, the vessel diameter and cost can be significantly reduced. At very high pressures, a point is reached where water no longer exhibits boiling behavior. Above this critical pressure [3200.11 psi (22.1 MPa)], the water temperature continuously increases with heat addi- tion. Steam generators can be designed to operate at pressures above this critical pressure. Drums and steam-water separation are no longer required and the steam generator operates effectively on the once- through principle. There are a large number of design methods used to evaluate the expected flow rate for a specific steam generator design and set of operating conditions. In addition, there are several criteria which establish the minimum required flow rate and maximum allowable steam content or quality in individual tubes, as well as the maximum allowable flow rates for the steam drum. System arrangement and key components Most applications of steam generators involve the production of electricity or the supply of process steam. In some cases, a combination of the two applications, called cogeneration, is used. In each application, the steam generator is a major part of a larger system that has many subsystems and components. Fig. 9 shows a modern coal-fired power generating facility; Fig. 10 identifies the major subsystems. Key subsystems in- clude fuel receiving and preparation, steam generator Fig. 8 Simple circulation systems.
- 45. Steam 41 / Steam Generation – An Overview 1-5 The Babcock & Wilcox Company and combustion, environmental protection, turbine- generator, and heat rejection including cooling tower. First, follow the fuel and products of combustion (flue gas) through the system. The fuel handling sys- tem stores the fuel supply (coal in this example), pre- pares the fuel for combustion and transports it to the steam generator. The associated air system supplies air to the burners through a forced draft fan. The steam generator subsystem, which includes the air heater, burns the fuel-air mixture, recovers the heat, and generates the controlled high pressure and high temperature steam. The flue gas leaves the steam generator subsystem and selective catalytic reduction (SCR) system if supplied, then passes through particu- late collection and sulfur dioxide (SO2) scrubbing sys- temswherepollutantsarecollectedandtheashandsolid scrubber residue are removed. The remaining flue gas is then sent to the stack through an induced draft fan. Next, follow the steam-water path. The steam gen- erator (boiler) evaporates water and supplies high temperature, high pressure steam, under carefully controlled conditions, to a turbine-generator set that produces the electricity. The steam may also be re- heated in the steam generator, after passing through part of a multi-stage turbine system, by running the exhaust steam back to the boiler convection pass (reheater not shown). Ultimately, the steam is passed from the turbine to the condenser where the remain- ing waste heat is rejected. Before the water from the condenser is returned to the boiler, it passes through several pumps and heat exchangers (feedwater heat- ers) to increase its pressure and temperature. The heat absorbed by the condenser is eventually rejected to the atmosphere by one or more cooling towers. These cool- ing towers are perhaps the most visible component in the power system (Fig. 9). The natural draft cooling tower shown is basically a hollow cylindrical structure which circulates air and moisture to absorb the heat rejected by the condenser. Such cooling towers exist at most modern power plant sites, both nuclear- and fossil fuel-fired. For an industrial power system, many of the same features are needed. However, the turbine-generator and heat rejection portions are replaced by the pro- cess application, such as radiant space heaters or heat exchangers. In a nuclear power system (Fig. 11), the fossil fuel- fired steam generator is replaced by a nuclear reactor vesseland,typically,twoormoresteamgenerators.The coal handling system is replaced by a nuclear reactor fuel bundle handling and storage facility, and the large scale air pollution control equipment is not needed. Fig. 9 Coal-fired utility power plant. Fig. 10 Coal-fired utility power plant schematic. SCR Air Heater Stack Particulate Collector Boiler Coal Pulverization Coal Supply Fuel Water from Heaters Induced Draft Fan Primary Air Fan Forced Draft Fan Air Water to Boiler Electricity Steam Substation Transformer Cooling Tower Turbine- Generator Condenser Pumps Makeup Pumps Condensate Pump High Pressure Heaters Low Pressure Heaters Feed Pump (Not Shown: Reheater, Ash and Reagent Handling and Sludge Disposal) Combustion Air Scrubber SO2
- 46. 1-6 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company Fossil steam generator classifications Modern steam generating systems can be classified byvariouscriteria.Theseincludeenduse,firingmethod, operating pressure, fuel, and circulation method. Utility steam generators are used primarily to gen- erate electricity in large central power stations. They are designed to optimize overall thermodynamic effi- ciency at the highest possible availability. New units are typically characterized by large, main steam flow rates with superheated steam outlet pressures from 1800 to 3860 psi (12.41 to 26.62 MPa) with steam tem- peratures at or above 1050F (566C). A key character- istic of newer units is the use of a reheater section to increase overall cycle efficiency. Industrial steam generators generally supply steam to processes or manufacturing activities and are de- signed with particular attention to: 1) process con- trolled (usually lower) pressures, 2) high reliability with minimum maintenance, 3) use of one or more locally inexpensive fuels, especially process byproducts or wastes, and 4) low initial capital and minimum operating costs. On a capacity basis, the larger users of such industrial units are the pulp and paper industry, municipal solid waste reduction indus- try, food processing industry, petroleum/petrochemi- cal industry, independent power producers and cogenerators, and some large manufacturing opera- tions. Operating pressures range from 150 to 1800 psi (1.04 to 12.41 MPa) with saturated or superheated steam conditions. Impact of energy source The primary fuel selected has perhaps the most sig- nificant impact on the steam generator system con- figuration and design. In the case of nuclear energy, a truly unique system for containing the fuel and the nuclear reaction products has been developed with an intense focus on safety and protecting the public from radiation exposure.Acceptable materials performance in the radiative environment and the long term ther- mal-hydraulic and mechanical performance are cen- tral to system design. When fossil, biomass, or byproduct fuels are burned, widely differing provi- sions must be made for fuel handling and prepara- tion, fuel combustion, heat recovery, fouling of heat transfersurfaces,corrosionofmaterials,andemissions control. For example, in a natural gas-fired unit (Fig.12), there is minimal need for fuel storage and handling. Only a small furnace is needed for combus- tion, and closely spaced heat transfer surfaces may be used because of lack of ash deposits (fouling). The cor- rosion allowance is relatively small and the emissions control function is primarily for NOx formed during the combustion process. The result is a relatively small, compact and economical design. If a solid fuel such as coal (which has a significant level of noncombustible ash) is used, the overall sys- tem is much more complex. This system could include extensive fuel handling and preparation facilities, a much larger furnace, and more widely spaced heat transfer surfaces. Additional components could be spe- cial cleaning equipment to reduce the impact of fouling and erosion, air preheating to dry the fuel and enhance combustion, more extensive environmental equipment, and equipment to collect and remove solid wastes. The impact of fuel alone on a utility boiler design is clearly indicated in Fig. 12, where both steam genera- tors produce the same steam flow rate. Further add- ing to the size and cost difference, but not shown, are the facts that the coal-fired boiler will be wider (dimen- sion not shown) and will require more flue gas cleanup equipment to meet emissions requirements. The particular challenge when burning different solid fuels is indicated in Fig. 13, where provision is made for burning both pulverized (finely ground) coal using the burners and for wood chips and bark which are burned on the moving grate (stoker) at the bottom of the unit. Impact of steam conditions The steam temperature and pressure for different boiler applications can have a significant impact on design. Fig. 14 identifies several typical boiler types, as well as the relative amount of heat input needed, for water heating, evaporation (boiling), superheat- ing, and reheating, if required. The relative amount of energy needed for evaporation is dramatically re- ducedasoperatingpressureisincreased.Asaresult,the relativeamountofphysicalheattransfersurface(tubes) dedicatedtoeachfunctioncanbedramaticallydifferent. Fossil fuel systems Fossil fuel steam generator components Modern steam generators are a complex configu- ration of thermal-hydraulic (steam and water) sections which preheat and evaporate water, and superheat steam. These surfaces are arranged so that: 1) the fuel can be burned completely and efficiently while mini- mizing emissions, 2) the steam is generated at the required flow rate, pressure and temperature, and 3) Fig. 11 Nuclear power plant schematic.
- 47. Steam 41 / Steam Generation – An Overview 1-7 The Babcock & Wilcox Company the maximum amount of energy is recovered. A rela- tively simple coal-fired utility boiler is illustrated in Fig. 15. The major components in the steam generat- ing and heat recovery system include: 1. furnace and convection pass, 2. steam superheaters (primary and secondary), 3. steam reheater, 4. boiler or steam generating bank (industrial units only), 5. economizer, 6. steam drum, 7. attemperator and steam temperature control sys- tem, and 8. air heater. These components are supported by a number of sub- systems and pieces of equipment such as coal pulver- izers, combustion system, flues, ducts, fans, gas-side cleaning equipment and ash removal equipment. The furnace is a large enclosed open space for fuel combustion and for cooling of the flue gas before it enters the convection pass. Excessive gas tempera- tures leaving the furnace and entering the tube bundles could cause particle accumulation on the tubes or excessive tube metal temperatures. The specific geometry and dimensions of the furnace are highly influenced by the fuel and type of combustion equip- ment. In this case, finely ground or pulverized coal is blown into the furnace where it burns in suspension. The products of combustion then rise through the upper furnace. The superheater, reheater and econo- mizer surfaces are typically located in the flue gas horizontal and vertical downflow sections of the boiler enclosure, called the convection pass. In modern steam generators, the furnace and con- vection pass walls are composed of steam- or water- cooled carbon steel or low alloy tubes to maintain wall metal temperatures within acceptable limits. These tubes are connected at the top and bottom by head- ers, or manifolds. These headers distribute or collect the water, steam or steam-water mixture. The furnace wall tubes in most modern units also serve as key steam generating components or surfaces. The tubes are welded together with steel bars to provide mem- brane wall panels which are gas-tight, continuous and rigid. The tubes are usually prefabricated into ship- pable membrane panels with openings for burners, observation doors, sootblowers (boiler gas-side surface cleaning equipment) and gas injection ports. Superheaters and reheaters are specially designed in-line tube bundles that increase the temperature of saturated steam. In general terms, they are simple single-phase heat exchangers with steam flowing in- side the tubes and the flue gas passing outside, gen- erally in crossflow. These critical components are manufactured from steel alloy material because of their high operating temperature. They are typically configured to help control steam outlet temperatures, keep metal temperatures within acceptable limits, and control steam flow pressure loss. The main difference between superheaters and reheaters is the steam pressure. In a typical drum boiler, the superheater outlet pressure might be 2700 psi (18.62 MPa) while the reheater outlet might be only 580 psi (4.0 MPa). The physical design and loca- tion of the surfaces depend upon the desired outlet temperatures, heat absorption, fuel ash characteris- tics and cleaning equipment. These surfaces can be either horizontal or vertical as shown. The super- heater and sometimes reheater are often divided into multiple sections to help control steam temperature and optimize heat recovery. The heat transfer surface in the furnace may not be sufficient to generate enough saturated steam for Fig. 12 Comparison of gas- and coal-fired steam generators.
- 48. 1-8 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company the particular end use. If this is the case, an additional bank of heat exchanger tubes called the boiler bank or steam generating bank is added. (See Fig. 13.) This is needed on many smaller, low pressure industrial boilers, but is not often needed in high pressure util- ity boilers. This boiler bank is typically composed of the steam drum on top, a second drum on the bottom, and a series of bent connecting tubes. The steam drum internals and tube sizes are arranged so that subcooled water travels down the tubes (farthest from the fur- nace) into the lower drum. The water is then distrib- uted to the other tubes where it is partially converted to steam and returned to the steam drum. The lower drum is often called the mud drum because this is where sediments found in the boiler water tend to settle out and collect. The economizer is a counterflow heat exchanger for recovering energy from the flue gas beyond the su- perheater and, if used, the reheater. It increases the temperature of the water entering the steam drum. The tube bundle is typically an arrangement of par- allel horizontal serpentine tubes with the water flow- ing inside but in the opposite direction (counterflow) to the flue gas. Tube spacing is as tight as possible to promote heat transfer while still permitting adequate tube surface cleaning and limiting flue gas-side pres- sure loss. By design, steam is usually not generated inside these tubes. The steam drum is a large cylindrical vessel at the top of the boiler, in which saturated steam is separated from the steam-water mixture leaving the boiler tubes. Drums can be quite large with diameters of 3 to 6 ft (0.9 to 1.8 m) and lengths approaching 100 ft (30.5 m). They are fabricated from thick steel plates rolled into cylinders with hemispherical heads. They house the steam-water separation equipment, purify the steam, mix the replacement or feedwater and chemi- cals, and provide limited waterstoragetoaccommodate small changes in unit load. Major connections to the steamdrumareprovidedtoreceivethesteam-watermix- ture from the boiler tubes, remove saturated steam, add replacementormakeupwater,andreturnthenearsatu- rated water back to the inlet of the boiler tubes. The steam temperature control system can be com- plex and include combinations of recirculating some of the flue gas to the bottom or top of the furnace, provid- ing special gas flow passages at the back end of the steamgenerator,adjustingthecombustionsystem,and adding water or low temperature steam to the high temperature steam flow (attemperation). The compo- nentmostfrequentlyusedforthelatteriscalledaspray attemperator.Inlargeutilityunits,attemperatorswith direct injection of water or low temperature steam are used for dynamic control because of their rapid re- sponse. They are specially designed to resist thermal shock and are frequently located at the inlet of the su- perheater or between superheater sections to better control the superheater outlet metal temperatures. Positioning of individual superheater sections can also help maintain proper outlet steam temperatures. The air heater is not a portion of the steam-water circuitry, but serves a key role in the steam generator system heat transfer and efficiency. In many cases, especially in high pressure boilers, the temperature of the flue gas leaving the economizer is still quite high. The air heater recovers much of this energy and adds it to the combustion air to reduce fuel use. De- signs include tubular, flat plate, and regenerative heat exchangers, among others. Steam-water flow system The steam-water components are arranged for the most economical system to provide a continuous sup- ply of steam. The circulation system (excluding reheat- er) for a natural circulation, subcritical pressure, drum type steam generator is shown in Fig. 16. Feed- Fig. 13 Large industrial boiler with multiple fuel capability. Fig. 14 Steam generator energy absorption by function.
- 49. Steam 41 / Steam Generation – An Overview 1-9 The Babcock & Wilcox Company water enters the bottom header (A) of the economizer and passes upward in the opposite direction to the flue gas. It is collected in an outlet header (B), which may also be located in the flue gas stream. The water then flows through a number of pipes which connect the economizer outlet header to the steam drum. It is sometimesappropriatetorunthesetubesvertically(B- C) through the convection pass to economizer outlet headers located at the top of the boiler. These tubes can then serve as water-cooled supports for the hori- zontal superheater and reheater when these banks span too great a distance for end support. The feed- water is injected into the steam drum (D) where it mixes with the water discharged from the steam-wa- ter separators before entering connections to the downcomer pipes (D-E) which exit the steam drum. The water travels around the furnace water wall circuits to generate steam. The water flows through the downcomer pipes (D-E) to the bottom of the fur- nace where supply tubes (E-F) route the circulating water to the individual lower furnace panel wall head- ers (F). The water rises through the furnace walls to individual outlet headers (G), absorbing energy to become a steam-water mixture. The mixture leaves the furnace wall outlet headers by means of riser tubes (G-D), to be discharged into the drum and steam-wa- ter separators. The separation equipment returns es- sentially steam-free water to the downcomer inlet con- nections. The residual moisture in the steam that leaves the primary steam separation devices is re- moved in secondary steam separators, and dry steam is discharged to the superheater through a number of drum outlet connections (H-I and H-J). The steam circuitry serves dual functions: cooling the convection pass enclosure, and generating the required superheated steam conditions. Steam from the drum passes through multiple connections to a header (I) supplying the roof tubes and, separately, to headers (J) supplying the membrane panels in the pendant convection pass (so named because the su- perheater/reheater vertical tubes are hanging from supports above). The steam flows through these mem- brane panels to outlet headers (K). Steam from these headers and the roof tube outlet headers (L) then pro- vides the cooling for the horizontal convection pass enclosure (L-M) (so named because the superheater/ reheater/economizer tubes are horizontal in this flue gas downpass). Steam flows downward through these panels and is collected in outlet headers (M) just up- stream of the economizer bank. Steam flow then rises through the primary super- heater and discharges through the outlet header (N) and connecting piping equipped with a spray attemperator (O). It then enters the secondary super- heater inlet header (P), flowing through the super- heater sections to an outlet header (Q). A discharge pipe (R) terminates outside of the boiler enclosure where the main steam lines route the steam flow to the control valves and turbine. Combustion system and auxiliaries Most of the non-steam generating components and auxiliaries used in coal-fired steam generators are part of the fuel preparation and combustion systems. These include: 1. fuel preparation: feeders and coal pulverizers, 2. combustionsystem:burners,flamescanners,light- ers, controls, windbox, 3. air-gas handling: fans, flues and ducts, dampers, control and measurement systems, silencers, and 4. other components and auxiliaries: sootblowers (heat transfer surface cleaning equipment), ash collection and handling equipment, control and monitoring equipment. Fig. 16 Coal-fired boiler steam-water circulation system. Fig. 15 Coal-fired utility boiler.
- 50. 1-10 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company Because of their intimate relationship with the steam generation process, many of these components are supplied with the boiler. If not, careful specification and interaction with the steam generator manufac- turer are critical. The combustion system has a dramatic impact on overall furnace design. Wall mounted burners are shown in Figs. 15 and 17. These are typical for large coal-, oil-, or gas-fired units today. However, a vari- ety of other systems are also used and are continuing to be developed to handle the variety of fuel charac- teristics and unit sizes. Other combustion systems in- clude stokers (Figs. 4 and 13), Cyclone furnaces, and fluidized-bed combustion units (Fig. 5). All have their strengths and weaknesses for particular applications. Key elements of these systems involve the need to control the formation and emission of pollutants, pro- vide complete efficient combustion, and handle inert material found in the fuel. The fuel characteristics play a central role in how these functions are met and how the equipment is sized and designed. Air-gas flow system Many of these auxiliaries are identified in Fig. 17 along with the air-gas flow path in the large coal-fired utility boiler. Air is supplied by the forced draft fan (A) to the air heater (B) where it is heated to recover energy and enhance combustion. Most of the hot air (typically 70 to 80%), called secondary air, passes di- rectly to the windboxes (C) where it is distributed to individual burners. The remaining 20 to 30%, called primary air, passes to the booster (or primary air) fan and then to the coal pulverizers (D) where the coal is dried and ground. The hot primary air then pneumati- cally conveys the pulverized coal to the burners (E) where it is mixed with the secondary air for combus- tion. The coal and air are rapidly mixed and burned in the furnace (F) and the flue gas then passes up through the furnace, being cooled primarily by radia- tion until it reaches the furnace exit (G). The gas then progressively passes through the secondary super- heater, reheater, primary superheater and econo- mizer before leaving the steamgeneratorenclosure(H). The gas passes through the air heater (B) and then through any pollution control equipment and induced draft fan (I) before being exhausted to the atmosphere. Emissions control A key element of fossil fuel-fired steam generator system design is environmental protection. A broad rangeofgovernmentregulationssetslimitsonprimary gaseous, liquid and solid waste emissions from the steam generating process. For coal-, oil-, and gas-fired units, the primary air pollutant emissions include sulfur dioxide (SO2), nitrogen oxides (NOx) and air- borne particulate or flyash. Water discharges include trace chemicals used to control corrosion and fouling as well as waste heat rejected from the condenser. Solid waste primarily involves the residual ash from the fuel andanyspentsorbentfromthepollutioncontrolsystems. The gaseous and solid waste from the fuel and com- bustion process can be minimized by fuel selection, control of the combustion process, and equipment lo- cated downstream of the steam generator. SO2 emis- sions may be reduced by using fuels which contain low levels of sulfur, by fluidized-bed combustors, or by using a post-combustion scrubber system. Combustion NOx emissions are typically controlled by using equip- ment such as special low NOx burners or fluidized-bed combustors. Where it is required to significantly re- duce NOx emissions (to levels lower than is practically achieved by combustion techniques alone), back-end or post-combustion techniques, such as selective cata- lytic reduction (SCR) or selective noncatalytic reduc- tion (SNCR) technologies, are employed. Flyash or air- borne particulate is collected by either a fabric filter (baghouse) or electrostatic precipitator (ESP) with re- moval efficiencies above 99%. The particulate collec- tion equipment and SO2 scrubbers produce solid byproduct streams which must be safely landfilled or used for some industrial applications. The water discharges are minimized by installing recirculating cooling systems. An example of this is cooling towers that reject the waste heat from the power cycle to the air, instead of to a water source. These are used on virtually all new fossil and nuclear power plants. Chemical discharges are minimized by specially designed zero discharge systems. A set of emissions rates before and after control for a typical 500 MW power plant is shown in Table 1. Nuclear steam generating systems Overview Nuclear steam generating systems include a series of highly specialized heat exchangers, pressure ves- sels, pumps and components which use the heat gen- erated by nuclear fission reactions to efficiently and Fig. 17 Coal-fired boiler air/gas flow path.
- 51. Steam 41 / Steam Generation – An Overview 1-11 The Babcock & Wilcox Company safely generate steam. The system is based upon the energy released when atoms within certain materials, such as uranium, break apart or fission. Fission oc- curs when a fissionable atom nucleus captures a free subatomic particle – a neutron. This upsets the inter- nal forces which hold the atom nucleus together. The nucleus splits apart producing new atoms as well as an average of two to three neutrons, gamma radia- tion and energy. The nuclear steam supply system (NSSS) is de- signed to serve a number of functions: 1) house the nuclear fuel, 2) stimulate the controlled fission of the fuel, 3) control the nuclear reaction rate to produce the required amount of thermal energy, 4) collect the heat and generate steam, 5) safely contain the reac- tion products, and 6) provide backup systems to pre- vent release of radioactive material to the environ- ment. Various systems have been developed to accom- plish these functions. The main power producing sys- tem in commercial operation today is the pressurized water reactor (PWR). A key difference between the nuclear and chemi- cal energy driven systems is the quantity of fuel. The energy released per unit mass of nuclear fuel is many orders of magnitude greater than that for chemical based fuels. For example, 1 lb (0.454 kg) of 3% en- riched uranium fuel produces about the same amount of thermal energy in a commercial nuclear system as 100,000 lb (45,360 kg) of coal in a fossil-fired steam system. While a 500 MW power plant must handle ap- proximately one million tons of coal per year, the nuclear plant will handle only 10 tons of fuel. The fossil fuel plant must be designed for a continuous fuel sup- ply process, while most nuclear plants use a batch fuel process, where about one third of the fuel is replaced during periodic outages. However, once the steam is generated, the balance of the power producing sys- tem (turbine, condenser, cooling system, etc.) is simi- lar to that used in the fossil fuel plant. Nuclear steam system components A typical nuclear steam system from The Babcock & Wilcox Company (B&W) is shown in Fig. 3 and a simplified schematic is shown in Fig. 18. This nuclear system consists of two coolant loops. The primary loop cools the reactor, transports heat to two or more steam generators (only one shown), and returns coolant to the reactor by four or more primary coolant pumps (only one shown). The coolant is high purity, subcooled, single-phase water flowing at very high rates [350,000 to 450,000 GPM (22,100 to 28,400 l/s)] at around 2200 psi(15.17MPa)andanaveragetemperatureofapproxi- mately 580F (304C). The primary loop also contains a pressurizer to maintain the loop pressure at design op- erating levels. The secondary loop includes the steam generation and interface with the balance of the power plant. High purity water from the last feedwater heater passes through the steam generator and is converted into steam. From the steam generator outlet, the satu- rated or superheated steam flows out of the contain- ment building to the high pressure turbine. The op- erating pressure is typically around 1000 psi (6.9 MPa). The balance of the secondary loop resembles fossil fuel-fired systems. (See Figs. 10 and 11.) The center of the NSSS is the reactor vessel and re- actor core (Fig. 19). The fuel consists of compressed pel- lets [for example, 0.37 in. (9.4 mm) diameter by 0.7 in. (18 mm) long] of 2.5 to 5% enriched uranium oxide. These pellets are placed in zircaloy tubes which are sealed at both ends to protect the fuel and to contain thenuclearreactionproducts.Thetubesareassembled into bundles with spacer and closure devices. These bundles are then assembled into the nuclear fuel core. The reactor enclosure (Fig. 19) is a low alloy steel pressure vessel lined with stainless steel for corrosion protection. The rest of the reactor includes flow distri- bution devices, control rods, core support structures, Table 1 Typical 500 MW Subcritical Coal-Fired Steam Generator Emissions and Byproducts* Power System Characteristics • 500 MW net • 196 t/h (49.4 kg/s) bituminous coal − 2.5% sulfur − 16% ash − 12,360 Btu/lb (28,749 kJ/kg) • 65% capacity factor Discharge Rate t/h (tm/h) Emission Typical Control Equipment Uncontrolled Controlled SOx as SO2 Wet limestone scrubber 9.3 (8.4) 0.3 (0.3) NOx as NO2 Low NOx burners and SCR 2.9 (2.6) 0.1 (0.1) CO2 Not applicable 485 (440) Flyash to air** Electrostatic precipitator or baghouse 22.9 (20.8) 0.05 (0.04) Thermal discharge to water sources Natural draft cooling tower 2.8 x 109 Btu/h (821 MWt) ∼0 (0) Ash to landfill** Controlled landfill 9.1 (8.3) 32 (29) Scrubber sludge: gypsum plus water Controlled landfill or wallboard quality gypsum 0 (0) 27.7 (25) * See Chapter 32, Table 1, for a modern 615 MW supercritical coal-fired steam generator. ** As flyash emissions to the air decline, ash to landfill increases.
- 52. 1-12 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company thermal shielding and moderator. The moderator in this case is water which serves a dual purpose. It re- duces the velocity of the neutrons thereby making the nuclear reactions more likely. It also serves as the cool- ant to maintain the core materials within acceptable temperature limits and transports thermal energy to the steam generators. The control rods contain neutron absorbing material and are moved into and out of the nuclear core to control the energy output. The steam generators can be of two types, once- through (Fig. 20) and recirculating (Fig. 21). In both types, the pressure vessel is a large heat exchanger designed to generate steam for the secondary loop from heat contained in the primary coolant. The primary coolant enters a plenum and passes through several thousand small diameter [approximately 0.625 in. (15.9 mm)] Inconel® tubes. The steam generator is a large, carbon steel pressure vessel. Specially designed tubesheets, support plates, shrouds, and baffles pro- vide effective heat transfer, avoid thermal expansion problems, and avoid flow-induced vibration. In the once-through steam generator (OTSG), Fig. 20, the secondary loop water flows from the bottom to the top of the shell side of the tube bundle and is con- tinuously converted from water to superheated steam. The superheated steam then passes to the high pres- sure turbine. In the recirculating steam generator (RSG), Fig. 21, water moves from the bottom to the top of the shell side ofthetubebundlebeingconvertedpartiallyintosteam. The steam-water mixture passes into the upper shell where steam-water separators supply saturated dry steam to the steam generator outlet. The steam is sent to the high pressure turbine. The water leaving the steam generator upper shell is mixed with feedwater and is returned to the bottom of the tube bundle. The pressurizer is a simple cylindrical pressure ves- sel which contains both water and steam at equilib- rium. Electrical heaters and spray systems maintain the pressure in the pressurizer vessel and the primary loop within set limits. The primary loop circulating pumps maintain high flow rates to the reactor core to control its temperature and transfer heat to the steam generators. A number of support systems are also provided. These include reactor coolant charging systems, makeup water addition, spent fuel storage cooling, and decay heat removal systems for when the reactor is shut down. Other specialized systems protect the re- actor system in the case of a loss of coolant event. The key function of these systems is to keep the fuel bundle temperature within safe limits if the primary coolant flow is interrupted. Nuclear steam system classifications A variety of reactor systems have been developed to recover thermal energy from nuclear fuel and to generate steam for power generation. These are usu- ally identified by their coolant and moderator types. The principal systems for power generation include: 1. Pressurized water reactor (PWR) This is the sys- tem discussed above, using water as both reactor coolant and moderator, and enriched uranium oxide as the fuel. 2. Boiling water reactor (BWR) The steam genera- tor is eliminated and steam is generated directly in the reactor core. A steam-water mixture cools and moderates the reactor core. Enriched uranium oxide fuel is used. Fig. 19 Reactor vessel and internals. Fig. 18 Nuclear steam system schematic.
- 53. Steam 41 / Steam Generation – An Overview 1-13 The Babcock & Wilcox Company 3. CANDU (PHWR) Heavy water (deuterium) is used as the moderator and primary loop coolant. The reactor configuration is unique but the steam generator is similar to the recirculating steam gen- erator for the PWR. Natural (not enriched) ura- nium oxide is used as the fuel. 4. Gas-cooled reactors These are a variety of gas- cooled reactors which are typically moderated by graphite and cooled by helium or carbon dioxide. 5. Breederreactors Theseareadvancedreactorsystems usingsodiumasthereactorcoolantwithnomodera- tor. These systems are specially designed to produce more fissionable nuclear fuel than they use. Engineered safety systems Safety is a major concern in the design, construc- tion and operation of nuclear power generating facili- ties. The focus of these efforts is to minimize the like- lihood of a release of radioactive materials to the en- vironment. Three approaches are used to accomplish this goal. First, the nuclear power industry has devel- oped one of the most extensive and rigorous quality control programs for the design, construction and maintenance of nuclear facilities. Second, reactor sys- tems are designed with multiple barriers to prevent radioactive material release. These include high tem- perature ceramic fuel pellets, sealed fuel rods, reactor vessel and primary coolant system, and the contain- ment building including both the carbon steel reactor containment vessel and the reinforced concrete shield building. The third approach includes a series of en- gineered safety systems to address loss of coolant con- ditions and maintain the integrity of the multiple barriers. These systems include: 1. emergency reactor trip systems including rapid in- sertion of control rods and the addition of soluble neutron poisons in the primary coolant to shut down the nuclear reaction, 2. high and low pressure emergency core cooling sys- tems to keep the reactor core temperature within acceptable limits and remove heat from the fuel in the event of a major loss of primary coolant or a small pipe break, 3. a heat removal system for the cooling water and containment building, and 4. spray and filtering systems to collect and remove radioactivity from the containment building. Because of the high power densities and decay heat generation, the reactor integrity depends upon the continuous cooling of the nuclear fuel rods. Multiple independent components and backup power supplies are provided for all critical systems.Fig. 20 Once-through steam generator. Fig. 21 Recirculating steam generator.
- 54. 1-14 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company Steam system design Steam generator interfaces The steam generator system’s primary function is to convert chemical or nuclear energy bound in the fuel to heat and produce high temperature, high pres- sure steam. The variety of fuel sources, the high tem- perature nature of these processes, and the large number of subsystem interfaces contribute to the chal- lenging nature of the design process. The initial steps in evaluating the steam generating system include es- tablishing key interfaces with other plant systems and with the power cycle. These are typically set by the end user or consulting engineer after an in-depth evaluation indicates: 1) the need for the expanded power supply or steam source, 2) the most economical fuel selection and type of steam producing system, 3) the plant location, and 4) the desired power cycle or process steam conditions. The key requirements fall into six major areas: 1. Steam minimum, nominal, and maximum flow rates; pressure and temperature; need for one or more steam reheat stages; auxiliary equipment steam usage; and future requirements. 2. Source of the steam flow makeup or replacement wa- ter supply, water chemistry and inlet temperature. 3. The type and range of fuels considered, including worst case conditions, and the chemical analyses (proximate and ultimate analyses) for each fuel or mixture of fuels. 4. Elevationabovesealevel,overallclimatehistoryand forecast,earthquakepotentialandspacelimitations. 5. Emissions control requirements and applicable government regulations and standards. 6. The types of auxiliary equipment; overall plant and boiler efficiency; access needs; evaluation penalties, e.g., power usage; planned operating modes including expected load cycling require- ments, e.g., peaking, intermediate or base load; and likely future plant use. When these interfaces are established, boiler design and evaluation may begin. Systematic approach There are a variety of evaluation approaches that can be used to meet the specific steam generator per- formance requirements. These include the multiple iterations commonly found in thermal design where real world complexities and nonlinear, noncontinuous interactions prevent a straightforward solution. The process begins by understanding the particular appli- cation and system to define conditions such as steam flow requirements, fuel source, operating dynamics, and emissions limits, among others. From these, the designer proceeds to assess the steam generator op- tions, interfaces, and equipment needs to achieve per- formance. Using a coal-fired boiler as an example, a systematic approach would include the following: 1. Specify the steam supply requirements to define the overall inputs of fuel, air and water, and the steam output conditions. 2. Evaluate the heat balances and heat absorption by type of steam generator surface. 3. Perform combustion calculations to define heat in- put and gas flow requirements. 4. Configure the combustion system to complete the combustion process while minimizing emissions (fuel preparation, combustion and air handling). 5. Configure the furnace and other heat transfer sur- faces to satisfy temperature, material, and perfor- mance tradeoffs while meeting the system control needs. 6. Size other water-side and steam-side components. 7. Specify the back-end tradeoffs on the final heat recovery devices such as water heaters (economiz- ers) and air heaters. 8. Check the steam generating system performance to ensure that the design criteria are met. 9. Verify overall unit performance. 10. Repeat steps 2 through 9 until the desired steam mass flow and temperature are achieved over the specified range of load conditions. 11. Use American Society of Mechanical Engineers (ASME) Code rules to design pressure parts to meettheanticipatedoperatingconditionsandcom- plete detailed mechanical design. 12. Design and integrate environmental protection equipment to achieve prescribed emissions levels. 13. Incorporate auxiliaries as needed, such as tube surface cleaning equipment, fans, instrumenta- tion and controls, to complete the design and as- sure safe and continuous operation. The life cycle and daily operation of the steam gen- erator (and the plant in which it will operate) are important elements to be considered from the begin- ning of the design and throughout the design process. Today, some steam generators will be required to op- erate efficiently and reliably for up to 60 years or more. During this time, many components will wear out because of the aggressive environment, so routine inspection of pressure parts is needed to assure con- tinued reliability. Unit operating procedures, such as the permitted severity and magnitude of transients, may be monitored to prevent reduced unit life. Oper- ating practices including water treatment, cycling op- eration procedures, and preventive maintenance pro- grams, among others, can significantly affect steam generator availability and reliability. Key unit com- ponents may be upgraded to improve performance. In each case, decisions made during the design phase and subsequent operation can substantially enhance the life and performance of the unit. System design example Now that the basic fossil fuel and nuclear steam generating systems have been described, it is appro- priate to explore the general design and engineering process. While each of the many systems requires spe- cialized evaluations, they share many common ele- ments. To illustrate how the design process works, a small industrial B&W PFI gas-fired boiler has been selected for discussion. (See Figs. 22 and 23.) Basically, the customer has one overriding need: when the valve is turned on, steam is expected to be
- 55. Steam 41 / Steam Generation – An Overview 1-15 The Babcock & Wilcox Company supplied at the desired pressure, temperature and flow rate. In this example, the customer specifies 400,000 lb/h (50.4 kg/s) of superheated steam at 600 psi (4.14 MPa) and 850F (454C). The customer has agreed to supply high purity feedwater at 280F (138C) and to supply natural gas as a fuel source. As with all steam generating systems, there are a number of additional constraints and requirements as discussed in Steam generator interfaces, but the major job of the steam generator or boiler is to supply steam. Combustion of the natural gas produces a stream of combustion products or flue gas at perhaps 3600F (1982C). To maximize the steam generator thermal efficiency, it is important to cool these gases as much as possible while generating the steam. The minimum flue gas outlet temperature is established based upon technical and economic factors (discussed below). For now, a 310F (154C) outlet temperature to the exhaust stack is selected. The approximate steam and flue gas temperature curves are shown in Fig. 24 and define the heat transfer process. The heat transfer surface for the furnace, boiler bank, superheater and air heater is approximately 69,000 ft2 (6410 m2 ). From a design perspective, the PFI boiler can be viewed as either a steam heater or gas cooler. The lat- ter approach is most often selected for design. The design fuel heat input is calculated by dividing the steam heat output by the target steam generator ther- mal efficiency. Based upon the resulting fuel flow, com- bustion calculations define the air flow requirements and combustion products gas weight. The heat trans- fer surface is then configured in the most economical way to cool the flue gas to the temperature necessary for the target steam generator efficiency. Before pro- ceedingtofollowthegasthroughthecoolingprocess,the amount of heat recovery for each of the different boiler surfaces (superheater and boiler) must be established. Fig. 25 illustrates the water heating process from an inlet temperature of 280F (138C) to the superheater steam outlet temperature of 850F (454C). This curve indicates that about 20% of the heat absorbed is used to raise the water from its inlet temperature to the saturation temperature of 490F (254C). 60% of the energy is then used to evaporate the water to produce saturated steam. The remaining 20% of the heat in- put is used to superheat or raise the steam tempera- ture to the desired outlet temperature of 850F (454C). The fuel and the combustion process selected set the geometry of the furnace. In this case, simple circular burners are used. The objective of the burners is to mix the fuel and air rapidly to produce a stable flame and complete combustion while minimizing the forma- tion of NOx emissions. Burners are available in sev- eral standardized sizes. The specific size and number are selected from past experience to provide the de- sired heat input rate while permitting the necessary level of load range control. The windbox, which dis- tributes the air to individual burners, is designed to provide a uniform air flow at low enough velocities to permit the burners to function properly. The furnace volume is then set to allow complete fuel combustion. The distances between burners and between the burners and the floor, roof, and side walls are determined from the known characteristics of the particular burner flame. Adequate clearances are specified to prevent flame impingement on the furnace surfaces, which could overheat the tubes and cause tube failures. Once the furnace dimensions are set, this volume is enclosed in a water-cooled membrane panel surface. This construction provides a gas-tight, all steel enclo- sure which minimizes energy loss, generates some steam and minimizes furnace maintenance. As shown in Fig. 23, the roof and floor tubes are inclined slightly to enhance water flow and prevent steam from collect- ing on the tube surface. Trapped steam could result in overheating of the tubes. Heat transfer from the flame to the furnace enclosure surfaces occurs primarily by thermal radiation.As a result, the heat input rates per Fig. 23 Small industrial boiler – sectional view. Fig. 22 Small PFI industrial boiler.
- 56. 1-16 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company unit area of surface are very high and relatively inde- pendent of the tubewall temperatures. Boiling water provides an effective means to cool the tubes and keep the tube metal temperatures within acceptable limits as long as the boiling conditions are maintained. Fig. 26 shows the effect of the furnace on gas tem- perature. The gas temperature is reduced from 3600 at point A to 2400F at point B (1982 to 1316C), while boiling takes place in the water walls (points 1 to 2).A large amount of heat transfer takes place on a small amount of surface. From the furnace, the gases pass through the furnace screen tubes shown in Fig. 23. The temperature drops a small amount [50F (28C)] from points B to C in Fig. 26, but more importantly, the superheater surface is partially shielded from the furnace thermal radiation. The furnace screen tubes are connected to the drum and contain boiling water. Next, the gas passes through the superheater where the gas temperature drops from 2350 at point C to 1750F at point D (1288 to 954C). Saturated steam from the drum is passed through the superheater tub- ing to raise its temperature from 490F (254C) satura- tiontemperaturetothe850F(454C)desiredoutlettem- perature (points 5 to 4). The location of the superheater and its configura- tion are critical in order to keep the steam outlet tem- perature constant under all load conditions. This in- volves radiation heat transfer from the furnace with convection heat transfer from the gas passing across the surface. In addition, where dirty gases such as combustion products from coal are used, the spacing of the superheater tubes is also adjusted to accommo- date the accumulation of fouling ash deposits and the use of cleaning equipment. After the superheater, almost half of the energy in the gas stream has been recovered with only a small amount of heat transfer surface [approximately 6400 ft2 (595 m2 )]. This is possible because of the large tem- perature difference between the gas and the boiling water or steam. The gas temperature has now been dra- matically reduced, requiring much larger heat transfer surfaces to recover incremental amounts of energy. The balance of the steam is generated by passing the gas through the boiler bank. (See Figs. 22 and 23.) This bank is composed of a large number of water- containing tubes that connect the steam drum to a lower (mud) drum. The temperature of the boiling water is effectively constant (points 5 to 6 in Fig. 26), while the gas temperature drops by almost 1000F (556C) to an outlet temperature of 760F (404C), be- tween points D and E. The tubes are spaced as closely as possible to increase the gas flow heat transfer rate. If a particulate-laden gas stream were present, the spacing would be set to limit erosion of the tubes, re- duce the heat transfer degradation due to ash depos- its, and permit removal of the ash. Spacing is also controlled by the allowable pressure drop across the bank. In addition, a baffle can be used in the boiler bank bundle to force the gas to travel at higher veloc- ity through the bundle, increase the heat transfer rate, and thereby reduce the bundle size and cost. To re- cover this additional percentage of the supplied en- ergy, the boiler bank contains more than 32,000 ft2 (3000 m2 ) of surface, or approximately nine times more surface per unit of energy than in the high tempera- ture furnace and superheater. At this point in the process, the temperature difference between the satu- rated water and gas is only 270F (150C), between points 6 and E in Fig. 26. Economics and technical limits dictate the type and arrangement of additional heat transfer surfaces. An economizer or water-cooled heat exchanger could be used to heat the makeup or feedwater and cool the gas. The lowest gas exit temperature possible is the inlet temperature of the feedwater [280F (138C)]. However, the economizer would have to be infinitely large to accomplish this goal. Even if the exit gas temperature is 310F (154C), the temperature difference at this point in the heat exchanger would only be 30F (17C), still making the heat exchanger relatively large. In- stead of incorporating an economizer, an air preheater could be used to recover the remaining gas energy and preheat the combustion air. This would reduce the Fig. 24 Industrial boiler – temperature versus heat transfer surface. Fig. 25 Steam-water temperature profile.
- 57. Steam 41 / Steam Generation – An Overview 1-17 The Babcock & Wilcox Company natural gas needed to heat the steam generator. Air heaters can be very compact. Also, air preheating can enhance the combustion of many difficult to burn fu- els such as coal. All of the parameters are reviewed to selectthemosteconomicalsolutionthatmeetsthetech- nical requirements. In this case, the decision has been made to use an air heater and not an economizer. The air heater is designed to take 80F (27C) ambient air (point 9) and increase the temperature to 570F (299C), at point 8. This hot air is then fed to the burners. At the same time, the gas temperature is dropped from 760F (404C) to the desired 310F (154C) outlet temperature (points E to F). If a much lower gas outlet temperature than 310F (154C) is used, the heat exchanger surfaces may become uneconomically large, although this is a case by case decision. In addition, for fuels such as oil or coal which can produce acid constituents in the gas stream (such as sulfur oxides), lower exit gas tem- peratures may result in condensation of these constitu- ents onto the heat transfer surfaces, and excessive corrosion damage. The gas is then exhausted through the stack to the atmosphere. Finally, the feedwater temperature increases from 280F (138C) to saturation temperature of 490F (254C). In the absence of an economizer, the feedwater is supplied directly to the drum where it is mixed with the water flowing through the boiler bank tubes and furnace. The flow rate of this circulating water in industrial units is approximately 25 times higher than the feedwater flow rate. Therefore, when the feedwater is mixed in the drum, it quickly ap- proaches the saturation temperature without appre- ciably lowering the temperature of the recirculating water in the boiler tubes. Reviewing the water portion of the system, the feed- water is supplied to the drum where it mixes with the recirculating water after the steam is extracted and sent to the superheater. The drum internals are spe- cially designed so that the now slightly subcooled water flows down through a portion of the boiler bank tubes to the lower or mud drum. This water is then distributed to the remainder of the boiler bank tubes (also called risers) and the furnace enclosure tubes where it is partially converted to steam (approximately 4% steam by weight). The steam-water mixture is then returned to the steam drum. Here, the steam- water mixture is passed through separators where the steam is separated from the water. The steam is then sent to the superheater, and from there to its end use. The remaining water is mixed with the feedwater and is again distributed to the downcomer tubes. Other steam producing systems A variety of additional systems also produce steam for power and process applications. These systems usually take advantage of low cost or free fuels, a com- bination of power cycles and processes, and recovery of waste heat in order to reduce overall costs. Ex- amples of these include: 1. Gas turbine combined cycle (CC) Advanced gas turbines with heat recovery steam generators as part of a bottoming cycle to use waste heat recov- ery and increase thermal efficiency. 2. Integrated gasification combined cycle (IGCC) Adds a coal gasifier to the CC to reduce fuel costs and minimizeairborneemissions. 3. Pressurized fluidized-bed combustion (PFBC) Includes higher pressure combustion with gas cleaning and expansion of the combustion prod- ucts through a gas turbine. 4. Blast furnace hood heat recovery Generates steam using the waste heat from a blast furnace. 5. Solar steam generator Uses concentrators to collect andconcentratesolarradiationandgeneratesteam. Common technical elements The design of steam generating systems involves the combination of scientific and technical fundamen- tals, empirical data, practical experience and designer insight. While technology has advanced significantly, it is still not possible to base the design of modern sys- tems on fundamentals alone. Instead, the fundamen- tals provide the basis for combining field data and empirical methods. Even given the wide variety of shapes, sizes and applications (see Fig. 27), steam generator design in- volves the application of a common set of technologies. The functional performance of the steam generator is established by combining thermodynamics, heat transfer, fluid mechanics, chemistry, and combustion science or nuclear science with practical knowledge of the fouling of heat transfer surfaces and empirical knowledge of the behavior of boiling water. The de- sign and supply of the hardware are aided by struc- tural design and advanced materials properties re- search combined with expertise in manufacturing technologies and erection skills to produce a quality, reliable product to meet the highly demanding system requirements.Fig. 26 Gas and steam temperature schematic.
- 58. 1-18 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company The ASME Boiler and Pressure Vessel Code is the firm basis from which steam generator pressure parts can be safely designed. Once built, the operation and maintenance of the steam generator are critical to ensure a long life and reliable service. Water chemis- try and chemical cleaning are increasingly recognized as central elements in any ongoing operating pro- gram. The impact of fuel and any residual flyash is important in evaluating the corrosion and fouling of heat transfer surfaces. The use of modern techniques to periodically inspect the integrity of the steam gen- erator tubes leads to the ability to extend steam gen- erator life and improve overall performance. These are accomplished by the application of engineered com- ponent modification to better meet the changing needs of the steam generating system. Finally, the control systems which monitor and operate many subsystems to optimize unit performance are important to main- tain system reliability and efficiency. All of these functions – functional performance, mechanical design, manufacture, construction, opera- tion, maintenance, and life extension – must be fully combined to provide the best steam generating sys- tem. Long term success depends upon a complete life cycle approach to the steam generating system. Steam generator system operators routinely require their equipment to operate continuously and reliably for more than 60 years in increasingly demanding con- ditions. Therefore, it is important to consider later boiler life, including component replacement, in the initial phases of boiler specification. Changes in de- sign to reduce initial capital cost must be weighed against their possible impact on future operation. Fig. 27 This energy complex in the northern U.S. includes four coal-fired steam systems, ranging from 80 to 330 MW, installed over a 25-year period. Bibliography Aschner, F.S., Planning Fundamentals of Thermal Power Plants, John Wiley & Sons, New York, New York, 1978. Axtman, W.H., and American Boiler Manufacturers As- sociation staff, “The American Boiler Industry: A Century of Innovation,” American Boiler Manufacturers Associa- tion (ABMA), Arlington, Virginia, 1988. “Boilers and auxiliary equipment,” Power, Vol. 132, No. 6, pp B-l to B-138, Platts/McGraw-Hill, New York, New York, June, 1988. Clapp, R.M., Ed., Modern Power Station Practice: Boil- ers and Ancillary Plant, Third Ed., Pergamon Press, Oxford, England, United Kingdom, April 1, 1993. Collier, J.G., and Hewitt, G.F., Introduction to Nuclear Power, Taylor and Francis Publishers, Washington, D.C., June 1, 2000. Elliot, T.C., Chen, K., Swanekamp, R.C., Ed., Standard Handbook of Powerplant Engineering, McGraw-Hill Com- pany, New York, New York, 1997.
- 59. Steam 41 / Steam Generation – An Overview 1-19 The Babcock & Wilcox Company Inconel is a trademark of the Special Metals Corporation group of companies. El-Wakil, M.M., Powerplant Technology, McGraw-Hill Primis Custom Publishing, New York, New York, 1984. Foster, A.R., and Wright, R.L., Basic Nuclear Engineer- ing, Pearson Allyn and Bacon, Boston, Massachusetts, January, 1983. Fraas, A.P., Heat Exchanger Design, Second Ed., Interscience, New York, New York, March, 1989. Gunn, D., and Horton, R., Industrial Boilers, Longman Scientific and Technical, Longman Science & Technology, London, England, United Kingdom, April, 1989. Hambling, P., Modern Power Station Practice: Turbines, Generators and Associated Plant, Third Ed., Pergamon Press, Oxford, England, United Kingdom, April 1, 1993. Jackson, A.W., “The How and Why of Boiler Design,” En- gineers Society of Western Pennsylvania Power Sympo- sium, Pittsburgh, Pennsylvania, February 15, 1967. Kakaç, S., Ed., Boilers, Evaporators and Condensers, Interscience, April 15, 1991. See Chapter 6, “Fossil Fuel- Fired Boilers: Fundamentals and Elements,” by J.B. Kitto and M.J. Albrecht. Li, K.W., and Priddy, A.P., Power Plant System Design, Wiley Text Books, New York, New York, February, 1985. Shields, C.D., Boilers: Types, Characteristics, and Func- tions, McGraw-Hill Company, New York, New York, 1961. Wiener, M., “The Latest Developments in Natural Circu- lation Boiler Design,” Proceedings of the American Power Conference, Vol. 39, pp. 336-348, 1977.
- 60. 1-20 Steam 41 / Steam Generation – An Overview The Babcock & Wilcox Company 750 MW once-through spiral wound universal pressure (SWUP™) coal-fired utility boiler. Catalyst Primary Air Fan Flue Gas Outlet Air Heater Steam Coil Air Heater Forced Draft Fan B&W Roll Wheel™ Pulverizers Low NO Burners x Ammonia Injection Grid Steam Separator Water Collection Tank Primary Superheater Economizer Platen Superheater Intermediate Superheater Final Superheater Final Reheater Furnace SCR Circulation Pump Spiral Transition Headers xNO Ports Primary Reheater Mix Bottle
- 61. Steam 41 / Thermodynamics of Steam 2-1 The Babcock & Wilcox Company Chapter 2 Thermodynamics of Steam Thermodynamics is the science which describes and defines the transformation of one form of energy into another – chemical to thermal, thermal to mechani- cal, and mechanical to thermal. The basic tenets in- clude: 1) energy in all of its forms must be conserved, and 2) only a portion of available energy can be con- verted to useful energy or work. Generally referred to as the first and second laws of thermodynamics, these tenets evolved from the early development of the steam engine and the efforts to formalize the obser- vations of its conversion of heat into mechanical work. Regardless of the type of work or form of energy under consideration, the terms heat, work, and energy have practical significance only when viewed in terms of systems, processes, cycles, and their surroundings. In the case of expansion work, the system is a fluid capable of expansion or contraction as a result of pres- sure, temperature or chemical changes. The way in which these changes take place is referred to as the process. A cycle is a sequence of processes that is ca- pable of producing net heat flow or work when placed between an energy source and an energy sink. The surroundings represent the sources and sinks which accommodate interchanges of mass, heat and work to or from the system. Steam may be viewed as a thermodynamic system which is favored for power generation and heat trans- fer. Its unique combination of high thermal capacity (specific heat), high critical temperature, wide avail- ability, and nontoxic nature has served to maintain this dominant position. High thermal capacity of a working fluid generally results in smaller equipment for a given power output or heat transfer. The useful temperature range of water and its high thermal ca- pacity meet the needs of many industrial processes and the temperature limitations of power conversion equipment. Properties of steam Before a process or cycle can be analyzed, reliable properties of the working fluid are needed. Key prop- erties include enthalpy, entropy, and specific volume. While precise definitions are provided later in this chapter, enthalpy is a general measure of the inter- nally stored energy per unit mass of a flowing stream, specific entropy is a measure of the thermodynamic potential of a system in the units of energy per unit mass and absolute temperature, and specific volume is the volume per unit mass. In the case of steam, a worldwide consensus of these and other thermophysical properties has been reached through the International Association for the Proper- ties of Steam. The most frequently used tabulation of steam properties is the American Society of Mechani- cal Engineers (ASME) Steam Tables.1,2 Selected data from this tabulation in English units are summarized in Tables 1, 2 and 3. Corresponding SI tabulations are provided inAppendix 1. These properties are now well described by formulas that have been agreed to by the International Association for the Properties of Water and Steam, and are available from a number of sources on the Internet as add-on functions to spreadsheets and other software products. The first two columns of Tables 1 and 2 define the unique relationship between pressure and tempera- ture referred to as saturated conditions, where liquid and vapor phases of water can coexist at thermody- namic equilibrium. For a given pressure, steam heated above the saturation temperature is referred to as su- perheated steam, while water cooled below the satu- ration temperature is referred to as subcooled or com- pressed water. Properties for superheated steam and compressed water are provided in Table 3. Reproduced from Reference 1, Fig. 1 shows the values of enthalpy and specific volume for steam and water over a wide range of pressure and temperature. Under superheated or subcooled conditions, fluid properties, such as enthalpy, entropy and volume per unit mass, are unique functions of temperature and pressure. However, at saturated conditions where mixtures of steam and water coexist, the situation is more complex and requires an additional parameter for definition. For example, the enthalpy of a steam- water mixture will depend upon the relative amounts of steam and water present. This additional param- eter is the thermodynamic equilibrium quality or sim- ply quality (x) defined by convention as the mass frac- tion of steam: x m m m s s w = + (1)
- 62. 2-2 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company Note: The following steam tables and Fig. 1 have been abstracted from ASME International Steam Tables for Industrial Use (copyright 2000 by The American Society of Mechanical Engineers), based on the IAPWS industrial formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97). Table 1 Properties of Saturated Steam and Saturated Water (Temperature) 1 Specific Volume, ft3 /lb Enthalpy,2 Btu/lb Entropy, Btu/lb F Water Evap Steam Water Evap Steam Water Evap Steam vf vfg vg Hf Hfg Hg sf sfg sg 32 0.08865 0.01602 3302 3302 -0.02 1075.2 1075.2 -0.00004 2.1869 2.1868 32 35 0.09998 0.01602 2946 2946 3.00 1073.5 1076.5 0.0061 2.1701 2.1762 35 40 0.12173 0.01602 2443 2443 8.03 1070.7 1078.7 0.0162 2.1427 2.1590 40 45 0.14757 0.01602 2035.6 2035.6 13.05 1067.8 1080.9 0.0262 2.1159 2.1421 45 50 0.17813 0.01602 1702.9 1702.9 18.07 1065.0 1083.1 0.0361 2.0896 2.1257 50 60 0.2564 0.01603 1206.0 1206.1 28.08 1059.4 1087.4 0.0555 2.0385 2.0941 60 70 0.3633 0.01605 867.2 867.2 38.08 1053.7 1091.8 0.0746 1.9894 2.0640 70 80 0.5074 0.01607 632.4 632.4 48.07 1048.0 1096.1 0.0933 1.9420 2.0353 80 90 0.6990 0.01610 467.4 467.4 58.05 1042.4 1100.4 0.1116 1.8964 2.0080 90 100 0.9504 0.01613 349.9 349.9 68.04 1036.7 1104.7 0.1296 1.8523 1.9819 100 110 1.2766 0.01617 265.0 265.0 78.02 1031.0 1109.0 0.1473 1.8098 1.9570 110 120 1.6949 0.01620 202.95 202.96 88.00 1025.2 1113.2 0.1647 1.7686 1.9333 120 130 2.2258 0.01625 157.09 157.10 97.99 1019.4 1117.4 0.1817 1.7288 1.9106 130 140 2.8929 0.01629 122.81 122.82 107.98 1013.6 1121.6 0.1985 1.6903 1.8888 140 150 3.723 0.01634 96.92 96.93 117.97 1007.8 1125.7 0.2151 1.6530 1.8680 150 160 4.747 0.01639 77.17 77.19 127.98 1001.9 1129.8 0.2313 1.6168 1.8481 160 170 6.000 0.01645 61.97 61.98 137.99 995.9 1133.9 0.2474 1.5816 1.8290 170 180 7.520 0.01651 50.15 50.17 148.01 989.9 1137.9 0.2631 1.5475 1.8106 180 190 9.350 0.01657 40.90 40.92 158.05 983.8 1141.8 0.2787 1.5143 1.7930 190 200 11.538 0.01663 33.59 33.61 168.10 977.6 1145.7 0.2940 1.4820 1.7760 200 212 14.709 0.01671 26.76 26.78 180.18 970.1 1150.3 0.3122 1.4443 1.7565 212 220 17.201 0.01677 23.12 23.13 188.25 965.0 1153.3 0.3241 1.4198 1.7440 220 230 20.795 0.01684 19.356 19.373 198.35 958.6 1157.0 0.3388 1.3899 1.7288 230 240 24.985 0.01692 16.299 16.316 208.47 952.1 1160.5 0.3534 1.3607 1.7141 240 250 29.843 0.01700 13.799 13.816 218.62 945.4 1164.0 0.3678 1.3322 1.7000 250 260 35.445 0.01708 11.743 11.760 228.79 938.6 1167.4 0.3820 1.3043 1.6862 260 270 41.874 0.01717 10.042 10.059 238.99 931.7 1170.7 0.3960 1.2769 1.6730 270 280 49.218 0.01726 8.627 8.644 249.21 924.7 1173.9 0.4099 1.2502 1.6601 280 290 57.567 0.01735 7.444 7.461 259.5 917.5 1177.0 0.4236 1.2239 1.6476 290 300 67.021 0.01745 6.449 6.467 269.8 910.2 1180.0 0.4372 1.1982 1.6354 300 310 77.68 0.01755 5.609 5.627 280.1 902.7 1182.8 0.4507 1.1728 1.6235 310 320 89.65 0.01765 4.897 4.915 290.4 895.0 1185.5 0.4640 1.1480 1.6120 320 340 118.00 0.01787 3.771 3.789 311.3 879.2 1190.5 0.4903 1.0994 1.5897 340 360 153.00 0.01811 2.940 2.958 332.3 862.5 1194.8 0.5162 1.0522 1.5684 360 380 195.71 0.01836 2.318 2.336 353.6 844.9 1198.5 0.5416 1.0062 1.5478 380 400 247.22 0.01864 1.8454 1.8640 375.1 826.4 1201.5 0.5667 0.9613 1.5280 400 420 308.71 0.01894 1.4818 1.5007 396.9 806.7 1203.6 0.5915 0.9171 1.5086 420 440 381.44 0.01926 1.1986 1.2179 419.0 785.9 1204.9 0.6161 0.8735 1.4896 440 460 466.7 0.0196 0.9755 0.9952 441.5 763.7 1205.2 0.6405 0.8304 1.4709 460 480 565.9 0.0200 0.7980 0.8180 464.4 739.9 1204.4 0.6648 0.7874 1.4522 480 500 680.5 0.0204 0.6551 0.6756 487.9 714.5 1202.3 0.6890 0.7445 1.4335 500 520 812.1 0.0209 0.5392 0.5601 511.9 687.0 1198.9 0.7133 0.7013 1.4145 520 540 962.2 0.0215 0.4441 0.4656 536.7 657.3 1194.0 0.7377 0.6575 1.3952 540 560 1132.7 0.0221 0.3654 0.3875 562.3 624.9 1187.2 0.7624 0.6128 1.3752 560 580 1325.4 0.0228 0.2995 0.3223 589.0 589.3 1178.2 0.7875 0.5668 1.3543 580 600 1542.5 0.0236 0.2438 0.2675 616.9 549.7 1166.6 0.8133 0.5187 1.3320 600 620 1786.1 0.0246 0.1961 0.2207 646.6 505.0 1151.6 0.8400 0.4677 1.3077 620 640 2059.2 0.0259 0.1543 0.1802 678.7 453.3 1132.0 0.8683 0.4122 1.2804 640 660 2364.8 0.0277 0.1167 0.1444 714.5 390.9 1105.3 0.8991 0.3491 1.2482 660 680 2707.3 0.0303 0.0809 0.1112 757.3 309.3 1066.6 0.9354 0.2714 1.2068 680 700 3092.9 0.0368 0.0378 0.0747 823.6 167.0 990.6 0.9910 0.1440 1.1350 700 705.1028 3200.1 0.0497 0 0.04975 897.5 0 897.5 1.0538 0 1.0538 705.1028 1. SI steam tables are provided in Appendix 1. 2. In the balance of Steam, enthalpy is denoted by H in place of h to avoid confusion with heat transfer coefficient. Temp F Temp F Press. psia
- 63. Steam 41 / Thermodynamics of Steam 2-3 The Babcock & Wilcox Company Table 2 Properties of Saturated Steam and Saturated Water (Pressure) 1 Internal Volume, ft3 /lb Enthalpy,2 Btu/lb Entropy, Btu/lb F Energy, Btu/lb Water Evap Steam Water Evap Steam Water Evap Steam Water Steam vf vfg vg Hf Hfg Hg sf sfg sg uf ug 0.0886 31.986 0.01602 3303.8 3303.8 -0.03 1075.2 1075.2 0 2.1869 2.1869 0 1021.0 0.0886 0.1 35.005 0.01602 2945.0 2945.0 3.01 1073.5 1076.5 0.0061 2.1701 2.1762 3.01 1022.0 0.1 0.15 45.429 0.01602 2004.3 2004.3 13.48 1067.6 1081.1 0.0271 2.1136 2.1407 13.48 1025.4 0.15 0.2 53.132 0.01603 1525.9 1525.9 21.20 1063.2 1084.4 0.0422 2.0734 2.1156 21.20 1028.0 0.2 0.3 64.452 0.01604 1039.4 1039.4 32.53 1056.8 1089.4 0.0641 2.0164 2.0805 32.53 1031.7 0.3 0.4 72.834 0.01606 791.8 791.9 40.91 1052.1 1093.0 0.0799 1.9758 2.0557 40.91 1034.4 0.4 0.5 79.549 0.01607 641.3 641.3 47.62 1048.3 1095.9 0.0925 1.9441 2.0366 47.62 1036.6 0.5 0.6 85.180 0.01609 539.9 539.9 53.24 1045.1 1098.3 0.1028 1.9182 2.0210 53.24 1038.4 0.6 0.7 90.05 0.01610 466.80 466.81 58.10 1042.3 1100.4 0.1117 1.8962 2.0079 58.10 1040.0 0.7 0.8 94.34 0.01611 411.56 411.57 62.39 1039.9 1102.3 0.1195 1.8770 1.9965 62.39 1041.4 0.8 0.9 98.20 0.01613 368.30 368.32 66.24 1037.7 1103.9 0.1264 1.8601 1.9865 66.23 1042.6 0.9 1 101.69 0.01614 333.49 333.51 69.73 1035.7 1105.4 0.1326 1.8450 1.9776 69.73 1043.7 1 2 126.03 0.01623 173.70 173.72 94.02 1021.7 1115.8 0.1750 1.7445 1.9195 94.01 1051.5 2 3 141.42 0.01630 118.69 118.70 109.39 1012.8 1122.2 0.2009 1.6849 1.8858 109.38 1056.3 3 4 152.91 0.01636 90.61 90.63 120.89 1006.1 1126.9 0.2198 1.6423 1.8621 120.87 1059.9 4 5 162.18 0.01641 73.507 73.52 130.16 1000.6 1130.7 0.2349 1.6090 1.8438 130.15 1062.7 5 6 170.00 0.01645 61.963 61.98 137.99 995.9 1133.9 0.2474 1.5816 1.8290 137.97 1065.1 6 7 176.79 0.01649 53.632 53.65 144.79 991.8 1136.6 0.2581 1.5583 1.8164 144.77 1067.1 7 8 182.81 0.01652 47.328 47.34 150.83 988.2 1139.0 0.2675 1.5381 1.8056 150.80 1068.9 8 9 188.22 0.01656 42.387 42.40 156.27 984.9 1141.1 0.2760 1.5201 1.7961 156.24 1070.5 9 10 193.16 0.01659 38.406 38.42 161.22 981.8 1143.1 0.2836 1.5040 1.7875 161.19 1072.0 10 14.696 211.95 0.01671 26.787 26.80 180.13 970.1 1150.3 0.3121 1.4445 1.7566 180.09 1077.4 14.696 15 212.99 0.01672 26.278 26.30 181.18 969.5 1150.7 0.3137 1.4413 1.7549 181.13 1077.7 15 20 227.92 0.01683 20.075 20.09 196.25 959.9 1156.2 0.3358 1.3961 1.7319 196.18 1081.8 20 30 250.30 0.01700 13.7312 13.748 218.9 945.2 1164.1 0.3682 1.3313 1.6995 218.8 1087.8 30 40 267.22 0.01715 10.4832 10.500 236.2 933.7 1169.8 0.3921 1.2845 1.6766 236.0 1092.1 40 50 280.99 0.01727 8.4998 8.517 250.2 924.0 1174.2 0.4113 1.2475 1.6588 250.1 1095.4 50 60 292.69 0.01738 7.1588 7.176 262.2 915.6 1177.8 0.4273 1.2169 1.6443 262.0 1098.1 60 70 302.92 0.01748 6.1896 6.207 272.8 908.0 1180.8 0.4412 1.1907 1.6319 272.5 1100.4 70 80 312.03 0.01757 5.4554 5.473 282.2 901.2 1183.3 0.4534 1.1678 1.6212 281.9 1102.3 80 90 320.27 0.01766 4.8792 4.897 290.7 894.8 1185.6 0.4644 1.1473 1.6117 290.4 1104.0 90 100 327.82 0.01774 4.4146 4.432 298.6 888.9 1187.5 0.4744 1.1288 1.6032 298.2 1105.5 100 120 341.26 0.01789 3.7107 3.729 312.6 878.1 1190.7 0.4920 1.0964 1.5883 312.2 1108.0 120 140 353.04 0.01802 3.2019 3.220 325.0 868.4 1193.4 0.5072 1.0685 1.5757 324.5 1110.0 140 160 363.55 0.01815 2.8163 2.834 336.1 859.4 1195.5 0.5207 1.0440 1.5647 335.6 1111.6 160 180 373.08 0.01827 2.5137 2.532 346.2 851.1 1197.3 0.5328 1.0220 1.5549 345.6 1113.0 180 200 381.81 0.01839 2.2696 2.288 355.5 843.3 1198.8 0.5439 1.0021 1.5460 354.9 1114.1 200 250 400.98 0.01865 1.8252 1.8439 376.2 825.4 1201.6 0.5679 0.9591 1.5270 375.3 1116.3 250 300 417.37 0.01890 1.5245 1.5434 394.0 809.4 1203.4 0.5883 0.9229 1.5111 393.0 1117.7 300 350 431.75 0.01913 1.3071 1.3262 409.8 794.6 1204.5 0.6060 0.8914 1.4974 408.6 1118.6 350 400 444.63 0.0193 1.14225 1.1616 424.2 780.9 1205.0 0.6217 0.8635 1.4853 422.7 1119.1 400 450 456.32 0.0196 1.01283 1.0324 437.3 767.9 1205.2 0.6360 0.8383 1.4743 435.7 1119.2 450 500 467.05 0.0198 0.90840 0.9282 449.5 755.5 1205.0 0.6490 0.8152 1.4643 447.7 1119.1 500 550 476.98 0.0199 0.82229 0.8422 460.9 743.6 1204.6 0.6611 0.7939 1.4550 458.9 1118.8 550 600 486.25 0.0201 0.75002 0.7702 471.7 732.2 1203.9 0.6723 0.7740 1.4464 469.5 1118.4 600 700 503.14 0.0205 0.63535 0.6559 491.6 710.3 1201.9 0.6928 0.7377 1.4305 489.0 1117.0 700 800 518.27 0.0209 0.54830 0.5692 509.8 689.5 1199.3 0.7112 0.7050 1.4162 506.7 1115.0 800 900 532.02 0.0212 0.47983 0.5011 526.7 669.4 1196.2 0.7279 0.6751 1.4030 523.2 1112.7 900 1000 544.65 0.0216 0.42446 0.4461 542.6 650.0 1192.6 0.7434 0.6472 1.3906 538.6 1110.0 1000 1100 556.35 0.0220 0.37869 0.4006 557.6 631.0 1188.6 0.7578 0.6211 1.3789 553.1 1107.0 1100 1200 567.26 0.0223 0.34014 0.3625 571.8 612.4 1184.2 0.7714 0.5963 1.3677 566.9 1103.7 1200 1300 577.50 0.0227 0.30718 0.3299 585.5 593.9 1179.5 0.7843 0.5727 1.3570 580.1 1100.1 1300 1400 587.14 0.0231 0.27861 0.3017 598.8 575.7 1174.4 0.7966 0.5499 1.3465 592.8 1096.3 1400 1500 596.27 0.0235 0.25357 0.2770 611.6 557.4 1169.0 0.8084 0.5279 1.3363 605.1 1092.1 1500 2000 635.85 0.0256 0.16255 0.1882 671.8 464.7 1136.5 0.8622 0.4242 1.2864 662.3 1066.9 2000 2500 668.17 0.0286 0.10208 0.1307 730.8 360.7 1091.5 0.9130 0.3199 1.2329 717.6 1031.1 2500 3000 695.41 0.0344 0.05015 0.0845 802.9 213.6 1016.5 0.9736 0.1849 1.1585 783.8 969.5 3000 3200.11 705.1028 0.0497 0 0.0498 897.5 0 897.5 1.0538 0 1.0538 868.0 868.0 3200.11 1. See Note 1, Table 1. 2. See Note 2, Table 1. Temp F Press. psia Press. psia
- 64. 2-4 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company Table 3 Properties of Superheated Steam and Compressed Water (Temperature and Pressure) 1 Temperature, F 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 0.0161 392.5 452.3 511.9 571.5 631.1 690.7 68.00 1150.2 1195.7 1241.8 1288.6 1336.1 1384.5 0.1295 2.0509 2.1152 2.1722 2.2237 2.2708 2.3144 0.0161 78.14 90.24 102.24 114.21 126.15 138.08 150.01 161.94 173.86 185.78 197.70 209.62 221.53 233.45 68.01 1148.6 1194.8 1241.3 1288.2 1335.9 1384.3 1433.6 1483.7 1534.7 1586.7 1639.6 1693.3 1748.0 1803.5 0.1295 1.8716 1.9369 1.9943 2.0460 2.0932 2.1369 2.1776 2.2159 2.2521 2.2866 2.3194 2.3509 2.3811 2.4101 0.0161 38.84 44.98 51.03 57.04 63.03 69.00 74.98 80.94 86.91 92.87 98.84 104.80 110.76 116.72 68.02 1146.6 1193.7 1240.6 1287.8 1335.5 1384.0 1433.4 1483.5 1534.6 1586.6 1639.5 1693.3 1747.9 1803.4 0.1295 1.7928 1.8593 1.9173 1.9692 2.0166 2.0603 2.1011 2.1394 2.1757 2.2101 2.2430 2.2744 2.3046 2.3337 0.0161 0.0166 29.899 33.963 37.985 41.986 45.978 49.964 53.946 57.926 61.905 65.882 69.858 73.833 77.807 68.04 168.09 1192.5 1239.9 1287.3 1335.2 1383.8 1433.2 1483.4 1534.5 1586.5 1639.4 1693.2 1747.8 1803.4 0.1295 0.2940 1.8134 1.8720 1.9242 1.9717 2.0155 2.0563 2.0946 2.1309 2.1653 2.1982 2.2297 2.2599 2.2890 0.0161 0.0166 22.356 25.428 28.457 31.466 34.465 37.458 40.447 43.435 46.420 49.405 52.388 55.370 58.352 68.05 168.11 1191.4 1239.2 1286.9 1334.9 1383.5 1432.9 1483.2 1534.3 1586.3 1639.3 1693.1 1747.8 1803.3 0.1295 0.2940 1.7805 1.8397 1.8921 1.9397 1.9836 2.0244 2.0628 2.0991 2.1336 2.1665 2.1979 2.2282 2.2572 0.0161 0.0166 11.036 12.624 14.165 15.685 17.195 18.699 20.199 21.697 23.194 24.689 26.183 27.676 29.168 68.10 168.15 1186.6 1236.4 1285.0 1333.6 1382.5 1432.1 1482.5 1533.7 1585.8 1638.8 1992.7 1747.5 1803.0 0.1295 0.2940 1.6992 1.7608 1.8143 1.8624 1.9065 1.9476 1.9860 2.0224 2.0569 2.0899 2.1224 2.1516 2.1807 0.0161 0.0166 7.257 8.354 9.400 10.425 11.438 12.446 13.450 14.452 15.452 16.450 17.448 18.445 19.441 68.15 168.20 1181.6 1233.5 1283.2 1332.3 1381.5 1431.3 1481.8 1533.2 1585.3 1638.4 1692.4 1747.1 1802.8 0.1295 0.2939 1.6492 1.7134 1.7681 1.8168 1.8612 1.9024 1.9410 1.9774 2.0120 2.0450 2.0765 2.1068 2.1359 0.0161 0.0166 0.0175 6.218 7.018 7.794 8.560 9.319 10.075 10.829 11.581 12.331 13.081 13.829 14.577 68.21 168.24 269.74 1230.5 1281.3 1330.9 1380.5 1430.5 1481.1 1532.6 1584.9 1638.0 1692.0 1746.8 1802.5 0.1295 0.2939 0.4371 1.6790 1.7349 1.7842 1.8289 1.8702 1.9089 1.9454 1.9800 2.0131 2.0446 2.0750 2.1041 0.0161 0.0166 0.0175 4.935 5.588 6.216 6.833 7.443 8.050 8.655 9.258 9.860 10.460 11.060 11.659 68.26 168.29 269.77 1227.4 1279.3 1329.6 1379.5 1429.7 1480.4 1532.0 1584.4 1637.6 1691.6 1746.5 1802.2 0.1295 0.2939 0.4371 1.6516 1.7088 1.7586 1.8036 1.8451 1.8839 1.9205 1.9552 1.9883 2.0199 2.0502 2.0794 0.0161 0.0166 0.0175 4.0786 4.6341 5.1637 5.6831 6.1928 6.7006 7.2060 7.7096 8.2119 8.7130 9.2134 9.7130 68.31 168.33 269.81 1224.1 1277.4 1328.1 1378.4 1428.8 1479.8 1531.4 1583.9 1637.1 1691.3 1746.2 1802.0 0.1295 0.2939 0.4371 1.6286 1.6872 1.7376 1.7829 1.8246 1.8635 1.9001 1.9349 1.9680 1.9996 2.0300 2.0592 0.0161 0.0166 0.0175 3.4661 3.9526 4.4119 4.8585 5.2995 5.7364 6.1709 6.6036 7.0349 7.4652 7.8946 8.3233 68.37 168.38 269.85 1220.8 1275.3 1326.8 1377.4 1428.0 1479.1 1530.8 1583.4 1636.7 1690.9 1745.9 1801.7 0.1295 0.2939 0.4370 1.6085 1.6686 1.7196 1.7652 1.8071 1.8461 1.8828 1.9176 1.9508 1.9825 2.0129 2.0421 0.0161 0.0166 0.0175 3.0060 3.4413 3.8480 4.2420 4.6295 5.0132 5.3945 5.7741 6.1522 6.5293 6.9055 7.2811 68.42 168.42 269.89 1217.4 1273.3 1325.4 1376.4 1427.2 1478.4 1530.3 1582.9 1636.3 1690.5 1745.6 1801.4 0.1294 0.2938 0.4370 1.5906 1.6522 1.7039 1.7499 1.7919 1.8310 1.8678 1.9027 1.9359 1.9676 1.9980 2.0273 0.0161 0.0166 0.0174 2.6474 3.0433 3.4093 3.7621 4.1084 4.4505 4.7907 5.1289 5.4657 5.8014 6.1363 6.4704 68.47 168.47 269.92 1213.8 1271.2 1324.0 1375.3 1426.3 1477.7 1529.7 1582.4 1635.9 1690.2 1745.3 1801.2 0.1294 0.2938 0.4370 1.5743 1.6376 1.6900 1.7362 1.7784 1.8176 1.8545 1.8894 1.9227 1.9545 1.9849 2.0142 0.0161 0.0166 0.0174 2.3598 2.7247 3.0583 3.3783 3.6915 4.0008 4.3077 4.6128 4.9165 5.2191 5.5209 5.8219 68.52 168.51 269.96 1210.1 1269.0 1322.6 1374.3 1425.5 1477.0 1529.1 1581.9 1635.4 1689.8 1745.0 1800.9 0.1294 0.2938 0.4369 1.5593 1.6242 1.6776 1.7239 1.7663 1.8057 1.8426 1.8776 1.9109 1.9427 1.9732 2.0025 0.0161 0.0166 0.0174 0.0186 2.1504 2.4662 2.6872 2.9410 3.1909 3.4382 3.6837 3.9278 4.1709 4.4131 4.6546 68.66 168.63 270.05 375.10 1263.5 1319.0 1371.6 1423.4 1475.3 1527.6 1580.6 1634.4 1688.9 1744.2 1800.2 0.1294 0.2937 0.4368 0.5667 1.5951 1.6502 1.6976 1.7405 1.7801 1.8173 1.8524 1.8858 1.9177 1.9482 1.9776 0.0161 0.0166 0.0174 0.0186 1.7665 2.0044 2.2263 2.4407 2.6509 2.8585 3.0643 3.2688 3.4721 3.6746 3.8764 68.79 168.74 270.14 375.15 1257.7 1315.2 1368.9 1421.3 1473.6 1526.2 1579.4 1633.3 1688.0 1743.4 1799.6 0.1294 0.2937 0.4307 0.5665 1.5703 1.6274 1.6758 1.7192 1.7591 1.7964 1.8317 1.8652 1.8972 1.9278 1.9572 00161 0.0166 0.0174 0.0186 1.4913 1.7028 1.8970 2.0832 2.2652 2.4445 2.6219 2.7980 2.9730 3.1471 3.3205 68.92 168.85 270.24 375.21 1251.5 1311.4 1366.2 1419.2 1471.8 1524.7 1578.2 1632.3 1687.1 1742.6 1798.9 0.1293 0.2936 0.4367 0.5664 1.5483 1.6077 1.6571 1.7009 1.7411 1.7787 1.8141 1.8477 1.8798 1.9105 1.9400 0.0161 0.0166 0.0174 0.0162 1.2841 1.4763 1.6499 1.8151 1.9759 2.1339 2.2901 2.4450 2.5987 2.7515 2.9037 69.05 168.97 270.33 375.27 1245.1 1307.4 1363.4 1417.0 1470.1 1523.3 1576.9 1631.2 1686.2 1741.9 1798.2 0.1293 0.2935 0.4366 0.5663 1.5282 1.5901 1.6406 1.6850 1.7255 1.7632 1.7988 1.8325 1.8647 1.8955 1.9250 0.0161 0.0166 0.0174 0.0186 0.9919 1.1584 1.3037 1.4397 1.5708 1.6992 1.8256 1.9507 2.0746 2.1977 2.3200 69.32 169.19 270.51 375.38 1231.2 1299.1 1357.7 1412.7 1466.6 1520.3 1574.4 1629.1 1684.4 1740.3 1796.9 0.1292 0.2934 .04364 0.5660 1.4921 1.5595 1.6123 1.6578 1.6690 1.7371 1.7730 1.8069 1.8393 1.8702 1.8998 1. See Notes 1 and 2, Table 1. Press., psia (sat. temp) V 1 H (101.74) S V 5 H (162.24) S V 10 H (193.21) S V 15 H (213.03) S V 20 H (227.96) S V 40 H (267.25) S V 60 H (292.71) S V 80 H (312.04) S V 100 H (327.82) S V 120 H (341.27) S V 140 H (353.04) S V 160 H (363.55) S V 180 H (373.08) S V 200 H (381.80) S V 250 H (400.97) S V 300 H (417.35) S V 350 H (431.73) S V 400 H (444.60) S V 500 H (467.01) S
- 65. Steam 41 / Thermodynamics of Steam 2-5 The Babcock & Wilcox Company Table 3 Properties of Superheated Steam and Compressed Water (Temperature and Pressure) 1 Temperature, F 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 0.0161 0.0166 0.0174 0.0186 0.7944 0.9456 1.0726 1.1892 1.3008 1.4093 1.5160 1.6211 1.7252 1.8284 1.9309 69.58 169.42 270.70 375.49 1215.9 1290.3 1351.8 1408.3 1463.0 1517.4 1571.9 1627.0 1682.6 1738.8 1795.6 0.1292 0.2933 0.4362 0.5657 1.4590 1.5329 1.5844 1.6351 1.6769 1.7155 1.7517 1.7859 1.8184 1.8494 1.8792 0.0161 0.0166 0.0174 0.0186 0.0204 0.7928 0.9072 1.0102 1.1078 1.2023 1.2948 1.3858 1.4757 1.5647 1.6530 69.84 169.65 270.89 375.61 487.93 1281.0 1345.6 1403.7 1459.4 1514.4 1569.4 1624.8 1680.7 1737.2 1794.3 0.1291 0.2932 0.4360 0.5655 0.6889 1.5090 1.5673 1.6154 1.6580 1.6970 1.7335 1.7679 1.8006 1.8318 1.8617 0.0161 0.0166 0.0174 0.0186 0.0204 0.6774 0.7828 0.8759 0.9631 1.0470 1.1289 1.2093 1.2885 1.3669 1.4446 70.11 169.88 271.07 375.73 487.88 1271.1 1339.2 1399.1 1455.8 1511.4 1566.9 1622.7 1678.9 1735.0 1792.9 0.1290 0.2930 0.4358 0.5652 0.6885 1.4869 1.5484 1.5980 1.6413 1.6807 1.7175 1.7522 1.7851 1.8164 1.8464 0.0161 0.0166 0.0174 0.0186 0.0204 0.5869 0.6858 0.7713 0.8504 0.9262 0.9998 1.0720 1.1430 1.2131 1.2825 70.37 170.10 271.26 375.84 487.83 1260.6 1332.7 1394.4 1452.2 1508.5 1564.4 1620.6 1677.1 1734.1 1791.6 0.1290 0.2929 0.4357 0.5649 0.6881 1.4659 1.5311 1.5822 1.6263 1.6662 1.7033 1.7382 1.7713 1.8028 1.8329 0.0161 0.0166 0.0174 0.0186 0.0204 0.5137 0.6080 0.6875 0.7603 0.8295 0.8966 0.9622 1.0266 1.0901 1.1529 70.63 170.33 271.44 375.96 487.79 1249.3 1325.9 1389.6 1448.5 1504.4 1561.9 1618.4 1675.3 1732.5 1790.3 0.1289 0.2928 0.4355 0.5647 0.6876 1.4457 1.5149 1.5677 1.6126 1.6530 1.6905 1.7256 1.7589 1.7905 1.8207 0.0161 0.0166 0.0174 0.0185 0.0203 0.4531 0.5440 0.6188 0.6865 0.7505 0.8121 0.8723 0.9313 0.9894 1.0468 70.90 170.56 271.63 376.08 487.75 1237.3 1318.8 1384.7 1444.7 1502.4 1559.4 1616.3 1673.5 1731.0 1789.0 0.1289 0.2927 0.4353 0.5644 0.6872 1.4259 1.4996 1.5542 1.6000 1.6410 1.6787 1.7141 1.7475 1.7793 1.8097 0.0161 0.0166 0.0174 0.0185 0.0203 0.4016 0.4905 0.5615 0.6250 0.6845 0.7418 0.7974 0.8519 0.9055 0.9584 71.16 170.78 271.82 376.20 487.72 1224.2 1311.5 1379.7 1440.9 1499.4 1556.9 1614.2 1671.6 1729.4 1787.6 0.1288 0.2926 0.4351 0.5642 0.6868 1.4061 1.4851 1.5415 1.5883 1.6298 1.6679 1.7035 1.7371 1.7691 1.7996 0.0161 0.0166 0.0174 0.0185 0.0203 0.3176 0.4059 0.4712 0.5282 0.5809 0.6311 0.6798 0.7272 0.7737 0.8195 71.68 171.24 272.19 376.44 487.65 1194.1 1296.1 1369.3 1433.2 1493.2 1551.8 1609.9 1668.0 1726.3 1785.0 0.1287 0.2923 0.4348 0.5636 0.6859 1.3652 1.4575 1.5182 1.5670 1.6096 1.6484 1.6845 1.7185 1.7508 1.7815 0.0161 0.0166 0.0173 0.0185 0.0202 0.0236 0.3415 0.4032 0.4555 0.5031 0.5482 0.5915 0.6336 0.6748 0.7153 72.21 171.69 272.57 376.69 487.60 616.77 1279.4 1358.5 1425.2 1486.9 1546.6 1605.6 1664.3 1723.2 1782.3 0.1286 0.2921 0.4344 0.5631 0.6851 0.8129 1.4312 1.4968 1.5478 1.5916 1.6312 1.6678 1.7022 1.7344 1.7657 0.0160 0.0165 0.0173 0.0185 0.0202 0.0235 0.2906 0.3500 0.3988 0.4426 0.4836 0.5229 0.5609 0.5980 0.6343 72.73 172.15 272.95 376.93 487.56 615.58 1261.1 1347.2 1417.1 1480.6 1541.1 1601.2 1660.7 1720.1 1779.7 0.1284 0.2918 0.4341 0.5626 0.6843 0.8109 1.4054 1.4768 1.5302 1.5753 1.6156 1.6528 1.6876 1.7204 1.7516 0.0160 0.0165 0.0173 0.0184 0.0201 0.0233 0.2488 0.3072 0.3534 0.3942 0.4320 0.4680 0.5027 0.5365 0.5695 73.26 172.60 273.32 377.19 487.53 614.48 1240.9 1353.4 1408.7 1474.1 1536.2 1596.9 1657.0 1717.0 1777.1 0.1283 0.2916 0.4337 0.5621 0.6834 0.8091 1.3794 1.4578 1.5138 1.5603 1.6014 1.6391 1.6743 1.7075 1.7389 0.0160 0.0165 0.0173 0.0184 0.0200 0.0230 0.1681 0.2293 0.2712 0.3068 0.3390 0.3692 0.3980 0.4259 0.4529 74.57 173.74 274.27 377.82 487.50 612.08 1176.7 1303.4 1386.7 1457.5 1522.9 1585.9 1647.8 1709.2 1770.4 0.1280 0.2910 0.4329 0.5609 0.6815 0.8048 1.3076 1.4129 1.4766 1.5269 1.5703 1.6094 1.6456 1.6796 1.7116 0.0160 0.0165 0.0172 0.0183 0.0200 0.0228 0.0982 0.1759 0.2161 0.2484 0.2770 0.3033 0.3282 0.3522 0.3753 75.88 174.88 275.22 378.47 487.52 610.08 1060.5 1267.0 1363.2 1440.2 1509.4 1574.8 1638.5 1701.4 1761.8 0.1277 0.2904 0.4320 0.5597 0.6796 0.8009 1.1966 1.3692 1.4429 1.4976 1.5434 1.5841 1.6214 1.6561 1.6888 0.0160 0.0165 0.0172 0.0183 0.0199 0.0227 0.0335 0.1588 0.1987 0.2301 0.2576 0.2327 0.3065 0.3291 0.3510 76.4 175.3 275.6 378.7 487.5 609.4 800.8 1250.9 1353.4 1433.1 1503.8 1570.3 1634.8 1698.3 1761.2 0.1276 0.2902 0.4317 0.5592 0.6788 0.7994 0.9708 1.3515 1.4300 1.4866 1.5335 1.5749 1.6126 1.6477 1.6806 0.0160 0.0164 0.0172 0.0183 0.0199 0.0225 0.0307 0.1364 0.1764 0.2066 0.2326 0.2563 0.2784 0.2995 0.3198 77.2 176.0 276.2 379.1 487.6 608.4 779.4 1224.6 1338.2 1422.2 1495.5 1563.3 1629.2 1693.6 1757.2 0.1274 0.2899 0.4312 0.5585 0.6777 0.7973 0.9508 1.3242 1.4112 1.4709 1.5194 1.5618 1.6002 1.6358 1.6691 0.0159 0.0164 0.0172 0.0182 0.0198 0.0223 0.0287 0.1052 0.1463 0.1752 0.1994 0.2210 0.2411 0.2601 0.2783 78.5 177.2 277.1 379.8 487.7 606.9 763.0 1174.3 1311.6 1403.6 1481.3 1552.2 1619.8 1685.7 1750.6 0.1271 0.2893 0.4304 0.5573 0.6760 0.7940 0.9343 1.2754 1.3807 1.4461 1.4976 1.5417 1.5812 1.6177 1.6516 0.0159 0.0164 0.0171 0.0181 0.0196 0.0219 0.0268 0.0591 0.1038 0.1312 0.1529 0.1718 0.1890 0.2050 0.2203 81.1 179.5 279.1 381.2 488.1 604.6 746.0 1042.9 1252.9 1364.6 1452.1 1529.1 1600.9 1670.0 1737.4 0.1265 0.2881 0.4287 0.5550 0.6726 0.7880 0.9153 1.1593 1.3207 1.4001 1.4582 1.5061 1.5481 1.5863 1.6216 0.0159 0.0163 0.0170 0.0180 0.0195 0.0216 0.0256 0.0397 0.0757 0.1020 0.1221 0.1391 0.1544 0.1684 0.1817 83.7 181.7 281.0 382.7 488.6 602.9 736.1 945.1 1188.8 1323.6 1422.3 1505.9 1582.0 1654.2 1724.2 0.1258 0.2870 0.4271 0.5528 0.6693 0.7826 0.9026 1.0176 1.2615 1.3574 1.4229 1.4748 1.5194 1.5593 1.5962 0.0158 0.0163 0.0170 0.0180 0.0193 0.0213 0.0248 0.0334 0.0573 0.0816 0.1004 0.1160 0.1298 0.1424 0.1542 86.2 184.4 283.0 384.2 489.3 601.7 729.3 901.8 1124.9 1281.7 1392.2 1482.6 1563.1 1638.6 1711.1 0.1252 0.2859 0.4256 0.5507 0.6663 0.7777 0.8926 1.0350 1.2055 1.3171 1.3904 1.4466 1.4938 1.5355 1.5735 1. See Notes 1 and 2, Table 1. Press., psia (sat. temp) V 600 H (486.20) S V 700 H (503.08) S V 800 H (518.21) S V 900 H (531.95) S V 1000 H (544.58) S V 1100 H (556.28) S V 1200 H (567.19) S V 1400 H (587.07) S V 1600 H (604.87) S V 1800 H (621.02) S V 2000 H (635.80) S V 2500 H (668.11) S V 3000 H (695.33) S V 3200 H (705.08) S V 3500 H S V 4000 H S V 5000 H S V 6000 H S V 7000 H S
- 66. 2-6 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company Fig. 1 Pressure-enthalpy chart for steam (English units).
- 67. Steam 41 / Thermodynamics of Steam 2-7 The Babcock & Wilcox Company where ms is the mass of steam and mw is the mass of water. The quality is frequently recorded as a percent steam by weight (% SBW) after multiplying by 100%. The mixture enthalpy (H ) (see Note below), entropy (s) and specific volume (v) of a steam-water mixture can then be simply defined as: H H x H Hf g f= + −( ) (2a) s s x s sf g f= + −( ) (2b) v v x v vf g f= + −( ) (2c) where the subscripts f and g refer to properties at satu- rated liquid and vapor conditions, respectively. The difference in a property between saturated liquid and vapor conditions is frequently denoted by the subscript fg; for example, Hfg = Hg – Hf. With these definitions, if the pressure or temperature of a steam-water mix- ture is known along with one of the mixture proper- ties, the quality can then be calculated. For example, if the mixture enthalpy is known, then: x H H Hf fg= −( ) / (3) Engineering problems deal mainly with changes or differences in enthalpy and entropy. It is not neces- sary to establish an absolute zero for these properties, although this may be done for entropy. The Steam Tables indicate an arbitrary zero internal energy and entropy for the liquid state of water at the triple point corresponding to a temperature of 32.018F (0.01C) and a vapor pressure of 0.08865 psi (0.6112 kPa). The triple point is a unique condition where the three states of water (solid, liquid and vapor) coexist at equilibrium. Properties of gases In addition to steam, air is a common working fluid for some thermodynamic cycles.As with steam, well de- fined properties are important in cycle analysis.Air and many common gases used in power cycle applications can usually be treated as ideal gases. An ideal gas is defined as a substance that obeys the ideal gas law: Pv RT= (4) where R is a constant which varies with gas species; P and T are the pressure and temperature, respec- tively. R is equal to the universal gas constant, R [1545 ft lb/lb-mole R (8.3143 kJ/kg mole K)], divided by the molecular weight of the gas. For dry air, R is equal to 53.34 lbf ft/lbm R (0.287 kJ/kg K). Values for other gases are summarized in Reference 3. The ideal gas law is commonly used in a first analysis of a process or cycle because it simplifies calculations. Final calcu- lations often rely on tabulated gas properties for greater accuracy. Tabulated gas properties are available from numer- ous sources. (See References 4 and 5 for examples.) Unfortunately, there is less agreement on gas proper- ties than on those for steam. The United States (U.S.) boiler industry customarily uses 80F (27C) and 14.7 psia (101.35 kPa) as the zero enthalpy of air and com- bustion products. A more general reference is one at- mosphere pressure, 14.696 psia (101.35 kPa), and 77F (25C). This is the standard reference point for heats of formation of compounds from elements in their standard states, latent heats of phase changes and free energy changes. Because of different engineering con- ventions, considerable care must be exercised when using tabulated properties. Selected properties for air and other gases are provided in Chapter 3, Table 3. Conservation of mass and energy Thermodynamic processes are governed by the laws of conservation of mass and conservation of energy ex- cept for the special case of nuclear reactions discussed in Chapter 47. These conservation laws basically state that the total mass and total energy (in any of its forms) can neither be created nor destroyed in a process. In an open flowing power system, where mass continually enters and exits a system such as Fig. 2, these laws can take the forms: Conservation of mass m m m1 2− = ∆ (5) Conservation of energy E E E Q W2 1− + = −∆ (6) Note: To avoid confusion with the symbol for heat trans- fer coefficient, enthalpy (Btu/lb or kJ/kg) is denoted by H in this chapter and the balance of Steam unless specially noted. Enthalpy is frequently denoted by h in thermody- namic texts. Fig. 2 Diagram illustrating thermodynamic processes.
- 68. 2-8 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company where m is the mass flow, ∆m is the change in inter- nal system mass, E is the total energy flowing into or out of the processes, ∆E is the change in energy stored in the system with time, Q is the heat added to the sys- tem, W is the work removed, and the subscripts 1 and 2 refer to inlet and outlet conditions respectively. For steady-state conditions ∆m and ∆E are zero. The conservation of energy states that a balance exists between energy, work, and heat quantities en- tering and leaving the system. This balance of energy flow is also referred to as the first law of thermody- namics. The terms on the left side of Equation 6 rep- resent stored energy entering or leaving the system as part of the mass flows and the accumulation of to- tal stored energy within the system. The terms on the right side are the heat transferred to the system, Q, and work done by the system, W. The stored energy components, represented by the term E, consist of the internally stored energy and the kinetic and poten- tial energy. In an open system, there is work required to move mass into the system and work done by the system to move mass out. In each case, the total work is equal to the product of the mass, the system pres- sure, and the specific volume. Separating this work from other work done by the system and including a breakdown of the stored energy, the energy conser- vation equation becomes: m u Pv V g z m u Pv V g z E Q W c c k 2 2 2 1 2 1 2 2 + + + − + + + + = −∆ (7) where m is the mass, u is the internal stored energy, P is the system pressure, V is the fluid velocity, v is the specific volume, z is the elevation, and Wk is the sum of the work done by the system. In this form, the work terms associated with mass moving into and out of the system (Pv) have been groupedwiththestoredenergycrossingthesystembound- ary. Wk represents all other work done by the system. For many practical power applications, the energy equation can be further simplified for steady-state pro- cesses. Because the mass entering and leaving the sys- tem over any time interval is the same, dividing Equa- tion 7 by the mass (m2 or m1 because they are equal) yields a simple balance between the change in stored energy due to inflow and outflow and the heat and work terms expressed on a unit mass basis. Heat and work expressed on a unit mass basis are denoted q and w,respectively.Theunsteadytermforsystemstoreden- ergy in Equation 7 is then set to zero. This yields the following form of the energy conservation equation: ∆ ∆ ∆ ∆u Pv V g z g g q w c c k+ ( ) + + = − 2 2 (8) Each ∆ term on the left in Equation 8 represents the difference in the fluid property or system charac- teristic between the system outlet and inlet. ∆u is the difference in internally stored energy associated with molecular and atomic motions and forces. Internally stored energy, or simply internal energy, accounts for all forms of energy other than the kinetic and potential energies of the collective molecule masses. This is possible because no attempt is made to absolutely define u. The term ∆(Pv) can be viewed as externally stored energy in that it reflects the work required to move a unit mass into and out of the system. The remaining terms of externally stored energy, ∆(V 2 /2gc) and ∆z, depend on physical aspects of the system. ∆(V 2 /2gc) is the difference in total kinetic energy of the fluid be- tween two reference points (system inlet and outlet). ∆zg/gc represents the change in potential energy due toelevation,whereg isthegravitationalconstant32.17 ft/s2 (9.8 m/s2 ) and gc is a proportionality constant for English units. The value of the constant is obtained from equivalence of force and mass times acceleration: Force mass acceleration = × gc (9) In the English system, by definition, when 1 lb force (lbf) is exerted on a 1 lb mass (lbm), the mass accelerates at the rate of 32.17 ft/s2 . In the SI system, 1 N of force is exerted by 1 kg of mass accelerating at 1 m/s2 . Therefore, the values of gc are: gc = 32 17 2 . lbm ft / lbf s (10a) gc = 1 2 kg m/Ns (10b) Because of the numerical equivalency between g and gc in the English system, the potential energy term in Equation 8 is frequently shown simply as ∆z. When SI unitsareused,thistermisoftenexpressedsimplyas∆zg because the proportionality constant has a value of 1. While many texts use the expression lbf to designate lb force and lbm to designate lb mass, this is not done inthistextbecauseitisbelievedthatitisgenerallyclear simply by using lb.As examples, the expression Btu/lb always means Btu/lb mass, and the expression ft lb/lb always means ft lb force/lb mass. Application of the energy equation requires dimen- sional consistency of all terms and proper conversion constants are inserted as necessary. For example, the terms u and q, usually expressed in Btu/lb or J/kg, may be converted to ft lb/lb or N m/kg when multi- plied by J, the mechanical equivalent of heat. This conversion constant, originally obtained by Joule’s ex- periments between 1843 and 1878, is defined as: J = 778.17 ft lbf / Btu (11a) J = 1 Nm/ J (11b) Particular attention should be given to the sign con- vention applied to heat and work quantities. Originat- ing with the steam engine analysis, heat quantities are defined as positive when entering the system and work (for example, shaft work) is positive when leav- ing the system. Because u and Pv of Equation 8 are system proper- ties, their sum is also a system property. Because these properties of state can not be changed independently of one another and because the combination (u + Pv) appears whenever mass enters or leaves the system,
- 69. Steam 41 / Thermodynamics of Steam 2-9 The Babcock & Wilcox Company it is customary to consider the sum (u + Pv) as a single property H, called enthalpy. H u Pv J= + ( )/ (12) where Pv is divided by J to provide consistent units. In steam applications,H is usually expressed in Btu/ lb or J/kg. The examples in the following section il- lustrate the application of the steady-state open sys- tem energy Equation 7 and the usefulness of enthalpy in the energy balance of specific equipment. Applications of the energy equation Steam turbine To apply the energy equation, each plant compo- nent is considered to be a system, as depicted in Fig. 2. In many cases, ∆z, ∆(V 2 /2gc) and q from throttle (1) to exhaust (2) of the steam turbine are small compared to (H2 − H1). This reduces Equation 8 to: u P v J u P v J w Jk2 2 2 1 1 1+ ( )− − ( ) =/ / / (13a) or H H w Jk2 1− = / (13b) Equation 13 indicates that the work done by the steam turbine, wk/J, is equal to the difference between the en- thalpy of the steam entering and leaving. However, H1 and H2 are seldom both known and further description of the process is required for a solution of most problems. Steam boiler The boiler does no work, therefore wk = 0. Because ∆z and ∆(V 2 /2gc) from the feedwater inlet (1) to the steam outlet (2) are small compared to (H2 – H1), the steady-state energy equation becomes: q H H= −2 1 (14) Based on Equation 14 the heat added, q (positive), in the boiler per unit mass of flow in is equal to the difference between H2 of the steam leaving and H1 of the feedwater entering. Assuming that the pressure varies negligibly through the boiler and the drum pressure is known, Equation 14 can be solved know- ing the temperature of the incoming feedwater. Water flow through a nozzle For water flowing through a nozzle, the change in specific volume is negligible. Commonly the change in elevation, ∆z, the change in internal energy, ∆u, the work done, wk, and the heat added, q, are negli- gible and the energy equation reduces to: V g V g P P vc c2 2 1 2 1 22 2/ /( ) − ( ) = −( ) (15) The increase in kinetic energy of the water is given by Equation 15 for the pressure drop (P1 – P2). If the approach velocity to the nozzle, V1, is zero, Equation 15 becomes: V g P P vc2 1 22= −( ) (16) The quantity (P1 – P2) v is often referred to as the static head. Flow of a compressible fluid through a nozzle In contrast to water flow, when steam, air or other compressible fluid flows through a nozzle, the changes in specific volume and internal energy are not negli- gible. In this case, assuming no change in elevation ∆z, Equation 8 becomes: V g V g H H Jc c2 2 1 2 1 22 2/ /( ) − ( ) = −( ) (17) If the approach velocity, V1, is zero, this further sim- plifies to: V g J H Hc2 1 22= −( ) (18) Fromthis,itisevidentthatthevelocityofacompress- ible fluid leaving a nozzle is a function of its entering andleavingenthalpies.Unfortunately,aswiththesteam turbine, H1 and H2 are seldom both known. Compressor If a compressible fluid moves through an adiabatic compressor (q = 0, a convenient approximation) and the change in elevation and velocity are small com- pared to (H2 – H1), the energy equation reduces to: − = −w J H Hk / 2 1 (19) Note that wk is negative because the compressor does work on the system. Therefore, the net effect of the compressor is expressed as an increase in fluid en- thalpy from inlet to outlet. Pump The difference between a pump and a compressor is that the fluid is considered to be incompressible for the pumping process; this is a good approximation for water. For an incompressible fluid, the specific volume is the same at the inlet and outlet of the pump. If the fluid friction is negligible, then the internal energy changes, ∆u, are set to zero and the energy equation can be expressed as: − = −( )w P P vk 2 1 (20) Because all real fluids are compressible, it is important to know what is implied by the term incompressible. The meaning here is that the isothermal compressibility, kT, given by k v v P T = − 1 δ δ (21) is assumed to be arbitrarily small and approaching zero. Because neither v nor P is zero, δv must be zero and v must be a constant. Also, for isothermal condi- tions (by definition) there can be no change in inter- nal energy, u, due to pressure changes only.
- 70. 2-10 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company Entropy and its application to processes The preceding examples illustrate applications of the energybalanceinproblemswhereafluidisusedforheat transferandshaftwork.Theyalsodemonstratetheuse- fulness of the enthalpy property. However, as was pointed out, H1 and H2 are seldom both known. Addi- tionalinformationisfrequentlyprovidedbythefirstand secondlawsofthermodynamicsandtheirconsequences. The first and second laws of thermodynamics The first law of thermodynamics is based on the energy conservation expressed by Equation 6 and, by convention, relates the heat and work quantities of this equation to internally stored energy, u. Strictly speaking, Equation 6 is a complete form of the first law of thermodynamics. However, it is frequently use- ful to use the steady-state formulation provided in Equation 8 and further simplify this for the special case of 1) no change in potential energy due to grav- ity acting on the mass, and 2) no change in kinetic energy of the mass as a whole. In a closed system where only shaft work is permitted, these simplifying assumptions permit the energy Equation 8 for a unit mass to be reduced to: ∆u q w Jk= − ( )/ (22a) or in differential form du q w Jk= − ( )δ δ / (22b) The first law treats heat and work as being inter- changeable, although some qualifications must apply. All forms of energy, including work, can be wholly con- verted to heat, but the converse is not generally true. Given a source of heat coupled with a heat-work cycle, such as heat released by high temperature combus- tion in a steam power plant, only a portion of this heat can be converted to work. The rest must be rejected to an energy sink, such as the atmosphere, at a lower temperature. This is essentially the Kelvin statement of the second law of thermodynamics. It can also be shown that it is equivalent to the Clausius statement wherein heat, in the absence of external assistance, can only flow from a hotter to a colder body. Concept and definition of entropy Heat flow is a function of temperature difference. If a quantity of heat is divided by its absolute tem- perature, the quotient can be considered a type of dis- tribution property complementing the intensity fac- tor of temperature. Such a property, proposed and named entropy by Clausius, is widely used in ther- modynamics because of its close relationship to the second law. Rather than attempt to define entropy (s) in an ab- solute sense, consider the significance of differences in this property given by: S S S q T 2 1 1 2 − = = ×∫ ∆ δ rev total system mass (23) where ∆S = change in entropy, Btu/R (J/K) qrev = reversible heat flow between thermodynamic equilibrium states 1 and 2 of the system, Btu/ lb (J/kg) T = absolute temperature, R (K) Entropy is an extensive property, i.e., a quantity of entropy, S, is associated with a finite quantity of mass, m. If the system is closed and the entire mass under- goes a change from state 1 to 2, an intensive property s is defined by S/m. The property s is also referred to as entropy, although it is actually specific entropy. If the system is open as in Fig. 2, the specific entropy is calculated by dividing by the appropriate mass. Use of the symbol δ instead of the usual differen- tial operator d is a reminder that q depends on the process and is not a property of the system (steam). δq represents only a small quantity, not a differen- tial. Before Equation 23 can be integrated, qrev must be expressed in terms of properties, and a reversible path between the prescribed initial and final equilib- rium states of the system must be specified. For ex- ample, when heat flow is reversible and at constant pressure, qrev = cpdT. This may represent heat added reversibly to the system, as in a boiler, or the equiva- lent of internal heat flows due to friction or other irreversibilities.Inthesetwocases,∆sisalwayspositive. The same qualifications for δ hold in the case of thermodynamic work. Small quantities of w similar in magnitude to differentials are expressed as δw. Application of entropy to a reversible process Reversible thermodynamic processes exist in theory only; however, they serve an important function of de- fining limiting cases for heat flow and work processes. The properties of a system undergoing a reversible pro- cess are constrained to be homogeneous because there arenovariationsamongsubregionsofthesystem.More- over, during interchanges of heat or work between a system and its surroundings, only corresponding poten- tial gradients of infinitesimal magnitude may exist. All actual processes are irreversible. To occur, they must be under the influence of a finite potential dif- ference. A temperature difference supplies this drive and direction for heat flow. The work term, on the other hand, is more complicated, because there are as many different potentials (generalized forces) as there are forms of work. However, the main concern here is expansion work for which the potential is clearly a pressure difference. Regardless of whether a process is to be considered reversible or irreversible, it must have specific begin- ning and ending points (limits) in order to be evalu- ated.Toapplythefirstandsecondlaws,thelimitsmust be equilibrium states. Nonequilibrium thermodynam- ics is beyond the scope of this text. Because the limits of real processes are to be equilibrium states, any pro- cess can be approximated by a series of smaller revers- ible processes starting and ending at the same states as the real processes. In this way, only equilibrium conditions are considered and the substitute processes can be defined in terms of the system properties. The
- 71. Steam 41 / Thermodynamics of Steam 2-11 The Babcock & Wilcox Company following lists the reversible processes for heat flow and work: Reversible Heat Flow Reversible Work Constant pressure, dP = 0 Constant pressure, dP = 0 Constant temperature,dT = 0 Constant temperature,dT = 0 Constant volume, dv = 0 Constant entropy, ds = 0 w = 0 q = 0 Thequalificationoftheseprocessesisthateachdescribes a path that has a continuous functional relationship on coordinate systems of thermodynamic properties. A combined form of the first and second laws is ob- tained by substituting δ qrev = Tds for δq in Equation 22b, yielding: du Tds wk= − δ (24) Because only reversible processes are to be used,δw should also be selected with this restriction. Revers- ible work for the limited case of expansion work can be written: δ w Pdvrev( ) = (25) In this case, pressure is in complete equilibrium with external forces acting on the system and is related to v through an equation of state. Substituting Equation 25 in 24, the combined ex- pression for the first and second law becomes: du Tds Pdv= − (26) Equation 26, however, only applies to a system in which the reversible work is entirely shaft work. To modify this expression for an open system in which flow work d(Pv) is also present, the quantity d(Pv) is added to the left side of Equation 25 and added as (Pdv + vdP) on the right side. The result is: du d Pv Tds Pdv Pdv vdP+ ( ) = − + + (27a) or dH Tds vdP= + (27b) The work term vdP in Equation 27 now represents re- versible shaft work in an open system, expressed on a unit mass basis. Because Tds in Equation 26 is equivalent to δq, its value becomes zero under adiabatic or zero heat trans- fer conditions (δq = 0). Because T can not be zero, it follows that ds = 0 and s is constant. Therefore, the maximum work from stored energy in an open sys- tem during a reversible adiabatic expansion is ∫ vdP at constant entropy. The work done is equal to the decrease in enthalpy. Likewise for the closed system, the maximum expansion work is –∫ Pdv at constant entropy and is equal to the decrease in internal en- ergy. These are important cases of an adiabatic isen- tropic expansion. Irreversible processes All real processes are irreversible due to factors such as friction, heat transfer through a finite temperature difference, and expansion through a process with a finite net force on the boundary. Real processes can be solved approximately, however, by substituting a series of reversible processes. An example of such a substitution is illustrated in Fig. 3, which represents the adiabatic expansion of steam in a turbine or any gas expanded from P1 to P2 to produce shaft work. T1, P1 and P2 are known. The value of H1 is fixed by T1 and P1 for a single-phase condition (vapor) at the in- let. H1 may be found from the Steam Tables, a T-s dia- gram (Fig. 3) or, more conveniently, from an H-s (Mol- lier) diagram, shown in the chapter frontispiece. From the combined first and second laws, the maximum en- ergy available for work in an adiabatic system is (H1 − H3), as shown in Fig. 3, where H3 is found by the adiabatic isentropic expansion (expansion at constant entropy) from P1 to P2. A portion of this available en- ergy, usually about 10 to 15%, represents work lost (wL) due to friction and form loss, limiting ∆H for shaft work to (H1 − H2). The two reversible paths used to arrive at point b in Fig. 3 (path a to c at constant en- tropy, s, and path c to b at constant pressure) yield the following equation: H H H H H H1 3 2 3 1 2−( ) − −( ) = − (28) Point b, identified by solving for H2, now fixes T2; v1 and v2 are available from separate tabulated values of physical properties. Note that ∆H 2-3 can be found from: ∆H Tds2 3 3 2 − = ∫ (29) or, graphically, the area on the T-s diagram (Fig. 3) under the curve P2 from points c to b. Areas bounded by reversible paths on the T-s diagram in general rep- Fig. 3 Irreversible expansion, state a to state b.
- 72. 2-12 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company resent q (heat flow per unit mass) between the sys- tem and its surroundings. However, the path a to b is irreversible and the area under the curve has no sig- nificance. The area under path c to b, although it has the form of a reversible quantity q, does not represent heat added to the system but rather its equivalent in internal heat flow.Asimilar situation applies to the re- lationship between work and areas under reversible paths in a pressure-volume equation of state diagram. Because of this important distinction between revers- ible and irreversible paths, care must be exercised in graphically interpreting these areas in cycle analysis. Returning to Fig. 3 and the path a to b, wL was con- sidered to be a percentage of the enthalpy change along the path a to c. In general, the evaluation should be handled in several smaller steps (Fig. 4) for the fol- lowing reason. Point b has a higher entropy than point c and, if expansion to a pressure lower than P2 (Fig. 3) is possible, the energy available for this additional expansion is greater than that at point c. In other words, a portion of wL (which has the same effect as heat added to the system) for the first expansion can be recovered in the next expansion or stage. This is the basis of the reheat factor used in analyzing ex- pansions through a multistage turbine. Since the pres- sure curves are divergent on an H-s or T-s diagram, the sum of the individual ∆Hs values (isentropic ∆H) for individual increments of ∆P (or stages in an irre- versible expansion) is greater than that of the revers- ible ∆Hs between the initial and final pressures (Fig. 4). Therefore the shaft work that can be achieved is greater than that calculated by a simple isentropic expansion between the two pressures. Principle of entropy increase Although entropy has been given a quantitative meaning in previous sections, there are qualitative aspects of this property which deserve special empha- sis. An increase in entropy is a measure of that por- tion of process heat which is unavailable for conver- sion to work. For example, consider the constant pres- sure reversible addition of heat to a working fluid with the resulting increase in steam entropy. The minimum portion of this heat flow which is unavailable for shaft work is equal to the entropy increase multiplied by the absolute temperature of the sink to which a part of the heat must be rejected (in accordance with the sec- ond law). However, because a reversible addition of heat is not possible, incremental entropy increases also occur due to internal fluid heating as a result of tem- perature gradients and fluid friction. Even though the net entropy change of any por- tion of a fluid moving through a cycle of processes is always zero because the cycle requires restoration of all properties to some designated starting point, the sum of all entropy increases has a special significance. These increases in entropy, less any decreases due to recycled heat within a regenerator, multiplied by the appropriate sink absolute temperature (R or K) are equal to the heat flow to the sink. In this case, the net entropy change of the system undergoing the cycle is zero, but there is an entropy increase of the surround- ings. Any thermodynamic change that takes place, whether it is a stand alone process or cycle of processes, results in a net entropy increase when both the sys- tem and its surroundings are considered. Cycles To this point, only thermodynamic processes have been discussed with minor references to the cycle. The next step is to couple processes so heat may be con- verted to work on a continuous basis. This is done by selectively arranging a series of thermodynamic pro- cesses in a cycle forming a closed curve on any sys- tem of thermodynamic coordinates. Because the main interest is steam, the following discussion emphasizes expansion or Pdv work. This relies on the limited dif- ferential expression for internal energy, Equation 26, and enthalpy, Equation 27. However, the subject of thermodynamics recognizes work as energy in tran- sit under any potential other than differential tem- perature and electromagnetic radiation. Carnot cycle Sadi Carnot (1796 to 1832) introduced the concept of the cycle and reversible processes. The Carnot cycle is used to define heat engine performance as it con- stitutes a cycle in which all component processes are reversible. This cycle, on a temperature-entropy dia- gram, is shown in Fig. 5a for a gas and in Fig. 5b for a two-phase saturated fluid. Fig. 5c presents this cycle for a nonideal gas, such as superheated steam, on Mollier coordinates (entropy versus enthalpy). Referring to Fig. 5, the Carnot cycle consists of the following processes: 1. Heat is added to the working medium at constant temperature (dT = 0) resulting in expansion work Fig. 4 Three-stage irreversible expansion – ∆Hs1 + ∆Hs2 + ∆Hs3 > ∆Hsac.
- 73. Steam 41 / Thermodynamics of Steam 2-13 The Babcock & Wilcox Company and changes in enthalpy. (For an ideal gas, changes in internal energy and pressure are zero and, therefore, changes in enthalpy are zero.) 2. Adiabatic isentropic expansion (ds = 0) occurs with expansion work and an equivalent decrease in en- thalpy. 3. Heat is rejected to the surroundings at a constant temperature and is equivalent to the compression work and any changes in enthalpy. 4. Adiabatic isentropic compression occurs back to the starting temperature with compression work and an equivalent increase in enthalpy. This cycle has no counterpart in practice. The only way to carry out the constant temperature processes in a one-phase system would be to approximate them through a series of isentropic expansions and constant pressure reheats for heat addition, and isentropic com- pressionswithaseriesofintercoolersforheatrejections. Another serious disadvantage of a Carnot gas engine would be the small ratio of net work to gross work (net work referring to the difference between the expansion work and the compression work, and gross work being expansion work). Even a two-phase cycle, such as Fig. 5b, would be subject to the practical mechanical difficul- ties of wet compression and, to a lesser extent, wet ex- pansion where a vapor-liquid mixture exists. Nevertheless, the Carnot cycle illustrates the basic principlesofthermodynamicsand,becausetheprocesses are reversible, the Carnot cycle offers the maximum thermodynamicefficiencyattainablebetweenanygiven temperatures of heat source and sink. The efficiency of the cycle is defined as the ratio of the net work output to the total heat input. Various texts refer to this ratio as either thermodynamic efficiency, thermal efficiency, or simply efficiency. Using the T-s diagram for the Carnot cycle shown in Fig. 5a, the thermodynamic efficiency depends solely on the temperatures at which heat addi- tion and rejection occur: η = − = − T T T T T 1 2 1 2 1 1 (30) where η =thermodynamic efficiency of the conversion from heat into work T1 =absolute temperature of heat source, R (K) T2 =absolute temperature of heat sink, R (K) The efficiency statement of Equation 30 can be ex- tended to cover all reversible cycles where T1 and T2 are defined as mean temperatures found by dividing the heat added and rejected reversibly by ∆s. For this reason, all reversible cycles have the same efficiencies when considered between the same mean tempera- ture limits of heat source and heat sink. Rankine cycle Early thermodynamic developments were centered around the performance of the steam engine and, for comparison purposes, it was natural to select a revers- ible cycle which approximated the processes related to its operation. The Rankine cycle shown in Fig. 6, proposed independently by Rankine and Clausius,Fig. 5 Carnot cycles.
- 74. 2-14 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company meets this objective.All steps are specified for the sys- tem only (working medium) and are carried out re- versibly as the fluid cycles among liquid, two-phase and vapor states. Liquid is compressed isentropically from points a to b. From points b to c, heat is added reversibly in the compressed liquid, two-phase and finally superheat states. Isentropic expansion with shaft work output takes place from points c to d and unavailable heat is rejected to the atmospheric sink from points d to a. The main feature of the Rankine cycle is that com- pression (pumping) is confined to the liquid phase, avoiding the high compression work and mechanical problems of a corresponding Carnot cycle with two- phase compression. This part of the cycle, from points a to b in Fig. 6, is greatly exaggerated, because the difference between the saturated liquid line and point b (where reversible heat addition begins) is too small to show in proper scale. For example, the temperature rise with isentropic compression of water from a satu- ration temperature of 212F (100C) and one atmo- sphere to 1000 psi (6.89 MPa) is less than 1F (0.6C). If the Rankine cycle is closed in the sense that the fluid repeatedly executes the various processes, it is termed a condensing cycle. Although the closed, con- densing Rankine cycle was developed to improve steam engine efficiency, a closed cycle is essential for any toxic or hazardous working fluid. Steam has the important advantage of being inherently safe. How- ever, the close control of water chemistry required in high pressure, high temperature power cycles also favors using a minimum of makeup water. (Makeup is the water added to the steam cycle to replace leak- age and other withdrawals.) Open steam cycles are still found in small units, some special processes, and heating load applications coupled with power. The con- densate from process and heating loads is usually re- turned to the power cycle for economic reasons. The higher efficiency of the condensing steam cycle is a result of the pressure-temperature relationship between water and its vapor state, steam. The lowest temperature at which an open, or noncondensing, steam cycle may reject heat is approximately 212F (100C), the saturation temperature corresponding to atmospheric pressure of 14.7 psi (101.35 kPa). The pressure of the condensing fluid can be set at or be- low atmospheric pressure in a closed cycle. This takes advantage of the much lower sink temperature avail- able for heat rejection in natural bodies of water and the atmosphere. Therefore, the condensing tempera- ture in the closed cycle can be 100F (38C) or lower. Fig. 7 illustrates the difference between an open and closed Rankine cycle. Both cycles are shown with nonideal expansion processes. Liquid compression takes place from points a to b and heat is added from points b to c. The work and heat quantities involved in each of these processes are the same for both cycles. Expansion and conversion of stored energy to work take place from points c to d´ for the open cycle and from c to d for the closed cycle. Because this process is shown for the irreversible case, there is internal fluid heating and an entropy increase. From points d´ to a, and d to a, heat is rejected in order to condense the steam. Because this last portion of the two cycles is shown as reversible, the shaded areas are proportional to the rejected heat. The larger amount of rejected heat for the open cycle is evident and is directly re- lated to the lower amount of work that can be done by the expansion process. Regenerative Rankine cycle The reversible cycle efficiency given by Equation 30, where T2 and T1 are mean absolute temperatures for rejecting and adding heat respectively, indicates only three choices for improving ideal cycle efficiency: decreasing T2, increasing T1, or both. Little can be done to reduce T2 in the Rankine cycle because of the limitations imposed by the temperatures of available rejected heat sinks in the general environment. Some T2 reduction is possible by selecting variable condenser pressures for very large units with two or more ex- haust hoods, because the lowest temperature in the condenser is set by the lowest temperature of the cool- ing water. On the other hand, there are many ways to increase T1 even though the steam temperature may be limited by high temperature corrosion and al- lowable stress properties of the material. One early improvement to the Rankine cycle was the adoption ofregenerativefeedwaterheating.Thisisdone by extracting steam from various stages in the turbine to heat the feedwater as it is pumped from the bottom of the condenser (hot well) to the boiler economizer. Fig. 8 is a diagram of a widely used supercritical pressure steam cycle showing the arrangement of vari- ous components including the feedwater heaters. This cycle also contains one stage of steam reheat, which is another method of increasing the mean T1. Regard- less of whether the cycle is high temperature, high pressure or reheat, regeneration is used in all mod- ern condensing steam power plants. It improves cycle efficiency and has other advantages, including lower volume flow in the final turbine stages and a conve- nient means of deaerating the feedwater. In the power plant heat balances shown in Fig. 8 and later in Fig. 10, several parameters require definition:Fig. 6 Temperature-entropy diagram of the ideal Rankine cycle.
- 75. Steam 41 / Thermodynamics of Steam 2-15 The Babcock & Wilcox Company DC: In the feedwater heater blocks, this parameter is the drain cooler approach temperature or the difference between the shell-side condensate outlet (drain) temperature and the feedwater inlet temperature. TD: In the feedwater heater blocks, this parameter is the terminal temperature difference or the differencebetweentheshell-sidesteaminlettem- perature and the feedwater outlet temperature. P: In the feedwater heater blocks, this parameter is the nominal shell-side pressure. The temperature-entropy diagram of Fig. 9 for the steam cycle of Fig. 8 illustrates the principle of regenera- tioninwhichthemeantemperaturelevelisincreasedfor heat addition. Instead of heat input starting at the hot well temperature of 101.1F (38.4C), the water entering the boiler economizer has been raised to 502F (261C) by the feedwater heaters. Fig. 9 also shows that the mean temperature level for heat addition is increased by reheating the steam after a portion of the expansion has taken place. Be- cause maximum temperatures are limited by physi- cal or economic reasons, reheating after partial expan- sion of the working fluid is also effective in raising the average T1. The hypothetical case of an infinite num- ber of reheat and expansion stages approaches a con- stant temperature heat addition of the Carnot cycle, at least in the superheat region. It would appear ben- eficial to set the highest temperature in the superheat reheat stage at the temperature limit of the working medium or its containment. However, merely increas- ing T1 may not improve efficiency. If the entropy in- crease accompanying reheat causes the final expan- sion process to terminate in superheated vapor, the mean temperature for heat rejection, T2, has also been increased unless the superheat can be extracted in a regenerative heater, adding heat to the boiler feedwater. Such a regenerative heater would have to operate at the expense of the very effective cycle. All of these factors, plus component design limitations, must be considered in a cycle analysis where the ob- jective is to optimize the thermodynamic efficiency within the physical and economic constraints of the equipment. In addition, there are constraints imposed by the economics of fuel selection and the environmen- tal impacts of fuel combustion that impact the design of the boiler/turbine regenerative cycle. Overall cycle characteristics, including efficiency, can also be illus- trated by plotting the cycle on a Mollier chart. (See chapter frontispiece and Fig. 4.) The procedure used in preparing Fig. 9 deserves special comment because it illustrates an important function of entropy. All processes on the diagram rep- resent total entropies divided by the high pressure steam flow rate. Total entropies at any point of the cycle are the product of the mass flowing past that point in unit time and the entropy per pound (specific entropy) corresponding to the pressure, temperature, and state of the steam. Specific entropy values are pro- vided by the Steam Tables such as those provided here in Tables 1, 2, and 3. If a point falls in the two-phase region, entropy is calculated in the same manner as enthalpy. That is, the value for evaporation is multi- plied by the steam quality (fraction of uncondensed steam) and added to the entropy value of water at saturation conditions corresponding to the pressure at that point in the system. Because there are different flow rates for the vari- ous cycle processes, small sections of individual T-s diagrams are superimposed in Fig. 9 on a base dia- gram that identifies saturated liquid and vapor pa- rameters. However, the saturation parameters can only be compared to specific points on the T-s diagram. These points correspond to the parts of the cycle rep- resenting heat addition to high pressure steam and the expansion of this steam in a high pressure tur- bine. In these parts of the cycle, the specific entropy of the fluid and the value plotted in the diagram are the same. At each steam bleed point of the intermedi- Fig. 7 Rankine cycles.
- 76. 2-16 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company ate and low pressure turbine, the expansion line should show a decrease in entropy due to reduced flow entering the next turbine stage. However, for conve- nience, the individual step backs in the expansion lines have been shifted to the right to show the re- heated steam expansion as one continuous process. Feedwater heating through the regenerators and compression by the pumps (represented by the zigzag lines in Fig. 9) result in a net entropy increase. How- ever, two factors are involved in the net increase, an entropyincreasefromtheheataddedtothefeedwaterand adecreaseresultingfromcondensingandcoolingthebleed steam and drain flows from higher pressure heaters. Consider an example in which the feedwater heater justbeforethedeaeratingheaterincreasesthetempera- ture of a 3,661,954 lb/h feedwater from 203.0 to 239.5F. From Table 1, this increases the enthalpy, H, of the feedwaterfrom171.2to208.0andincreasestheentropy, s, from 0.2985 to 0.3526. The total entropy increase per lb of high pressure steam flowing at 4,813,813 lb/h is: s s m m 2 1 0 3526 0 2985 3 661 954 4 813 −( ) = −( ) feedwater HPsteam . . , , , ,8813 0 0412= . Btu/lb F (31) The feedwater temperature rises 36.5F and the to- tal heat absorbed is: H H m2 1 208 0 171 2 3 661 954 134 759 907 −( ) = −( ) = feedwater Btu/h . . , , , , (32) On the heat source side of the balance, 132,333 lb/ h of steam are bled from the low pressure turbine at 28.8 psig. This steam has an enthalpy of 1200.3 and Fig. 8 Supercritical pressure, 3500 psig turbine cycle heat balance (English units).
- 77. Steam 41 / Thermodynamics of Steam 2-17 The Babcock & Wilcox Company an entropy of 1.7079. The steam is desuperheated and condensed according to the following equation: H H m 2 1 1200 3 134 759 = − = − heat absorbed by feedwater LP steam . , ,9907 132 333 182 0 , .= Btu/lb (33) Interpolating Table 1, the low pressure steam is cooled to 213.0F at Hf = 181.2 Btu/lb. The correspond- ing entropy of the heater drain is 0.3136 Btu/lb F. Therefore, the entropy decrease is: s s m m 1 2 1 7079 0 3136 132 333 −( ) = −( ) LP steam HP steam 4,813,81 . . , 33 Btu/lb F= 0 0383. (34) This heater shows a net entropy increase of 0.0412 − 0.0383 = 0.0029 Btu/lb F. Recall that an increase in entropy represents heat energy that is unavailable for conversion to work. Therefore, the net entropy increase through the feedwater heater is the loss of available energy that can be attributed to the pressure drop required for flow and temperature difference. These differences are necessary for heat transfer. The quantity of heat ren- dered unavailable for work is the product of the en- tropy increase and the absolute temperature of the sink receiving the rejected heat. Available energy From the previous feedwater heater example, there is a derived quantity, formed by the product of the corresponding entropy and the absolute temperature of the available heat sink, which has the nature of a property. The difference between H (enthalpy) and Tos is another derived quantity called available energy. e H T so= − (35) where e = available energy, Btu/lb (kJ/kg) H = enthalpy, Btu/lb (kJ/kg) To = sink temperature, R (K) s = entropy, Btu/lb R (kJ/kg K) Available energy is not a property because it can not be completely defined by an equation of state; rather, it is dependent on the sink temperature. How- ever, a combined statement of the first and second laws of thermodynamics indicates that the difference in the available energy between two points in a reversible process represents the maximum amount of work (on a unitmassbasis)thatcanbeextractedfromthefluiddue to the change of state variables H and s between the two points. Conceptually then, differences in the value of Tos represent energy that is unavailable for work. The concept of available energy is useful in cycle analysis for optimizing the thermal performance of various components relative to overall cycle efficiency. In this way small, controllable changes in availabil- ity may be weighed against larger, fixed unavailable heat quantities which are inherent to the cycle. By comparing actual work to the maximum reversible work calculated from differences in available energy, the potential for improvement is obtained. Rankine cycle efficiency As with the Carnot cycle efficiency, the Rankine cycle efficiency (η) is defined as the ratio of the net work (Wout – Win) produced to the energy input (Qin): η = −Wout in in W Q (36) For the simple cycle shown in Fig. 7, the work terms and the energy input are defined as: W m H Ht w c dout = −( )η (37) W m H H m v P P w b a p w a b a p in = −( ) ≅ −( ) / / η η (38) Q m H Hw c bin = −( ) (39) where Ha – d are the enthalpies defined in Fig. 7, mw is the water flow rate, Pa – b are the pressures at points a Fig. 9 Steam cycle for fossil fuel temperature-entropy diagram – single reheat, seven-stage regenerative feedwater heating – 3500 psig, 1000F/1000F steam.
- 78. 2-18 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company and b, va is the water specific volume at point a, while ηt and ηp are the efficiencies of the turbine and boiler feed pump respectively. Substituting Equations 37, 38 and 39 into Equa- tion 36 and canceling the mass flow rate, mw , which is the same in all three cases provide the following overall thermodynamic efficiency (ηth): η η η th t c d a b a p c b H H v P P H H = −( )− −( ) −( ) / (40) In even a simple power producing facility using the Rankine cycle, several other factors must also be con- sidered: 1. Not all of the chemical energy supplied to the boiler from the fuel is absorbed by the steam – typically 80 to 85% of the energy input is absorbed. 2. A variety of auxiliary equipment such as fans, soot- blowers, environmental protection systems, water treatment equipment, and fuel handling systems, among others use part of the power produced. 3. Electrical generators and motors are not 100% ef- ficient. Incorporating these general factors into Equation 40 for a simple power cycle yields the net generating efficiency, ηnet: η η η η η ηnet aux = −( )− −( ) − −( ) g t c d b a p m c b b H H v P P w H H 1 / / (41) where waux is the auxiliary power usage, ηb is the boiler efficiency, while ηg and ηm are the electrical generator and motor efficiencies, both typically 0.98 to 0.99. The gross power efficiency can be evaluated from Equa- tion 41 with waux set at zero. The evaluation of efficiency in modern high pres- sure steam power systems is more complex. Provision in the evaluation must be made for steam reheat or Fig. 10 Subcritical pressure, 2400 psig turbine cycle heat balance (English units).
- 79. Steam 41 / Thermodynamics of Steam 2-19 The Babcock & Wilcox Company double reheat, and turbine steam extraction for regen- erative feedwater heating, among others. This evalu- ation is based upon a steam turbine heat balance or steam cycle diagram such as that shown in Fig. 8 for a 3500 psig (24.13 MPa) supercritical pressure fossil fuel-fired unit, or Fig. 10 for a 2400 psig (16.55 MPa) subcritical pressure unit. The subcritical pressure unit shown has a single reheat, six closed feedwater heat- ers and one open feedwater heater. Rankine cycle heat rate Heat rate is a term frequently used to define vari- ous power plant efficiencies. If the electrical genera- tion used is the net output after subtracting all auxil- iary electrical power needs, then Equation 42 defines the net heat rate using English units. If the auxiliary electrical usage is not deducted, Equation 42 defines the gross heat rate. Heat rate Total fuel heat input (Btu/h) Electrical generati = oon (kW) (42) Heat rate is directly related to plant efficiency, η, by the following relationships: Net heat rate Btu/kWh net = 3412 14. η (43a) Gross heat rate Btu/kWh gross = 3412 14. η (43b) Steam cycle in a nuclear plant Fig. 11 illustrates a Rankine cycle whose thermal energy source is a pressurized water nuclear steam system. High pressure cooling water is circulated from a pressurized water reactor to a steam generator. Therefore, heat produced by the fission of enriched uranium in the reactor core is transferred to feedwater supplied to the steam generator which, in turn, supplies steam for the turbine. The steam gen- erators of a nuclear plant are shell and tube heat ex- changers in which the high pressure reactor coolant flows inside the tubes and lower pressure feedwater is boiled outside of the tubes. For the pressurized wa- ter reactor system, the Rankine cycle for power genera- tiontakesplaceentirelyinthenonradioactivewaterside (secondary side) that is boiling and circulating in the steam system; the reactor coolant system is simply the heat source for the power producing Rankine cycle. The steam pressure at the outlet of the steam gen- erator varies among plants due to design differences and ranges from 700 to 1000 psi (4.83 to 6.90 MPa). Nominally, a nuclear steam system by The Babcock & Wilcox Company (B&W) with a once-through steam generator provides slightly superheated steam at 570F (299C) and 925 psi (6.38 MPa). Steam flow from the once-through generator reaches the high pressure turbine at about 900 psi (6.21 MPa) and 566F (297C). More prevalent are nuclear steam systems that use a recirculating steam generator. In this design, feedwater is mixed with saturated water coming from the steam generator’s separators before entering the tube bundle and boiling to generate steam. This boil- ing steam-water mixture reaches a quality of 25 to 33% at the end of the heat exchanger and enters the steam generator’s internal separators. The separators return the liquid flow to mix with incoming feedwater and direct the saturated steam flow to the outlet of the steam generator. Inevitably, a small amount of mois- ture is formed by the time the steam flow reaches the high pressure turbine. Even though the once-through steam generator is capable of providing superheated steam to the turbine, the pressure and temperature limitations of nuclear plant components must be observed. As a result, the expansion lines of the power cycle lie largely in the wet steam region. This is essentially a saturated or nearly saturated steam cycle. The expansion lines for the nuclear steam system shown in Fig. 11 (featuring a once-through steam generator) are plotted on an enthalpy-entropy or H-s diagram in Fig. 12. The superheated steam is delivered to the turbine at a temperature only 34F (19C) above saturation.Al- though this superheat improves cycle efficiency, large quantities of condensed moisture still exist in the tur- bine. For example, if expansion from the initial con- ditions shown in Fig. 12 proceed down one step to the back pressure of 2.0 in. Hg [approximately 1.0 psi (6.9 kPa)] the moisture formed would exceed 20%.At best, steam turbines can accommodate about 15% moisture content. High moisture promotes erosion, especially in the turbine blades, and reduces expansion efficiency. In addition to mechanical losses from momentum exchanges between slow moving condensate particles, high velocity steam and rotating turbine blades, there is also a thermodynamic loss resulting from the con- densate in the turbine. The expansion of the steam is too rapid to permit equilibrium conditions to exist when condensation is occurring. Under this condition, the steam becomes subcooled, retaining a part of the avail- able energy which would be released by condensation. Fig. 11 indicates two methods of moisture removal used in this cycle and Fig. 12 shows the effect of this moisture removal on the cycle. After expansion in the high pressure turbine, the steam passes through a moisture separator, which is a low pressure drop sepa- rator external to the turbine. After passing through this separator, the steam is reheated in two stages, first by bleed steam and then by high pressure steam to 503F (262C), before entering the low pressure turbine. Here a second method of moisture removal, in which grooves on the back of the turbine blades drain the moisture from several stages of the low pressure tur- bine, is used. The separated moisture is carried off with the bleed steam. Internal moisture separation reduces erosion and affords a thermodynamic advantage due to the diver- gence of the constant pressure lines with increasing enthalpy and entropy. This can be shown by the use of available energy, e, as follows. Consider the mois- ture removal stage at 10.8 psi in Fig. 12. After expan- sion to 10.8 psi, the steam moisture content is 8.9%. Internal separation reduces this to approximately 8.2%. Other properties are as follows:
- 80. 2-20 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company End of After Moisture Expansion Extraction P 10.8 psi 10.8 psi H 1057.9 Btu/lb 1064.7 Btu/lb s 1.6491 Btu/lb F 1.6595 Btu/lb F To (at 2 in. Hg) 560.8 R 560.8 R Tos 924.8 Btu/lb 930.7 Btu/lb e = H – Tos 133.1 Btu/lb 134.0 Btu/lb The increase in available energy, ∆e, due to moisture extraction is 134.0 − 133.1 = 0.9 Btu/lb of steam. The values of moisture and enthalpy listed are given for equilibrium conditions without considering the nonequilibrium effects that are likely to exist within the turbine. These effects can be empirically accounted for by the isentropic efficiency of the expan- sion line. An important point to observe from this ex- ample is the need to retain a sufficient number of sig- nificant digits in the calculations. Frequently, the evaluationofthermodynamicprocessesresultsinwork- ing with small differences between large numbers. Supercritical steam cycles As previously pointed out, cycle thermodynamic ef- ficiency is improved by increasing the mean tempera- ture of the heat addition process. This temperature can be increased when the feedwater pressure is increased because the boiler inlet pressure sets the saturation temperature in the Rankine cycle. If the pressure is increased above the critical point of 3200.1 psi (22.1 MPa), heat addition no longer results in the typical boiling process in which there is an interface between the steam and water. Rather, the fluid can be treated as a single phase as it passes through the process where properties change from those of a liquid to a gas without an interface. Additional heating super- heats the steam and expansion in a first stage (high pressure) turbine can occur entirely in a superheated state. This is referred to as a supercritical steam cycle, originally given the name Benson Super Pressure Plant when first proposed in the 1920s. The first com- mercial unit featuring the supercritical cycle and two stages of reheat was placed in service in 1957. The steam cycle of a typical supercritical plant is shown in Fig. 13. In this T-s diagram, point a repre- sents the outlet of the condensate pump. Between points a and b, the condensate is heated in the low pressure feedwater heater using saturated liquid and/ or steam extracted from the steam turbines. Point b corresponds to the high pressure feedwater pump in- let. The pump increases the pressure to 4200 psi (28.96 MPa), obtaining conditions of point c. Between points Fig. 11 Power cycle diagram, nuclear fuel: reheat by bleed and high pressure steam, moisture separation, and six-stage regenerative feedwater heating – 900 psi, 566F/503F (6.21 MPa, 297C/262C) steam.
- 81. Steam 41 / Thermodynamics of Steam 2-21 The Babcock & Wilcox Company c and d, additional feedwater heating is provided by steam extracted from the high and low pressure tur- bines. Point d corresponds to the supercritical boiler inlet. Due to the nature of the fluid, the supercritical boiler is a once-through design, having no need for separation equipment. The Universal Pressure, or UP® , boiler design used in the supercritical unit is de- scribed further in Chapter 26. For the supercritical cycle shown, the steam arrives at the high pressure turbine at 3500 psi (24.1 MPa) and 1050F (566C). Ex- pansion in this turbine is complete at point f, which corresponds to a superheated condition. Steam ex- hausted from the high pressure turbine is then re- heated in the boiler to approximately 1040F (560C), before entering the low pressure turbine at approxi- mately 540 psi (3.7 MPa); this corresponds to point g on the T-s diagram. The low pressure turbine expands the steam to point h on the diagram. The cycle is com- pleted by condensing the exhaust from the low pressure turbine to a slightly subcooled liquid, and a condensate pump delivers the liquid to the low pressure feedwater heater, which corresponds to point a in the T-s diagram. The high pressure of the feedwater in the supercritical cycle requires a substantially higher power input to the feedwater pump than that required by the saturated Rankine cycle. In a typical Rankine cycle with a steam pressure of 2400 psi (16.55 MPa), the pump power input requires approximately 2% of the turbine output. This may increase to as much as 3% in the supercritical unit. However, this increase is justified by the improved thermodynamic efficiency of the cycle. In general, with equivalent plant param- eters (fuel type, heat sink temperature, etc.), the supercritical steam cycle generates about 4% more net power output than the subcritical pressure regenera- tive Rankine steam cycle. Process steam applications In steam power plants generating only electric power, economically justifiable thermodynamic effi- ciencies range up to about 42% in fossil fuel plants (higher in combined cycle plants discussed later in this chapter) and 34% in nuclear plants. Therefore, typi- cally more than half of the heat released from the fuel must be transferred to the environment. Energy resources may be more efficiently used by operating multipurpose steam plants, where steam is exhausted or extracted from the cycle at a sufficient pressure for use in an industrial process or space heat- ing application. With these arrangements, an overall thermal utilization of 65% or greater is possible. Com- bination power and process installations have been common for many years, but the demand for process steam is not sufficient to permit the use of these com- bined cycles in most central station electric power gen- erating plants. However, in regions where waste dis- posal and renewable energy sources have become sig- nificant environmental issues, the use of cogeneration, biomass and waste-to-energy installations have been successfully tied together with district heating and Fig. 13 Supercritical steam cycle with one reheat. Fig. 12 Steam cycle for nuclear fuel on a Mollier chart: reheat by bleed and high pressure steam, moisture separation and six-stage regenera- tive feedwater heating – 900 psi, 566F/503F steam (English units).
- 82. 2-22 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company other process steam application projects. In recent years, the most successful of these have been in Eu- ropean municipalities. Gas turbine cycle In the thermodynamic cycles previously described, the working fluid has been steam used in a Rankine cycle. The Rankine cycle efficiency limit is dictated by the ratio of the current maximum and minimum cycle temperatures. The current maximum temperature of the steam Rankine cycle is approximately 1200F (649C), which is set primarily by material constraints at the elevated pressures of the steam cycles. One means of extending the efficiency limit is to replace the working fluid with air or gas. The gas turbine system in its simplest form consists of a compressor, combustor and turbine, as shown in Fig. 14. Because of its simplicity, low capital cost and short lead time, gas turbine systems are being used by some utilities to add capacity in smaller increments. Use of the gas turbine system in conjunction with the steam Rank- ine cycle is also an effective means of recovering some of the heat lost when combustion gases are released to the atmosphere at high temperatures. In the simple gas turbine system shown in Fig. 14, air is compressed then mixed with fuel and burned in a combustor. The high temperature gaseous combus- tion products enter the turbine and produce work by expansion. A portion of the work produced by the tur- bine is used to drive the compressor and the remain- der is available to produce power. The turbine exhaust gases are then vented to the atmosphere. To analyze the cycle, several simplifying assumptions are made. First, although the combustion process changes the composition of the working fluid, the fluid is treated as a gas of single composition throughout, anditiscon- sidered an ideal gas to obtain simple relationships be- tweenpointsinthesystem.Second,thecombustionpro- cess is approximated as a simple heat transfer process in which the heat input to the working fluid is deter- minedbythefuelheatingvalues.Aresultofthisapproxi- mation is that the mass flow rate through the system remains constant. The final approximation is to assume that each of the processes is internally reversible. If the turbine expansion is complete with the ex- haust gas at the same pressure as the compressor in- let air, the combination of processes can be viewed as a cycle. The simplifying assumptions above result in the idealized gas turbine cycle referred to as the air- standard Brayton cycle. Fig. 15 shows the cycle on T- s and P-v diagrams, which permit determining the state variables at the various cycle locations. The idealized cycle assumes an isentropic process between points 1 and 2 (compression) and between 3 and 4 (expansion work). The temperature rise between points 2 and 3 is calculated by assuming the heat ad- dition due to combustion is at a constant pressure. In the analysis, the pressure ratio between points 1 and 2 is given by the compressor design and is assumed to be known. To determine the temperature at point 2, a relationship between the initial and final states of an isentropic ideal gas process is obtained as follows. First, the general definitions of constant pressure and constant volume specific heats, respectively, are: c H T p p = ∂ ∂ (44) c u T v v = ∂ ∂ (45) Strictly speaking, the specific heat values vary with temperature. In practice, however, they are assumed to be constant to facilitate the calculations. The two constants are related in that their difference equals the gas constant in the ideal gas law (Pv = RT ): c c Rp v− = (46) The ratio of the constant pressure and constant volume specific heats is designated the specific heat ratio, k. k c cp v= / (47) From these definitions, changes in enthalpy and in- ternal energy for an ideal gas can be calculated from: dH c dTp= (48) du c dTv= (49) Although expressed to relate differential changes in enthalpy and temperature, the concept of specific heat can be used to calculate finite enthalpy changes as long as the change in temperature is not excessive. When higher accuracy is required, tabulated enthalpy values should be used. Recalling Equation 26, the combined expression of the first and second laws of thermodynamics, setting ds = 0 for the isentropic process, and inserting the change in internal energy given by Equation 49, the former equation may be written: Tds du Pdv c dT Pdvv= + = + = 0 (50) Substituting the ideal gas law (in differential form, RdT = Pdv + vdP) and using the specific heat ratio defi- nition, Equation 50 becomes: Fig. 14 Simple gas turbine system.
- 83. Steam 41 / Thermodynamics of Steam 2-23 The Babcock & Wilcox Company dP P kdv v + = 0 (51) Integrating this yields: Pvk = constant (52) From Equation 52 and the ideal gas law, the fol- lowing relationship between pressures and tempera- tures in an isentropic process is obtained, and the tem- peratures at points 2 and 4 are determined. T T T T P P k k 2 1 3 4 2 1 1 = = −( )/ (53) With this, the temperature and pressure (state vari- ables) at all points in the cycle are determined. The turbine work output, wt, required compressor work, wc, and heat input to the process, qb, are calculated as: w c T Tt p= −( )3 4 (54) w c T Tc p= −( )2 1 (55) q c T Tb v= −( )3 2 (56) As in other cycle analyses described to this point, the cycle efficiency η is calculated as the net work pro- duced divided by the total heat input to the cycle and is given by: η = −w w q t c b (57) in which qb is the heat input in the combustor (burner) per unit mass of gas (the working fluid) flowing through the system. For the ideal cycle, this can also be expressed in terms of gas temperatures by using Equation 48 to express the enthalpy change in the combustor and Equations 54 and 55 for the turbine and compressor work: η = − − − 1 4 1 3 2 T T T T c c p v (58) The actual gas turbine cycle differs from the ideal cycle due to inefficiencies in the compressor and tur- bine and pressure losses in the system. The effects of these irreversible aspects of the real gas turbine cycle are shown in the T-s diagram in Fig. 16.An isentropic compression would attain the point 2s, whereas the real compressor attains the pressure P2, with an en- tropy corresponding to point 2 on the T-s diagram; like- wise the turbine expansion attains point 4 rather than 4s. Constant-pressure lines on the diagram for pres- sures P2 and P3 illustrate the effect of pressure losses in the combustor and connecting piping, and the de- viation of the process between points 4 and 1 from a constant-pressure process illustrates the effect of com- pressor inlet and turbine exhaust pressure losses on the cycle efficiency. Points along the real cycle are determined by cal- culating the temperature T2s from Equation 53 as: T T P P s k k 2 1 2 1 1 = −( )/ (59) Using the compressor efficiency provided by the manu- facturer and solving for enthalpy or temperature at the compressor outlet yields the following: ηc s sT T T T H H H H = − − = − − 2 1 2 1 2 1 2 1 (60) Despite the significant advances in the mechani- cal efficiency of compressor and turbine designs (both on the order of 80% or greater), the overall cycle effi- ciency of a real gas turbine system is relatively low (30 to 35%) due to the high exhaust gas temperature and because a significant portion of the turbine out- put is used for compressor operation. The cycle effi- ciency may be increased by using a heat exchanger to preheat the air between the compressor and com- bustor. This heat is supplied by the turbine exhaust gas in a manner similar to that of the Rankine cycle regenerative heat exchangers. However, the higher efficiency is achieved in a system with a lower pres- sure ratio across the compressor and turbine, which in turn lowers the net work output for a given com- bustion system. The lower net output and extra hard- ware cost must be weighed in each case against the thermodynamic efficiency improvement. One of the key benefits of the gas turbine cycle is its ability to operate at much higher temperatures than the Rankine steam cycle. Gas turbines typically operate with an inlet temperature of 1800 to 2200F (982 to 1204C) and some turbine designs with com- plex internal cooling systems have been operated as high as 2300F (1260C), raising the thermodynamic efficiency. With the ability to operate at elevated tem- peratures and to use combustion gases as a working fluid, some gas turbine systems are operated in con- junction with the steam Rankine cycle. Combined cycles and cogeneration As seen in the previous discussions of the Rankine and Brayton cycles, the gas turbine Brayton cycle ef- ficiently uses high temperature gases from a combus- tion process but discharges its exhaust gas at a rela- Fig. 15 Air-standard Brayton cycle.
- 84. 2-24 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company tively high temperature; in the Brayton cycle, this con- stitutes wasted heat. On the other hand, the steam turbine Rankine cycle is unable to make full use of the highest temperatures. Combined cycles are de- signed to take advantage of the best features of these two cycles to improve the overall thermodynamic effi- ciency of the plant. Advanced combined cycles, in which the gas turbine exhaust is used as a heat source for a steam turbine cycle, can achieve overall thermal efficiencies in excess of 50%, generally representing a 15% improvement in the cycle efficiency compared to the gas turbine alone. Waste heat boilers In its simplest form, the combined cycle plant is a gas turbine (Brayton cycle) plant enhanced by pass- ing the turbine exhaust through a steam generator, as shown in Fig. 17. The steam generator uses the hot turbine exhaust as a heat source for a steam turbine Rankine cycle. Electric power is generated from the mechanical work provided by the gas turbine and the steam turbine. In concept, the steam generator in the combined cycle is recovering the otherwise wasted heat from the gas turbine exhaust, and therefore it is referred to as a heat recovery steam generator or a waste heat boiler. (See Chapter 27.) More recent ap- plications of the combined cycle have incorporated supplemental firing in the waste heat boiler to elevate the steam temperature and, therefore, to improve the steam cycle performance. Thermodynamic efficiency is defined as the work output of the two cycles divided by the total heat supplied (Qtotal): η = −( ) + −( ) W W W W QGT STout in out in total/ (61) where the subscripts GT and ST refer to gas turbine and steam turbine, respectively. Another approach to combining the gas and steam cycles, in which the steam generator serves as the com- bustion chamber for the gas turbine cycle, is shown in Fig. 18. In this arrangement, the principal heat source to the gas and steam cycle is the combustion process taking place in the steam generator. The gas- eous combustion products are expanded in the gas turbine and the steam generated in the boiler tubes is expanded in the steam turbine.Although not shown in Fig. 18, the heat contained in the gas turbine ex- haust may be recovered by using either a regenera- tive heat exchanger in the gas turbine cycle or a feedwater heater in the steam cycle.Apressurized flu- idized-bed combustion combined cycle is a specific example of this approach to combining the gas and steam cycles. (See Chapter 17.) Cogeneration In the most general sense, cogeneration is the pro- duction of more than one useful form of energy (ther- mal, mechanical, electrical, etc.) simultaneously from a single fuel. In practice, cogeneration refers to gen- erating electricity while principally performing an in- dustrial function such as space heating, process heat- ing or fuel gasification. Cogeneration systems are di- vided into two basic arrangements, topping and bot- toming cycles. A topping cycle is shown in Fig. 19. In this system the fuel is used for power generation in a steam boiler or gas turbine cycle combustor, and the waste heat from the power generation cycle supports an indus- trial process. The most common topping cycle is one in which a boiler generates steam at a higher pressure than that needed for the process or space conditioning application. The high pressure steam is then expanded in a turbine to a pressure that is appropriate for the application, generating electricity in the expansion process. Steam turbines, gas turbines and reciprocat- ing engines are commonly used in topping cycles. A bottoming cycle is most commonly associated with the recovery or waste heat boiler. In the bottoming cycle, fuel is not supplied directly to the power gener- ating cycle. Rather, steam is generated from a waste Fig. 17 Simple combined cycle plant. Fig. 16 T-s diagram of an actual gas turbine system. Fig. 18 Pressurized combustion combined cycle plant.
- 85. Steam 41 / Thermodynamics of Steam 2-25 The Babcock & Wilcox Company heat source and then expanded in a turbine to pro- duce work or to generate electricity. Steam is fre- quently used in the bottoming cycle because of its ability to condense at low temperatures in the closed Rankine cycle. The bottoming cycle is shown in Fig. 20. The steam Rankine cycle used as a bottoming cycle has been illustrated previously in the descriptions of combined cycle plants. Combustion processes To this point, cycles have been compared based on the thermodynamic efficiency achieved, i.e., the net work produced divided by the total heat input to the cycle. To complete the evaluation of a combustion- based cycle, however, the performance must be ex- pressed in terms of fuel consumption. In addition, the ability of the different machines to make full use of the combustion energy varies with temperatures reached in the combustion chamber and with disso- ciation of the combustion products. The energy release during combustion is illustrated by considering the combustion of carbon (C) and oxy- gen (O2) to form carbon dioxide (CO2): C O CO+ →2 2 If heat is removed from the combustion chamber and the reactants and products are maintained at 25C and 0.1 MPa (77F and 14.5 psi) during the process, the heat transfer from the combustion chamber would be 393,522 kJ per kmole of CO2 formed. From the first law applied to the process, the heat transfer is equal to the difference in enthalpy between the reactants and products: q w H HP R− = − (62) The subscripts R and P refer to reactants and prod- ucts, respectively.Assuming that no work is done in the combustion chamber and expressing the enthalpy of reactantsandproductsonapermolebasis,thisbecomes: Q n H n HP P R R= − ∑∑ (63) The number of moles of each element or molecular species entering or leaving the chamber, nR or nP re- spectively, is obtained from the chemical reaction equa- tion. By convention, the enthalpy of elements at 25C and 0.1 MPa (77F and 14.5 psi) are assigned the value of zero. Consequently, the enthalpy of CO2 at these conditions is –393,522 kJ/kmole (the negative sign is due to the convention of denoting heat transferred from a control volume as negative). This is referred to as the enthalpy of formation and is designated by the symbol Hf o . The enthalpy of CO2 (and other molecular species) at other conditions is found by adding the change in enthalpy between the desired condition and the standard state to the enthalpy of formation. [Note that some tables may not use 25C and 0.1 MPa (77F and 14.5 psi) as the standard state when listing the enthalpy of formation.] Ideal gas behavior or tabu- lated properties are used to determine enthalpy changes from the standard state. The stoichiometrically balanced chemical reaction equationprovidestherelativequantitiesofreactantsand products entering and leaving the combustion chamber. Thefirstlawanalysisisusuallyperformedonapermole or unit mass of fuel basis. The heat transfer from a com- bustion process is obtained from a first law analysis of thecombustionprocess,giventhepressureandtempera- ture of the reactants and products. Unfortunately, even in the case of complete combustion as assumed in the previous example, the temperature of the combustion products must be determined by additional calculations discussed later in this section. The combustion of fossil or carbon based fuel is com- monly accompanied by the formation of steam or water (H2O) as in the reaction: CH 2O CO 2H O2 2 24 + → + Again, the difference in enthalpy between the reac- tants and products is equal to the heat transfer from the combustion process. The heat transfer per unit mass of fuel (methane in this example) is referred to as the heating value of the fuel. If the H2O is present as liquid in the products, the heat transferred is re- ferred to as the higher heating value (HHV). The term lower heating value (LHV) is used when the H2O is present as a vapor. The difference between these two values is frequently small (about 4% for most hydro- carbon fuels) but still significant. When the efficiency Fig. 19 Topping cycle. Fig. 20 Bottoming cycle.
- 86. 2-26 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company of a cycle is expressed as a percentage of the fuel’s heating value, it is important to know whether the HHV or LHV is used. As noted, one of the difficulties in completing the first law analysis of the combustion process is deter- mining the temperature of the products. In some ap- plications an upper limit of the combustion tempera- ture may be estimated. From the first law, this can occur if the combustion process takes place with no change in kinetic or potential energy, with no work and with no heat transfer (adiabatically). Under these assumptions, the first law indicates that the sum of the enthalpies of the reactants equals that of the prod- ucts. The temperature of the products is then deter- mined iteratively by successively assuming a product temperature and checking the equality of the reactant and product enthalpies. For a given fuel and reactants at the specified inlet temperature and pressure, this procedure determines the highest attainable combus- tion temperature, referred to as the adiabatic combus- tion or flame temperature. Gibbs free energy An important thermodynamic property derived from a combinationofotherproperties(justasenthalpy was derived from u, P and v) is Gibbs free energy (g), which is also frequently referred to as free energy: g H Ts= − (64) Free energy g is a thermodynamic potential similar to enthalpy and internal energy because in any ther- modynamic process, reversible or irreversible, differ- ences in this quantity depend only on initial and fi- nal states of the system. The usefulness of free energy is particularly evident from the following expression of the combined first and secondlaws,expressedforareversibleprocesswithneg- ligible changes in kinetic and potential energy: W m H T s m H T s o o rev = −( ) − −( ) ∑ ∑ 1 1 1 2 2 2 (65) When applied to a combustion process in which the reactantsandproductsareintemperatureequilibrium with the surroundings, this becomes: W n g n gR R P Prev = −∑ ∑ (66) This equation indicates the maximum value of revers- ible work that can be obtained from the combustion of a given fuel. The reversible work is maximized when the reactants constitute a stoichiometrically bal- anced mixture (no excess air). The quantities nR and nP are obtained from the chemical reaction equation and g is expressed on a per mole basis in Equation 66. From this, one might expect to express the efficiency of a cycle that extracts energy from a combustion pro- cess as a percentage of the Gibbs free energy decrease, rather than in terms of the heating value of the fuel. It is uncommon for this to be done, however, because the difference between the free energy decrease and the heating value of hydrocarbon fuels is small and be- cause the use of fuel heating value is more widespread. Free energy is more commonly used to determine the temperature reached in burning fuel, including the effects of dissociation. The problem of dissociation is illustrated by again considering the combustion of carbon and oxygen to form CO2. If the temperature of the combustion process is high enough, the CO2 dis- sociates to form CO and O2 according to the reaction: CO CO O2 2↔ + 1 2 As the dissociation reaction occurs from left to right (from all CO2 to none), the sum of the reactant free energies and that of the products vary. Equilibrium of this reaction is reached when the sum of the free ener- gies is a minimum. The equilibrium point (degree of dissociation) varies with the combustion temperature. While the process of iteratively determining a mini- mum free energy point is suited for computer calcula- tions, the equilibrium conditions of the dissociation reaction at an assumed temperature can also be de- termined using tabulated values of a constant relat- ing the species involved in the reaction. This constant is known as the equilibrium constant Keq, which for ideal gases is given by: K P P P eq B b C c A a = ( ) ( ) ( ) (67) where PA, PB and PC are the partial pressures, i.e., the products of total pressure and mole fractions in the mixture, of the reactants and products. The exponents represent the number of moles present for each spe- cies (A, B and C) in the stoichiometric balance equa- tion as follows: aA bB cC↔ + (68) Equations 67 and 68 yield simultaneous equations for the mole fractions a, b and c. For nonideal gas re- actions, the partial pressures are replaced by what are known as fugacities (the tendencies of a gas to expand or escape). Thermodynamic properties and relation- ships for the compounds and their elements encoun- tered in the combustion process are available in the literature. One of the best sources for this information is the JANAF Thermochemical Tables, published by the U.S. Department of Commerce.6 These tables in- clude log10 values of the equilibrium constants for tem- peratures from 0 to 6000K. To continue the carbon-oxygen combustion example, the overall chemical reaction, including dissociation, is now written as: C O CO CO O+ → + +2 2 2a b c in which the coefficients a, b and c represent the mole fractions of the product components as determined by the solution to the dissociation reaction at the assumed combustion temperature. The overall reaction equa- tion is now used to check the assumed temperature
- 87. Steam 41 / Thermodynamics of Steam 2-27 The Babcock & Wilcox Company by adding the enthalpies of the combustion products at the assumed temperature, noting that the enthalpy per mole must be multiplied by the corresponding mole fraction a, b, or c for each product species. The com- bustion temperature is determined when the sum of product enthalpies minus that of the reactants equals the heat transfer to the surroundings of the combus- tion chamber. The convective and radiative heat transfer from the combustion products to the cham- ber and eventually to the working fluid of the cycle at the assumed combustion temperature are discussed in Chapter 4. 1. Parry, W.T., et al., ASME International Steam Tables for Industrial Use, Based on IAPWS-IF97, The American Society of Mechanical Engineers, New York, New York, January, 2000. 2. ASME Steam Properties for Industrial Use, Based on IAPWS-IF97, Professional Version 1.1, The American So- ciety of Mechanical Engineers, New York, New York, 2003. 3. Weast, R.C., et al., CRC Handbook of Chemistry and Physics, 70th Ed., CRC Press, Inc., Boca Raton, Florida, 1989. References 4. Keenan, J.H., Chao, J., and Kaye, J., Gas Tables: Thermodynamic Properties of Air Products of Combus- tion and Component Gases Compressible Flow Functions, Second Ed., John Wiley & Sons, New York, New York, June, 1983. 5. Vargaftik, N.B., Tables on the Thermophysical Prop- erties of Liquids and Gases: In Normal and Dissociated States, Second Ed., John Wiley & Sons, New York, New York, November, 1975. 6. Chase, Jr., M.W., et al., JANAF Thermochemical Tables, Fourth Ed., American Chemical Society, Ameri- can Institute of Physics, New York, New York, 1998.
- 88. 2-28 Steam 41 / Thermodynamics of Steam The Babcock & Wilcox Company Mollier diagram (H-s) for steam.
- 89. Steam 41 / Fluid Dynamics 3-1 The Babcock & Wilcox Company Chapter 3 Fluid Dynamics In the production and use of steam there are many fluid dynamics considerations. Fluid dynamics ad- dresses steam and water flow through pipes, fittings, valves, tube bundles, nozzles, orifices, pumps and tur- bines, as well as entire circulating systems. It also con- siders air and gas flow through ducts, tube banks, fans, compressors and turbines plus convection flow of gases due to draft effect. The fluid may be a liquid or gas but, regardless of its state, the essential property of a fluid is that it yields under the slightest shear stress. This chapter is limited to the discussion of Newtonian liquids, gases and vapors where any shear stress is directly proportional to a velocity gradient normal to the shear force. The ratio of the shear stress to the ve- locity gradient is the property viscosity represented by the symbol µ. Liquids and gases are recognized as states of mat- ter. In the liquid state, a fluid is relatively incompress- ible, having a definite volume. It is also capable of forming a free surface interface between itself and its vapor or any other fluid with which it does not mix. On the other hand, a gas is highly compressible. It expands or diffuses indefinitely and is subject only to the limi- tations of gravitational forces or an enclosing vessel. The term vapor generally implies a gas near satu- ration conditions where the liquid and the gas phase coexist at essentially the same temperature and pres- sure, during a process such as vaporization or boiling. In a similar sense the term gas denotes a highly su- perheated steam. Sometimes steam may be treated as an ideal gas and careful judgment is needed when doing so. Fluid dynamics principles normally consider the fluid to be a continuous region of matter, a continuum, and a molecular model is not required except for rare instances. However, one property is noteworthy to con- sider due to the effect on steam generation fluid flow and due to intermolecular forces. Surface tension, σ, is a liquid property of the vapor-liquid interface and is the energy per unit area required to extend the in- terface. Surface tension is important in two-phase sys- tems, such as a mixture flowing in a boiler tube, and relates to the shape and flow regime of the bubble in- terface and also to the heat transfer area of droplets. Vapor bubbles increase the resistance to fluid flow. The surface tension of water is dependent on tempera- ture and its value goes to zero at the critical tempera- ture (705.47 F, 374.15C). Supercritical water is con- sidered single phase in fluid dynamic analysis due to zero surface tension. The recommended correlation1 for the surface ten- sion of water and its vapor, σ, is: σ = × −( ) − − − 235 8 10 1 0 625 3 1 256 . / . . N m T T T T T T c c (1) where Tc = 647.15K and T is the fluid temperature in K. Water in steam generators operating at supercriti- cal pressure (above 3200.1 psia, 22.1 MPa) will be- have as a single phase fluid converting from liquid to steam without creating bubbles. At the critical pres- sure and critical temperature, the density of water and steam are identical and there is no distinguishable in- terface at equilibrium conditions. Surface tension is also related to the latent heat of vaporization which also decreases to zero at the critical temperature.2 This chapter discusses single phase fluid flow. Chapter 5 pertains to two-phase fluid flow that occurs in boiling tube circuits. Fundamental relationships Three fundamental laws of conservation apply to fluid dynamic systems: conservation of mass, momen- tum and energy. With the exception of nuclear reac- tions where minute quantities of mass are converted into energy, these laws must be satisfied in all flow- ingsystems.Fundamentalmathematicalrelationships for these principles are presented in several different forms that may be applied in particular fluid dynamic situations to provide an appropriate solution method. However, full analytical solutions are frequently too complex without the use of a computer. Simplified forms of the full equations can be derived by apply- ing engineering judgment to drop negligible terms and consider only terms of significant magnitude for cer-
- 90. 3-2 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company tain classes of problems. Fluid dynamics problems can be classified as compressible or incompressible, viscous or inviscid. Engineering practice is based upon apply- ing various assumptions and empirical relationships in order to obtain a practical method of solution. A more complete discussion of the derivation of these conservation law relationships and vector notation representing three dimensional spaces may be found in References 3, 4, 5 and 6. Conservation of mass The law of conservation of mass simply states that the rate of change in mass stored in a system must equal the difference in the mass flowing into and out of the system. The continuity equation of mass for one dimensional single phase flow in a variable area chan- nel or stream tube is: A t AV x V A x A V x ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ = ρ ρ ρ ρ 0 (2) In its simplest form in x, y and z three dimensional Cartesian coordinates, conservation of mass for a small fixed control volume is: ∂ ∂ + ∂ ∂ + ∂ ∂ = − ∂ ∂x u y v z w t ρ ρ ρ ρ (3) where u, v and w are the fluid velocities in the x, y and z coordinate directions; t is time and ρ is the fluid density.An important form of this equation is derived by assuming steady-state (∂ /∂t = 0) and incompress- ible (constant density) flow conditions: ∂ ∂ + ∂ ∂ + ∂ ∂ = u x v y w z 0 (4) Although no liquid is truly incompressible, the as- sumption of incompressibility simplifies problem solu- tions and is frequently acceptable for engineering practice considering water and oils. Another relationship useful in large scale pipe flow systems involves the integration of Equation 3 around the flow path for constant density, steady-state con- ditions. For only one inlet (subscript 1) and one outlet (subscript 2): m A V A V= =ρ ρ1 1 1 2 2 2 (5) where ρ is the average density, V is the average ve- locity, A is the cross-sectional area, and m is the mass flow rate. Conservation of momentum The law of conservation of momentum is a repre- sentation of Newton’s Second Law of Motion – the mass of a particle times its acceleration is equal to the sum of all of the forces acting on the particle. In a flow- ing system, the equivalent relationship for a fixed (con- trol) volume becomes: the rate of change in momen- tum entering and leaving the control volume is equal to the sum of the forces acting on the control volume. The conservation of momentum for one dimensional single phase flow in a variable area channel or stream tube is: 1 1 0 2 g G t A x G A P A g g P x c f c ∂ ∂ + ∂ ∂ + + + ∂ ∂ = ρ τ ρ θsin (6) where P = pressure, psia (MPa) G = mass flux, G = ρV, lb/h ft2 (kg/s m2 ) A = flow area of channel ft2 (m2 ) ρ = density lb/ft3 (kg/m3 ) τ = wallshearstress,lb/ft2 (N/m2 )(refertoEquation26) Pf = channel wetted perimeter, ft (m) g = 32.17 ft /s2 (9.8 m /s2 ) gc = 32.17 lbm ft/lbf s2 (1 kg m /N s2 ) θ = angle of channel inclination for x distance This relationship is useful in calculating steam gen- erator tube circuit pressure drop. The conservation of momentum is a vector equa- tion and is direction dependent, resulting in one equa- tion for each coordinate direction (x, y and z for Car- tesian coordinates), providing three momentum equa- tions for each scaler velocity component, u, v and w. Thefullmathematicalrepresentationofthemomen- tum equation is complex and is of limited direct use in many engineering applications, except for numerical computational models. As an example, in the x coordi- nate direction, the full momentum equation becomes: ρ ρ ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ = − ∂ ∂ + ∂ ∂ u t u u x v u y w u z f P x x x Term 1 Term 2 Term 3 2 33 2µ µ ∂ ∂ − ∂ ∂ − ∂ ∂ + ∂ ∂ ∂ ∂ + ∂ ∂ u x v y w z y v x u y Term 4 + ∂ ∂ ∂ ∂ + ∂ ∂ z w x u z µ (7) where ƒx is the body force in the x direction, P is the pressure, and µ is the viscosity. This equation and the corresponding equations in the y and z Cartesian co- ordinates represent the Navier-Stokes equations which are valid for all compressible Newtonian fluids with variable viscosity. Term 1 is the rate of momen- tum change. Term 2 accounts for body force effects such as gravity. Term 3 accounts for the pressure gra- dient. The balance of the equation accounts for mo-
- 91. Steam 41 / Fluid Dynamics 3-3 The Babcock & Wilcox Company mentum change due to viscous transfer. Term 1 is sometimes abbreviated as ρ(Du /Dt) where Du /Dt is defined as the substantial derivative of u. For a func- tion β (scaler or vector), D /Dt is the substantial de- rivative operator on function β defined as: D Dt t u x v y w z t β β β β β β β = ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ + ∇vi (8) where the vector gradient or grad or del operator on function β is defined as: ∇β or grad β or del β = i ∂ β/∂x + j ∂ β/∂y + k ∂ β/∂z For the special case of constant density and viscosity, this equation reduces to (for the x coordinate direction): Du Dt f P x u x u y u z x= − ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ 1 2 2 2 2 2 2 ρ µ ρ (9) The y and z coordinate equations can be developed by substituting appropriate parameters for velocity u, pressure gradient ∂P / ∂x, and body force ƒx. Where vis- cosity effects are negligible (µ = 0), the Euler equation of momentum is produced (x direction only shown): Du Dt f P x x= − ∂ ∂ 1 ρ (10) Energy equation (first law of thermodynamics) The law of conservation of energy for nonreacting fluids states that the energy transferred into a sys- tem less the mechanical work done by the system must be equal to the rate of change in stored energy, plus the energy flowing out of the system with a fluid, minus the energy flowing into the system with a fluid. A single scaler equation results. The one dimensional single phase flow energy equation for a variable area channel or stream tube is: ρ τ ∂ ∂ + ∂ ∂ = ′′ + ′′′ + ∂ ∂ H t G H x q P A q J PH 1 (11) where P = pressure, psia (MPa) G = mass flux, lb/h ft2 (kg/s m2 ) A = flow area of channel, ft2 (m2 ) ρ = density, lb/ft3 (kg/m3 ) τ = wall shear stress, lb/ft2 (N/m2 ) PH = channel heated area, ft2 (m2 ) x = channel distance, ft (m) for x distance H = enthalpy, Btu/lb (kJ/kg) J = mechanical equivalent of heat = 778.17 ft lbf/ Btu (1 N m/J) q′′ = heat flux at boundary, Btu/h ft2 (W/m2 ) q′′′ = internal heat generation, Btu/h ft3 (W/m) A general form of the energy equation for a flow- ing system using an enthalpy based formulation and vector notation is: ρ µDH Dt q DP Dt k T gc = ′′′ + + ∇ ∇ +i Φ Term1 Term Term Term Term2 3 4 5 (12) where ρ is the fluid density, H is the enthalpy per unit mass of a fluid, T is the fluid temperature, q′′′ is the internal heat generation, k is the thermal conductiv- ity, and Φ is the dissipation function for irreversible work.6 Term 1 accounts for net energy convected into the system, Term 2 accounts for internal heat genera- tion, Term 3 accounts for work done by the system, Term 4 addresses heat conduction, and Term 5 ac- counts for viscous dissipation. As with the momentum equations, the full energy equation is too complex for most direct engineering applications except for use in numerical models. (See Chapter 6.) As a result, specialized forms are based upon various assumptions and engineering approxi- mations.As discussed in Chapter 2, the most common form of the energy equation for a simple, inviscid (i.e., frictionless) steady-state flow system with flow in at location 1 and out at location 2 is: JQ W J u u P v P v g V V Z Z g gc c − = −( ) + −( ) + −( ) + −( ) 2 1 2 2 1 1 2 2 1 2 2 1 1 2 (13a) or JQ W J H H g V V Z Z g gc c − = −( ) + −( ) + −( ) 2 1 2 2 1 2 2 1 1 2 (13b) where Q = heat added to the system, Btu lbm (J/kg) (See Note below) W = work done by the system, ft-lbf/lbm (N m/kg) J = mechanical equivalent of heat = 778.17 ft lbf/ Btu (1 N m/J) u = internal energy, Btu/lbm (J/kg) P = pressure, lbf/ft2 (N/m2 ) υ = specific volume, ft3 /lbm (m3 /kg) V = velocity, ft /s (m/s) Z = elevation, ft (m) H = enthalpy = u + Pυ/J, Btu/lbm (J/kg) g = 32.17 ft /s2 (9.8 m /s2 ) gc = 32.17 lbm ft/lbf s2 (1 kg m /N s2 ) Note: Where required for clarity, the abbreviation lb is aug- mented by f (lbf) to indicate pound force and by m (lbm) to indicate pound mass. Otherwise lb is used with force or mass indicated by the context.
- 92. 3-4 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company Energy equation applied to fluid flow (pressure loss without friction) The conservation laws of mass and energy, when simplified for steady, frictionless (i.e., inviscid) flow of an incompressible fluid, result in the mechanical en- ergy balance referred to as Bernoulli’s equation: P v Z g g V g P v Z g g V gc c c c 1 1 1 2 2 2 2 2 2 2 + + = + + (14) The variables in Equation 14 are defined as follows with the subscripts referring to location 1 and loca- tion 2 in the system: P = pressure, lbf/ft2 (N/m2 ) υ = specific volume of fluid, ft3 /lbm (m3 /kg) Z = elevation, ft (m) V = fluid velocity, ft/s (m/s) Briefly, Equation 14 states that the total mechani- cal energy present in a flowing fluid is made up of pres- sure energy, gravity energy and velocity or kinetic energy; each is mutually convertible into the other forms. Furthermore, the total mechanical energy is constant along any stream-tube, provided there is no friction, heat transfer or shaft work between the points considered. This stream-tube may be an imaginary closed surface bounded by stream lines or it may be the wall of a flow channel, such as a pipe or duct, in which fluid flows without a free surface. Applications of Equation 14 are found in flow mea- surements using the velocity head conversion result- ing from flow channel area changes. Examples are the venturi, flow nozzle and various orifices. Also, pitot tube flow measurements depend on being able to com- pare the total head, Pυ + Z + (V2 /2 gc ), to the static head, Pυ + Z, at a specific point in the flow channel. Descriptions of metering instruments are found in Chapter 40. Bernoulli’s equation, developed from strictly mechanical energy concepts some 50 years before any precise statement of thermodynamic laws, is a special case of the conservation of energy equa- tion or first law of thermodynamics in Equations 13a and b. Applications of Equation 13 to fluid flow are given in the examples on water and compressible fluid flow through a nozzle under the Applications of the En- ergy Equation section in Chapter 2. Equation 18, Chapter 2 is: V g J H H C H Hc2 1 2 1 22= −( ) = − (15) where V2 = downstream velocity, ft/s (m/s) gc = 32.17 lbm ft/lbf s2 = 1 kg m/Ns2 J = 778.26 ft lbf/Btu = 1 Nm/J H1 = upstream enthalpy, Btu/lb (J/kg) H2 = downstream enthalpy, Btu/lb (J/kg) C = 223.8 lbm/Btu × ft/s (1.414 kg/J × m/s) This equation relates fluid velocity to a change in en- thalpy under adiabatic (no heat transfer), steady, in- viscid (no friction) flow where no work, local irrevers- ible flow pressure losses, or change in elevation occurs. The initial velocity is assumed to be zero and compress- ible flow is permitted. If the temperature (T) and pres- sure (P ) of steam or water are known at points 1 and 2, Equation 15 provides the exit velocity using the en- thalpy (H) values provided in Tables 1, 2 and 3 of Chap- ter 2. If the pressure and temperature at point 1 are known but only the pressure at point 2 is known, the outlet enthalpy (H2) can be evaluated by assuming con- stant entropy expansion from points 1 to 2, i.e., S1 = S2. Ideal gas relationships There is another method that can be used to deter- mine velocity changes in a frictionless adiabatic ex- pansion. This method uses the ideal gas equation of state in combination with the pressure-volume rela- tionship for constant entropy. From the established gas laws, the relationship be- tween pressure, volume and temperature of an ideal gas is expressed by: Pv T= R (16a) or Pv M T= R (16b) where P = absolute pressure, lb/ft2 (N/m2 ) υ = specific volume, ft3 /lb of gas (m3 /kg) M = molecular weight of the gas, lb/lb-mole (kg/kg-mole) T = absolute temperature, R (K) R = gas constant for specific gas, ft lbf/lbm R (N m/kg K) MR = R = the universal gas constant = 1545 ft lb/lb-mole R (8.3143 kJ/kg-mole K) The relationship between pressure and specific vol- ume along an expansion path at constant entropy, i.e., isentropic expansion, is given by: Pvk = constant (17) Because P1 and υ1 in Equation 13 are known, the con- stant can be evaluated from P1υ1 k . The exponent k is constant and is evaluated for an ideal gas as: k c cp v= =/ specific heat ratio (18) where cp = specificheatatconstantpressure,Btu/lbF(J/kgK) cv = specific heat at constantvolume,Btu/lbF(J/kgK) = (u1 – u2)/(T1 – T2) For a steady, adiabatic flow with no work or change in elevation of an ideal gas, Equations 13, 16, 17 and 18canbecombinedtoprovidethefollowingrelationship: V V g k k P v P P c k k 2 2 1 2 1 1 2 1 1 2 1 1− = − − − (19)
- 93. Steam 41 / Fluid Dynamics 3-5 The Babcock & Wilcox Company When V1 is set to zero and using English units Equa- tion 19 becomes: V k k P v P P k k 2 1 1 2 1 1 8 02 1 1= − − − . , ft/s (20) Equations 19 and 20 can be used for gases in pres- sure drop ranges where there is little change in k, pro- vided values of k are known or can be calculated. Equation 20 is widely used in evaluating gas flow through orifices, nozzles and flow meters. It is sufficiently accurate for most purposes to de- termine velocity differences caused by changes in flow area by treating a compressible fluid as incompress- ible. This assumption only applies when the difference in specific volumes at points 1 and 2 is small compared to the final specific volume. The accepted practice is to consider the fluid incompressible when: v v v2 1 2 0 05−( ) </ . (21) Because Equation 14 represents the incompressible energy balance for frictionless adiabatic flow, it may be rearranged to solve for the velocity difference as follows: V V g Pv Zg gc c2 2 1 2 2− = ( ) + ∆ ∆ / 22) where ∆(Pυ) = pressure head difference between locations 1 and 2 = (P1 – P2) υ, ft (m) ∆Z = head (elevation) difference between loca- tions 1 and 2, ft (m) V = velocity at locations 1 and 2, ft/s (m/s) When the approach velocity is approximately zero, Equation 22 in English units becomes: V gh h2 2 8 02= = . , ft/s (23) In this equation, h, in ft head of the flowing fluid, re- places ∆(Pυ) + ∆Z. If the pressure difference is mea- sured in psi, it must be converted to lb/ft2 to obtain Pυ in ft. Pressure loss from fluid friction So far, only pressure changes associated with the kinetic energy term, V2 /2 gc, and static pressure term, Z, have been discussed. These losses occur at constant flow where there are variations in flow channel cross- sectional area and where the inlet and outlet are at different elevations. Fluid friction and, in some cases heat transfer with the surroundings, also have impor- tant effects on pressure and velocity in a flowing fluid. The following discussion applies to fluids flowing in channels without a free surface. When a fluid flows, molecular diffusion causes momentum interchanges between layers of the fluid that are moving at different velocities. These inter- changes are not limited to individual molecules. In most flow situations there are also bulk fluid inter- changes known as eddy diffusion. The net result of all inelastic momentum exchanges is exhibited in shear stresses between adjacent layers of the fluid. If the fluid is contained in a flow channel, these stresses are eventually transmitted to the walls of the chan- nel. To counterbalance this wall shear stress, a pres- sure gradient proportional to the bulk kinetic energy, V2 / 2 gc, is established in the fluid in the direction of the bulk flow. The force balance is: π τ π D dP D dxw 2 4 ( ) = ( ) (24) where D = tube diameter or hydraulic diameter Dh ft (m) Dh = 4 × (flow area)/(wetted perimeter) for circu- lar or noncircular cross-sections, ft (m) dx = distance in direction of flow, ft (m) τw = shear stress at the tube wall, lb/ft2 (N/m2 ) Solving Equation 24 for the pressure gradient (dP / dx): dP dx D w= 4 τ (25) This pressure gradient along the length of the flow channel can be expressed in terms of a certain num- ber of velocity heads, ƒ, lost in a length of pipe equiva- lent to one tube diameter. The symbol ƒ is called the friction factor, which has the following relationship to the shear stress at the tube wall: τw c f v V g = 4 1 2 2 (26) Equation 25 can be rewritten, substituting for τw from Equation 26 as follows: dP dx D f v V g f D v V gc c = = 4 4 1 2 1 2 2 2 (27) The general energy equation, Equation 13, expressed as a differential has the form: du VdV g d Pv dQ dW c k+ + ( ) = − (28a) or du VdV g Pdv vdP dQ dW c k+ + + = − (28b) Substituting Equation 26 of Chapter 2 (du = Tds – Pdυ) in Equation 28 yields: Tds VdV g vdP dQ dW c k+ + = − (29) The term Tds represents heat transferred to or from the surroundings, dQ, and any heat added internally to the fluid as the result of irreversible processes. These processes include fluid friction or any irrevers-
- 94. 3-6 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company ible pressure losses resulting from fluid flow. (See Equation 29 and explanation, Chapter 2.) Therefore: Tds dQ dQF= + (30) where dQF is the heat equivalent of fluid friction and any local irrecoverable pressure losses such as those from pipe fittings, bends, expansions or contractions. Substituting Equation 30 into Equation 29, cancel- ing dQ on both sides of the equation, setting dWk equal to 0 (no shaft work), and rearranging Equation 29 results in: dP VdV vg dQ vc F = − − (31) Three significant facts should be noted from Equa- tion 31 and its derivation. First, the general energy equation does not accommodate pressure losses due to fluid friction or geometry changes. To accommodate these losses Equation 31 must be altered based on the first and second laws of thermodynamics (Chapter 2). Second, Equation 31 does not account for heat trans- fer except as it may change the specific volume, υ, along the length of the flow channel. Third, there is also a pressure loss as the result of a velocity change. This loss is independent of any flow area change but is dependent on specific volume changes. The pressure loss is due to acceleration which is always present in compressible fluids. It is generally negligible in incom- pressible flow without heat transfer because friction heating has little effect on fluid temperature and the accompanying specific volume change. Equation 27 contains no acceleration term and applies only to friction and local pressure losses. There- fore, dQF/υ in Equation 31 is equivalent to dP of Equation 27, or: dQ v f dx D V v g F c = 2 2 (32) Substitution of Equation 32 into Equation 31 yields: dP VdV vg f D V v g dx c c = − − 2 2 (33) From Equation 5, the continuity equation permits definition of the mass flux, G, or mass velocity or mass flow rate per unit area [lb/h ft2 (kg/m2 s)] as: V v G= = constant (34) Substituting Equation 34 into Equation 33 for a flow channel of constant area: dP G g dv f G g v D dx c c = − −2 2 2 2 2 (35) Integrating Equation 35 between points 1 and 2, lo- cated at x = 0 and x = L, respectively: P P G g v v f G g D vdx c c L 1 2 2 2 1 2 0 2 2 2 1 − = −( ) + ∫ (36) The second term on the right side of Equation 36 may be integrated provided a functional relationship be- tween υ and x can be established. For example, where the heat absorption rate over the length of the flow channel is constant, temperature T is approximately linear in x, or: dx L T T dT= −2 1 (37) and vdx L T T vdT Lv L av0 2 1 1 2 ∫ ∫= − = (38) The term υaυ is an average specific volume with re- spect to temperature, T. v v v v vav R= +( ) = +( )φ φ2 1 1 1 (39) where υR = υ2/υ1 φ = averaging factor In most engineering evaluations, υ is almost lin- ear in T and φ ≈ l/2. Combining Equations 36 and 37, and rewriting υ 2 – υ 1 as υ 1 (υ R – 1): P P G g v v f L D G g v v c R c R 1 2 2 1 2 1 2 2 1 2 1 − = −( ) + +( )φ (40) Equation 40 is completely general. It is valid for com- pressible and incompressible flow in pipes of constant cross-section as long as the function T = F(x) can be as- signed. The only limitation is that dP/dx is negative at every point along the pipe. Equation 33 can be solved for dP/dx making use of Equation 34 and the fact that P1υ1 can be considered equal to P2υ2 for adiabatic flow over a short section of tube length. The result is: dP dx Pf D g Pv V c = − /2 1 2 (41) At any point where V 2 = gcPυ, the flow becomes choked because the pressure gradient is positive for velocities greater than (gcPυ)0.5 . The flow is essentially choked by excessive stream expansion due to the drop in pres- sure. The minimum downstream pressure that is ef- fective in producing flow in a channel is: P V v g v G gc c2 2 2 2 2 = =/ / (42) Dividing both sides of Equation 40 by G2 υ l / 2gc, the pressure loss is expressed in terms of velocity heads. One velocity head equals: ∆P V g Cv V g Cc c (one velocity head) = 2 2 2 2 = ρ (43)
- 95. Steam 41 / Fluid Dynamics 3-7 The Babcock & Wilcox Company where ∆P = pressure drop equal to one velocity head, lb/ in.2 (N/m2 ) V = velocity, ft/s (m/s) υ = specific volume, ft3 /lb (m3 /kg) gc = 32.17 lbm ft/lbf s2 = 1 kg m/N s2 C = 144 in.2 /ft2 (1 m2 /m2 ) ρ = density, lb/ft3 (kg/m3 ) In either case, ƒ represents the number of velocity heads (Nvh) lost in each diameter length of pipe. The dimensionless parameter defined by the pres- sure loss divided by twice Equation 43 is referred to as the Euler number: Eu P V gc= ( )∆ / /ρ 2 (44) where ρ is the density, or l/υ . Two other examples of integrating Equation 35 have wide applications in fluid flow. First, adiabatic flow through a pipe is considered. Both H and D are constant and Plυ l m = P2υ 2 m where m is the exponent for constant enthalpy. Values of m for steam range from 0.98 to 1.0. Therefore, the assumption Pυ = con- stant = P1υ 1 is sufficiently accurate for pressure drop calculations. This process is sometimes called isother- malpressuredropbecauseaconstanttemperatureideal gas expansion also requires a constant enthalpy. For Pυ = P1υ1, the integration of Equation 35 reduces to: P P G g v v v v n v v f L D G g v v v v c c 1 2 2 1 2 1 2 2 1 2 1 2 1 2 2 2 2 2 2 − = + + + (45) Neither P2 nor υ2 are known in most cases, therefore Equation 45 is solved by iteration.Also, the term 2υ1 υ2 /(υ1 + υ2) can usually be replaced by the numerical av- erage of the specific volumes – υav = 1 /2 υ1(PR + 1) where PR = P1 /P2 = υ2/υ1. The maximum high side error at PR = 1.10 is 0.22% and this increases to 1.3% at PR = 1.25. It is common practice to use a numerical average for the specific volume in most fluid friction pressure drop calculations. However, where the lines are long, P2 should be checked by Equation 42. Also, where heat transfer is taking place, P2 is seldom constant along the flow channel and appropriate averaging factors should be used. Computation using small zone subdivisions along the length of the tube circuit is recommended to limit errors in widely varying property values. The second important example considering flow under adiabatic conditions assumes an almost incom- pressible fluid, i.e., υ1 is approximately equal to υ2.(See Equation 21.) Substituting υ for υ1 and υ2 in Equa- tion 45, the result is: P P f L D G g v c 1 2 2 2 − = (46) All terms in Equations 45 and 46 are expressed in consistent units. However, it is general practice and often more convenient to use mixed units. For ex- ample, a useful form of Equation 46 in English units is: ∆P f L D v G e = 105 2 (47) where ∆P = fluid pressure drop, psi ƒ = friction factor from Fig. 1, dimensionless L = length, ft De = equivalent diameter of flow channel, in. (note units) υ = specific volume of fluid, ft3 /lb G = mass flux of fluid, lb/h ft2 Friction factor The friction factor (ƒ) introduced in Equation 26, is defined as the dimensionless fluid friction loss in ve- locity heads per diameter length of pipe or equivalent diameter length of flow channel. Earlier correlators in this field, including Fanning, used a friction factor one fourth the magnitude indicated by Equation 26. This is because the shear stress at the wall is proportional to one fourth the velocity head. All references to ƒ in this book combine the factor 4 in Equation 25 with ƒ as has been done by Darcy, Blasius, Moody and others. The friction factor is plotted in Fig. 1 as a function of the Reynolds number, a dimensionless group of vari- ables defined as the ratio of inertial forces to viscous forces. The Reynolds number (Re) can be written: Re or or= ρ µ ν µ VD VD GDe e e (48) where ρ = density of fluid, lbm/ft3 (kg/m3 ) ν = kinematic viscosity = µ /ρ, ft2 /h (m2 /s) µ = viscosity of fluid, lbm/ft h (kg/m s) V = velocity of fluid, ft/h (m/s) G = mass flux of fluid, lb/h ft2 (kg/m2 s) De = equivalent diameter of flow channel, ft (m) Fluid flow inside a closed channel occurs in a viscous or laminar manner at low velocity and in a turbulent manner at high velocities. Many experiments on fluid friction pressure drop, examined by dimensional analysis and the laws of similarity, have shown that the Reynolds number can be used to characterize a flow pattern. Examination of Fig. 1 shows that flow is laminar at Reynolds numbers less than 2000, gen- erally turbulent at values exceeding 4000 and com- pletely turbulent at higher values. Indeterminate con- ditions exist in the critical zone between Reynolds numbers of 2000 and 4000. Fluid flow can be described by a system of simulta- neous partial differential equations. (See earlier Fun- damental relationships section.) However, due to the complexity of these equations, solutions are generally only available for the case of laminar flow, where the only momentum changes are on a molecular basis. For laminar flow, integration of the Navier-Stokes equa-
- 96. 3-8 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company tion with velocity in the length direction only gives the following equation for friction factor: f = 64/Re (49) The straight line in the laminar flow region of Fig. 1 is a plot of this equation. It has been experimentally determined that the friction factor is best evaluated by using the Reynolds number to define the flow pattern.Afactor ε/De is then introduced to define the relative roughness of the channel surface. The coefficient ε expresses the aver- age height of roughness protrusions equivalent to the sand grain roughness established by Nikuradse.6 The friction factor values in Fig. 1 and the ε/De values in Fig. 2 are taken from experimental data as correlated by Moody.7 Laminar flow Laminar flow is characterized by the parallel flow- ing of individual streams like layers sliding over each other. There is no mixing between the streams except for molecular diffusion from one layer to the other. A small layer of fluid next to the boundary wall has zero velocity as a result of molecular adhesion forces. This establishes a velocity gradient normal to the main body of flow. Because the only interchanges of momentum in laminar flow are between the molecules of the fluid, the condition of the surface has no effect on the ve- locity gradient and therefore no effect on the friction factor. In commercial equipment, laminar flow is usu- ally encountered only with more viscous liquids such as the heavier oils. Turbulent flow When turbulence exists, there are momentum in- terchanges between masses of fluid. These inter- changes are induced through secondary velocities, irregular fluctuations or eddys, that are not parallel to the axis of the mean flow velocity. In this case, the condition of the boundary surface, roughness, does have an effect on the velocity gradient near the wall, which in turn affects the friction factor. Heat trans- fer is substantially greater with turbulent flow (Chap- ter 4) and, except for viscous liquids, it is common to induce turbulent flow with steam and water without Fig. 1 Friction factor/Reynolds number relationship for determining pressure drop of fluids flowing through closed circuits (pipes and ducts).
- 97. Steam 41 / Fluid Dynamics 3-9 The Babcock & Wilcox Company excessive friction loss. Consequently, it is customary to design for Reynolds numbers above 4000 in steam generating units. Turbulence fluctuations in the instantaneous ve- locity introduce additional terms to the momentum conservation equation called Reynolds stresses. These fluctuations influence the mean motion and increase the flow resistance in a manner producing an increase in the apparent viscosity. Analysis of turbulent flow must consider the impact of the fluctuating velocity component along with the mean flow velocity or re- sort to empirical methods that account for the addi- tional momentum dissipation.4, 6, 8 Velocity ranges Table 1 lists the velocity ranges generally encoun- tered in the heat transfer equipment as well as in duct and piping systems of steam generating units. These values, plus the specific volumes from the ASME Steam Tables (see Chapter 2) and the densities listed in Tables 2 and 3 in this chapter, are used to establish mass velocities for calculating Reynolds numbers and fluid friction pressure drops. In addition, values of viscosity, also required in calculating the Reynolds number, are given in Figs. 3, 4 and 5 for selected liq- uids and gases. Table 4 lists the relationship between various units of viscosity. Resistance to flow in valves and fittings Pipelines and duct systems contain many valves and fittings. Unless the lines are used to transport fluids over long distances, as in the distribution of process steam at a factory or the cross country transmission of oil or gas, the straight runs of pipe or duct are rela- tively short. Water, steam, air and gas lines in a power plant have relatively short runs of straight pipe and many valves and fittings. Consequently, the flow re- sistance due to valves and fittings is a substantial part of the total resistance. Methods for estimating the flow resistance in valves and fittings are less exact than those used in estab- lishing the friction factor for straight pipes and ducts. In the latter, pressure drop is considered to be the re- sult of the fluid shear stress at the boundary walls of the flow channel; this leads to relatively simple bound- ary value evaluations. On the other hand, pressure losses associated with valves, fittings and bends are mainly the result of impacts and inelastic exchanges Fig. 2 Relative roughness of various conduit surfaces. (SI conver- sion: mm = 25.4 X in.) Table 1 Velocities Common in Steam Generating Systems Velocity Nature of Service ft/min m/s Air: Air heater 1000 to 5000 5.1 to 25.4 Coal and air lines, pulverized coal 3000 to 4500 15.2 to 22.9 Compressed air lines 1500 to 2000 7.6 to 10.2 Forced draft air ducts 1500 to 3600 7.6 to 18.3 Forced draft air ducts, entrance to burners 1500 to 2000 7.6 to 10.2 Ventilating ducts 1000 to 3000 5.1 to 15.2 Crude oil lines [6 to 30 in. (152 to 762 mm)] 60 to 3600 0.3 to 18.3 Flue gas: Air heater 1000 to 5000 5.1 to 25.4 Boiler gas passes 3000 to 6000 15.2 to 30.5 Induced draft flues and breaching 2000 to 3500 10.2 to 17.8 Stacks and chimneys 2000 to 5000 10.2 to 25.4 Natural gas lines (large interstate) 1000 to 1500 5.1 to 7.6 Steam: Steam lines High pressure 8000 to 12,000 40.6 to 61.0 Low pressure 12,000 to 15,000 61.0 to 76.2 Vacuum 20,000 to 40,000 101.6 to 203.2 Superheater tubes 2000 to 5000 10.2 to 25.4 Water: Boiler circulation 70 to 700 0.4 to 3.6 Economizer tubes 150 to 300 0.8 to 1.5 Pressurized water reactors Fuel assembly channels 400 to 1300 2.0 to 6.6 Reactor coolant piping 2400 to 3600 12.2 to 18.3 Water lines, general 500 to 750 2.5 to 3.8
- 98. 3-10 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company of momentum. These losses are frequently referred to as local losses or local nonrecoverable pressure losses. Even though momentum is conserved, kinetic ener- gies are dissipated as heat. This means that pressure losses are influenced mainly by the geometries of valves, fittings and bends. As with turbulent friction factors, pressure losses are determined from empiri- cal correlations of test data. These correlations may be based on equivalent pipe lengths, but are prefer- ably defined by a multiple of velocity heads based on the connecting pipe or tube sizes. Equivalent pipe length calculations have the disadvantage of being dependent on the relative roughness (ε/D) used in the correlation. Because there are many geometries of valves and fittings, it is customary to rely on manu- facturers for pressure drop coefficients. It is also customary for manufacturers to supply valve flow coefficients (CV) for 60F (16C) water. These are expressed as ratios of weight or volume flow in the fully open position to the square root of the pressure drop. These coefficients can be used to relate velocity head losses to a connecting pipe size by the following expression: N kD Cv V= 4 2 / (50) Table 3 Physical Properties of Gases at 14.7 psi (0.101 MPa)** Instantaneous Specific Heat Temperature Density, cp cv k, Gas F lb/ft3 Btu/lb F Btu/lb F cp/cv Air 70 0.0749 0.241 0.172 1.40 200 0.0601 0.242 0.173 1.40 500 0.0413 0.248 0.180 1.38 1000 0.0272 0.265 0.197 1.34 CO2 70 0.1148 0.202 0.155 1.30 200 0.0922 0.216 0.170 1.27 500 0.0634 0.247 0.202 1.22 1000 0.0417 0.280 0.235 1.19 H2 70 0.0052 3.440 2.440 1.41 200 0.0042 3.480 2.490 1.40 500 0.0029 3.500 2.515 1.39 1000 0.0019 3.540 2.560 1.38 Flue gas* 70 0.0776 0.253 0.187 1.35 200 0.0623 0.255 0.189 1.35 500 0.0429 0.265 0.199 1.33 1000 0.0282 0.283 0.217 1.30 CH4 70 0.0416 0.530 0.406 1.30 200 0.0334 0.575 0.451 1.27 500 0.0230 0.720 0.596 1.21 1000 0.0151 0.960 0.836 1.15 * From coal; 120% total air; flue gas molecular weight 30. ** SI conversions: T, C = 5/9 (F-32); ρ, kg/m3 = 16.02 x lbm/ ft3 ; cp, kJ/kg K = 4.187 x Btu/lbm F. Table 4 Relationship Between Various Units of Viscosity Part A: Dynamic (or Absolute) Viscosity, µ Pa s Centipoise N s kg 0.01 g lbm lbm lbf s m2 m s cm s ft s ft h ft2 1.0 1000 672 x 10−3 2420 20.9 x 10−3 0.001 1.0 672 x 10−6 2.42 20.9 x 10−6 1.49 1488 1.0 3600 0.0311 413 x 10−6 0.413 278 x 10−6 1.0 8.6 x 10−6 47.90 47,900 32.2 115,900 1.0 Part B: Kinematic Viscosity, ν = µ/ρ Centistoke m2 0.01 cm2 ft2 ft2 s s s h 1.0 106 10.8 38,800 10−6 1.0 10.8 x 10−6 0.0389 92.9 x 10−3 92,900 1.0 3600 25.8 x 10−6 25.8 278 x 10−6 1.0 = Table 2 Physical Properties of Liquids at 14.7 psi (0.101 MPa) Density Specific Heat Liquid Temperature F (C) lb/ft3 (kg/m3 ) Btu/lb F (kJ/kg C) Water 70 (21) 62.4 (999.4) 1.000 (4.187) 212 (100) 59.9 (959.3) 1.000 (4.187) Automotive oil 70 (21) SAE 10 55 to 57 (881 to 913) 0.435 (1.821) SAE 50 57 to 59 (913 to 945) 0.425 (1.779) Mercury 70 (21) 846 (13,549) 0.033 (0.138) Fuel oil, #6 70 (21) 60 to 65 (961 to 1041) 0.40 (1.67) 180 (82) 60 to 65 (961 to 1041) 0.46 (1.93) Kerosene 70 (21) 50 to 51 (801 to 817) 0.47 (1.97)
- 99. Steam 41 / Fluid Dynamics 3-11 The Babcock & Wilcox Company where Nυ = number of velocity heads, dimensionless k = units conversion factor: for CV based upon gal/min/(∆ρ)1/2 , k = 891 D = internal diameter of connecting pipe, in. (mm) CV = flow coefficient in units compatible withk and D: for k = 891, CV = gal/min/(∆ρ)1/2 CV and corresponding values of Nυ for valves apply only to incompressible flow. However, they may be ex- trapolated for compressible condition using an average specific volume between P1 and P2 for ∆P values as high as 20% of P1. This corresponds to a maximum pressure ratio of 1.25. The ∆P process for valves, bends and fit- tings is approximately isothermal and does not require the most stringent limits set by Equation 21. When pressure drop can be expressed as an equiva- lent number of velocity heads, it can be calculated by the following formula in English units: ∆P N v G v= 12 105 2 (51) where ∆P = pressure drop, lb/in.2 Nυ = number of equivalent velocity heads, dimen- sionless υ = specific volume, ft3 /lb G = mass flux, lb/ft2 h Anotherconvenientexpression,inEnglishunitsonly, for pressure drop in air (or gas) flow evaluations is: ∆P N B T G v= + × 30 460 1 73 10 105 3 2 . (52) where ∆P = pressure drop, in. wg B = barometric pressure, in. Hg T = air (or gas) temperature, F Equation 52 is based on air, which has a specific volume of 25.2 ft3 /lb at 1000R and a pressure equiva- lent to 30 in. Hg. This equation can be used for other gases by correcting for specific volume. The range in pressure drop through an assortment ofcommercialfittingsisgiveninTable5.Thisresistance to flow is presented in equivalent velocity heads based ontheinternaldiameteroftheconnectingpipe.Asnoted, pressure drop through fittings may also be expressed as the loss in equivalent lengths of straight pipe. Contraction and enlargement irreversible pressure loss The simplest sectional changes in a conduit are con- verging or diverging boundaries. Converging bound- aries can stabilize flow during the change from pres- sure energy to kinetic energy, and local irrecoverable flow losses (inelastic momentum exchanges) can be practically eliminated with proper design. If the in- cluded angle of the converging boundaries is 30 deg (0.52 rad) or less and the terminal junctions are smooth and tangent, any losses in mechanical energy are largely due to fluid friction. It is necessary to con- sider this loss as 0.05 times the velocity head, based on the smaller downstream flow area. Fig. 4 Absolute viscosities of some common gases at atmospheric pressure.Fig. 3 Absolute viscosities of some common liquids (Pa s = 0.000413 X lbm/ft h).
- 100. 3-12 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company When the elevation change (Z2 – Z1) is zero, the mechanical energy balance for converging boundaries becomes: P v V g P v V g N V gc c c c 1 1 2 2 2 2 2 2 2 2 2 + = + + (53) Subscripts 1 and 2 identify the upstream and down- stream sections. Nc, the contraction loss factor, is the number of velocity heads lost by friction and local non- recoverable pressure loss in contraction. Fig. 6 shows values of this factor. When there is an enlargement of the conduit sec- tion in the direction of flow, the expansion of the flow stream is proportional to the kinetic energy of the flowing fluid and is subject to a pressure loss depend- ing on the geometry. Just as in the case of the con- traction loss, this is an irreversible energy conversion to heat resulting from inelastic momentum ex- changes. Because it is customary to show these losses as coefficients of the higher kinetic energy term, the mechanical energy balance for enlargement loss is: P v V g P v V g N V gc c e c 1 1 2 2 2 2 1 2 2 2 2 + = + + (54) The case of sudden enlargement [angle of divergence β = 180 deg (π rad)] yields an energy loss of (V1 - V2)2 / 2gc. This can also be expressed as: N A A e = − 1 1 2 2 (55) where A1 and A2 are the upstream and downstream cross-sectional flow areas, respectively and (A1 < A2). Even this solution, based on the conservation laws, depends on qualifying assumptions regarding static Fig. 6 Contraction loss factor for β>30 deg (Nc = 0.05 for β≤30 deg). Table 5 Resistance to Flow of Fluids Through Commercial Fittings* Fitting Loss in Velocity Heads L-shaped, 90 deg (1.57 rad) standard sweep elbow 0.3 to 0.7 L-shaped, 90 deg (1.57 rad) long sweep elbow 0.2 to 0.5 T-shaped, flow through run 0.15 to 0.5 T-shaped, flow through 90 deg (1.57 rad) branch 0.6 to 1.6 Return bend, close 0.6 to 1.7 Gate valve, open 0.1 to 0.2 Check valve, open 2.0 to 10.0 Globe valve, open 5.0 to 16.0 Angle valve, 90 deg (1.57 rad) open 3.0 to 7.0 Boiler nonreturn valve, open 1.0 to 3.0 * See Fig. 9 for loss in velocity heads for flow of fluids through pipe bends. Fig. 5 Absolute viscosities of saturated and superheated steam.
- 101. Steam 41 / Fluid Dynamics 3-13 The Babcock & Wilcox Company pressures at the upstream and downstream faces of the enlargement. Experimental values of the enlargement loss fac- tor, based on different area ratios and angles of diver- gence, are given in Fig. 7. The differences in static pressures caused by sudden and gradual changes in section are shown graphically in Fig. 8. The pressure differences are shown in terms of the velocity head at the smaller area plotted against section area ratios. Flow through bends Bends in a pipeline or duct system produce pressure losses caused by both fluid friction and momentum exchanges which result from a change in flow direc- tion. Because the axial length of the bend is normally included in the straight length friction loss of the pipe- line or duct system, it is convenient to subtract a cal- culated equivalent straight length friction loss from experimentally determined bend pressure loss factors. These corrected data form the basis of the empirical bend loss factor, Nb. The pressure losses for bends in round pipe in ex- cess of straight pipe friction vary slightly with Rey- nolds numbers below 150,000. For Reynolds numbers above this value, they are reasonably constant and depend solely on the dimensionless ratio r/D, the ra- tio of the centerline radius of the bend to the internal diameter of the pipe. For commercial pipe, the effect of Reynolds number is negligible. The combined ef- fect of radius ratio and bend angle, in terms of veloc- ity heads, is shown in Fig. 9. Flow through rectangular ducts The loss of pressure caused by a direction change in a rectangular duct system is similar to that for cy- lindrical pipe. However, an additional factor, the shape of the duct in relation to the direction of bend, must be taken into account. This is called the aspect ratio, which is defined as the ratio of the width to the depth of the duct, i.e., the ratio b/d in Fig. 10. The bend loss for the same radius ratio decreases as the aspect ratio increases,becauseofthesmallerproportionateinfluence of secondary flows on the stream. The combined effect of radius and aspect ratios on 90 deg (1.57 rad) duct bends is given in terms of velocity heads in Fig. 10. The loss factors shown in Fig. 10 are average val- ues of test results on ducts. For the given range of aspect ratios, the losses are relatively independent of the Reynolds number. Outside this range, the varia- tion with Reynolds number is erratic. It is therefore recommended that Nb values for b/d = 0.5 be used for all aspect ratios less than b/d = 0.5, and values for b/ d = 2.0 be used for ratios greater than b/d = 2.0. Losses for bends other than 90 deg (1.57 rad) are customar- ily considered to be proportional to the bend angle. Turning vanes The losses in a rectangular elbow duct can be re- duced by rounding or beveling its corners and by in-Fig. 7 Enlargement loss factor for various included angles. Fig. 8 Static pressure difference resulting from sudden and gradual changes in section.
- 102. 3-14 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company stalling turning vanes. With rounding or beveling, the overall size of the duct can become large; however, with turning vanes, the compact form of the duct is preserved. A number of turning vane shapes can be used in a duct. Fig. 11 shows four different arrangements. Seg- mented shaped vanes are shown in Fig. 11a, simple curved thin vanes are shown in Fig. 11b, and concen- tric splitter vanes are shown in Fig. 11c. In Fig. 11c, the vanes are concentric with the radius of the duct. Fig. 11d illustrates simple vanes used to minimize flow separation from a square edged duct. The turning vanes of identical shape and dimen- sion, Fig. 11b, are usually mounted within the bend of an elbow. They are generally installed along a line or section of the duct and are placed from the inner corner to the outside corner of the bend. Concentric turning vanes, Fig. 11c, typically installed within the bend of the turn, are located from one end of the turn to the other end. The purpose of the turning vanes in an elbow or turn is to deflect the flow around the bend to the inner wall of the duct. When the turning vanes are appropriately designed, the flow distribution is improved by reduc- ing flow separation from the walls and reducing the formation of eddy zones in the downstream section of thebend.Thevelocitydistributionoverthedownstream cross-section of the turn is improved (see Fig. 12), and the pressure loss of the turn or elbow is decreased. The main factor in decreasing the pressure losses and obtaining equalization of the velocity field is the elimination of an eddy zone at the inner wall of the turn. For a uniform incoming flow field, the largest effect of decreasing the pressure losses and establish- ing a uniform outlet flow field for a turn or elbow is achieved by locating the turning vanes closer to the inner curvature of the bend. (See Figs. 11d and 12c.) For applications requiring a uniform velocity distri- bution directly after the turn, a full complement or normal arrangement of turning vanes (see Fig. 12b) is required. However, for many applications, it is suf- ficient to use a reduced number of vanes, as shown in Fig. 12c. For nonuniform flow fields, the arrangement of turning vanes is more difficult to determine. Many times, numerical modeling (see Chapter 6) and flow testing of the duct system must be done to determine the proper vane locations. Fig. 9 Bend loss for round pipe, in terms of velocity heads. Fig. 10 Loss for 90 deg (1.57 rad) bends in rectangular ducts.
- 103. Steam 41 / Fluid Dynamics 3-15 The Babcock & Wilcox Company Pressure loss A convenient chart for calculating the pressure loss resulting from impact losses in duct systems convey- ing air (or flue gas) is shown in Fig. 13. When mass flux and temperature are known, a base velocity head in inches of water at sea level can be obtained. Flow over tube banks Bare tube The transverse flow of gases across tube banks is an example of flow over repeated major cross- sectional changes. When the tubes are staggered, sec- tional and directional changes affect the resistance. Experimental results and the analytical conclusions of extensive research by The Babcock & Wilcox Com- pany (B&W) indicate that three principal variables other than mass flux affect this resistance. The pri- mary variable is the number of major restrictions, i.e., the number of tube rows crossed, N. The second vari- able is the friction factor ƒ which is related to the Reynolds number (based on tube diameter), the tube spacing diameter ratios, and the arrangement pattern (in-line or staggered). The third variable is the depth factor, Fd (Fig. 14), which is applicable to banks less than ten rows deep. The friction factors ƒ for various in-line tube patterns are given in Fig. 15. The product of the friction factor, the number of major restrictions (tube rows) and the depth factor is, in effect, the summation of velocity head losses through the tube bank. N f N Fv d= (56) The Nυ value established by Equation 56 may be used in Equations 51 or 52 to find the tube bank pres- sure loss. Some test correlations indicate ƒ values higher than the isothermal case for cooling gas and lower for heating gas. Finned tube In some convective boiler design ap- plications, extended surface tube banks are used. Many types of extended surface exist, i.e., solid heli- cal fin, serrated helical fin, longitudinal fin, square fin anddifferenttypesofpinstuds.Forfurnaceapplications, the cleanliness of the gas or heat transfer medium dic- tateswhetheranextendedsurfacetubebankcanbeused and also defines the type of extended surface. Several different tube bank calculation methods exist for extended surface, and many are directly re- lated to the type of extended surface that is used. Various correlations for extended surface pressure loss can be found in References 9 through 15. In all cases, a larger pressure loss per row of bank exists with an extended surface tube compared to a bare tube. For in-line tube bundles, the finned tube resistance per row of tubes is approximately 1.5 times that of the bare tube row. However, due to the increased heat trans- fer absorption of the extended surface, a smaller num- ber of tube rows is required. This results in an overall bank pressure loss that can be equivalent to a larger but equally absorptive bare tube bank. Flow through stacks or chimneys The flow of gases through stacks or chimneys is es- tablished by the natural draft effect of the stack and/ or the mechanical draft produced by a fan. The resis- tance to this flow, or the loss in mechanical energy be- Fig. 11 Turning vanes in elbows and turns: a) segmented, b) thin concentric, c) concentric splitters, and d) slotted (adapted from Idelchik, Reference 12). Fig. 12 Velocity profiles downstream of an elbow: a) without vanes, b) with typical vanes, and c) with optimum vanes (adapted from Idelchik, Reference 12). Fig. 13 Mass flux/velocity head relationship for air.
- 104. 3-16 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company tween the bottom and the top of the stack, is a result of the friction and stack exit losses.Application examples of these losses are given in Chapter 25. Pressure loss in two-phase flow Evaluation of two-phase steam-water flows is much more complex.As with single-phase flow, pressure loss occurs from wall friction, acceleration, and change in elevation. However, the relationships are more com- plicated. The evaluation of friction requires the assess- ment of the interaction of the steam and water phases. Acceleration is much more important because of the large changes in specific volume of the mixture as water is converted to steam. Finally, large changes in average mixture density at different locations signifi- cantly impact the static head. These factors are pre- sented in detail in Chapter 5. Entrainment by fluid flow Collecting or transporting solid particles or a sec- ond fluid by the flow of a primary fluid at high veloc- ity is known as entrainment. This is usually accom- plished with jets using a small quantity of high pres- sure fluid to carry large quantities of another fluid or solid particles. The pressure energy of the high pres- sure fluid is converted into kinetic energy by nozzles, with a consequent reduction of pressure. The mate- rial to be transported is drawn in at the low pressure zone, where it meets and mixes with the high veloc- ity jet. The jet is usually followed by a parallel throat section to equalize the velocity profile. The mixture then enters a diverging section where kinetic energy is partially reconverted into pressure energy. In this case, major fluid flow mechanical energy losses are an example of inelastic momentum exchanges occurring within the fluid streams. Theinjector isajetpumpthatusescondensingsteam as the driving fluid to entrain low pressure water for delivery against a back pressure higher than the pres- sure of the steam supplied. The ejector, similar to the injector, is designed to entrain gases, liquids, or mix- tures of solids and liquids for delivery against a pres- sure less than that of the primary fluid. In a water- jet aspirator, water is used to entrain air to obtain a partial vacuum. In the Bunsen type burner, a jet of gas entrains air for combustion. In several instances, entrainment may be detrimental to the operation of steam boilers. Particles of ash entrained by the prod- ucts of combustion, when deposited on heating sur- faces, reduce thermal conductance, erode fan blades, and add to pollution when discharged into the atmo- sphere. Moisture carrying solids, either in suspension or in solution, are entrained in the stream. The solids may be carried through to the turbine and deposited on the blades, decreasing turbine capacity and effi- ciency. In downcomers or supply tubes, steam bubbles are entrained in the water when the drag on the bubbles is greater than the buoyant force. This re- duces the density in the pumping column of natural circulation boilers. Fig. 14 Draft loss depth factor for number of tube rows crossed in convection banks. Fig. 15 Friction factor (f ) as affected by Reynolds number for various in-line tube patterns; crossflow gas or air.
- 105. Steam 41 / Fluid Dynamics 3-17 The Babcock & Wilcox Company Boiler circulation An adequate flow of water and steam-water mix- ture is necessary for steam generation and control of tube metal temperatures in all circuits of a steam gen- erating unit. At supercritical pressures this flow is produced mechanically by pumps.At subcritical pres- sures, circulation is produced by the force of gravity or pumps, or a combination of the two. The elements of single-phase flow discussed in this chapter, two- phase flow discussed in Chapter 5, heat input rates, and selected limiting design criteria are combined to evaluate the circulation in fossil-fired steam genera- tors. The evaluation procedures and key criteria are presented in Chapter 5. 1. Meyer, C.A., et al., ASME Steam Tables, Sixth Ed., American Society of Mechanical Engineers, New York, New York, 1993. 2. Tabor, D., Gases, Liquids and Solids: and Other States of Matter, First Ed., Penguin Books, Ltd., Harmondsworth, England, United Kingdom, 1969. 3. Lahey, Jr., R.T., and Moody, F.J., The Thermal-Hy- draulics of a Boiling Water Nuclear Reactor, Ameri- can Nuclear Society, Hinsdale, Ilinois, 1993. 4. Rohsenow, W., Hartnett, J., and Ganic, E., Handbook of Heat Transfer Fundamentals, McGraw-Hill Com- pany, New York, 1985. 5. Burmeister, L.C., Convective Heat Transfer, Second Ed., Wiley-Interscience, New York, New York, 1993. 6. Schlichting, H.T. Gersten, K., and Krause, E., Boundary-Layer Theory, Eighth Ed., Springer-Verlag, New York, New York, 2000. 7. Moody, L.F., “Friction Factors for Pipe Flow,” Trans- actions of the American Society of Mechanical Engi- neers (ASME), Vol. 66, 8, pp. 671-684, November, 1944. 8. Hinze, J.O., Turbulence: An Introduction to Its Mechanism and Theory, Second Ed., McGraw-Hill Company, New York, New York, 1975. References 9. Briggs, D.E., and Young, E.H., “Convective heat transfer and pressure drop of air flowing across trian- gular pitch banks of finned tubes,” Chemical Engineer- ing Progress Symposium Series (Heat Transfer), AIChE, Vol. 41, No. 41, pp. l-10, Houston, Texas, 1963. 10. Grimison, E.D., “Correlation and utilization of new data on flow resistance and heat transfer for crossflow of gases over tube banks,” Transactions of ASME, Process Industries Division, Vol. 59, pp. 583-594, New York, New York, 1937. 11. Gunter, A.Y., and Shan, W.A., “A general correlation of friction factors for various types of surfaces in cross- flow,” Transactions of ASME, Vol. 67, pp. 643-660, 1945. 12. Idelchik, I.E., Handbook of Hydraulic Resistance, Third Ed., Interpharm/CRC, New York, New York, November, 1993. 13. Jakob, M., Discussion appearing in Transactions of ASME, Vol. 60, pp. 384-386, 1938. 14. Kern, D.Q., Process Heat Transfer, p. 555, McGraw- Hill Company, New York, New York, December, 1950. 15. Wimpress, R.N., Hydrocarbon Processing and Petro- leum Refiner, Vol. 42, No. 10, pp. 115-126, Gulf Pub- lishing Company, Houston, Texas, 1963.
- 106. 3-18 Steam 41 / Fluid Dynamics The Babcock & Wilcox Company Laser velocity measurements in a steam generator flow model.
- 107. Steam 41 / Heat Transfer 4-1 The Babcock & Wilcox Company Chapter 4 Heat Transfer Heat transfer deals with the transmission of ther- mal energy and plays a central role in most energy conversion processes. Heat transfer is important in fossil fuel combustion, chemical reaction processes, electrical systems, nuclear fission and certain fluid systems. It also occurs during everyday activities in- cluding cooking, heating and refrigeration, as well as being an important consideration in choosing cloth- ing for different climates. Although the fundamentals of heat transfer are simple, practical applications are complex because real systemscontainirregulargeometries,combinedmodes of heat transfer and time dependent responses. Fundamentals Basic modes of heat transfer There are three modes of heat transfer: conduction, convection and radiation. One or more of these modes controls the amount of heat transfer in all applications. Conduction Temperature is a property that indi- cates the kinetic energy possessed by the molecules of a substance; the higher the temperature the greater the kinetic energy or molecular activity of the sub- stance. Molecular conduction of heat is simply the transfer of energy due to a temperature difference between adjacent molecules in a solid, liquid or gas. Conduction heat transfer is evaluated using Fourier’s law: q kA dT dx c = − (1) The flow of heat, qc, is positive when the tempera- ture gradient, dT/dx, is negative. This result, consis- tent with the second law of thermodynamics, indicates that heat flows in the direction of decreasing tempera- ture. The heat flow, qc, is in a direction normal (or per- pendicular) to an area, A, and the gradient, dT/dx, is the change of temperature in the direction of heat flow. The thermal conductivity, k, a property of the mate- rial, quantifies its ability to conduct heat. A range of thermal conductivities is listed in Table 1. The discrete form of the conduction law is written: q kA L T T= −( )1 2 (2) Fig. 1 illustrates positive heat flow described by this equation and shows the effect of variable thermal con- ductivity on the temperature distribution. The group- ing kA/L is known as the thermal conductance, Kc; the inverse L/kA is known as the thermal resistance, Rc and Kc = 1/Rc. A special case of conduction is the thermal contact resistanceacrossajointbetweensolidmaterials.Atthe interface of two solid materials the surface to surface contact is imperfect from the gap that prevails due to surface roughness. In nuclear applications with fuel pellets and fuel cladding, surface contact resistance can have a major impact on heat transfer. If one di- mensional steady heat flow is assumed, the heat trans- fer across a gap is defined by: q T T Rct = −1 2 (3) where the quantity Rct is called the thermal contact resistance, 1/hctA, and hct is called the contact coeffi- cient. T1 and T2 are the average surface temperatures on each side of the gap. Tabulated values of the con- tact coefficient are presented in References 1 and 2. Table 1 Thermal Conductivity, k, of Common Materials Material Btu/h ft F W/m C Gases at atmospheric pressure 0.004 to 0.70 0.007 to 1.2 Insulating materials 0.01 to 0.12 0.02 to 0.21 Nonmetallic liquids 0.05 to 0.40 0.09 to 0.70 Nonmetallic solids (brick, stone, concrete) 0.02 to 1.5 0.04 to 2.6 Liquid metals 5.0 to 45 8.6 to 78 Alloys 8.0 to 70 14 to 121 Pure metals 30 to 240 52 to 415
- 108. 4-2 Steam 41 / Heat Transfer The Babcock & Wilcox Company Nomenclature A surface area, ft2 (m2 ) cp specific heat at constant pressure, Btu/lb F (J/kg K) Cf cleanliness factor, dimensionless Ct thermal capacitance, Btu/ft3 F (J/m3 K) C electrical capacitance, farad D diameter, ft (m) De equivalent diameter, ft (m) Eb blackbody emissive power, Btu/h ft2 (W/m2 ) F radiation configuration factor, dimensionless F heat exchanger arrangement factor, dimensionless Fa crossflow arrangement factor, dimensionless Fd tube bundle depth factor, dimensionless Fpp fluid property factor, see text FT fluid temperature factor, dimensionless F total radiation exchange factor, dimensionless g acceleration of gravity, 32.17 ft/s2 (9.8 m/s2 ) G incident thermal radiation, Btu/h ft2 (W/m2 ) G mass flux or mass velocity, lb/h ft2 (kg/m2 s) h heat transfer coefficient, Btu/h ft2 F (W/m2 K) hc crossflow heat transfer coef., Btu/h ft2 F (W/m2 K) hct contact coefficient, Btu/h ft2 F (W/m2 K) hc ′ crossflow velocity and geometry factor, see text hl longitudinal heat transfer coef., Btu/h ft2 F (W/m2 K) h l ′ longitudinal flow velocity and geometry factor, see text H enthalpy, Btu/lb (J/kg) Hfg latent heat of vaporization, Btu/lb (J/kg) I electrical current, amperes J radiosity, Btu/h ft2 (W/m2 ) k thermal conductivity, Btu/h ft F (W/m K) K thermal conductance, Btu/h F (W/K) Ky mass transfer coefficient, lb/ft2 s (kg/m2 s) L beam length, ft (m) L, length or dimension, ft (m) Lh fin height, ft (m) Lt fin spacing, ft (m) m mass flow rate, lb/h (kg/s) p pressure or partial pressure, atm (Pa) P temp. ratio for surface arrgt. factor, dimensionless q heat flow rate, Btu/h (W) ′′′q volumetric heat generation rate, Btu/h ft3 (W/m3 ) qrel heat release, Btu/h ft3 (W/m3 ) r radius, ft (m) R electrical resistance (ohms) R temp. ratio for surface arrgt. factor, dimensionless R thermal resistance, h F/Btu (K/W) R radiative resistance, 1/ft2 (1/m2 ) Rf fouling factor, h ft2 F/Btu (m2 K/W) S total exposed surface area for a finned surface, ft2 (m2 ) Sf fin surface area; sides plus peripheral area, ft2 (m2 ) SH source term for internal heat generation, Btu/h ft3 (W/m3 ) t time, s or h, see text (s) T temperature, F or R (C or K) T° temperature at initial time, F (C) ∆t time interval, s ∆T temperature difference, F (C) ∆TLMTD log mean temperature difference, F (C) u,v,w velocity in x, y, z coordinates respectively, ft/s (m/s) U overall heat transfer coef., Btu/h ft2 F (W/m2 K) V electrical voltage, volts V velocity, ft/s (m/s) V volume, ft3 (m3 ) x dimension, ft (m) x,y,z dimensions in Cartesian coordinate system, ft (m) ∆x change in length, ft (m) Y Schmidt fin geometry factor, dimensionless Yg concentration in bulk fluid, lb/lb (kg/kg) Yi concentration at condensate interface, lb/lb (kg/kg) Z Schmidt fin geometry factor, dimensionless α absorptivity, or total absorptance, dimensionless β volume coefficient of expansion, 1/R (1/K) Γ effective diffusion coefficient, lb/ft s (kg/m s) ε emissivity, or total emittance, dimensionless η Schmidt fin efficiency, dimensionless µ dynamic viscosity, lbm/ft s (kg/m s) ρ density, lb/ft3 (kg/m3 ) ρ reflectivity, dimensionless σ Stefan-Boltzmann constant, 0.1713 × 10-8 Btu/h ft2 R4 (5.669 × 10-8 W/m2 K4 ) τ transmissivity, dimensionless Subscripts: b bulk c conduction ct contact cv convection e node point east eff effective f film or fin fd fully developed g gas i inside or ith parameter j jth parameter o outside p node point under evaluation r radiation s surface sg surface to gas w node point west w wall δ liquid film surface (gas liquid interface) ∞ free stream conditions ⊥ perpendicular to flow parallel to flow Dimensionless groups: Gr g T T L hL k s = −( ) = = ∞β ρ µ 2 3 2 Grashof number Nu Nusselt number Pe Re PPr Peclet number Pr Prandtl number Ra Gr Pr Rayleigh numb = = c k p µ eer Re Reynolds number St Nu Re Pr Stanton number = = = = ρ µ µ V L G L h c Gp
- 109. Steam 41 / Heat Transfer 4-3 The Babcock & Wilcox Company Examples include 300 Btu/h ft2 F (1.7 kW/m2 K) be- tween two sections of ground 304 stainless steel in air and 25,000 Btu/h ft2 F (142 kW/m2 K) between two sections of ground copper in air. The factors are usu- ally unknown for specific applications and estimates need to be made. There are two principal contributions across the gap – solid to solid conduction at the points of contact and thermal conduction through the en- trapped gases in the void spaces. Convection Convection heat transfer within a fluid (gas or liquid) occurs by a combination of molecular conduction and macroscopic fluid motion. Convection occurs adjacent to heated surfaces as a result of fluid motion past the surface as shown in Fig. 2. Natural convection occurs when the fluid motion is due to buoyancy effects caused by local density dif- ferences. In the top portion of Fig. 2, the fluid motion is due to heat flow from the surface to the fluid; the fluid density decreases causing the lighter fluid to rise and be replaced by cooler fluid. Forced convection re- sults when mechanical forces from devices such as fans give motion to the fluids. The rate of heat transfer by convection, qcv, is defined: q hA T Tcv s f= −( ) (4) where h is the local heat transfer coefficient, A is the surface area, Ts is the surface temperature and Tƒ is the fluid temperature. Equation 4 is known as Newton’s Law of Cooling and the term hAs is the con- vection conductance, Kcv. The heat transfer coefficient, h, is also termed the unit conductance, because it is defined as the conductance per unit area. Average heat transfer coefficients over a surface are used in most engineering applications. This convective heat transfer coefficient is a function of the thermal and fluid dynamic properties and the surface geometry.Ap- proximate ranges are shown in Table 2. Radiation Radiation is the transfer of energy be- tween bodies by electromagnetic waves. This trans- fer, unlike conduction or convection, requires no in- tervening medium. The electromagnetic radiation, in the wavelength range of 0.1 to 100 micrometers, is produced solely by the temperature of a body. Energy at the body’s surface is converted into electromagnetic waves that emanate from the surface and strike an- other body. Some of the thermal radiation is absorbed by the receiving body and reconverted into internal energy, while the remaining energy is reflected from or transmitted through the body. The fractions of ra- diation reflected, transmitted and absorbed by a sur- face are known respectively as the reflectivity, ρ, trans- missivity, τ, and absorptivity α. The sum of these frac- tions equals one: Fig. 2 Natural and forced convection. Above, boundary layer on a vertical flat plate. Below, velocity profiles for laminar and turbulent boundary layers in flow over a flat plate. (Vertical scale enlarged for clarity.) Table 2 Typical Convective Heat Transfer Coefficients, h Condition Btu/h ft2 F W/m2 C Air, free convection 1 to 5 6 to 30 Air, forced convection 5 to 50 30 to 300 Steam, forced convection 300 to 800 1800 to 4800 Oil, forced convection 5 to 300 30 to 1800 Water, forced convection 50 to 2000 300 to 12,000 Water, boiling 500 to 20,000 3000 to 120,000Fig. 1 Temperature-thickness relationships corresponding to different thermal conductivities, k.
- 110. 4-4 Steam 41 / Heat Transfer The Babcock & Wilcox Company ρ τ α+ + = 1 (5) All surfaces absorb radiation, and all surfaces whose temperatures are above absolute zero emit thermal ra- diation. Surfaces in boilers are typically opaque, which do not allow transmission of any radiation (τ = 0). Thermal radiation generally passes through gases such as dry air with no absorption taking place. These nonabsorbing, or nonparticipating, gases do not af- fect the radiative transfer. Other gases, like carbon di- oxide, water vapor and carbon monoxide, to a lesser degree, affect radiative transfer and are known as participating gases. These gases, prevalent in the flue gases of a boiler, affect the heat transfer to surfaces and the distribution of energy absorbed in the boiler. All bodies continuously emit radiant energy in amounts which are determined by the temperature and the nature of the surface. A perfect radiator, or blackbody, absorbs all of the incident thermal radia- tion, G, reaching its surface: q A Gr + = (6) and emits radiant energy at the maximum theoreti- cal limit according to the Stefan-Boltzmann law: q A Tr s − = σ 4 (7) σ is the Stefan-Boltzmann constant 0.1713 × 10-8 Btu/ h ft2 R4 (5.669 × 10-8 W/m2 K4 ), and Ts is the absolute temperature of the surface, R (K). The product σ Ts 4 is also known as the blackbody emissive power, Eb. The net radiative heat transfer of a blackbody is the dif- ference between absorbed and emitted radiant energy: q q q A G Tr r r s= − = −+ − ( )σ 4 (8) The radiation from a blackbody extends over the whole range of wavelengths, although the bulk of it in boiler applications is concentrated in a band from 0.1 to 20 micrometers. The wavelength at which the maximum radiation intensity occurs is inversely pro- portional to the absolute temperature of the body; this is known as Wien’s law. A real radiator absorbs less than 100% of the en- ergy incident on it and emits less than the maximum theoretical limit. The net heat transfer by radiation from a real surface can be expressed by: q A G Tr s= −( )α ε σ 4 (9) where ε is the total emissivity and α is the total ab- sorptivity. If the emissivity and absorptivity are inde- pendent of wavelength, the surface is termed a non- selective radiator, or gray surface. According to Kirchoff’s law, emissivity and absorptivity are always equal for a gray surface: ε α= (10) Therefore, a can be eliminated from Equation 9, and emissivity is all that is needed to describe the radia- tion properties of the surface. Table 3 shows some rep- resentative values of emissivity. If all surfaces are as- sumed to be gray, a simpler treatment of radiation is possible. For two surface enclosures, this treatment involves introducing a total exchange factor, F12, which depends on the configuration (geometry), the emissivities and the surface areas.3 If the emissivity depends on wavelength, the sur- face is termed a selective or non-gray radiator.Accord- ing to Kirchhoff’s law, spectral emissivity and spec- tral absorptivity are always equivalent, ελ =αλ, for non- gray surfaces. Total emissivity is the integrated aver- age of ελ over the spectrum of emitted radiation, and total absorptivity is the integrated average of αλ over the spectrum of incident radiation. The terms emis- sivity and emittance (and corresponding terms absorp- tivity and absorptance) are commonly interchanged in the literature. For convenience, the term emittance is used here for total emissivity and absorptance is used for total absorptivity, of non-gray surfaces. For non-gray surfaces, the emittance can be ex- pressed as a function of the surface temperature ε (Ts), and absorptance as a function of the incident radia- tion or flame temperature, α (Tf). Based on Kirchhoff ’s law, plots of ε vs Ts may be interpreted as plots of α vs Tf if the physical state of the surface is unchanged. An analysis of non-gray conditions re- quires temperature dependent emittance and absorp- tance, or spectral property calculations which are more complicated. An example of non-gray radiators in a boileraretheashdepositsonwaterwallheatingsurfaces. The net radiation heat transfer between two black- body surfaces which are separated by a vacuum or nonparticipating gas is written: q A F T T12 1 12 1 4 2 4 = −( )σ (11) A1 is the surface area; F12 is the geometric shape fac- tor and represents the fraction of radiant energy leav- ing surface 1 that directly strikes surface 2.As will be discussed later for radiation between two surfaces, F12 is the exchange factor for two surfaces based on the geometric arrangement only, and F12 is the exchange factor that includes the effects of emissivity for gray surfaces, and participating media between the sur- faces. For blackbody surfaces (ε1 = ε2 = 1) and nonpar- ticipating media, F12 = F12. T1 and T2 are the surface temperatures. Since the net energy at surface 1 must balance the net energy at surface 2, we can write: q q12 21= − (12) Using Equations 11 and 12, the following results: A F A F1 12 2 21= (13) Table 3 Representative Values of Emissivity Polished metals 0.01 < ε < 0.08 Metals, as-received 0.1 < ε < 0.2 Metals oxidized 0.25 < ε < 0.7 Ceramic oxides 0.4 < ε < 0.8 Special paints 0.9 < ε < 0.98+
- 111. Steam 41 / Heat Transfer 4-5 The Babcock & Wilcox Company Unsteady-state conduction So far only steady-state conduction, where temperatures vary from point to point but do not change with time, has been discussed. All unsteady-state conduction involves heat storage. For instance, in heating a furnace, enough heat must be supplied to bring the walls to the operating tem- perature and also to make up for the steady-state losses of normal operation. In large power boilers that run for long periods of time, heat storage in the walls and boiler metal is an insignificant fraction of the to- tal heat input. In small boilers with refractory settings that are operated only part time, or in furnaces that are frequently heated and cooled in batch process work, heat stored in the walls during startup may be a considerable portion of the total heat input. Unsteady-stateconductionisimportantwhenequal- izing boiler drum temperature during pressure rais- ing and reducing periods. When boiler pressure is raised, the water temperature rises. The inner surface of the steam drum is heated by contact with the wa- ter below the water line and by the condensation of steam above the water line. The inside and outside drum temperatures are increased by unsteady-state conduction. During this transient heatup period, tem- perature differentials across the drum wall (or ther- mal gradients) will be larger than during steady-state operation. Larger thermal gradients result in higher thermal stresses as discussed in Chapter 8. The rate of temperature and pressure increase must therefore be controlled to maintain the thermal stresses within acceptable levels in order to protect the drum. During pressure reducing periods, the inside of the drum be- low the water line is cooled by boiler water while the top of the drum is cooled by radiation to the water, by the steam flow to the outlet connections, and by un- steady-state conduction through the drum walls. Unsteady-state conduction occurs in heating or cool- ing processes where temperatures change with time. Examples include heating billets, quenching steel, op- erating regenerative heaters, raising boiler pressure, and heating and cooling steam turbines. By introduc- ing time as an additional variable, conduction analy- ses become more complicated. For unsteady heat flow, theonedimensionalthermalenergyequationbecomes: ρ c T t x k T x p ∂ ∂ = ∂ ∂ ∂ ∂ (21) The left side of the equation represents the rate of energy storage. The two boundary temperatures at x = 0 and L, and the initial temperature, T = To , are sufficient to find a solution. Other boundary conditions involving radiation, convection, or specified heat flux at x = 0 or L can also be applied.3 A general form of the energy equation for multi- dimensional applications is: ρ c T t k Tp ∂ ∂ = ∇⋅ ∇( ) (22) where ∇·(k∇T) is defined in Equations 19 and 20. Con- ditions on the boundary as a function of time, and initial temperatureofthesystem,aresufficienttofind a solution. This equation, known as the principle of reciprocity, guarantees conservation of the radiant heat transfer between two surfaces. The following rule applies to the surfaces of an enclosure: Fij j =∑ 1 (14) stating that the total fraction of energy leaving sur- face i to all other ( j) surfaces must equal 1. Many texts include the calculation of geometric shape fac- tors, commonly named shape factors or configura- tion factors.1,2 Radiation balances for participating and nonparticipating media are presented later in the chapter. Governing equations Energy balances The solution of a heat transfer problem requires defining the system which will be analyzed. This usually involves idealizing the actual system by defining a schematic control volume of the modeled system. A net energy balance on the control volume reflects the first law of thermodynamics and can be stated: energy in energy out stored energy− = (15) For a steady flow of heat, the balance simplifies to: heat in = heat out (16) The laws governing the flow of heat are used to ob- tain equations in terms of material temperature or fluid enthalpy. Steady-stateconduction Thebasiclawsforeachheat transfer mode and the energy balance provide the tools needed to write the governing equations for rectan- gular and cylindrical heat transfer systems. For ex- ample, for the plane wall shown in Fig. 1, the steady flow energy balance for a slice of thickness, dx, is: q q q q dq dx dx1 2 0− = − + = (17) After substituting Equation 1, this is rewritten as: d dx kA dT dx = 0 (18) The conditions at the boundaries, T = T1 at x = 0 and T = T2 at x = L, provide closure. The general symbolic form of the equation in three dimensions can be rep- resented, vector notation: ∇ ⋅ ∇( ) =k T 0 (19) or in x, y, z Cartesian coordinates: ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ = x k T x y k T y z k T z 0 (20) This assumes there is no net heat storage or heat gen- eration in the wall.
- 112. 4-6 Steam 41 / Heat Transfer The Babcock & Wilcox Company Electrical analogy The basic laws of conduction, convection and radiation can frequently be rear- ranged into equations of the form: q T T Rt = −1 2 (23) This equation can be compared to Ohm’s law for elec- trical circuits (I = V/R). The heat transfer or heat flow from point 1 to 2 (q) is analogous with current (I ), the temperature difference (T1 – T2) is analogous with voltage (V), and the thermal resistance (Rt) is analo- gous with electrical resistance (R). Thermal resistance is defined as the reciprocal of thermal conductance, Kt. Table 4 contains analog thermal resistances used in many applications. For systems with unsteady-state conduction gov- erned by Equation 21 or 22, an electrical analogy can be written: q C dT dt t= (24) where Ct is the thermal capacitance, ρ cpV. This equa- tion can be compared with its electrical equivalent: I C dV dt = (25) where C is the electrical capacitance. Kirchhoff’s law for electrical circuits provides the last analogy needed. In heat transfer notation this would be: q q∑ = stored (26) This is an expression of the first law of thermodynam- ics which states that all heat flows into a point equal the rate of energy storage. Consider the composite system and the equivalent thermal circuit shown in Fig. 3. The concepts of resis- tance and conductance are particularly useful when more than one mode of heat transfer or more than one material or boundary is involved. When two modes of heat transfer, such as convection and radiation, oc- cur simultaneously and independently, the combined conductance, K, is the sum of the individual conduc- tances, Kcv and Kr. These individual conductances are essentially heat flows in parallel. When the heat flows are in series, the resistances, not the conductances, are additive. The total or equivalent thermal resistance can then be substituted into Equation 23 to calculate the total heat flow. Flowing systems Boilershavecomplexdistributions of flow, temperature and properties. In the basic ex- ample depicted in Fig. 4, there is steady flow into and out of the system, which is lumped into a single control volume. This leads to a balance of energy written as: m H m H m H m H1 1 2 2 3 3 4 4+ + = (27) where m is the mass flow rate at each inlet or outlet and H is the fluid enthalpy. As discussed in Chapter 3, the full energy equation sets the net energy entering a system (from mass flow into and out of the system) equal to the internal heat generation, plus the work done by the system, plus energy conducted into the system, plus a viscous dis- sipation term (see Chapter 3, Equation 12). Viscous dissipation and work done in the boiler system can both usually be neglected. For steady-state conditions, Fig. 3 Temperature distribution in composite wall with fluid films. ∆x n (r2/r1) kA 2πkl 1 1 hA 2πr2lh T2−T3 T2−T3 23A2 σ(T2 4 −T3 4 ) 23(2πr2l) σ(T2 4 −T3 4 ) Table 4 Summary of Thermal Resistances Rectangular Cylindrical Geometries Geometries and Surfaces and Surfaces Conduction, Rc Convection, Rcv from surface Radiation, Rr from surface Heat flow Body of conductivity, k, and area, A, normal to heat flow T2 T1 h, A ∆ x T3 Heat flow T3 T1 T2 r1 r2 l
- 113. Steam 41 / Heat Transfer 4-7 The Babcock & Wilcox Company the energy equation in terms of fluid enthalpy and in vector notation can then be written as: ∇⋅( ) = ∇⋅ ∇( ) +ρuH H SHΓ Convection Conduction Internal heat genneration (28) The parameter Γ is an effective diffusion coefficient that includes molecular diffusion and turbulent diffu- sion. SH is internal heat generation per unit volume. Rearranging Equation 28 and replacing enthalpy with temperature (dH = cp dT) the energy equation becomes: ρc u T k T Sp eff H⋅∇ = ∇⋅ ∇ +( ) (29) The parameter keff = cpΓ is effective thermal conduc- tivity. Using x, y, z Cartesian coordinates, the equa- tion is expressed: ρc u T x v T y w T z x k T x y k T y p eff eff ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ + z k T z Seff H (30) In boiler applications, internal heat generation (SH) includes radiation absorption and emission from par- ticipating gases, and heat release from combustion. The complete velocity field and thermal boundary conditions are necessary to find a solution to the fluid temperature field. Equations 28 or 29 can be used with single phase flow or can be used with multiple phase flow (gas-solid or steam-water) by using mass averaged enthalpy or temperature. The development and application of the energy equation in rectangular, cylindrical and spheri- cal coordinates are discussed in References 1 and 2. Most boiler applications are too complex for an al- gebraic solution of the energy equation. However, the continuity and momentum equations discussed in Chapter 3 (Equations 3 to 10) are combined with the energy equation to form a fundamental part of the computational models discussed in Chapter 6. A nu- merical solution to this equation can then be readily achieved for many complex problems involving radia- tion and combustion. Radiation balances for enclosures Nonparticipatingmedia ReferringtoEquation11,thenet radiation between two blackbody surfaces can be written: q A F T T12 1 12 1 4 2 4 = −( )σ (31) The term F12 is the geometric shape factor and is shown for two common geometries in Fig. 5. Use of the tabulated values for more complex problems is dem- onstrated in the example problems under Applica- tions. Equation 31 has limited value in boilers, because most fireside surfaces are not blackbodies. This equa- tion is better used to obtain estimates of radiation heat transfer, because it describes the maximum theoreti- cal rate of energy transfer between two surfaces. For the theory of radiation heat transfer in enclo- sures, see Reference 4. The energy striking a surface, called the incident energy, G, is the total energy strik- ing a surface from all other surfaces in the enclosure. The energy leaving a surface, called the radiosity, J, is comprised of the energy emitted from the surface (Eb) Fig. 5 Shape factors, Fij, for calculating surface-to-surface radiation heat transfer. Fig. 4 Energy balance for a flowing system.
- 114. 4-8 Steam 41 / Heat Transfer The Babcock & Wilcox Company and the reflected incident energy. These terms are re- lated by: J E Gb= +ε ρ (32) The net radiation heat transfer from a surface is found as follows: q A J G= −( ) (33) Combining Equations 32 and 33 leads to the electri- cal analogy listed first in Table 5. This circuit equiva- lent describes the potential difference between the surface at an emissive power, evaluated at Ts, and the surface radiosity. To evaluate the radiative heat trans- fer, the radiosity must first be determined. The net energy between surface i and surface j is the differ- ence between the outgoing radiosities: q A F J Jij i ij i j= −( ) (34) The electrical analogy of the net exchange between two surfaces is listed in Table 5. The sum of similar terms for all surfaces in the enclosure yields the cir- cuit diagram in the table and the equation: q A F J Ji i ij j N i j= −( ) = ∑1 (35) The rules for electrical circuits are useful in finding the net radiation heat transfer. Consider the electri- cal circuit for radiation heat transfer between two gray walls shown in Fig. 6. The rules for series circuits can be used to determine the net heat transfer: q E E R R R b b 12 2 1 1 2 3 = − + + (36) where R A R A F R A 1 1 1 1 2 1 12 3 2 2 2 1 1 1 = − = = −ε ε ε ε , , Total radiation exchange factors for common two-sur- face geometries encountered in boiler design are listed in Table 6. Participating media On the fire side of the boiler, the mixture of gases and particles absorbs, emits, and scatters radiant energy. When a uniform temperature- bounding surface encloses an isothermal gas volume, the radiant heat transfer can be treated as one zone, with absorption and emission from the participating gas mixture.Theincidentradiationonthesurfacesismadeup of the emitted energy from the gas, εg Ebg, and incoming energy from the surrounding walls, (1 − αg) Js. Therefore, the incident radiation is defined by: G E Js g bg g s= + −( )ε α1 (37) Table 6 Common Gray Two-Surface Enclosures Large (Infinite) Parallel Planes A1 = A2 = A F12 = 1 Long (Infinite) Concentric Cylinders A1 = r1 A2 r2 F12 = 1 Concentric Spheres A1 = r1 2 A2 r2 2 F12 = 1 Small Convex Object in a Large Cavity A1 ≈ 0 A2 F12 = 1 Note: The net heat flow is calculated from q12 = σA1 12(T1 4 −T2 4 ) 1 1 + 1 −1 ε1 ε2 12 = 1 1 + 1−ε2 r1 ε1 ε2 r2 12 = 1 1 + 1−ε2 r1 2 ε1 ε2 r2 12 = 12 = ε1 r1 r2 r1 r2 A1,T1,ε1 A2,T2,ε2 A1,T1,ε1 A2,T2,ε2 Table 5 Network Equivalents for Radiative Exchange in Enclosures with Gray Surfaces Circuit Description Equivalent Resistance Net exchange Ri = 1−εi at surface Ai εi Net exchange 1 between surfaces Rij = i and j Ai Fij Net exchange 1 between Rik = surface i and Ai Fik all other surfaces Ebi Ri Ji Rij Ji Jj Ji J1 J2 Jk Jj Fig. 6 Electric circuit analogy for thermal radiation.
- 115. Steam 41 / Heat Transfer 4-9 The Babcock & Wilcox Company The energy leaving the surface is made up of direct emission, εs Ebs, and reflected incident energy, (1−εs)Gs. Therefore, the radiosity is: J E Gs s bs s s= + −( )ε ε1 (38) The solution of Equations 37 and 38 yields values for the incoming and the outgoing heat fluxes (q /As). The netheattransferbetweenthesurfaceandgasbecomes: q J G A E E sg s s s s g bg g bs g s = − = −( ) − −( ) −( ) ε ε α α ε1 1 1 (39) The calculation of absorptivity is described in the ex- amples at the end of the chapter. When the surfaces are radiatively black, εs = 1 and Equation 39 becomes: q A E Esg s g bg g bs= −( )ε α (40) The procedures presented here provide the basis for engineering estimates which are described with ex- amples at the end of the chapter. However, boiler en- closure wall and gas temperatures generally vary from wall to wall and even from point to point.Amulti-zone, three-dimensionalnumericalanalysisisthenrequired, becausesimpleexpressionsofsurfaceheattransferand participating media can not be solved analytically. Numerical analysis of radiation heat transfer in multi-dimensional applications with absorption, emis- sion and scattering is routinely applied with commer- cially available computational fluid dynamics (CFD) software. This involves the solution of an integral-dif- ferential equation for radiation intensity as a func- tion of position, direction, and wavelength. The radia- tive transport equation (RTE) accounts for loss in in- tensity by absorption and scattering and gain in in- tensity by emission and scattering. Boundary condi- tions are applied for absorption, emission, and reflec- tion at the surface. Integration of the equation over the blackbody spectrum simplifies the transport equa- tion by eliminating the dependence on wavelength. The RTE for total (spectrally integrated) radiation intensity uses total radiative properties for gases, par- ticles, and surfaces. Heat transfer properties and correlations Thermal conductivity, specific heat and density Thermalconductivity,k,isamaterialpropertythatis expressed in Btu/h ft F (W/m K) and is dependent on thechemicalcompositionandphysicalcharacteristicsof the substance. The relative order of magnitude of val- ues for various substances is shown in Table 7. Thermal conductivities are generally highest for solids, lower for liquidsandloweryetforgases.Insulatingmaterialshave the lowest conductivities of solid materials. Thermal conductivities of pure metals generally decrease with an increase in temperature, while al- loy conductivities may either increase or decrease. (See Fig. 7.) Conductivities of several steels and alloys are shown in Table 7. Thermal conductivities of various refractory materials are shown in Chapter 23, Fig. 10. For many heat transfer calculations it is sufficiently ac- curate to assume a constant thermal conductivity that correspondstotheaveragetemperatureofthematerial. The effective thermal conductivity of ash deposits on water wall heating surfaces varies widely depend- ing on temperature, composition, heating cycle and physical characteristics of the deposits. The lower limit is close to the thermal conductivity of air or lower (0.03 Btu/h ft F or 0.05 W/m K), and the upper limit does not exceed values for refractory materials (1.4 Btu/h ft F or 2.4 W/m K). The effective thermal conductiv- ity of a friable particulate layer is near the lower limit and is fairly independent of temperature below 1650 to 2200F (899 to 1204C) at which sintering usually occurs.Above this temperature, particlesfusetogether andthermalcontactbetweenparticlesincreases,result- inginasharpincreaseinthermalconductivity.Thehigh- est conductivity is achieved with complete melting. The physical changes caused by fusion and melting are ir- reversible upon cooling, and thermal conductivity of fused deposits decreases with decreasing temperature. Table 7 Properties of Various Substances at Room Temperature (see Note 1) ρ cp k lb Btu Btu ft3 lb F h ft F METALS Copper 559 0.09 223 Aluminum 169 0.21 132 Nickel 556 0.12 52 Iron 493 0.11 42 Carbon steel 487 0.11 25 Alloy steel 18Cr 8Ni 488 0.11 9.4 NONMETAL SOLIDS Limestone 105 ~0.2 0.87 Pyrex glass 170 ~0.2 0.58 Brick K-28 27 ~0.2 0.14 Plaster 140 ~0.2 0.075 Kaowool 8 ~0.2 0.016 GASES Hydrogen 0.006 3.3 0.099 Oxygen 0.09 0.22 0.014 Air 0.08 0.24 0.014 Nitrogen 0.08 0.25 0.014 Steam (see Note 2) 0.04 0.45 0.015 LIQUIDS Water 62.4 1.0 0.32 Sulfur dioxide (liquid) 89.8 0.33 0.12 Notes: 1. SI conversions: ρ, 1 lb/ft3 = 16.018 kg/m3 ; cp, 1 Btu/lb F = 4.1869 kJ/kg K; k, 1 Btu/h ft F = 1.7307 W/m K. 2. Reference temperature equals 32F (0C) except for steam which is referenced at 212F (100C).
- 116. 4-10 Steam 41 / Heat Transfer The Babcock & Wilcox Company Thermal conductance of ash deposits (k/x) is less sen- sitive to changing conditions than thermal conductivity. As the deposit grows in thickness (x), thermal conduc- tivity (k) also increases due to fusion and slagging. The neteffectisthatunitthermalconductancemayonlyvary by a factor of four, 25 to 100 Btu/h ft2 F (142 to 568 W/ m2 C), while variations in thermal conductivity are an order of magnitude larger. The thermal effects of coal- ash deposits are further described by Wall et al.5 The thermal conductivity of water ranges from 0.33 Btu/h ft F (0.57 W/m K) at room temperature to 0.16 Btu/h ft F (0.28 W/m K) near the critical point. Water properties are relatively insensitive to pressure, par- ticularly at pressures far from the critical point. Most other nonmetallic liquid thermal conductivities range from 0.05 to 0.15 Btu/h ft F (0.09 to 0.26 W/m K). In addition, thermal conductivities of most liquids de- crease with temperature. The thermal conductivities of gases increase with temperature and are independent of pressure at nor- mal boiler conditions. These conductivities generally decrease with increasing molecular weight. The rela- tively high conductivity of hydrogen (a low molecu- lar weight gas) makes it a good cooling medium for electric generators. The relatively low conductivity of argon (a high molecular weight gas) makes a good insulating medium for thermal pane windows. When calculating the conductivity of nonhomo- geneous materials, the designer must use an apparent thermal conductivity to account for the porous or lay- ered construction materials. In boilers and furnaces with refractory walls, thermal conductivity may vary from site to site due to variations in structure, compo- sition, density, or porosity when the materials were in- stalled. The thermal conductivities of these materials are strongly dependent on their apparent bulk den- sity (mass per unit volume). For higher temperature insulations, the apparent thermal conductivity of fi- brous insulations and insulating firebrick decreases as bulk density increases, because the denser mate- rial attenuates the radiation. However, an inflection occurs at some point at which a further increase in den- sity increases the thermal conductivity due to conduc- tion in the solid material. Theory shows that specific heats of solids and liq- uids are generally independent of pressure. Table 7 lists specific heats of various metals, alloys and nonhomogeneous materials at 68F (20C). These val- ues may be used at other temperatures without sig- nificant error. The temperature dependence of the specific heat for gases is more pronounced than for solids and liquids. In boiler applications, pressure dependence may gen- erally be neglected. Tables 8a and 8b give specific heat data for air and other gases. In the case of steam and water, property variations (specific heat and thermal conductivity) can be signifi- cant over the ranges of temperature and pressure found in boilers. It is therefore recommended that the properties as compiled in the American Society of Mechanical Engineers (ASME) Steam Tables6 be used. Radiation properties Bodies that are good radiation absorbers are equally good emitters and Kirchhoff’s law states that, for gray surfaces at thermal equilibrium, their emissivities are equal to their absorptivities.Ablackbody is one which absorbs all incident radiant energy while reflecting or transmitting none of it. The absorptivity and emissiv- ity of a blackbody are, by definition, each equal to one. This terminology does not necessarily mean that the body appears to be black. Snow, for instance, absorbs only a small portion of the incident visible light, but to the longer wavelengths (the bulk of thermal radia- tion), snow is almost a blackbody. At a temperature of 2000F (1093C) a blackbody glows brightly, because a non-negligible part of its radiation is in the visible range. Bodies are never completely black, but a hole through the wall of a large enclosure can be used to approximate blackbody conditions, because radiation entering the hole undergoes multiple reflections and absorptions. Asaresult,mostoftheradiationisretained in the enclosure, and surfaces are treated as gray. Fortunately, a number of commercial surfaces, par- ticularly at high temperatures, have emissivities of 0.80 to 0.95 and behave much like blackbodies. Typi- cal average emissivity values are noted in Table 9. Although emissivity depends on the surface composi- tion and roughness and wavelength of radiation, the wavelength dependence is often neglected in practi- cal boiler calculations and surfaces are treated as gray. Ash deposits The emittance and thermal proper- ties of furnace ash deposits have a large effect on boiler heat transfer. The emittance depends on the tempera- ture, chemical composition, structure and porosity of the particulate layer, and whether deposits are par- tially fused or molten. The same ash at different loca- tions within the same boiler (or the same location in different boilers) may have significantly different values of surface emittance. Reported values in the ThermalConductivity,Btu/hftF(W/mK) 0 40 (69) 30 (52) 20 (35) 10 (17) 100 (38) 300 (149) 500 (260) 700 (371) 900 (482) 1100 (593) 1500 (816) 1300 (704) Temperature, F (C) Alloy 600 Carbon Steel, SA210A1, SA106A,B,C Alloy 625 Alloy 800 Alloy 825 Low Alloy (1-1/4 Cr-1/2 Mo-Si) SA213T2,T12,T11 Stainless Steel SA213TP304 Low Alloy (2-1/4 Cr-1Mo) SA213T22 Medium Alloy (9Cr-1Mo-V) SA213T9, T91 Stainless Steel SA213TP309, TP310, TP316, TP317, TP321, TP347 Fig. 7 Thermal conductivity, k, of some commonly used steels and alloys. (1 Btu/h ft F = 1.7307 W/m K)
- 117. Steam 41 / Heat Transfer 4-11 The Babcock & Wilcox Company literature claim emittances between 0.5 and 0.9 for most ash and slag deposits. The effect of coal ash composition, structure, and temperature on deposit emittance5,7 is shown in Fig. 8.Afriable particulate material has low emittance be- cause radiation is scattered (and reflected) from indi- vidual particles and does not penetrate beyond a thin layer (~1 mm) near the surface. Emittance of friable ash deposits decreases with increasing surface tem- perature, until sintering and fusion changes the struc- ture of the deposit. A sharp increase in emittance is associated with ash fusion as particles grow together (pores close) and there are fewer internal surfaces to scatter radiation. Completely molten ash or slag is partially transparent to radiation, and emittance may depend upon substrate conditions. The emittance of completely fused deposits (molten or frozen slag) on oxidized carbon steel is about 0.9. Emittance increases Table 8a Properties of Selected Gases at 14.696 psi (101.33 kPa) (see Note 1) cp k µ T ρ Btu/ Btu/ lbm/ F lb/ft3 lb F h ft F ft h Pr Air 0 0.0860 0.239 0.0133 0.0400 0.719 100 0.0709 0.240 0.0154 0.0463 0.721 300 0.0522 0.243 0.0193 0.0580 0.730 500 0.0413 0.247 0.0231 0.0680 0.728 1000 0.0272 0.262 0.0319 0.0889 0.730 1500 0.0202 0.276 0.0400 0.1080 0.745 2000 0.0161 0.286 0.0471 0.1242 0.754 2500 0.0134 0.292 0.0510 0.1328 0.760 3000 0.0115 0.297 0.0540 0.1390 0.765 Carbon Dioxide (CO2) 0 0.1311 0.184 0.0076 0.0317 0.767 100 0.1077 0.203 0.0100 0.0378 0.767 300 0.0793 0.226 0.0149 0.0493 0.748 500 0.0628 0.247 0.0198 0.0601 0.750 1000 0.0413 0.280 0.0318 0.0828 0.729 1500 0.0308 0.298 0.0420 0.1030 0.731 2000 0.0245 0.309 0.0500 0.1188 0.734 2500 0.0204 0.316 0.0555 0.1300 0.739 3000 0.0174 0.322 0.0610 0.1411 0.745 Water Vapor (H2O) 212 0.0372 0.451 0.0145 0.0313 0.974 300 0.0328 0.456 0.0171 0.0360 0.960 500 0.0258 0.470 0.0228 0.0455 0.938 1000 0.0169 0.510 0.0388 0.0691 0.908 1500 0.0127 0.555 0.0570 0.0889 0.866 2000 0.0100 0.600 0.0760 0.1091 0.861 2500 0.0083 0.640 0.0960 0.1289 0.859 3000 0.0071 0.670 0.1140 0.1440 0.846 Oxygen (O2) 0 0.0953 0.219 0.0131 0.0437 0.730 100 0.0783 0.220 0.0159 0.0511 0.707 300 0.0577 0.227 0.0204 0.0642 0.715 500 0.0457 0.235 0.0253 0.0759 0.705 1000 0.0300 0.253 0.0366 0.1001 0.691 1500 0.0224 0.264 0.0465 0.1195 0.677 2000 0.0178 0.269 0.0542 0.1414 0.701 2500 0.0148 0.275 0.0624 0.1594 0.703 3000 0.0127 0.281 0.0703 0.1764 0.703 Nitrogen (N2) 0 0.0835 0.248 0.0132 0.0380 0.713 100 0.0686 0.248 0.0154 0.0440 0.710 300 0.0505 0.250 0.0193 0.0547 0.710 500 0.0400 0.254 0.0232 0.0644 0.704 1000 0.0263 0.269 0.0330 0.0848 0.691 1500 0.0196 0.284 0.0423 0.1008 0.676 2000 0.0156 0.292 0.0489 0.1170 0.699 2500 0.0130 0.300 0.0565 0.1319 0.700 3000 0.0111 0.305 0.0636 0.1460 0.701 Note: 1. SI conversions: T(C) = [T(F) − 32]/1.8; ρ, 1 lb/ft3 = 16.018 kg/m3 ; cp, 1 Btu/lb F = 4.1869 kJ/kg K; k, 1 Btu/h ft F = 1.7307 W/m K; µ, 1 lbm/ft h = 0.0004134 kg/m s. Table 8b Properties of Selected Gases at 14.696 psi (101.33 kPa) (see Note 1) cp k µ T ρ Btu/ Btu/ lbm/ F lb/ft3 lb F h ft F ft h Pr Flue gas − natural gas (see Note 2) 300 0.0498 0.271 0.0194 0.0498 0.694 500 0.0394 0.278 0.0237 0.0593 0.694 1000 0.0259 0.298 0.0345 0.0803 0.694 1500 0.0193 0.317 0.0452 0.0989 0.693 2000 0.0154 0.331 0.0555 0.1160 0.692 2500 0.0128 0.342 0.0651 0.1313 0.691 3000 0.0109 0.351 0.0742 0.1456 0.689 Flue gas − fuel oil (see Note 3) 300 0.0524 0.259 0.0192 0.0513 0.692 500 0.0415 0.266 0.0233 0.0608 0.694 1000 0.0273 0.287 0.0336 0.0817 0.696 1500 0.0203 0.304 0.0436 0.1001 0.697 2000 0.0162 0.316 0.0531 0.1169 0.697 2500 0.0134 0.326 0.0618 0.1318 0.696 3000 0.0115 0.334 0.0700 0.1459 0.695 Flue gas − coal (see Note 4) 300 0.0537 0.254 0.0191 0.0519 0.691 500 0.0425 0.261 0.0232 0.0615 0.693 1000 0.0279 0.282 0.0333 0.0824 0.697 1500 0.0208 0.299 0.0430 0.1007 0.699 2000 0.0166 0.311 0.0521 0.1173 0.700 2500 0.0138 0.320 0.0605 0.1322 0.701 3000 0.0118 0.328 0.0684 0.1462 0.701 Notes: 1. SI conversions: T(C) = [T(F) − 32]/1.8; ρ, 1 lb/ft3 = 16.018 kg/m3 ; cp, 1 Btu/lb F = 4.1869 kJ/kg K; k, 1 Btu/h ft F = 1.7307 W/m K; µ, 1 lbm/ft h = 0.0004134 kg/m s. 2. Flue gas composition by volume (natural gas, 15% excess air): 71.44% N2, 2.44% O2, 8.22% CO2, 17.9% H2O. 3. Flue gas composition by volume (fuel oil, 15% excess air): 74.15% N2, 2.54% O2, 12.53% CO2, 0.06% SO2, 10.72% H2O. 4. Flue gas composition by volume (coal, 20% excess air): 74.86% N2, 3.28% O2, 13.97% CO2, 0.08% SO2, 7.81% H2O.
- 118. 4-12 Steam 41 / Heat Transfer The Babcock & Wilcox Company with increasing particle size of friable particulate de- posits (Fig. 8a), because larger particles have less ca- pacity to back-scatter incident radiation. Emittance increases with increasing iron oxide (Fe2O3) and un- burned carbon content of the ash (Fig. 8b) because these components have a greater capacity to absorb radiation. Low emittance of some lignitic ash depos- its, known as reflective ash, may be attributed to low Fe2O3 content, although this alone is not a reliable indicator of a reflective ash. Emittance is also indi- rectly dependent upon oxidizing and reducing envi- ronment of the flue gas, due to the effect on the melt- ing characteristics and unburned carbon content in the ash. The thermal and radiative effects of coal-ash deposits are further described by Wall et al.5 Combustion gases Although many gases, such as oxygen and nitrogen, absorb or emit only insignificant amounts of radiation, others, such as water vapor, carbon dioxide, sulfur dioxide and carbon monoxide, substantially absorb and emit. Water vapor and car- bon dioxide are important in boiler calculations be- cause of their presence in the combustion products of hydrocarbon fuels. These gases are selective radiators. They emit and absorb radiation only in certain bands (wavelengths) of the spectrum that lie outside of the visible range and are consequently identified as nonluminous radiators. Whereas the radiation from a furnace wall is a surface phenomenon, a gas radi- ates and absorbs (within its absorption bands) at ev- ery point throughout the furnace. Furthermore, the emissivity of a gas changes with temperature, and the presence of one radiating gas may have characteris- tics that overlap with the radiating characteristics of another gas when they are mixed. The energy emit- ted by a radiating gaseous mixture depends on gas temperature, the partial pressures, p, of the constitu- ents and a beam length, L, that depends on the shape and dimensions of the gas volume. An estimate of the mean beam length is L = 3.6 V/A for radiative trans- fer from the gas to the surface of the enclosure, where V is the enclosure volume and A is the enclosure sur- face area. The factor 3.6 is approximate, and values between 3.4 to 3.8 have been recommended depend- ing on the actual geometry.4 Figs. 9 and 10 show the emissivity for water vapor and carbon dioxide.8 The accuracy of these charts has gainedgreateracceptancethanthemorewidelyknown chartsofHottel,4 particularlyathightemperaturesand short path lengths. The effective emissivity of a water vapor-carbon dioxide mixture is calculated as follows: ε ε ε ε= + −H O CO2 2 ∆ (41) where ∆ε is a correction factor that accounts for the effect of overlapping spectral bands. This equation neglects pressure corrections and considers boilers op- erating at approximately 1 atm. The factors shown in Fig. 11 depend on temperature, the partial pressures, p, of the constituents and the beam length, L. The pres- ence of carbon monoxide and sulfur dioxide can typi- cally be neglected in combustion products, because CO and SO2 are weakly participating and overlap with the infrared spectrum of H2O and CO2. When using Figs. 9 to 11 to evaluate absorptivity, α, of a gas, Hottel4 recommends modification of the pL product by a surface to gas temperature ratio. This is illustrated in Example 6 at the end of this chapter. Table 9 Normal Emissivities, ε, for Various Surfaces13 (see Note 1) Material Emissivity, ε Temp., F Description Aluminum 0.09 212 Commercial sheet Aluminum oxide 0.63 to 0.42 530 to 930 Aluminum Varying age and Al paint 0.27 to 0.67 212 content Brass 0.22 120 to 660 Dull plate Copper 0.16 to 0.13 1970 to 2330 Molten Copper 0.023 242 Polished Cuprous oxide 0.66 to 0.54 1470 to 2012 Iron 0.21 392 Polished, cast Iron 0.55 to 0.60 1650 to 1900 Smooth sheet Iron 0.24 68 Fresh emeried Iron oxide 0.85 to 0.89 930 to 2190 Steel 0.79 390 to 1110 Oxidized at 1100F Steel 0.66 70 Rolled sheet Steel 0.28 2910 to 3270 Molten Steel (Cr-Ni) 0.44 to 0.36 420 to 914 18-8 rough, after heating Steel (Cr-Ni) 0.90 to 0.97 420 to 980 25-20 oxidized in service Brick, red 0.93 70 Rough Brick, fireclay 0.75 1832 Carbon, lamp- black 0.945 100 to 700 0.003 in. or thicker Water 0.95 to 0.963 32 to 212 Note: 1. SI conversion: T(C) = [T(F) − 32]/1.8; 1 in. = 25.4 mm. Fig. 8 Effect of coal ash composition, structure and temperature on deposit emittance.5,7 0.9 1100900 Increasing Absorption 700500300100 0.4 0.5 0.6 0.7 0.8 0.9 (b) Surface Temperature, T , C With Carbon With Fe O Colorless Increasing Particle Size 1.0 0.8 0.7 0.6 0.5 0.4 (a) 211-422 µm 211 µm 104- <44 µm 53-104 µm Cooling Particulates Heating Fused Sintering Fusion 1.0 TotalEmissivityorEmittance,
- 119. Steam 41 / Heat Transfer 4-13 The Babcock & Wilcox Company Radiation properties of gases can be calculated more accurately based on fundamental models for spectral gas radiation. The exponential wide band model9 pre- dicts spectral absorption and emission properties of single and multi-component gases including H2O, CO2, CO, CH4, NO, and SO2 as a function of tempera- ture and pressure. Diatomic gases N2, O2 and H2 may contribute to the total gas volume and pressure of the mixture, but are considered transparent to infrared radiation. Radiation properties are conveniently ex- pressed as emission and absorption coefficients that dependonlocalvariationsingascomposition,tempera- ture, and pressure. This approach is suitable for nu- mericalmodelingofradiationwithparticipatingmedia, which requires frequent evaluation of gas properties at a large number of control volumes. Entrained particles Combustion usually involves some form of particulate that is entrained in combus- tion gases. Particles are introduced as the fuel which undergo transformations of combustion and/or are formed by the processes of condensation and agglom- eration of aerosol particles. Entrained particles have asignificantroleinradiationheattransferbecausethey absorb, emit, and scatter radiation. Scattering effec- tively extends the beam length of radiation in an en- closure,becausethebeamchangesdirectionmanytimes before it reaches a wall. Radiation from entrained par- ticles depends on the particle shape, size distribution, chemicalcomposition,concentration,temperature,and the wavelength of incident radiation. Particulates in boilers are comprised of unreacted fuel (coal, oil, black liquor), char, ash, soot, and other aerosols. Soot is an example of an aerosol that con- 0.05 1.0 0.06 0.07 0.04 0.03 0.02 0.01 0.00 0.0 0.2 0.4 0.6 0.8 90 bar cm 30 bar cm 60 bar cm 90 bar cm 1700F (925C) and Above p L + p L = 120 bar cm p p + p Fig. 11 Radiation heat transfer correction factor associated with mixtures of water vapor and carbon dioxide.8 (1 bar-cm = 0.0324 ft-atm) Fig.10 Emissivity of carbon dioxide at one atmosphere total pressure: pcL= partial pressure in atmospheres x mean beam length in feet.8 (1 bar-cm = 0.0324 ft-atm; T(F) = [T(C) x 1.8] + 32) EmissivityofCarbonDioxide 0.005 0.05 0.10 0.20 0.30 0.01 2200200016001200800200 1000 1400 1800400 600 Carbon Dioxide Total Pressure 1 bar Partial Pressure 0 bar 0.3 bar cm 0.15 bar cm 2 bar cm 4 bar cm 15 bar cm 40 bar cm 8 bar cm 1 bar cm 0.6 bar cm 100 bar cm Temperature, C (T)F = (T(C) x 1.8) + 32 0.04 0.03 0.02 p c L = 0.5 bar cm Fig. 9 Emissivity of water vapor at one atmosphere total pressure: pwL= partial pressure in atmospheres x mean beam length in feet.8 (1 bar-cm = 0.0324 ft-atm; T(F) = [T(C) x 1.8] + 32) EmissivityofWaterVapor 0.70 0.50 0.10 0.05 0.01 2200200016001200800200 Temperature, C T(F) = (T(C) x 1.8) + 32 1000 1400 1800400 600 Water Vapor Total Pressure 1 bar Partial Pressure 0 bar 40 bar cm 80 bar cm 150 bar cm 400 bar cm 10 bar cm 20 bar cm 3 bar cm 0.5 bar cm 1.5 bar cm 6 bar cm0.08 0.04 0.03 0.02 0.20 p w L = 0.2 bar cm
- 120. 4-14 Steam 41 / Heat Transfer The Babcock & Wilcox Company tributes to radiation from gas flames in boilers. Ne- glecting the effect of soot on radiation heat transfer in the flame could lead to significant errors in the cal- culated flame temperature, and radiation heat trans- fer to the furnace walls in the flame zone. Ash is an example of particulate that contributes to radiation in coal-firedboilers.Scatteringbyashparticleseffectively redistributes radiation in the furnace, and smooths out variations in radiation heat flux, analogous to the way a cloud distributes solar radiation on the earth. The absorption and emission characteristics of flyash par- ticles increase, and scattering decreases with the rela- tive amount of iron oxide or residual carbon, which acts as a coloring agent in the ash. Analytical methods such as Equation 39 that de- pend upon emissivity and absorptivity of the partici- pating media are inaccurate when particles other than soot are involved, because the effects of scatter- ing are neglected. Numerical methods which solve the general form of the radiative transport equation in- clude the effects of scattering (see Numerical methods). Mie Theory10 is a general method for calculating the radiation properties of spherical particles as a func- tion of particle composition, concentration, diameter and wavelength. Rigorous calculations by this method can only be performed with the aid of a computer and require that optical properties (complex refractive in- dex as a function of wavelength) of the particle mate- rials are known. The complex refractive index of lig- nite, bituminous, and anthracite coals, and corre- sponding properties of char and ash have been mea- sured, as well as other materials that are typically en- countered in combustion systems. Radiation properties ofparticlesareconvenientlyexpressedastotalemission, absorption, and scattering efficiencies that depend on particlecomposition,diameterandtemperature.Particle properties must be combined with gas properties in an analysis of radiation with participating media. Working formulas for convection heat transfer Heat transfer by convection between a fluid (gas or liquid) and a solid is expressed by Equation 4. This equation is a definition of the heat transfer coefficient but is inadequate in describing the details of the con- vectivemechanisms.Onlyacomprehensivestudyofthe flow and heat transfer would define the dependence of the heat transfer coefficient along the surface. In the literature, simple geometries have been modeled and predictions agree well with experimental data. How- ever, for the more complex geometries encountered in boiler analysis, correlations are used that have been developed principally from experimental data. Convective heat transfer near a surface takes place by a combination of conduction and mass transport. In thecaseofheatflowingfromaheatedsurfacetoacooler fluid, heat flows from the solid first by conduction into a fluid element, raising its internal energy. The heated element then moves to a cooler zone where heat flows from it by conduction to the cooler surrounding fluid. Fluid motion can occur in two ways. If the fluid is set in motion due to density differences arising from temperature variations, free or natural convection occurs. If the motion is externally induced by a pump or fan, the process is referred to as forced convection. Convective heat transfer can occur in laminar or turbulent flows. For laminar flow, the fluid moves in layers, or lamina, with each element following an or- derly path. In turbulent flow, prevalent in boiler pas- sages, the local motion of the fluid is chaotic and sta- tistical treatment is used to establish average velocity and heat transfer values. Experimental studies have confirmed that a flow field can be divided into two zones: a viscous zone adjacent to the surface and a nonviscous zone removed from the heat transfer surface. The viscous, heated zone is termed the boundary layer region. The hydro- dynamic boundary layer is defined as the distance from the wall at which the local velocity reaches 99% of the velocity far from the wall. At the entrance of a pipe or duct, the boundary layer begins to grow; this flow portion is called the developing region. Downstream, when the viscous region fills the pipecoreorgrowstoamaximum,theflowistermedfully developed. Developing region heat transfer coefficients are larger than the fully developed values. In many applications it is sufficient to assume that the hydrody- namic and thermal boundary layers start to grow at the same location, although this is not always the case. Flow over a body (around a circular cylinder) is termed external flow, while flow inside a confined re- gion, like a pipe or duct, is termed internal flow. Natural or free convection A fluid at rest, exposed to a heated surface, will be at a higher temperature and lower density than the surrounding fluid. The differences in density, because of this difference in temperature, cause the lighter, warmer fluid elements to circulate and carry the heat elsewhere. The complex relationships governing this typeofconvectiveheattransferarecoveredextensively in other texts.1 Experimental studies have confirmed thatthemaindimensionlessparametersgoverningfree convection are the Grashof and Prandtl numbers: Gr = −( )∞g T T Lsβ ρ µ 2 3 2 (42) Pr = c k p µ (43) The Grashof number is a ratio of the buoyant to vis- cous forces. The Prandtl number is the ratio of the dif- fusion of momentum and heat in the fluid. The prod- uct, Gr Pr, is also called the Rayleigh number, Ra. In boiler system designs, air and flue gases are the important free convection heat transfer media. For these designs, the equation for the convective heat transfer coefficient h is: h C T Ts= −( )∞ 1 3/ (44) This correlation is applicable when the Rayleigh num- ber, Ra, is greater than 109 , which is generally recog-
- 121. Steam 41 / Heat Transfer 4-15 The Babcock & Wilcox Company nized as the transition between laminar and turbu- lent flow. Values of the constant C in the equation are listed below: Geometry Btu h ft F2 4/3 W m K2 4/3 Horizontal plate facing upward 0.22 1.52 Vertical plates or pipes more than 1 ft (0.3 m) high 0.19 1.31 Horizontal pipes 0.18 1.24 The correlation generally produces convective heat transfer coefficients in the range of 1 to 5 Btu/h ft2 F (5.68 to 28.39 W/m2 K). Forced convection Dimensionless numbers Forced convection implies the use of a fan, pump or natural draft stack to in- duce fluid motion. Studies of many heat transfer sys- tems and numerical simulation of some simple geom- etries confirm that fluid flow and heat transfer data may be correlated by dimensionless numbers. Using these principles, scale models enable designers to pre- dict field performance. For simple geometries, a mini- mum of dimensionless numbers is needed for model- ing. More complex scaling requires more dimension- less groups to predict unit performance. The Reynolds number is used to correlate flow and heat transfer in closed conduits. It is defined as: Re = = ρ µ µ V L GL (45) where L is a characteristic length of the conduit or an obstacle in the flow field. This dimensionless group represents the ratio of inertial to viscous forces. The Reynolds number is only valid for a continu- ous fluid filling the conduit. The use of this param- eter generally assumes that gravitational and inter- molecular forces are negligible compared to inertial and viscous forces. The characteristic length, termed equivalent hy- draulic diameter, is different for circular and noncircular conduits. For circular conduits, the inside diameter (ID) is used. For noncircular ducts, the equivalent diameter becomes: De = ×4 Flow cross-sectional area Wetted perimeter (46) This approach, used to compare dynamically similar fluidsingeometricallysimilarconduitsofdifferentsize, yieldsequalReynoldsnumbersfortheflowsconsidered. At low velocities, the viscous forces are strong and laminar flow predominates, while at higher velocities, theinertialforcesdominateandthereisturbulentflow. In closed conduits, such as pipes and ducts, the transi- tion to turbulent flow occurs near Re = 2000. The gen- erally accepted range for transition to turbulent flow undercommontubeflowconditionsis2000<Re<4000. For fluid flow over a flat external surface, the char- acteristic length for the Reynolds number is the sur- face length in the direction of the flow, x. Transition to turbulence is generally considered for Re ≥ 105 . In the case of flow over a tube, the outside diameter (OD), D, is the characteristic length. In tube bundles with crossflow, transition generally occurs at Re > 100. Experimental studies have confirmed that the con- vective heat transfer coefficient can be functionally characterized by the following dimensionless groups: Nu = ( )f Re, Pr (47) where Nu is the Nusselt number, Re is the Reynolds number and Pr is the Prandtl number. The Nusselt number, a ratio of the wall temperature gradient to reference gradients, is defined as follows: Nu = hL k (48) The previously discussed Prandtl number, represent- ing a ratio of the diffusion of momentum and heat in the fluid, is also the ratio of the relative thickness of viscous and thermal boundary layers. For air and flue gases, Pr < 1.0 and the thermal boundary layer is thicker than the viscous boundary layer. In the literature, correlations are also presented using other dimensionless groups; the Peclet and Stanton numbers are the most common. The Peclet number is defined as follows: Pe = Re Pr (49) The Stanton number is defined in terms of the Nusselt, Reynolds and Prandtl numbers: St Nu = Re Pr (50) Laminar flow inside tubes For heating or cooling of viscous fluids in horizontal or vertical tubes with con- stant surface temperature and laminar flow conditions (Re < 2300), the heat transfer coefficient, or film con- ductance,canbedeterminedbythefollowingequation:11 Nu = 1 86 1 3 0 14 . Re Pr / . D L b w µ µ (51) or h k D GD c k D L b p b b w = 1 86 1 3 0 14 . / . µ µ µ µ (52) where the parameter G = ρV is defined as the mass flux or mass flow rate per unit area and tube diameter, D, is the characteristic length used in the evaluation of the Reynolds number. The ratio of viscosities (µb /µw) is a correction factor that accounts for temperature depen- dent fluid properties. Properties in Equations 51 and 52 are evaluated at an average bulk fluid temperature, except µw which is evaluated at the wall temperature. For low viscosity fluids, such as water and gases, a more complex equation is required to account for the effects of natural convection at the heat transfer sur-
- 122. 4-16 Steam 41 / Heat Transfer The Babcock & Wilcox Company face. This refinement is of little interest in industrial practice because water and gases in laminar flow are rarely encountered. Turbulent flow Studies of turbulent flow indicate several well defined regions as shown in Fig. 12. Next to the heat transfer surface is a very thin laminar flow region, less than 0.2% of the characteristic length, where the heat flow to or from the surface is by mo- lecular conduction. The next zone, known as the buffer layer, is less than 1% of the characteristic length and is a mixture of laminar and turbulent flow. Here the heat is transferred by a combination of convection and conduction. In the turbulent core, which comprises roughly 98% of the cross-section, heat is transferred mainly by convection. In turbulent flow, the local but chaotic motion of the fluid causes axial and radial motion of fluid elements. This combination of motions sets up eddies, or local swirling motions, augmenting the heat transfer from the core to the laminar sublayer. The laminar flow in the sublayer and the laminar component in the buffer layer act as a barrier, or film, to the heat transfer pro- cess. Increasing the fluid velocity has been found to decrease this film thickness, reducing the resistance to heat transfer. Turbulent flow in tubes The distance required to obtain hydrodynamically and thermally fully devel- oped turbulent flow is shorter than that for laminar flow. The flow length needed to achieve hydrodynami- cally fully developed conditions is variable and de- pends upon the specific Reynolds number (operating conditions) and surface geometry. It typically varies from 6 to 20 diameters (x/D). Fully developed ther- mal flow for gases and air, important in boiler analy- sis, occurs at similar x/D ratios. However, for liquids, the ratio is somewhat higher and increases with the Prandtl number. Extensive research data using low viscosity gases and liquids have been correlated. The following equa- tion12 is recommended for fully developed flow with small to moderate temperature differences: Nufd n = 0 023 0 8 . Re Pr. (53) with n = 0.4 for heating of the fluid and n = 0.3 for cool- ing of the fluid, and properties evaluated at the bulk temperature. Equation 53 applies to gases and liquids in the range 0.7 < Pr < 160, which covers all fluids in boileranalysis.Iftheconditionsarenotfullydeveloped, the correlation is corrected as shown below:13 Nu Nu= + ( ) fd D x1 0 7 / . (54) with the stipulation that 2 ≤ x/D ≤ 20. These correla- tions should only be used for small to moderate tem- perature differences. A correlation by Seider and Tate11 is widely used for heating or cooling of a fluid and larger tempera- ture differences.All of the properties are evaluated at the bulk temperature, except µw which is evaluated at the wall temperature: Nufd b w = 0 027 0 8 1 3 0 14 . Re Pr. / . µ µ (55) The foregoing correlations may be applied for both constant surface temperature and heat flux conditions to a good approximation. For boiler applications involving turbulent flow in tubes, Equation 53 is rewritten with the temperature ratio added to convert the properties from a bulk to film temperature basis: Nufd f f b f T T = 0 023 0 8 0 4 0 8 . Re Pr. . . (56) All properties are evaluated at the film temperature (Tƒ), which is defined as the arithmetic mean tempera- ture between the wall temperature (Tw) and the bulk fluid temperature (Tb): Tƒ = (Tw + Tb)/ 2 with all tem- peratures in absolute units (R or K). Equation 56 is rewritten using parametric groupings: h G D c k T T l e p f b f = 0 023 0 8 0 2 0 4 0 6 0 4 0 . . . . . . µ ..8 (57) which can be expressed in the form: h h F Fl l pp T= ′ (58) Figs. 13 to 17 display the various factors that make up the right side of Equation 58. Unlike non-dimen- sional parameters (Nu, Re, Pr), these terms do not have any physical significance and are dependent upon the choice of engineering units. The physical properties factor, Fpp, combines all of the properties of the fluid into one term, and is evaluated at the gas film temperature for a particular fluid (gas, air or steam). Note that if Fpp for steam can not be obtained from Fig. 16, it can be calculated with values of cp, k and µ evaluated at the film temperature from the ASME Steam Tables.6 Turbulent cross flow around tubes The most impor- tant boiler application of convection is heat transfer from the combustion gases to the tubular surfaces in the convection passes. Perhaps the most complete and authoritative research on heat transfer of tubes in crossflow was completed in an extensive program con- ducted by The Babcock & Wilcox Company (B&W).14 The following correlation was adapted from this study for different fluids:Fig. 12 Structure of turbulent flow field near a solid boundary.
- 123. Steam 41 / Heat Transfer 4-17 The Babcock & Wilcox Company Nu = 0 321 0 61 0 33 . Re Pr. . f f a dF F (59) The last terms are an arrangement factor, Fa, and a depth factor Fd, that correct the results from the base configuration ( /D0 = 2.0, ⊥ /D0 = 1.75, number of rows ≥ 10) which by definition Fa = Fd = 1. The equa- tion applies to heating and cooling of fluids for clean tubes in crossflow. Equation 59 is rewritten using parametric groupings shown below: h G D c k F Fc p f a d= 0 321 0 61 0 39 0 33 0 67 0 28 . . . . . . µ (60) which can be expressed in the form: h h F F Fc c pp a d= ′ (61) Figs. 18 to 23 display the various factors that make up the right side of Equation 61. Unlike non-dimen- sional parameters (Nu, Re, Pr), these terms do not Fig. 14 Effect of film temperature, Tf, and moisture on the physical properties factor, Fpp, for gas; turbulent flow inside tubes or longitudinal flow over tubes (English units only). Fig. 15 Effect of film temperature, Tf, and moisture on the physical properties factor, Fpp, for air; turbulent flow inside tubes or longitudi- nal flow over tubes (English units only). Fig. 16 Effect of film temperature, Tf, and pressure on the physical properties factor, Fpp, for steam; turbulent flow inside tubes or longitudinal flow over tubes (English units only). Fig. 13 Basic convection velocity and geometry factor, ′hl , for air, gas or steam; turbulent flow inside tubes or longitudinal flow over tubes (English units only).
- 124. 4-18 Steam 41 / Heat Transfer The Babcock & Wilcox Company have any physical significance and are dependent upon the choice of engineering units. The physical properties factor, Fpp, similar to the one previously defined, is evaluated at the gas film temperature for a particular fluid (gas or air). The mass flux or mass flow per unit area, G, and the Reynolds numbers used in Equations 59 and 60 and Figs. 18, 21 and 22 are calculated based on flow conditions at the minimum free area (maximum velocity) between tubes. The arrangement factor, Fa, depends on the geomet- ric configuration of tubes, the ratio of tube spacing to diameter, Reynolds number, and the presence of ash in the flue gas. Values of Fa for clean tube conditions with air or flue gas without ash are given in Fig. 21. Values of Fa for commercially clean tube conditions with ash-laden flue gas are given in Fig. 22. The depth factor, Fd, accounts for entrance effects for banks of tubes which are less than ten rows deep in the direction of gas flow. For undisturbed flow [flow that is straight and uninterrupted for at least 4 ft (1.2 m) before entering a tube bank] approaching a bank of less than ten rows, the film conductance must in- clude the correction factor, Fd, shown in Fig. 23. Fd is unity when the tube bank is preceded by a bend, screen, damper or another tube bank in close proximity. Turbulent longitudinal flow around tubes Correla- tions that were developed based on turbulent flow in tubes (Equations 56 and 57, and Figs. 13 to 17) can also be applied for external flow parallel to tubes. In this case, the equivalent diameter De (defined by Equation 46) is used in the evaluation of Reynolds number. For flow parallel to a bank of circular tubes arranged on rectangular spacing, the equivalent di- ameter becomes: D D De o o= − 4 1 2 π (62) where Do is the tube outside diameter and 1 and 2 are the centerline spacing between tubes. The mass flux or mass flow per unit area, G, in Equations 56 and 57, and Fig. 13 is calculated based on the free area between tubes. Fig. 19 Effect of film temperature, Tf, and moisture on the physical properties factor, Fpp, for gas in turbulent crossflow over tubes (English units only). Fig. 20 Effect of film temperature, Tf, and moisture on the physical properties factor, Fpp, for air in crossflow over tubes (English units only). Fig. 17 Temperature factor, FT, for converting mass velocity from bulk to film basis for air, gas or steam; turbulent flow inside tubes or longitudinal flow over tubes. 100 1000 0.1 1 10 D = Outside Tube Diameter, in. 5 4 3 2 1 0.5 G = Mass Flux of Gas or Air, 1000 lb/h ft 200 100 300 500 10 50 20 30 1 2 3 5 h = 0.321 G /D Crossflow h=BasicConvectionVelocityandGeometryFactor forCrossflow Fig. 18 Basic crossflow convection velocity and geometry factor, h′c, for gas or air (English units only).
- 125. Steam 41 / Heat Transfer 4-19 The Babcock & Wilcox Company General heat transfer topics Heat exchangers Boiler systems contain many heat exchangers. In these devices, the fluid temperature changes as the fluids pass through the equipment. With an energy balance specified between two locations, 1 and 2: q mc T Tp= −( )2 1 (63) the change in fluid temperature can be calculated: T T q mcp2 1= + ( )/ (64) It is therefore appropriate to define a mean effective temperature difference governing the heat flow. This difference is determined by performing an energy bal- ance on the energy lost by the hot fluid and that en- ergy gained by the cold fluid. An equation of the form: q UA F T= ∆ LMTD (65) is obtained where the parameters U, A and F define the overall heat transfer coefficient, surface area, and ar- Fig. 23 Heat transfer depth factor for number of tube rows crossed in convection banks. (Fd = 1.0 if tube bank is immediately preceded by a bend, screen or damper.) rangement correction factor, respectively. The term ∆TLMTD, known as the log mean temperature difference, is defined as: ∆ ∆ ∆ ∆ ∆ T T T n T T LMTD = − ( ) 1 2 1 2/ (66) ∆T1 istheinitialtemperaturedifferencebetweenthehot and cold fluids (or gases), while ∆T2 defines the final temperature difference between these media. The pa- Fig. 22 Arrangement factor, Fa, as affected by Reynolds number for various in-line tube patterns, commercially clean tube conditions for crossflow of ash-laden gases. 2 F=ArrangementFactorforIn-LineTubeBanks 0.9 0.8 0.7 0.6 0.5 0.9 0.8 0.7 0.6 0.5 0.4 0.9 0.8 0.7 0.6 0.5 0.4 0.3 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 1.0 2.0 3.0 4.0 5.0 6.05.54.53.52.51.5 2 - 3 1.5 1.5 1.25 1 3 1.25 1.8 1.25-1.5 Reynolds No. = 40,000 Reynolds No. = 20,000 1 2 3 1 1 Reynolds No. = 8,000 1.82 3 Reynolds No. = 2,000 2 1.25-1.5 3 Tube Spacing Transverse to Gas Flow Outside Tube Diameter Tube Spacing in Direction of Gas Flow Outside Tube Diameter Curves Denoted By: Fig. 21 Arrangement factor, Fa, as affected by Reynolds number for various in-line tube patterns, clean tube conditions for crossflow of air or natural gas combustion products. 3 F=ArrangementFactorforIn-LineTubeBanks 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 2 1.0 2.0 3.0 4.0 5.0 6.05.54.53.52.51.5 2 - 3 1 1.5 1.8 3 1.25 Reynolds No. = 2,000 Reynolds No. = 8,000 Reynolds No. = 20,000 Reynolds No. = 40,000 2 1.8 1.5 1.25 1 1 3 1.25-1.5 3 1 2 2 1.25-1.5 Tube Spacing in Direction of Gas Flow Outside Tube Diameter Curves Denoted By: Tube Spacing Transverse to Gas Flow Outside Tube Diameter
- 126. 4-20 Steam 41 / Heat Transfer The Babcock & Wilcox Company rameterUinEquation65definestheoverallheattrans- fer coefficient for clean surfaces and represents the unit thermal resistance between the hot and cold fluids: 1 1 1 UA h A R h Ai i w o oclean = + + (67) For surfaces that are fouled, the equation is written: 1 1 UA R A UA R A f i i f o o = + +, , clean (68) where Rf,i is the reciprocal effective heat transfer co- efficient of the fouling on the inside surface, (l / UA) is the thermal resistance and Rf,o is the reciprocal heat transfer coefficient of the fouling on the outside sur- face. Estimates of overall heat transfer coefficients and fouling factors are listed in Tables 10 and 11. Actual fouling factors are site specific and depend on water chemistry and other deposition rate factors. Overall heat transfer coefficients can be predicted using: 1) the fluid conditions on each side of the heat transfer surface with either Equation 56 or 59, 2) the known materials of the heat transfer surface, and 3) the foul- ing factors listed in Table 11. Often the heat exchanger tube wall resistance (Rw) is small compared to the sur- face resistances and can be neglected, leading to the following equation for a clean surface: U h h h h D D i o i o o i = + ( )/ (69) This equation assumes that area, A in product UA, is based on the outside diameter of the tube, Do. The difficulty in quantifying fouling factors for gas-, oil- and coal-fired units has led to use of a cleanliness factor. This factor provides a practical way to provide extra surface to account for the reduction in heat trans- fer due to fouling. In gas-fired units, experience indi- cates that gas-side heat transfer coefficients are higher as a result of the cleanliness of the surface. In oil- and coal-fired units that are kept free of slag and deposits, a Table 11 Selected Fouling Factors Type of Fluid h ft2 F/Btu m2 K/W Sea water above 125F (50C) 0.001 0.0002 Treated boiler feedwater above 125F (50C) 0.001 0.0002 Fuel oil 0.005 0.0010 Alcohol vapors 0.0005 0.0001 Steam, non-oil bearing 0.0005 0.0001 Industrial air 0.002 0.0004 lower value is used. For units with difficult to remove deposits, values are reduced further. There are three general heat transfer arrange- ments: parallel flow, counterflow and crossflow, as shown in Fig. 24. In parallel flow, both fluids enter at the same relative location with respect to the heat transfer surface and flow in parallel paths over the heating surface. In counterflow, the two fluids enter at opposite ends of the heat transfer surface and flow in opposite directions over the surface. This is the most efficient heat exchanger although it can also lead to the highest tube wall metal temperatures. In crossflow, the paths of the two fluids are, in general, perpendicu- lar to one another. Fig. 24 shows the flow arrangements and presents Equation 66 written specifically for each case. The ar- rangement correction factor, F, is 1.0 for parallel and counterflow cases. For crossflow and multi-pass ar- rangements, the correction factors are shown in Figs. 25 and 26. Extended surface heat transfer The heat absorption area in boilers can be increased using longitudinally and circumferentially finned tubes. Finned, or extended, tube surfaces are used on the flue gas side. In regions prone to fouling, the fins must be spaced to permit cleaning. Experimental data on actual finned or extended surfaces are preferred for design purposes; the data should be collected at conditions similar to those expected to be encountered. However, in place of these data, the method by Schmidt15 generally describes the heat transfer across finned tubes. It is based on heat transfer to the un- derlying bare tube configuration, and it treats the tube as if it has zero fin height. Schmidt’s correlation for the gas-side conductance to tubes with helical, rect- angular, circular, or square fins is as follows: h h Z S S f c f f = − −( ) 1 1 η (70) where hc is the heat transfer coefficient of the bare tubes in crossflow defined by Equations 59 and 60, and Z is the geometry factor defined as: Z L L h t = − 1 0 18 0 63 . . (71) Table 10 Approximate Values of Overall Heat Transfer Coefficients Physical Situation Btu/h ft2 F W/m2 K Plate glass window 1.10 6.20 Double plate glass window 0.40 2.30 Steam condenser 200 to 1000 1100 to 5700 Feedwater heater 200 to 1500 1100 to 8500 Water-to-water heat exchanger 150 to 300 850 to 1700 Finned tube heat exchanger, water in tubes, air across tubes 5 to 10 30 to 55 Water-to-oil heat exchanger 20 to 60 110 to 340 Steam-to-gas 5 to 50 30 to 300 Water-to-gas 10 to 20 55 to 110
- 127. Steam 41 / Heat Transfer 4-21 The Babcock & Wilcox Company Sf represents the fin surface area including both sides and the peripheral area, while S represents the ex- posed bare tube surface between the fins plus the fin surface, Sf. The ratio Lh/Lt is the fin height divided by the clear spacing between fins. Fin efficiency, ηf, is shown in Fig. 27 as a function of the parameter X, defined as: X L Zh k Lh c f t= ( )2 / (72) for helical fins, and X r Y Zh k Lc f t= ( )2 / (73) for rectangular, square or circular fins. The param- eter Y is defined in Fig. 28. The overall conductance can be written: 1 1 1 UA C A h R A hf o f o w i c i = + + , , (74) The parameter Cf is the surface cleanliness factor. NTU method There are design situations for which the perfor- mance of the heat exchanger is known, but the fluid temperaturesarenot.Thisoccurswhenselectingaunit for which operating flow rates are different than those Fig. 25 Arrangement correction factors for a single-pass, crossflow heat exchanger with both fluids unmixed. Fig. 26 Arrangement correction factors for a single-pass, crossflow heat exchanger with one fluid mixed and the other unmixed (typical tubular air heater application). Fig. 24 Mean effective temperature difference.
- 128. 4-22 Steam 41 / Heat Transfer The Babcock & Wilcox Company previously tested. The outlet temperatures can only be found by trial and error using the methods previously presented. These applications are best handled by the net transfer unit (NTU) method that uses the heat exchanger effectiveness (see Reference 16). Heat transfer in porous materials Porosity is an important factor in evaluating the ef- fectiveness of insulation materials. In boiler applica- tions, porous materials are backed up by solid walls or casings,sothatthereisminimalflowthroughthepores. Heat flow in porous insulating materials occurs by conduction through the material and by a combina- tion of conduction and radiation through the gas-filled voids. In most refractory materials, the Grashof- Prandtl (Raleigh) number is small enough that neg- ligible convection exists although this is not the case in low density insulations [< 2 lb/ft3 (32 kg/m3 )]. The relative magnitudes of the heat transfer mechanisms depend, however, on various factors including poros- ity of the material, gas density and composition fill- ing the voids, temperature gradient across the mate- rial, and absolute temperature of the material. Analytical evaluation of the separate mechanisms is complex, but recent experimental studies at B&W have shown that the effective conductivity can be approximated by: k a bT cTeff = + + 3 (75) Experimental data can be correlated through this form, where a, b and c are correlation coefficients. The heat flow is calculated using Equation 1; k is replaced by keff and T is the local temperature in the insulation. Fig. 28 Coefficient Y as a function of ratio R/r for fin efficiency. In high temperature applications, heat transfer across the voids occurs mainly by radiation and the third term of Equation 75 dominates. In low tempera- ture applications, heat flow by conduction dominates and the first two terms of Equation 75 are controlling. Film condensation When a pure saturated vapor strikes a surface of lower temperature, the vapor condenses and a liquid film is formed on the surface. If the film flows along the surface because of gravity alone and a condition of laminar flow exists throughout the film thickness, then heat transfer through this film is by conduction only. As a result, the thickness of the condensate film has a direct effect on the quantity of heat transferred. The film thickness, in turn, depends on the flow rate of the condensate. On a vertical surface, because of drainage, the thickness of the film at the bottom will be greater than at the top. Film thickness increases as a plate surface is inclined from the vertical position. As the film temperature increases, its thickness decreases primarily due to increased drainage veloc- ity. In addition, the film thickness decreases with in- creasing vapor velocity in the direction of drainage. Mass diffusion and transfer Heat transfer can also occur by diffusion and mass transfer. When a mixture of a condensable vapor and a noncondensable gas is in contact with a surface that is below the dew point of the mixture, some conden- sation occurs and a film of liquid is formed on the sur- face. An example of this phenomenon is the conden- sation of water vapor on the outside of a metal con- tainer. As vapor from the main body of the mixture diffuses through the vapor-lean layer, it is condensed on the cold surface as shown in Fig. 29. The rate of condensation is therefore governed by the laws of gas diffusion. The heat transfer is controlled by the laws of conduction and convection. The heat transferred across the liquid layer must equal the heat transferred across the gas film plus the latent heat given up at the gas-liquid interface due to condensation of the mass transferred across the gas film. An equation relating the mass transfer is: h T T h T T K H Y Yi g g i y fg g iδ δ−( ) = −( ) + −( ) (76) where T and Y define the temperatures and concen- trations respectively identified in Fig. 29, hδ is the heat transfer coefficient across the liquid film, hg is the heat transfer coefficient across the gas film, and Ky is the mass transfer coefficient. Hfg is the latent heat of vaporization. Heat transfer due to mass transfer is important in de- signing cooling towers and humidifiers, where mixtures of vapors and noncondensable gases are encountered. Evaporation or boiling The phenomenon of boiling is discussed in Chap- ters 1 and 5, where the heat transfer advantages of nucleate boiling are noted. Natural-circulation fossil fuel boilers are designed to operate in the boiling range. In this range, the heat transfer coefficient var- Fig. 27 Fin efficiency as a function of parameter X.
- 129. Steam 41 / Heat Transfer 4-23 The Babcock & Wilcox Company ies from 5000 to 20,000 Btu/h ft2 F (28,392 to 113,568 W/m2 K). This is not a limiting factor in the design of fossil fuel boilers provided scale and other deposits are prevented by proper water treatment, and provided the design avoids critical heat flux (CHF) phenomena. (See Chapter 5.) In subcritical pressure once-through boilers, water is completely evaporated (dried out) in the furnace wall tubes which are continuous with the superheater tubes. These units must be designed for subcooled nucleate boiling, nucleate boiling, and film boiling, depending on fluid conditions and expected maximum heat absorption rates. Fluidized-bed heat transfer The heat transfer in gas-fluidized particle beds used in somecombustionsystemsiscomplex,involvingparticle-to- surfacecontact,generalconvectionandparticle-to-surface thermal radiation. Correlations for heat transfer to tube bundles immersed in fluidized beds aresummarizedin Chapter 17. Numerical modeling Advances in computers have enabled B&W to math- ematicallymodelcomplexheattransfersystems.These models provide a tool for analyzing thermal systems inexpensively and rapidly. Although empirical meth- ods and extensive equipment testing continue to pro- vide information to designers, numerical simulation of boiler components, e.g., membrane walls, will become increasinglyimportantascomputertechnologyevolves. (See Chapter 6.) Conduction The energy equation for steady-state heat flow was previously defined as Equation 19 and is more gen- erally written as Equation 20. Solutions of these equa- tions for practical geometries are difficult to obtain except in idealized situations. Numerical methods permit the consideration of additional complex effects including irregular geometries, variable properties, and complex boundary conditions. Conduction heat flow through boiler membrane walls, refractory lin- ings with several materials, and steam drum walls are several applications for these methods. The approach is to divide the heat transfer system into subvolumes called control volumes (Fig. 30). (See References 16 and 17.) The governing equation is integrated, or av- eraged, over the subvolume, leading to an expression of the form: T T R T T R q V c T T t e p pe w p pw p p p p p o − + − + ′′′ = − ∆ (77) where the subscripts denote the neighbor locations as points on a compass. If the steady-state solution is de- sired, the right hand side of the equation, c T T tp p p o −( ) / ∆ , whichaccountsforchangesinstoredenergyissettozero. A solution is then obtained numerically. Equation 77 is a discrete form of the continuous differential equa- tion. The modeled geometry is subdivided and equa- tions of this form are determined for each interior volume. The electrical analogy of the equation is ap- parent. First, each term is an expression of heat flow into a point using Fourier’s law by Equation 1 and, second, Kirchhoff’s law for electrical circuits, Equa- tion 26, is used to determine the net flow of heat into any point. The application of the electrical analogy is straightforward for any interior volume once the subvolumes are defined. At the boundaries, tempera- ture or heat flow is defined. For unsteady-state problems, asequenceofsolutions isobtainedforthetimeinterval∆t,withTp o beingthenode temperature at the beginning of the interval and Tp being the temperature at the end of the interval. Ref- erences 16 and 17 explore these models in depth. Vari- ous computer codes are commercially available to per- form the analysis and display the results. Radiation Numerical methods provide accurate estimates of radiative transfer in the absorbing and scattering media that is ubiquitous in the combustion and post- Fig. 29 Simultaneous heat and mass transfer in the dehumidification of air. Fig. 30 Control volume layout for a plane wall with notation for heat flow to node 3 and steady-state solution.
- 130. 4-24 Steam 41 / Heat Transfer The Babcock & Wilcox Company combustion zones of a boiler. Many numerical meth- ods have the advantage of incorporating complex geo- metrical description of the enclosure walls. These methods solve the radiation transport equation (RTE) in two and three dimensions and include the effects of absorption, emission, and scattering media, for gray or non-gray enclosure walls. Numerical models start by dividing the volume and surfaces of an enclosure into multiple control volumes and surface elements (as described in Chapter 6). Radiation properties of gases and particles are evaluated at each control volume, and may vary with local composition and temperature of the combustion mixture. Emissivity and tempera- ture of the walls may also vary with local conditions, for each surface element of the enclosure. The solu- tion of the RTE is generally carried out for the entire radiative spectrum for greatest numerical efficiency. However, if increased accuracy is required, the spec- trum can be divided into discrete bands correspond- ing with the bands of gaseous radiation and the RTE is solved for each band separately. Radiative heat transfer in furnaces can be calculated by one of several numerical methods, which are de- scribedinReference10.Thesimplestoftheseisthezonal method,4 an extension of the network exchange method described previously in this chapter. The enclosure is divided into a finite number of isothermal volume and surface area zones. Exchange factors for all combina- tions of volume to volume, volume to surface, and sur- face to surface exchange are precalculated. This analy- sisleadstoasetofsimultaneousequationsforunknown radiant heat fluxes, which are solved numerically. The discrete ordinates method is perhaps the most robust approach for numerical analysis of radiation heat transfer in boilers. The angular dependence of radiation is first expressed in spherical coordinates, and is divided into a finite number of discrete direc- tions for solving the RTE. The equations are trans- formed into a set of simultaneous partial differential equations, one for each direction, that are solved nu- merically. The accuracy of the method increases with the number of directions that are used in the approxi- mation (typically 12, 24, or 48). Discrete ordinates was developed and optimized for thermal radiation in multi-dimensional geometries by the pioneering work at B&W.18 Since then, it has gained in popularity, and is now used in many commercial computational fluid dynamics (CFD) codes. The numerical solution for radiation leads to the distribution of radiant intensity or radiant heat flux, for a given temperature field. This solution is coupled to the energy equation and temperature of the gas- particle mixture. The energy equation (Equation 28 or 29) can be solved numerically for gas-particle tem- perature field using the methods described in Chap- ter6.Radiationabsorptionandemissionisrepresented by the internal heat generation term, SH. Wall tem- perature is determined from an energy balance for convection and radiation heat transfer to the surface, and heat conduction through the wall. Several itera- tions between radiation, gas-particle energy, and wall temperature will ultimately yield a converged solution in which an overall energy balance is achieved. Design considerations Furnaces Fossil-fuel fired boiler designers need to evaluate furnace wall temperature and heat flux, flue gas tem- perature, and furnace exit gas temperature. These pa- rametersarerequiredtodeterminematerialsandtheir limits, and to size heat transfer surface. An analytical solution for heat transfer in a steam generating furnace is extremely complex. It is not pos- sible to calculate furnace outlet temperatures by theo- retical methods alone. Nevertheless, this temperature must be correctly predicted because it determines the designofthesuperheaterandothersystemcomponents. In a boiler, all of the principal heat transfer mecha- nisms take place simultaneously. These mechanisms are intersolid radiation between suspended solid par- ticles, tubes, and refractory materials; nonluminous gas radiation from the products of combustion; con- vection from the gases to the furnace walls; and con- duction through ash deposits on tubes. Fuel variation is significant. Pulverized coal, gas, oil or waste-fuel firing may be used. In addition, dif- ferent types of the same fuel also cause variations. Coal, for example, may be high volatile or low vola- tile, and may have high or low ash and moisture con- tents. The ash fusion temperature may also be high or low, and may vary considerably with the oxidizing properties of the furnace atmosphere. Furnace geometry is complex. Variations occur in the burner locations and spacing, in the fuel bed size, in the ash deposition, in the type of cooling surface, in the furnace wall tube spacing, and in the arch and hopper arrangements. Flame shape and length also affect the distribution of radiation and heat absorp- tion in the furnace. High intensity, high mixing burners produce bushy flames and promote large high temperature zones in the lower furnace. Lower intensity, controlled mixing burners frequently have longer flames that delay com- bustion while controlling pollutant formation. Surface characteristics vary. The enclosing furnace walls may include any combination of fuel arrange- ments,refractorymaterial,studdedtubes,spacedtubes backed by refractory, close-spaced tubes, membrane con- struction or tube banks. Emissivities of these surfaces are different. The water-cooled surface may be covered with fluid slag or dry ash in any thickness, or it may be clean. Temperature varies throughout the furnace. Fuel andairenteratrelativelylowtemperatures,reachhigh temperatures during combustion, and cool again as the products of combustion lose heat to the furnace enclo- sure. All temperatures change with load, excess air, burner adjustment and other operating conditions. Accurate estimates of furnace exit gas temperature are important. For example, high estimates may lead to over-estimating the heat transfer surface, while low estimates may cause operational problems. These are discussed in Chapter 19. Empirical methods Considering the fuel type, fir- ing rate and furnace configuration, empirical meth- ods as illustrated in Fig. 31 have long been used to
- 131. Steam 41 / Heat Transfer 4-25 The Babcock & Wilcox Company predict local absorption rates in the furnace. These methods, although largely empirical, contain engi- neering models which are based on fundamentals. Data and operating experience are used to tune the models employed in the design envelope. Fig. 31 shows typical vertical and horizontal heat flux distributions for furnace walls. Deviations in the heat flux distribution are caused by unbalanced firing, variations in tube surface condition, differences in slagging, load changes, sootblower opera- tionandothervariationsinunitoperation.Atypicalupset heat flux distribution is shown in Fig. 31. These upset factors are typically a function of vertical/horizontal lo- cation, firing method and fuel, and furnace configura- tion. They are derived from operating experience. The heat flux applied to the tubes in the furnace wall is also nonuniform in the circumferential direc- tion. As shown in Fig. 32, the membrane wall is ex- posed to the furnace on one side while the opposite side is typically insulated to minimize heat loss. The result- ing heat flux distribution depends upon the tube out- side diameter, wall thickness, and spacing, as well as the web thickness and materials. The fluid tempera- ture and inside heat transfer coefficient have second- ary effects. This distribution can be evaluated using commercially available computer codes. To correlate data and calculations for different fur- naces,methodsforcomparingtherelativeeffectiveness of different furnace wall surfaces are needed. The ef- fectiveness and spacing of tubes compared to a com- pletelywater-cooledsurfaceareshowninFig.33.Awall of flat-studded tubes is considered completely water- cooled. The effectiveness of expected ash covering, com- pared with completely water-cooled surfaces, can also be estimated. The entire furnace envelope can then be evaluated in terms of equivalent cold surface. The heat energy supplied by the fuel and by the preheated combustion air, corrected for unburned com- bustibleloss,radiationloss,andmoisturefromthefuel, may be combined into a single variable, known as heat available. The heat available divided by the equiva- lent flat projected furnace enclosure plus furnace Fig. 32 Typical circumferential heat flux distribution for a furnace membrane wall panel tube. Fig. 31 Typical vertical and horizontal heat flux distributions for furnace walls. Fig. 33 Furnace wall area effectiveness factor (1.0 for completely water-cooled surface). A reduced area (equivalent cold surface) is determined from these curves for walls not completely water cooled. (Adapted from Hottel4 .)
- 132. 4-26 Steam 41 / Heat Transfer The Babcock & Wilcox Company platen area is called the furnace heat release rate. The heat input from fuel divided by the furnace volume is called the furnace liberation rate. The furnace exit plane defines the boundary of the furnace volume and flat projected furnace enclosure area. The furnace exit plane area and back spacing between the furnace platen tubes are included in the flat projected area calculation. For furnace platens and membrane wall furnace enclosure, the effectiveness factor for all ex- amples given in this and other chapters is equal to 1.00. Furnace exit gas temperature (FEGT) is primarily a function of heat release rate rather than liberation rate. The furnace exit is commercially defined as be- ing located at the face of the first tube bank having a tube spacing of less than 15 in. (38.1 cm) side centers because, as can be inferred from Fig. 39, convection conductance typically becomes the predominant heat transfer mode at this side spacing. The furnace exit plane, generally used for the accurate calculation of overall heat transfer, is normally set at the face of the first tube bank having a tube spacing of 36 in. (91.4 cm) side centers or less in order to include the convec- tion conductance in the heat transfer calculations. At tube side centers of 36 in. (91.4 cm) or less, the convec- tion conductance is too significant to ignore as a portion oftotalheattransfer.TheapproximaterelationofFEGT to heat release rate at the furnace exit plane for a typi- cal pulverized bituminous coal is given in Fig. 34. Furnace exit gas temperatures and related heat absorption rates, as functions of furnace heat release rate for most pulverized coal-fired furnaces, lie within the shaded bands shown in Figs. 35 and 36. The lim- its indicated serve only as a general guide and may vary due to combustion system type, burner and air port placement, stoichiometry, fuel characteristics and cleaning cycle. The bands for dry ash and for slag-tap furnaces overlap between 100,000 and 150,000 Btu/ h ft2 (315,460 to 473,190 W/m2 ), but different types of coal are involved. To be suitable for a slag-tap furnace, a bituminous coal should have an ash viscosity of 250 poises at 2450F (1343C) or lower. In the overlapping range, dry ash and slag-tap both have about the same heat absorption rate, or dirtiness factor, as shown in Fig. 36. Both bands are rather broad, but they cover a wide range of ash characteristics and a considerable diversity in waterwall construction and dirtiness. The heat leaving the furnace is calculated from the exiting gas flow rate (the gas enthalpy values evalu- ated at the furnace exit gas temperature) plus the net radiative transfer at the furnace exit. The heat ab- sorbed in the furnace is the difference between the heat available from the fuel, including the preheated combustion air, and heat leaving the furnace. Numerical methods Empirical design methods are gradually being supplemented with numerical meth- ods, as the level of detail increases and confidence is improved. Radiation heat transfer in furnace enclo- sures can now be solved on computers, in combina- tion with turbulent flow, energy, and combustion. Ra- diation properties of gases, particles, and fuel specific properties of ash deposits can be included in the analy- sis with more advanced engineering models and cor- relations. The effects of spectral radiation from gases and particles can also be included to improve accuracy of the analysis. Detailed results include the three-di- mensional distribution of radiation intensity, gas tem- perature, and heat flux on the furnace walls. Numeri- Fig. 35 General range of furnace exit gas temperature for dry ash and slag-tap pulverized coal-fired furnaces. 2600 (1427) 2200 (1204) 1800 (982) 1400 (760) FurnaceExitGasTemperature,F(C) 100 (315) Heat Release Rate, 1000 Btu/h ft2 (kW/m2) 200 (631) 300 (946) 400 (1262) 500 (1577) 0 3000 (1649) 3400 (1871) Slag-Tap Dry Ash Fig. 34 Approximate relationship of furnace exit gas temperatures to heat release rate for a typical pulverized bituminous coal. 2800 (1538) 2600 (1427) 2200 (1204) 2400 (1316) 2000 (1093) 1800 (982) 1600 (871) 1400 (760) 0 (-18) FurnaceExitGasTemperature,F(C) 0 20 (63) 60 (189) 100 (315) 140 (442) 180 (568) 220 (694) Heat Release Rate, 1000 Btu/h ft2 (kW/m2)
- 133. Steam 41 / Heat Transfer 4-27 The Babcock & Wilcox Company cal methods have the potential for more accurate pre- diction of heat flux distribution on furnace walls and convective surfaces. However, further validation of results and improvements in computational efficiency are needed to make numerical methods more practi- cal for routine engineering applications. A numerical model was created for the furnace of a 560 MW supercritical steam pressure boiler firing high volatile eastern United States bituminous coal.Asche- matic of the furnace is shown in Fig. 37. The sloping furnace walls of the ash hopper, the furnace nose, and the horizontal section of the convection pass were in- cluded in the model. Inlet fuel, inlet air and exit streams were properly located around the boundaries. An example of the predicted heat flux distribution is shown in Fig. 38. The predicted furnace exit gas tem- perature for this case was 2242F (1228C), while the observed average value was 2276F (1247C). Relative magnitudes of convective and radiative heat transfer at various locations are shown in Fig. 39 for a 650 MW boiler. The furnace area is dominated by radiation while the back-end heat transfer surfaces in the di- rectionofflowareincreasinglydominatedbyconvection. Convection banks Tube spacing and arrangement In addition to heat absorption and resistance to gas flow, other important factors must be considered in establishing the opti- mum tube spacing and arrangement for a convection surface. These are slagging or fouling of surfaces, ac- cessibility for cleaning, and space occupied. A large longitudinal spacing relative to the transverse spac- ing is usually undesirable because it increases the space requirement without improving performance. These are discussed further in Chapter 21. Tube diameter For turbulent flow, the heat trans- fer coefficient is inversely proportional to a power of the tube diameter. In Equations 57 and 60 the expo- nent for longitudinal flow is 0.20; for cross flow it is 0.39. These equations indicate that the tube diameter should be minimized for the most effective heat trans- fer. However, this optimum tube diameter may require Fig. 38 Numerical model – predicted furnace wall flat projected heat flux distribution. (1 W/m2 = 0.317 Btu/h ft2 ) Fig. 37 560 MW utility boiler schematic used for numerical model (see Fig. 38). Fig. 36 General range of furnace heat absorption rates for dry ash and slag-tap pulverized coal-fired furnaces.
- 134. 4-28 Steam 41 / Heat Transfer The Babcock & Wilcox Company an arrangement that is expensive to fabricate, diffi- cult to install, or costly to maintain. A compromise between heat transfer effectiveness and manufactur- ing, erection, and service limitations is therefore nec- essary in selecting tube diameter. Penetration of radiation A convection bank of tubes bordering a furnace or a cavity acts as a blackbody radiant heat absorber. Some of the impinging heat, however, radiates through the spaces between the tubes of the first row and may penetrate as far as the fourth row. The quantity of heat penetration can be established by geometric or analytical methods. The effect of this penetration is especially important in establishing tube temperatures for superheaters lo- cated close to a furnace or high temperature cavity. Consider 2.0 in. (50.8 mm) OD tubes placed in an ar- ray of tubes on a 6.0 in. (152.4 mm) pitch. Fig. 33, curve 1 can be used to estimate the remaining radia- tion. For a given radiant heat flux, 45% is absorbed in the first tube row, and 55% passes to the second row. 45% of this reduced amount is again absorbed in the second tube row. After the fourth row, less than 10% of the initial radiation remains. Effect of lanes Lanes in tube banks, formed by the omission of rows of tubes, may decrease the heat ab- sorption considerably. These passages act as bypasses for flowing hot gases and radiation losses. Although the overall efficiency decreases, the high mass flow through the lanes increases the absorption rate of the adjacent tubes. Critical tube temperatures in super- heaters or steaming conditions in economizers may develop. Whenever possible, lanes should be avoided within tube banks and between tube banks and walls; however, this is not always possible. A calculation ac- counting for the lanes is necessary in such cases. Heat transfer to water Water heat transfer coefficient The heat transfer co- efficient for water in economizers is so much higher than the gas-side heat transfer coefficient that it can be neglected in determining economizer surface. Boiling water heat transfer coefficient The combined gas-side heat transfer coefficient (convection plus intertube radiation) seldom exceeds 30 Btu/h ft2 F (170 W/m2 K) in boiler design practice. The heat transfer coefficient for boiling water [l0,000 Btu/h ft2 F (56,784 W/m2 K)] is so much larger that it is generally ne- glected in calculating the resistance to heat flow, al- though Equation 4 in Chapter 5 can be used to calcu- late this value. Effect of scale Water-side and steam-side scale de- posits provide high resistance to heat flow. As scale thickness increases, additional heat is required to maintain a given temperature inside a furnace tube. This leads to high metal temperatures and can cause tube failure. Deposition of scale and other contami- nants is prevented by good feedwater treatment and proper operating practices. Heat transfer to steam In superheaters, the steam- side convection constitutes a significant resistance to heat flow.Although this resistance is much lower than the gas-side resistance, it can not be neglected in com- puting the overall heat flow resistance or the heat transfer rate. It is particularly significant in calculat- ing superheater tube temperatures, because the mean tube wall temperature is equal to the steam tempera- ture plus the temperature drop through the steam film plus half of the metal temperature drop. Thesteam-sideheattransfercoefficientiscalculated from Equation 58 using information from Figs. 13, 16 and 17. If the steam heat transfer coefficient is desig- nated as h, the film temperature drop, ∆Tf, is q/(hA), using the outside surface area of the tube as the base in each expression. It is imperative to prevent scale deposits in super- heater tubes. Because of its high resistance to heat flow and due to the elevated temperatures, even a thin layer of scale may be sufficient to overheat and fail a tube. Cavities Cavities are necessary between tube banks of steam generating units for access, for sootblowers, and for possible surface addition. Hot flue gas radiates heat to the boundary surfaces while passing through the cavity. The factors involved in calculating heat trans- fer in cavities are as follows. Temperature level Radiation from nonluminous gases to boundary surfaces and radiation to the gas by the surroundings increase approximately by the fourth power of their respective absolute tempera- tures. Remembering that Eb = σ T4 , Equations 39 and 40 illustrate this relationship. Gas composition Carbon dioxide and water vapor are the normal constituents of flue gases which emit nonluminous radiation in steam generating units. The concentrations of these constituents depend on the fuel burned and the amount of excess air. Particles in the gas The particles carried by flue gases receive heat from the gas by radiation, convec- tion, and conduction, and emit heat by radiation to the furnace enclosure. Size of cavity The heat transfer rate increases with cavity size. Thick layers of gas radiate more vigorously than thin layers. The shape of the cavity can also com- plicate heat transfer calculations. Fig. 39 Comparison of radiative and convective heat transfer contributions to absorption in various locations within a large utility boiler (SH = superheater; RH = reheater; 1 in. = 2.54 cm). Surfaces in Zone 60 (189.3) 50 (157.7) 40 (126.1) 30 (94.6) 20 (63.1) 10 (31.5) 0 HeatFlux,1000Btu/hft2(kW/m2) 1 2 3 4 5 6 7 8 9 10 Convective Radiative 1 6 8 97 10 2 3 5 24in.SHPlatens Cavity 12in.SH 9in.RH Cavity 9in.RH Cavity 48-54in.Platens+Enclosure 4
- 135. Steam 41 / Heat Transfer 4-29 The Babcock & Wilcox Company Receiving surface Arefractory surface forming part of a cavity boundary reaches a high temperature by convection and radiation from the flue gas. It also reradiates heat to the gas and to the other walls of the enclosure. Reradiation from a clean, heat-absorbing surface is small unless the receiving surface tempera- ture is high, as is the case with superheaters and reheaters.Ash or slag deposits on the tube reduce heat absorption and increase reradiation. In boiler design, there are two significant effects of cavity radiation: 1) the temperature of flue gas drops, from several degrees up to 40F (22C), in passing across a cavity, and 2) gas radiation increases the heat ab- sorption rates for the tubes forming the cavity bound- aries. The second effect influences superheater tube temperatures and the selection of alloys. Insulation The calculation of heat transfer through insulation follows the principles outlined for conduction through a composite wall. Refer to Chapter 23 for more infor- mation regarding insulating materials. Hot face temperature In a furnace with tube-to-tube walls, the hot face temperature of the insulation is the saturation temperature of the water in the tubes. If the inner face of the furnace wall is refractory, the hot face in- sulationtemperaturemustbecalculatedusingradiationand convection heat transfer principles on the gas side of the furnace wall, or estimated using empirical data. Heat loss and cold face temperature The heat loss to the surroundings and the cold face temperature de- crease as the insulation thickness increases. However, once an acceptable layer of insulation is applied, ad- ditional amounts are not cost effective. Standard com- mercial insulation thicknesses should be used in the composite wall. The detailed calculation of overall heat loss by ra- diation and convection from the surfaces of a steam generating unit (usually called radiation loss) is te- dious and time consuming. A simple approximate method is provided by the chart prepared from the American Boiler Manufacturers Association (ABMA) original. (See Chapter 23, Fig. 12.) Ambient air conditions Low ambient air tempera- ture and high air velocities reduce the cold face tem- perature. However, they have only a small effect on total heat loss, because surface film resistance is a minor part of the total insulation resistance. Combined heat loss rates (radiation plus convection) are given in Chapter 23, Fig. 11, for various temperature dif- ferences and air velocities. The effect of surface film resistance on casing temperature and on heat loss through casings is shown in Chapter 23, Fig. 15. Temperaturelimitsandconductivities Refractoryorin- sulating material suitable for high temperature appli- cationsisusuallymoreexpensiveandlesseffectivethan low temperature materials. It is therefore customary to use several layers of insulation. The lower cost, more effective insulation is used in the cool zones; the higher cost materials are used only where demanded by high operating temperatures. Thermal conductivities for re- fractoryandinsulatingmaterials,andtemperaturesfor which they are suitable, are shown in Chapter 23, Fig. 10. Applications Example 1 – Conduction through a plane wall If a flat plate is heated on one side and cooled on the other, the heat flow rate in the wall, shown in Fig. 1, is given by Equation 2. The rate of heat flow through a 0.25 in. thick steel plate with 1 ft2 surface area and ∆T = 25F may be evaluated with Equation 2 as follows: q k A T L = = × × = ∆ 30 1 25 0 25 12 36 000 . / , Btu/h (78) where the thermal conductivity, k, for steel is 30 Btu/h ft F. Example 2 – Heat flow in a composite wall with convection The heat flow through a steel wall which is insu- lated on both sides is shown in Fig. 3. This example demonstrates the procedure for combining thermal resistances. In addition to the thermal resistance of the firebrick, steel, and insulation, the heat flow is impeded by the surface resistances. Consider a 600 ft2 surface with gases at 1080F or 1540R on the inside exposed to an ambient temperature of 80F on the out- side. The thermal conductivities of the firebrick, steel flue and insulation are assumed to be k1 = 0.09, k2 = 25, and k3 = 0.042 Btu/h ft F, respectively. These as- sumptions are verified later. The layer thicknesses are ∆x1 = 4 in., ∆x2 = 0.25 in., and ∆x3 = 3 in. The heat transfer coefficients for convection are hcv,i = 5.0 Btu/ h ft2 F on the inside surface hcv,o = 2.0 Btu/h ft2 F on the outside surface. Where the temperature difference between the radiating gas, Tg, and a surface, Ts, is small, the radiation heat transfer coefficient can be estimated by: h F T T F Tr g s g≅ +( ) ≈4 0 2 4 3 3 . /σ ε σ ε (79a) where Tg and Ts are the absolute temperatures, R (K). In this example, the surface emissivity is assumed close to 1.0 and F = 1.0 resulting in: hr = ×( ) +( ) = − 4 0 0 1713 10 1080 460 25 8 3 . . Btu/h ft F2 (79b) Using the Req shown in Fig. 3 and values of R evalu- ated using Table 4: R Aeq = + + + + + = 1 5 1 25 1 5 1 25 4 12 0 09 0 25 12 25 3 12 0 042 1 2. . . 00 033 3 70 0 000833 5 95 0 5 10 18 . . . . . . + + + + = h ft F Btu 2 (80) It is clear that the firebrick and insulation control the overall resistance; the steel resistance can be ne-
- 136. 4-30 Steam 41 / Heat Transfer The Babcock & Wilcox Company glected. If the successive material layers do not make good thermal contact with each other, there will be interface resistances due to the air space or film. These resistances may be neglected in composite walls of insulating materials. However, they must be included in calculations if the layer resistances are small com- pared to the interface resistances. An example of this is heat transfer through a boiler tube with internal oxide deposits. The heat flow can be computed using Equation 23: q T T R A T T R A f eq f eq = − = − = − = ∞ ∞ 600 1080 80 10 18 58 939 . , Btu h (81) To determine if the correct thermal conductivities were assumed and if the temperature levels are within allowable operating limits of the material, it is neces- sary to calculate the temperatures at the material in- terfaces. Solving Equation 81 for temperature and sub- stitutingindividualresistancesandlocaltemperatures: T T q A R Af f1 1080 59 939 0 033 600 1077= − ( ) = − ( )( ) = , . F (82) T T q A R A2 1 1 1077 58 939 3 70 600 713= − = − =( ) ( )( ), . F (83) T T q A R A3 2 2 713 58 939 0 000833 600 713= − = − =( ) ( )( ), . F (84) T T q A R A4 3 3 713 58 939 5 95 600 129= − = − =( ) ( )( ), . F (85) T T q A R A∞ ∞ = − = − =( ) ( )( ) 4 129 58 939 0 5 600 80 , . F (86) The small temperature difference between the radi- ating gas and the surface (Tf – T1 = 3F ) verifies the as- sumption for using Equation 79a. Had the temperature difference been larger, then the full equation for the ra- diation resistance in Table 4 may have been required. The negligible resistance of the steel flue is reflected in the temperature drop T2 – T3 = 0. If the calculated interface temperatures indicate the conductivity was chosen improperly, new conductivities are defined using the mean temperature of each material. For example, a new firebrick conductivity is determined using 0.5 (T1 + T2). Example 3 – Heat flow in an insulated pipe Heat flow in cylindrical geometries is important in evaluating boiler heat transfer. Refer to the example steam line shown in Fig. 40. The resistances in Table 4 for cylindrical geometries must be used. The ther- mal analogy for the pipe in Fig. 40 can be written: R h r l ln r r k l ln r r k l h r l eq i = ( ) + ( ) + ( ) + ( ) 1 2 2 2 1 2 1 2 1 2 3 2 3 0 3 π π π π / / (87) A 3 in. Schedule 40 steel pipe (k = 25 Btu/h ft F) is covered with 0.75 in. insulation of k = 0.10 Btu/h ft F. This pipe has a 3.07 in. ID and a 3.50 in. OD. The pipe transports fluid at 300F and is exposed to an ambient temperature of 80F. With an inside heat transfer coefficient of 50 Btu/h ft2 F and an outside heat transfer coefficient of 4 Btu/h ft2 F, the thermal resistance and heat flow per unit length are: R l ln ln eq = ( ) + ( ) + 1 50 2 3 07 2 12 3 50 3 07 2 25 5 0 3 5 π π. / . . . . ( ) + ( ) 2 0 1 1 4 2 5 0 2 12 π π . . / (88) R leq = + + + = 0 0249 0 000834 0 568 0 191 0 785 . . . . . h ft F Btu (89) The overall resistance is dominated by the insula- tion resistance and that of the outer film boundary layer. The resistance of the metal pipe is negligible. q l = − = 300 80 0 785 280 . Btu/h ft (90) Fig. 40 Example of heat flow in an insulated pipe.
- 137. Steam 41 / Heat Transfer 4-31 The Babcock & Wilcox Company Example 4 – Heat flow between a small object and a large cavity Consider an unshielded thermocouple probe with an emissivity of 0.8 inserted in a duct at 240F carry- ing combustion air. If the thermocouple indicates a temperature of 540F and the surface heat transfer coefficient, h, between the thermocouple and gas is 20 Btu/h ft2 F, the true gas temperature can be estimated. The thermocouple temperature must be below the gas temperature because heat is lost to the walls. Under steady-state conditions, an energy balance equates the radiant heat loss from the thermocouple to the wall and the rate of heat flow from the gas to the thermocouple. Using Table 6, the heat flow between the thermo- couple and the cavity becomes: q A = ×( ) × +( ) − +( ) = − 0 8 0 1713 10 540 460 240 460 1041 4 8 4 4 . . . Btu/h ft2 (91) The true gas temperatures becomes: T q A h Tg t= + = + = / .1041 4 20 540 592F (92) Similar analyses can be performed for thermocouples shielded with reflective foils in high temperature envi- ronments. This practice prevents thermocouple heat lossesandincorrecttemperaturereadings.Theheatflow from a shielded thermocouple is calculated as follows: q N qshielded no shield= +( ) 1 1 (93) where N is the number of concentric layers of material. Example 5 – Heat flow between two surfaces An estimate of the maximum radiant heat transfer between two surfaces can be determined using Equa- tion 11. This approximation is valid when the walls are considered black and any intervening absorbing gases are neglected. If two 5 × 10 ft black rectangles, directly opposed,arespaced10ftapartwithtemperaturesof940 and 1040F, the energy exchange is estimated as follows. The energy from surface 1 directly striking surface 2 is defined by the shape factor F12. Referring to Fig. 5, this factor F12 is 0.125, indicating that 87.5% of the energy leaving surface 1 strikes a surface other than surface 2. The net heat flow is: q A F T T12 1 12 1 4 2 4 8 4 50 0 125 0 1713 10 1040 460 940 = −( ) = ( ) ×( ) × +( ) − − σ . . ++( ) = 460 13 071 4 12q , Btu/h (94) Intervening gases and/or gray walls further reduce the net heat flow. Example 6 – Radiation from a hot gas to furnace walls Consider a furnace with a volume of 160,000 ft3 and a heat transfer surface area of 19,860 ft2 . The gas tra- versing the furnace (Tg) is at 2540F (1393C) and the furnace walls (Ts) are at 1040F (560C). The radiant heat transfer rate can be estimated using Equation 40, assuming the walls are radiatively black (εs = 1). If the products of combustion at one atmosphere con- sist of 10% carbon dioxide, 5% water vapor, and 85% nitrogen, Figs. 9 to 11 can be used to estimate the gas emissivity and absorptivity. The beam length is L = 3.6 V/A = 29.0 ft. Then for H2O, pwL = (29.0) (0.05) = 1.45 ft-atm (45 bar-cm) and from Fig. 9 at 1393C the emissivity is found to be 0.22. For CO2, pcL = (29.0) (0.l0) = 2.90 ft-atm (89 bar-cm) and from Fig. 10, at 1393C, the emissivity is found to be 0.16. The correc- tion ∆ε is determined from Fig. 11. The total gas emis- sivity is then found from Equation 41: ε ε ε εg g= + −H O CO2 2 ∆ (95) εg = + − =0 22 0 16 0 06 0 32. . . . (96) Hottel4 suggests calculating the absorptivity of the gas using modified pressure length parameters: F p L T T w w s g = = ( )( ) + + = 0 05 29 1040 460 2540 460 0 73 . . ft-atm (or 22 barr-cm) (97) F p L T T c c s g = = ( )( ) + + = 0 10 29 1040 460 2540 460 1 45 . . ft-atm (or 45 baar-cm) (98) α εH O H O2 2 = ( ) × = + + F T T T w s g s , . .0 45 0 21 2540 460 1040 460 00 45 0 29 . .= (99) α εCO CO2 2 = ( ) × = + + F T T T c s g s , . .0 65 0 15 2540 460 1040 460 00 65 0 24 . .= (100) ∆ ∆α εg sT= ( ) = 0 04. (101) α α α αg g= + − =H O CO2 2 ∆ 0 49. (102)
- 138. 4-32 Steam 41 / Heat Transfer The Babcock & Wilcox Company The net rate of heat flow calculated from Equation 40: q A E Esg g bg g bs= −( ) = −( ) = × ε α σ σ19 860 0 32 3000 0 49 1500 797 10 4 4 6 , . . Btuu/h (103) In estimating boiler heat transfer, the beam lengths are large, effecting large pL values. Proprietary data are used to estimate the heat transfer for these val- ues, and extrapolation of the curves in Figs. 9 to 11 is not recommended. Example 7 – Radiation in a cavity Radiation in a cavity containing absorbing gases can be analyzed with the concepts previously pre- sented. These concepts are useful in analyzing sur- face to surface heat transfer. Examples include boiler wall to boiler wall, platen to platen, and boiler wall to boiler enclosure heat exchanges. Table 5 (and Refer- ence 4) contains the thermal resistances used in con- structing the thermal circuit in Fig. 41. Note the re- sistance between surface 1 and 2 decreases as the transmission in the gas, τ12, increases to a transpar- ent condition τ12 = 1. At τ12 near zero, the gases are opaque, and the resistance is very large. As the gas emissivitydecreases,thethermalcircuitreducestoFig. 6 and Equation 36. The solution of the circuit in Fig. 41 is found using Kirchhoff’s rule for nodes J1 and J2. The equations are solved simultaneously for J1 and J2: E J A J J A F E J A b bg g 1 1 1 1 1 2 1 1 12 12 1 1 1 1 1 1 0 − − + − + − = ε ε τ ε (104) Fig. 41 Example of radiation in a cavity. E J A J J A F E J A b bg b g 2 2 2 2 2 1 2 1 12 12 2 1 2 1 1 1 0 − − + − + − = ε ε τ ε (105) The net heat flow between the surfaces is: q A F J J12 1 12 12 1 2= −( )τ (106) Hottel4 demonstrates the procedures for finding the beam length to determine F12, εg1, and εg2. 1. Roshenow, W.M., Hartnett, J.P., and Ganic, E.N., Handbook of Heat Transfer Fundamentals, Second Ed., McGraw-Hill, Inc., New York, New York, 1985. 2. Roshenow, W.M., Hartnett, J.P., and Ganic, E.N., Handbook of Heat Transfer Applications, Second Ed., McGraw-Hill, Inc., New York, New York, 1985. 3. Kreith, F., and Bohn, M.S., Principles of Heat Trans- fer, Fourth Ed., Harper and Row, New York, New York, 1986. 4. Hottel, H.C., and Sarofim, A.F., Radiative Transfer, McGraw-Hill, Inc., New York, New York, 1967. 5. Wall, T.F., Bhattacharya, S.P., Zhang, D.K., et al., “The Properties and Thermal Effects of Ash Deposits in Coal-Fired Furnaces,” Progress in Energy and Combus- tion Science, Vol. 19, pp. 487-504, 1993. 6. Meyer, C.A., et al., ASME Steam Tables: Thermody- namic and Transport Properties of Steam, Sixth Ed., American Society of Mechanical Engineers, New York, New York, 1993. References 7. Boow, J., and Goard, P.R.C., “Fireside Deposits and Their Effect on Heat Transfer in a Pulverized Fuel-Fired Boiler: Part III. The Influence of the Physical Character- istics of the Deposit on its Radiant Emittance and Effec- tive Thermal Conductance,” Journal of the Institute of Fuel, pp. 412-419, Vol. 42, No. 346, 1969. 8. Leckner, B., “Spectral and Total Emissivity of Water Vapor and Carbon Dioxide,” Combustion and Flame, Vol. 19, pp. 33-48, 1972. 9. Edwards, D.K., “Molecular Gas Band Radiation,” Ad- vances in Heat Transfer, Vol. 12, Academic Press, New York, New York, pp. 115-193, 1964. 10. Modest, M.F., Radiative Heat Transfer, McGraw-Hill, Inc., New York, New York, 1993. 11. Sieder, E.N., and Tate, G.E., “Heat Transfer and Pres- sure Drop of Liquids in Tubes,” Industrial & Engineering Chemistry Research (I&EC), Vol. 28, p. 1429, 1936. 12. Dittus, F.W., and Boelter, L.M.K., University of Cali- fornia Publications on Engineering, Vol. 2, p. 443, Berke- ley, California, 1930.
- 139. Steam 41 / Heat Transfer 4-33 The Babcock & Wilcox Company Pyrex is a trademark of Corning Incorporated. 13. McAdams, W., Heat Transmission, Third Ed., McGraw-Hill, Inc., New York, New York, 1954. 14. Grimison, E.D., “Correlation and Utilization of New Data on Flow Resistance and Heat Transfer for Crossflow of Gases over Tube Banks,” Transactions of the American Society of Mechanical Engineers, Vol. 59, pp. 583-594, 1937. 15. Schmidt, T.F., “Wärme leistung von berippten Flächen,” Mitt. des Kältetechn. Institut der T.H. Karlshruhe, Vol. 4, 1949. 16. Incropera, F., and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Third Ed., John Wiley & Sons, New York, New York, 1990. 17. Patankar, S., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, Inc., New York, New York, 1980. 18. Fiveland, W. A., “Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclo- sures,” Transactions of the American Society of Mechani- cal Engineers Journal of Heat Transfer, Vol. 106, pp. 699- 706, 1984.
- 140. 4-34 Steam 41 / Heat Transfer The Babcock & Wilcox Company Wall-fired utility boiler furnace under construction.
- 141. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-1 The Babcock & Wilcox Company Chapter 5 Boiling Heat Transfer, Two-Phase Flow and Circulation A case of heat transfer and flow of particular inter- est in steam generation is the process of boiling and steam-water flow. The boiling or evaporation of wa- ter is a familiar phenomenon. In general terms, boil- ing is the heat transfer process where heat addition to a liquid no longer raises its temperature under con- stant pressure conditions; the heat is absorbed as the liquid becomes a gas. The heat transfer rates are high, making this an ideal cooling method for surfaces ex- posed to the high heat input rates found in fossil fuel boilers, concentrated solar energy collectors and the nuclear reactor fuel bundles. However, the boiling phenomenon poses special challenges such as: 1) the sudden breakdown of the boiling behavior at very high heat input rates, 2) the potential flow rate fluctuations which may occur in steam-water flows, and 3) the ef- ficient separation of steam from water. An additional feature of boiling and two-phase flow is the creation of significant density differences between heated and unheated tubes. These density differences result in water flowing to the heated tubes in a well designed boiler natural circulation loop. Most fossil fuel steam generators and all commer- cial nuclear steam supply systems operate in the pres- sure range where boiling is a key element of the heat transfer process. Therefore, a comprehensive under- standing of boiling and its various related phenom- ena is essential in the design of these units. Even at operating conditions above the critical pressure, where water no longer boils but experiences a continuous transition from a liquid-like to a gas-like fluid, boil- ing type behavior and special heat transfer charac- teristics occur. Boiling process and fundamentals Boiling point and thermophysical properties The boiling point, or saturation temperature, of a liquid can be defined as the temperature at which its vapor pressure is equal to the total local pressure. The saturation temperature for water at atmospheric pres- sure is 212F (100C). This is the point at which net vapor generation occurs and free steam bubbles are formed from a liquid undergoing continuous heating. As discussed in Chapter 2, this saturation tempera- ture (Tsat) is a unique function of pressure. TheAmeri- can Society of Mechanical Engineers (ASME) and the International Association for the Properties of Steam (IAPS) have compiled extensive correlations of thermo- physical characteristics of water. These characteristics include the enthalpy (or heat content) of water, the enthalpy of evaporation (also referred to as the latent heat of vaporization), and the enthalpy of steam. As the pressure is increased to the critical pressure [3200 psi (22.1 MPa)], the latent heat of vaporization declines to zero and the bubble formation associated with boil- ing no longer occurs. Instead, a smooth transition from liquid to gaseous behavior occurs with a continuous in- crease in temperature as energy is applied. Two other definitions are also helpful in discussing boiling heat transfer: 1. Subcooling For water below the local saturation temperature, this is the difference between the saturation temperature and the local water tem- perature (Tsat – T ). 2. Quality This is the flowing mass fraction of steam (frequently stated as percent steam by weight or %SBW after multiplying by 100%): x m m m = + steam water steam (1) where msteam = steam flow rate, lb/h (kg/s) mwater = water flow rate, lb/h (kg/s) Thermodynamically, this can also be defined as: x H H H or H H H H f fg f g f = − − − (2) where H = local average fluid enthalpy, Btu/lb (J/kg) Hf = enthalpy of water at saturation, Btu/lb (J/kg) Hg = enthalpy of steam at saturation, Btu/lb (J/kg) Hfg = latent heat of vaporization, Btu/lb (J/kg) When boiling is occurring at saturated, thermal equilibrium conditions, Equation 2 provides the frac- tional steam flow rate by mass. For subcooled condi-
- 142. 5-2 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company tions where H < Hf, quality (x) can be negative and is an indication of liquid subcooling. Forconditionswhere H > Hg, this value can be greater than 100% and repre- sents the amount of average superheat of the steam. Boiling curve Fig. 1 illustrates a boiling curve which summarizes the results of many investigators. This curve provides the results of a heated wire in a pool, although the characteristicsaresimilarformostsituations.Theheat transfer rate per unit area, or heat flux, is plotted versus the temperature differential between the metal surface and the bulk fluid. From points A to B, con- vection heat transfer cools the wire and boiling on the surface is suppressed. Moving beyond point B, which is also referred to as the incipient boiling point, the temperature of the fluid immediately adjacent to the heated surface slightly exceeds the local saturation temperature of the fluid while the bulk fluid remains subcooled. Bubbles, initially very small, begin to form adjacent to the wire. The bubbles then periodically collapse as they come into contact with the cooler bulk fluid. This phenomenon, referred to as subcooled boil- ing, occurs between points B and S on the curve. The heat transfer rate is quite high, but no net steam gen- eration occurs. From points S to C, the temperature of the bulk fluid has reached the local saturation tem- perature. Bubbles are no longer confined to the area immediately adjacent to the surface, but move into the bulk fluid. This region is usually referred to as the nucleate boiling region, and as with subcooled boil- ing, the heat transfer rates are quite high and the metal surface is only slightly above the saturation temperature. As point C is approached, increasingly large sur- face evaporation rates occur. Eventually, the vapor generation rate becomes so large that it restricts the liquid return flow to the surface. The surface eventu- ally becomes covered (blanketed) with an insulating layer of steam and the ability of the surface to trans- fer heat drops. This transition is referred to as the critical heat flux (CHF), departure from nucleate boil- ing (DNB), burnout, dryout, peak heat flux, or boil- ing crisis. The temperature response of the surface un- der this condition depends upon how the surface is being heated. In fossil fuel boiler furnaces and nuclear reactor cores, the heat input is effectively independent of surface temperature. Therefore, a reduction in the heat transfer rate results in a corresponding increase in surface temperature from point D to D′ in Fig. 1. In some cases, the elevated surface temperature is so high that the metal surface may melt. If, on the other hand, the heat input or heat transfer rate is depen- dent upon the surface temperature, typical of a nuclear steam generator, the average local tempera- ture of the surface increases as the local heat trans- fer rate declines. This region, illustrated in Fig. 1 from points D to E, is typically referred to as unstable film boiling or transition boiling. Because a large surface temperature increase does not occur, the main conse- quences are a decline in heat transfer performance per unit surface area and less overall energy transfer. The actual local phenomenon in this region is quite com- plex and unstable as discrete areas of surface fluctu- ate between a wetted boiling condition and a steam blanketed, or dry patch, condition. From position E through D′ to F, the surface is effectively blanketed by an insulating layer of steam or vapor. Energy is transferred from the solid surface through this layer by radiation, conduction and microconvection to the liquid-vapor interface. From this interface, evapora- tion occurs and bubbles depart. This heat transfer region is frequently referred to as stable film boiling. In designing steam generating systems, care must be exercised to control which of these phenomena oc- cur. In high heat input locations, such as the furnace area of fossil fuel boilers or nuclear reactor cores, it is important to maintain nucleate or subcooled boiling to adequately cool the surface and prevent material failures. However, in low heat flux areas or in areas where the heat transfer rate is controlled by the boil- ing side heat transfer coefficient, stable or unstable film boiling may be acceptable. In these areas, the resultant heat transfer rate must be evaluated, any temperature limitations maintained and only allow- able temperature fluctuations accepted. Flow boiling Flow or forced convective boiling, which is found in virtually all steam generating systems, is a more com- plex phenomenon involving the intimate interaction of two-phase fluid flow, gravity, material phenomena and boiling heat transfer mechanisms. Fig. 2 is a clas- sic picture of boiling water in a long, uniformly heated, circular tube. The water enters the tube as a subcooled liquid and convection heat transfer cools the tube. The point of incipient boiling is reached (point 1 in Fig. 2). This results in the beginning of subcooled boiling and bubbly flow. The fluid temperature continues to rise until the entire bulk fluid reaches the saturation tem- perature and nucleate boiling occurs, point 2. At this location, flow boiling departs somewhat from the simple pool boiling model previously discussed. The steam-water mixture progresses through a series ofFig. 1 Boiling curve – heat flux versus applied temperature difference.
- 143. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-3 The Babcock & Wilcox Company flow structures or patterns: bubbly, intermediate and annular. This is a result of the complex interaction of surface tension forces, interfacial phenomena, pres- sure drop, steam-water densities and momentum ef- fects coupled with the surface boiling behavior. While boiling heat transfer continues throughout, a point is reached in the annular flow regime where the liquid film on the wall becomes so thin that nucleation in the film is suppressed, point 3. Heat transfer then occurs through conduction and convection across the thin annular film with surface evaporation at the steam- water interface. This heat transfer mechanism, called convective boiling, also results in high heat transfer rates. It should also be noted that not all of the liquid is on the tube wall.Aportion is entrained in the steam core as dispersed droplets. Eventually, an axial location, point 4, is reached where the tube surface is no longer wetted and CHF or dryout occurs. This is typically associated with a temperature rise. The exact tube location and magni- tude of this temperature, however, depend upon a variety of parameters, such as the heat flux, mass flux, geometry and steam quality. Fig. 3 illustrates the effect of heat input rate, or heat flux, on CHF loca- tion and the associated temperature increase. From points 4 to 5 in Fig. 2, post-CHF heat transfer, which is quite complex, occurs. Beyond point 5, all of the liq- uidisevaporatedandsimpleconvectiontosteamoccurs. Boiling heat transfer evaluation Engineeringdesignofsteamgeneratorsrequiresthe evaluation of water and steam heat transfer rates un- der boiling and nonboiling conditions. In addition, the identification of the location of critical heat flux (CHF) is important where a dramatic reduction in the heat transfer rate could lead to: 1) excessive metal tempera- tures potentially resulting in tube failures, 2) an un- acceptable loss of thermal performance, or 3) unaccept- able temperature fluctuations leading to thermal fa- Fig. 3 Tube wall temperatures under different heat input conditions. Fig. 2 Simplified flow boiling in a vertical tube (adapted from Collier1 ).
- 144. 5-4 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company tigue failures. Data must also be available to predict therateofheattransferdownstreamofthedryoutpoint. CHF phenomena are less important than the heat transferratesforperformanceevaluation,butaremore important in defining acceptable operating conditions. As discussed in Chapter 4, the heat transfer rate per unit area or heat flux is equal to the product of tem- perature difference and a heat transfer coefficient. Heat transfer coefficients Heat transfer correlations are application (surface and geometry) specific and The Babcock & Wilcox Company (B&W) has developed extensive data for its applications through experimental testing and field experience. These detailed correlations remain propri- etary to B&W. However, the following generally avail- able correlations are provided here as representative of the heat transfer relationships. Single-phase convection Several correlations for forced convection heat transfer are presented in Chap- ter 4. Forced convection is assumed to occur as long as the calculated forced convection heat flux is greater than the calculated boiling heat flux (point 1 in Fig. 2): ′′ > ′′q qForced Convection Boiling (3) While not critical in most steam generator applica- tions, correlations are available which explicitly de- fine this onset of subcooled boiling and more accurately define the transition region.1 Subcooled boiling In areas where subcooled boil- ing occurs, several correlations are available to char- acterize the heat transfer process. Typical of these is the Jens and Lottes2 correlation for water. For inputs with English units: ∆T q esat P = ′′( ) − 60 106 1 4 900 / / / (4a) and for inputs with SI units: ∆T q esat P = ′′( ) − 25 1 4 6 2/ / . (4b) where ∆Tsat = Tw – Tsat, F (C) Tw = wall temperature, F (C) Tsat = saturated water temperature, F (C) ′′q = heat flux, Btu/h ft2 (MWt/m2 ) P = pressure, psi (MPa) Another relationship frequently used is that developed by Thom.3 Nucleate and convective boiling Heat transfer in the saturated boiling region occurs by a complex combi- nation of bubble nucleation at the tube surface (nucle- ate boiling) and direct evaporation at the steam-wa- ter interface in annular flow (convective boiling). At low steam qualities, nucleate boiling dominates while at higher qualities convective boiling dominates. While separate correlations are available for each range, the most useful relationships cover the entire saturated boiling regime. They typically involve the summation of appropriately weighted nucleate and convective boiling components as exemplified by the correlation developed by J.C. Chen and his colleagues.4 While such correlations are frequently recommended for use in saturated boiling systems, their additional precision is not usually required in many boiler or reactor ap- plications. For general evaluation purposes, the subcooled boiling relationship provided in Equation 4 is usually sufficient. Post-CHF heat transfer As shown in Fig. 3, substan- tial increases in tube wall metal temperatures are possible if boiling is interrupted by the CHF phenom- enon. The maximum temperature rise is of particular importance in establishing whether tube wall over- heating may occur. In addition, the reliable estima- tion of the heat transfer rate may be important for an accurate assessment of thermal performance. Once the metal surface is no longer wetted and water droplets are carried along in the steam flow, the heat transfer process becomes more complex and includes: 1) con- vective heat transfer to the steam which becomes su- perheated, 2) heat transfer to droplets impinging on the surface from the core of the flow, 3) radiation di- rectly from the surface to the droplets in the core flow, and 4) heat transfer from the steam to the droplets. This process results in a nonequilibrium flow featur- ing superheated steam mixed with water droplets. Current correlations do not provide a good estimate of the heat transfer in this region, but computer models show promise. Accurate prediction requires the use of experimental data for similar flow conditions. Reflooding A key concept in evaluating emergency core coolant systems for nuclear power applications is reflooding. In a loss of coolant event, the reactor core can pass through critical heat flux conditions and can become completely dry. Reflooding is the term for the complex thermal-hydraulic phenomena involved in rewetting the fuel bundle surfaces as flow is returned to the reactor core. The fuel elements may be at very elevated temperatures so that the post-CHF, or steam blanketed,conditionmaycontinueeveninthepresence of returned water flow. Eventually, the surface tem- perature drops enough to permit a rewetting front to wash over the fuel element surface. Analysis includes transient conduction of the fuel elements and the in- teractionwiththesteam-waterheattransferprocesses. Critical heat flux phenomena Critical heat flux is one of the most important pa- rameters in steam generator design. CHF denotes the set of operating conditions (mass flux, pressure, heat flux and steam quality) covering the transition from the relatively high heat transfer rates associated with nucleate or forced convective boiling to the lower rates resulting from transition or film boiling (Figs. 1 and 2). These operating conditions have been found to be geometry specific. CHF encompasses the phenomena of departure from nucleate boiling (DNB), burnout, dryout and boiling crisis. One objective in recirculat- ing boiler and nuclear reactor designs is to avoid CHF conditions. In once-through steam generators, the objective is to design to accommodate the temperature increase at the CHF locations. In this process, the heat flux profile, flow passage geometry, operating pressure
- 145. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-5 The Babcock & Wilcox Company and inlet enthalpy are usually fixed, leaving mass flux, local quality, diameter and some surface effects as the more easily adjusted variables. Factors affecting CHF Critical heat flux phenomena under flowing conditions found in fossil fuel and nuclear steam generators are affected by a variety of parameters.5 The primary parameters are the operat- ing conditions and the design geometries. The oper- ating conditions affecting CHF are pressure, mass flux and steam quality. Numerous design geometry factors include flow passage dimensions and shape, flow path obstructions, heat flux profile, inclination and wall surface configuration. Several of these effects are il- lustrated in Figs. 3 through 7. Fig. 3 illustrates the effect of increasing the heat input on the location of the temperature excursion in a uniformly heated vertical tube cooled by upward flow- ing water. At low heat fluxes, the water flow can be al- most completely evaporated to steam before any tem- perature rise is observed. At moderate and high heat fluxes, the CHF location moves progressively towards the tube inlet and the maximum temperature excur- sion increases.At very high heat fluxes, CHF occurs at a low steam quality and the metal temperature excur- sion can be high enough to melt the tube. At extremely high heat input rates, CHF can occur in subcooled water. Avoiding this type of CHF is an important de- sign criterion for pressurized water nuclear reactors. Many large fossil fuel boilers are designed to oper- ate between 2000 and 3000 psi (13.8 and 20.7 MPa). In this range, pressure has a very important effect, shown in Fig. 4, with the steam quality limit for CHF falling rapidly near the critical pressure; i.e., at con- stant heat flux, CHF occurs at lower steam qualities as pressure rises. Many CHF correlations have been proposed and are satisfactory within certain limits of pressure, mass velocity and heat flux. Fig. 5 is an example of a corre- lation which is useful in the design of fossil fuel natu- ral circulation boilers. This correlation defines safe and unsafe regimes for two heat flux levels at a given pres- sure in terms of steam quality and mass velocity. Ad- ditional factors must be introduced when tubes are used in membrane or tangent wall construction, are inclined from the vertical, or have different inside di- ameter or surface configuration. The inclination of the flow passage can have a particularly dramatic effect on the CHF conditions as illustrated in Fig. 6.6 Ribbed tubes Since the 1930s, B&W has investi- gated a large number of devices, including internal twisters, springs and grooved, ribbed and corrugated tubes to delay the onset of CHF. The most satisfactory overall performance was obtained with tubes having helical ribs on the inside surface. Two general types of rib configurations have been developed: 1. single-lead ribbed (SLR) tubes (Fig. 8a) for small internal diameters used in once-through subcriti- cal pressure boilers, and 2. multi-lead ribbed (MLR) tubes (Fig. 8b) for larger in- ternal diameters used in natural circulation boilers. Both of these ribbed tubes have shown a remark- able ability to delay the breakdown of boiling. Fig. 7 Fig. 5 Steam quality limit for CHF as a function of mass flux.Fig. 4 Steam quality limit for CHF as a function of pressure.
- 146. 5-6 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company compares the effectiveness of a ribbed tube to that of a smooth tube in a membrane wall configuration. This plot is different from Fig. 5 in that heat flux is given as an average over the flat projected surface. This is more meaningful in discussing membrane wall heat absorption. The ribbed bore tubes provide a balance of improved CHF performance at an acceptable increase in pres- sure drop without other detrimental effects. The ribs generate a swirl flow resulting in a centrifugal action which forces the water to the tube wall and retards entrainment of the liquid. The steam blanketing and film dryout are therefore prevented until substantially higher steam qualities or heat fluxes are reached. Because the ribbed bore tube is more expensive than a smooth bore tube, its use involves an economic bal- ance of several design factors. In most instances, there is less incentive to use ribbed tubes below 2200 psi (15.2 MPa). Evaluation CHF is a complex combination of ther- mal-hydraulic phenomena for which a comprehensive theoretical basis is not yet available. As a result, ex- perimental data are likely to continue to be the basis for CHF evaluations. Many data and correlations de- fine CHF well over limited ranges of conditions and geometries. However, progress is being made in de- veloping more general evaluation procedures for at least the most studied case – a uniformly heated smooth bore tube with upward flowing water. To address this complex but critical phenomenon in the design of reliable steam generating equipment, B&W has developed an extensive proprietary data- base and associated correlations.Agraphical example is shown in Fig. 5 for a fossil fuel boiler tube. A B&W correlation7 for nuclear reactor fuel rod bundle subchannel analysis is shown in Table 1. CHF criteria Anumber of criteria are used to assess the CHF margins in a particular tube or tube bundle geometry.8 These include the CHF ratio, flow ratio and quality margin, defined as follows: 1. CHF ratio minimum value of CHF heat flux upset heat flux = 2. flow ratio minimum value of min. design mass flux mass flux = at CHF 3. quality margin CHF quality max. design quality= − The CHF ratios for a sample fossil fuel boiler are illustrated in Fig. 9 for a smooth bore tube ′′ ′′( )q qB A/ and a ribbed bore tube ′′ ′′( )q qC A/ . The graph indicates the relative increase in local heat input which can be tol- erated before the onset of CHF conditions. A similar relationship for a nuclear reactor fuel rod application is shown in Fig. 10. Fig. 6 Effect of inclination on CHF at 700,000 lb/h ft2 (950 kg/m2 s).6 Fig. 7 Steam quality limit for CHF in smooth and ribbed bore tubes. Fig. 8a Single-lead ribbed tube. Fig. 8b Multi-lead ribbed tube.
- 147. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-7 The Babcock & Wilcox Company Supercritical heat transfer Unlike subcritical pressure conditions, fluids at su- percritical pressures experience a continuous transi- tion from water-like to steam-like characteristics. As a result, CHF conditions and boiling behavior would not be expected. However, at supercritical pressures, especially in the range of 1 < P/Pc < 1.15 where Pc is the critical pressure, two types of boiling-like behav- ior have been observed: pseudo-boiling and pseudo- film boiling. Pseudo-boiling is an increase in heat transfer coefficient not accounted for by traditional convection relationships. In pseudo-film boiling, a dramatic reduction in the heat transfer coefficient is observed at high heat fluxes. This is similar to the critical heat flux condition at subcritical pressures. These behaviors have been attributed to the sharp changes in fluid properties as the transition from water-like to steam-like behavior occurs. Fluid properties In the supercritical region, the ther- mophysical properties important to the heat transfer process, i.e., conductivity, viscosity, density and spe- cific heat, experience radical changes as a certain pres- sure-dependent temperature is approached and ex- ceeded. This is illustrated in Fig. 11. The transition temperature, referred to as the pseudo-critical tem- perature, is defined as the temperature where the specific heat, cp, reaches its maximum. As the operat- ing pressure is increased, the pseudo-critical tempera- ture increases and the dramatic change in the ther- mophysical properties declines as this temperature is approached and exceeded. Heat transfer rates Because of the significant changes in thermophysical properties (especially in specific heat) near the pseudo-critical temperature, a modified approach to evaluating convective heat transfer is needed.Anumber of correlations have been developedandarepresentativerelationshipforsmooth bore tubes is:9 hD k D G H H T T k i w i w w b w b w w = × − − 0 00459 0 923 . . µ µ 0 613 0 231. . υ υ b w (5) Fig. 9 Fossil boiler CHF ratio = minimum value of critical heat flux divided by upset heat flux. Fig. 10 Nuclear reactor CHF ratio = minimum value of critical heat flux divided by design heat flux. Table 1 B&W2 Reactor Rod Bundle Critical Heat Flux (CHF) Correlation7 (a − bDi ) A1 (A2G)A3+A4(P−2000) − A9GxCHF Hfg q"CHF = A5 (A6G)A7+A8(P−2000) where a = 1.15509 A = area, in.2 b = 0.40703 Di = equivalent diameter = 4A/Per A1 = 0.37020 x 108 G = mass flux, lb/h ft2 A2 = 0.59137 x 10−6 Hfg = latent heat of vaporization, A3 = 0.83040 Btu/lb A4 = 0.68479 x 10−3 P = pressure, psi A5 = 12.710 Per = wetted perimeter, in. A6 = 0.30545 x 10−5 xCHF = steam quality at CHF condi- A7 = 0.71186 tions, fraction steam by weight A8 = 0.20729 x 10−3 q"CHF = heat flux at CHF conditions, A9 = 0.15208 Btu/h ft2
- 148. 5-8 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company where h = heat transfer coefficient, Btu/h ft2 F (W/m2 K) k = thermal conductivity, Btu/h ft F (W/m K) Di = inside tube diameter, ft (m) G = mass flux, lb/h ft2 (kg/m2 s) µ = viscosity, lb/ft h (kg/m s) H = enthalpy, Btu/lb (J/kg) T = temperature, F (C) υ = specific volume, ft3 /lb (m3 /kg) The subscripts b and w refer to properties evaluated at the bulk fluid and wall temperatures respectively. This correlation has demonstrated reasonable agreement with experimental data from tubes of 0.37 to 1.5 in. (9.4 to 38.1 mm) inside diameter and at low heat fluxes. Pseudo-boiling For low heat fluxes and bulk fluid temperatures approaching the pseudo-critical tem- perature, an improvement in the heat transfer rate takes place. The enhanced heat transfer rate observed is sometimes referred to as pseudo-boiling. It has been attributed to the increased turbulence resulting from the interaction of the water-like and steam-like fluids near the tube wall. Pseudo-film boiling Potentially damaging tem- perature excursions associated with a sharp reduction in heat transfer can be observed at high heat fluxes. This temperature behavior is similar to the CHF phe- nomenon observed at subcritical conditions and is re- ferred to as pseudo-film boiling. This phenomenon has been attributed to a limited ability of the available turbulence to move the higher temperature steam-like fluid away from the tube wall into the colder, higher density (water-like) fluid in the bulk stream. A phe- nomenon similar to steam blanketing occurs and the wall temperature increases in response to the rela- tively constant applied heat flux. Single-lead ribbed (SLR) bore tubes are very effec- tive in suppressing the temperature peaks encoun- tered in smooth bore tubes.10 Two-phase flow Flow patterns As illustrated in Fig. 2, two-phase steam-water flow may occur in many regimes or structures. The transi- tion from one structure to another is continuous rather than abrupt, especially under heated conditions, and is strongly influenced by gravity, i.e., flow orientation. Because of the qualitative nature of flow pattern iden- tification, there are probably as many flow pattern descriptions as there are observers. However, for ver- tical, heated, upward, co-current steam-water flow in a tube,fourgeneralflowpatternsaregenerallyrecognized (see Fig. 12): 1. Bubbly flow Relatively discrete steam bubbles are dispersed in a continuous liquid water phase. Bubble size, shape and distribution are dependent upon the flow rate, local enthalpy, heat input rate and pressure. 2. Intermediate flow This is a range of patterns be- tween bubbly and annular flows; the patterns are also referred to as slug or churn flow. They range from: a) large bubbles, approaching the tube size in diameter, separated from the tube wall by thin annular films and separated from each other by slugs of liquid which may also contain smaller bubbles, to b) chaotic mixtures of large nonsym- metric bubbles and small bubbles. 3. Annular flow A liquid layer is formed on the tube wall with a continuous steam core; most of the liq- Fig. 11 Thermophysical properties of water (English units). Fig. 12 Flow pattern – upward, co-current steam-water flow in a heated vertical tube.
- 149. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-9 The Babcock & Wilcox Company uid is flowing in the annular film. At lower steam qualities, the liquid film may have larger ampli- tude waves adding to the liquid droplet entrain- ment and transport in the continuous steam core. At high qualities, the annular film becomes very thin, bubble generation is suppressed and the large amplitude waves disappear. 4. Mist flow A continuous steam core transports en- trained water droplets which slowly evaporate until a single-phase steam flow occurs. This is also referred to as droplet or dispersed flow. In the case of inclined and horizontal co-current steam-water flow in heated tubes, the flow patterns arefurthercomplicatedbystratificationeffects.Athigh flow rates, the flow patterns approach those of verti- cal tubes. At lower rates, additional distinct flow pat- terns (wavy, stratified and modified plug) emerge as gravity stratifies the flow with steam concentrated in the upper portion of the tube. This can be a problem where inclined tubes are heated from the top. CHF or dryout conditions occur at much lower steam quali- ties and lower heat input rates in such inclined or horizontal tubes. Additional complexity in patterns is observed when two-phase flow occurs in parallel or crossflow tube bundles. The tubes, baffles, support plates and mix- ing devices further disrupt the flow pattern formation. Flow maps The transitions from one flow regime to another are quite complex, with each transition rep- resenting a combination of factors. However, two di- mensional flow maps provide at least a general indi- cation of which flow pattern is likely under given op- erating conditions. The maps generally are functions of superficial gas and liquid velocities.An example for vertical, upward, steam-water co-current flow is pro- vided in Fig. 13.11 The axes in this figure represent the superficial momentum fluxes of the steam (y-axis) and water (x-axis). A sample flow line is shown begin- ning at nearly saturated water conditions and end- ing with saturated steam conditions. The tube expe- riences bubbly flow only near its inlet. This is followed by a brief change to intermediate flow before annu- lar flow dominates the heated length. Other flow maps are available for arrangements such as downflow tubes, inclined tubes and bundles. Flow maps, however, are only approximations provid- ing guidance in determining the relevant flow struc- ture for a given situation. Pressure loss The local pressure loss, ∆P [lb/ft2 (Pa)] or gradient δP/δl [lb/ft2 /ft (Pa/m)] in a two-phase steam-water system may be represented by: ∆ ∆ ∆ ∆ ∆P P P P Pf a g l= + + + (6a) or − = − − − + δ δ δ δ δ δ δ δ P l P l P l P l P f a g l∆ (6b) The ∆Pf and –(δ P/δ l)f terms account for local wall friction losses. The ∆Pa and –(δ P/δ l)a terms address the momentum or acceleration loss incurred as the volume increases due to evaporation. The hydraulic or static head loss is accounted for by ∆Pg and –(δ P/ δ l)g. Finally, all of the local losses due to fittings, con- tractions, expansions, bends, or orifices are included in ∆Pl. The evaluation of these parameters is usually made using one of two models: homogeneous flow or separated flow. A parameter of particular importance when evalu- ating the pressure loss in steam-water flows is void fraction. The void fraction can be defined by time-av- eraged flow area ratios or local-volume ratios of steam to the total flow. The area-based void fraction, α, can be defined as the ratio of the time-averaged steam flow cross-sectional area (Asteam) to the total flow area (Asteam + Awater): α = + A A A steam steam water (7) Using the simple continuity equation, the relation- ship between quality, x, and void fraction is: α ρ ρ = + −( ) x x x Sg f 1 (8) where S = ratio of the average cross-sectional velocities of steam and water (referred to as slip) ρg = saturated steam density, lb/ft3 (kg/m3 ) ρf = saturated water density, lb/ft3 (kg/m3 ) Fig. 13 Flow pattern map for vertical upward flow of water.11
- 150. 5-10 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company If the steam and water are moving at the same veloc- ity, S = 1 (no slip). Obviously, the relationship between void fraction and quality is also a strong function of system pressure. This relationship is illustrated in Fig. 14. The difference between the homogeneous and separated flow models is illustrated by the shaded band. The upper bound is established by the homo- geneous model and the lower bound by the separated flow model. Homogeneous model The homogeneous model is the simpler approach and is based upon the premise that the two-phase flow behavior can be directly mod- eled after single-phase behavior (see Chapter 3) if appropriate average properties are determined. The temperature and velocities of steam and water are assumed equal. The mixed weight averaged specific volume (υ) or the inverse of the homogeneous density (1/ρhom) is used: υ υ υ= −( ) +f gx x1 (9a) or 1 1 ρ ρ ρhom = −( ) + x x f g (9b) where υf = saturated water specific volume, ft3 /lb (m3 /kg) υg = saturated steam specific volume, ft3 /lb (m3 /kg) ρf = saturated water density, lb/ft3 (kg/m3 ) ρg = saturated steam density, lb/ft3 (kg/m3 ) x = steam quality This model provides reasonable results when high or low steam qualities exist, when high flow rates are present, or at higher pressures. In these cases, the flow is reasonably well mixed. The friction pressure drop (∆Pf) can be evaluated by the equations provided in Chapter 3 using the mix- ture thermophysical properties. The pressure differ- ence due to elevation (∆Pg) can be evaluated as: ∆P g g Lg c = ± ρ θhom sin (10) where g = acceleration of gravity, ft/s2 (m/s2 ) gc = 32.17 lbm ft/lbf s2 (1 kg m/N s2 ) L = length, ft (m) θ = angle from the horizontal The constant gc is discussed in Chapter 2. A pressure gain occurs in downflow and a pressure loss occurs in upflow. The acceleration loss can be evaluated by: ∆P G g a c = − 2 1 1 ρ ρout in (11) where G = mass flux, lb/s ft2 (kg/m2 s) ρout = outlet homogeneous density, lb/ft3 (kg/m3 ) ρin = inlet homogeneous density, lb/ft3 (kg/m3 ) Separated flow model In the steady-state sepa- rated flow model, the steam and water are treated as separate streams under the same pressure gradient but different velocities and differing properties. When the actual flow velocities of steam and water are equal, the simplest separated flow models approach the ho- mogeneous case. Using one of several separated flow models1 with unequal velocities, the pressure drop components (in differential form) are: − = − δ δ δ δ φ P l P lf LO LO 2 (friction) (12) − = δ δ υP l f D G gLO i f c 2 2 (single-phase friction) (13) − = + −( ) −( ) δ δ δ δ υ α υ α P l G g l x x a c g f 2 2 2 1 0 1 0 . . (accelerration) (14) − = + −( ) δ δ θ α υ α υ P l g gg c g f sin .1 0 (static head)(15) ∆ ΦP K G g l f c = 2 2 υ (local losses) (16) where Φ and φLO 2 = appropriate two-phase multipliers G = mass flux, lb/s ft2 (kg/m2 s) f = fanning friction factor (see Chapter 3) Di = tube inside diameter, ft (m) g = acceleration of gravity, ft/s2 (m/s2 ) gc = 32.17 lbm ft/lbf s2 (1 kg m/N s2 ) Fig. 14 Void fraction – quality relationship (homogeneous model, upper bound; separated flow model, lower bound).
- 151. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-11 The Babcock & Wilcox Company υf = liquid specific volume, ft3 /lb (m3 /kg) υg = vapor specific volume, ft3 /lb (m3 /kg) x = steam quality α = void fraction θ = angle from the horizontal K = loss coefficient While ∆Pl usually represents just the irreversible pres- sure loss in single-phase flows, the complexity of two- phase flows results in the loss of ∆Pl typically represent- ing the reversible and irreversible losses for fittings. To evaluate the individual pressure losses from Equations 12 through 16 and Equation 6b, it is nec- essary to calculate φLO 2 , α and Φ. Unfortunately, these factors are not well defined. Specific correlations and evaluations can only be used where experimental data under similar condi- tions provide confidence in the prediction. Proprietary correlations used by B&W are based upon experimen- tal data and practical experience. For straight vertical tubes, generally available rep- resentative relationships include: 1. Acceleration loss The void fraction can frequently be evaluated with the homogeneous model (S = 1 in Equation 8). 2. Friction loss and void fraction Typical two-phase multiplier, φLO 2 , and void fraction, α, relationships are presented by Thom,12 Martinelli-Nelson,13 Zuber-Findlay14 and Chexal-Lellouche.15 For illus- tration purposes the correlations of Thom are pre- sented in Figs. 15 and 16. These curves can be ap- proximated by: φ υ υLO g f x x x x 2 0 5 0 97303 1 0 97303 1 = −( )+ × −( )+ . . . + −( ) 0 5 2 0 0 027 1 . . . x (17) and α γ γ = + −( ) x x1 1 (18) where γ = (υg /υf)n n = (0.8294 – 1.1672/P) P = pressure, psi υg = saturated steam specific volume, ft3 /lb υf = saturated liquid specific volume, ft3 /lb x = steam quality Instabilities Instability in two-phase flow refers to the set of operating conditions under which sudden changes in flow direction, reduction in flow rate and oscillating flow rates can occur in a single flow passage. Often in manifolded multi-channel systems, the overall mass flow rate can remain constant while oscillating flows in individual channels still may occur. Such unstable conditions in steam generating systems can result in: 1. unit control problems, including unacceptable variations in steam drum water level, 2. CHF/DNB/dryout, 3. tube metal temperature oscillation and thermal fatigue failure, and 4. accelerated corrosion attack. Two of the most important types of instabilities in steam generator design are excursive instability, in- cluding Ledinegg and flow reversal, and density wave/pressure drop oscillations. The first is a static in- stability evaluated using steady-state equations while the last is dynamic in nature requiring the inclusion of time dependent factors. Fig. 15 Thom two-phase friction multiplier.12 Fig. 16 Thom void fraction correlation (>3% SBW).12
- 152. 5-12 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company Excursiveandflowreversalinstabilityevaluation The excursive instability is characterized by conditions where small perturbations in operating parameters result in a large flow rate change to a separate steady- state level. This can occur in both single channel and multi-channel manifolded systems. Excursive insta- bilities can be predicted by using the Ledinegg crite- ria.16 Instability may occur if the slope of the pressure drop versus flow characteristic curve (internal) for the tube becomes less than the slope of the supply (or applied) curve at any intersection point: δ δ δ δ ∆ ∆P G P G ≤ internal applied (19) The stable and unstable situations are illustrated in Fig. 17. As shown in the figure for unstable condi- tions, if the mass flow rate drops below point B then the flow rate continues to fall dramatically because the applied pumping head is less than that needed to move the fluid. For slightly higher mass flow rates (higher than point B), a dramatic positive flow excursion oc- curs because the pumping head exceeds the flow sys- tem requirement. In most systems, the first term in Equation 19 is generally positive and the second is negative. There- fore, Equation 19 predicts stability. However, in two- phasesystems,thermal-hydraulicconditionsmaycom- bine to produce a local area where (δ∆P/δG)internal is negative and the potential for satisfying Equation 19 and observing an instability exists.Aheated tube flow characteristic showing a potential region of instabil- ity is illustrated in Fig. 18 where multiple flow rates can occur for a single applied pressure curve. Operat- ing at point B is unstable with small disturbances re- sulting in a shift to pointAor point C. More intense dis- turbances could result in flow shifts between A and C. For the relatively small subcooling found at the en- trance to tube panels in recirculating drum boilers and due to the relatively low exit steam qualities, negative slope regions in the pressure drop versus flow curves are typically not observed for positive flow cases. How- ever, for once-through fossil fuel boilers and nuclear steam generators with high subcooling at the inlet and evaporation to dryness, negative slope regions in the upflow portion of the pressure drop characteristic may occur. Steps can be taken to avoid operation in any re- gion where the circuit internal δ∆P/δG ≤ 0. General effects of operating and design parameters on the pres- sure drop versus mass flow curves include: Parameter Increased Effect on ∆P Comment heat input decrease more stable inlet ∆P increase more stable pressure increase more stable In situations where static instability may occur, the inlet pressure drop can be increased by adding an orifice or flow restriction to modify the overall flow characteristic as shown in Fig. 18. Fig. 17 Stable and unstable flow-pressure drop characteristics. Fig. 18 Pressure drop characteristics showing unstable region.
- 153. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-13 The Babcock & Wilcox Company Densitywave/pressuredropinstability Densitywave instabilities involve kinematic wave propagation phe- nomena. Regenerative feedback between flow rate, vapor generation rate and pressure drop produce self sustaining alternating waves of higher and lower den- sity mixture that travel through the tube. This dy- namic instability can occur in single tubes that con- tain two-phase flows. In addition, when multiple tubes are connected by inlet and outlet headers, a more com- plex coupled channel instability, which is driven by density wave oscillations, may occur. Vertical heat flux distribution is a particularly sensitive parameter in dynamic instability evaluation. Density wave oscillations can be predicted by the application of feedback control theory. A number of computer codes have been developed to provide these predictions. In addition, instability criteria, which use a series of dimensionless parameters to reduce the complexity of the evaluation, have been developed. Effects of operating and design parameters on the density wave instability include: Parameter Increased Change in stability mass flux improved heat flux reduced pressure improved inlet ∆P improved inlet subcooling improved (large subcooling) reduced (small subcooling) Steam-water separation Subcritical pressure recirculating boilers and steam generators are equipped with large cylindrical vessels called steam drums. Their primary objective is to per- mit separation of the saturated steam from the steam- water mixture leaving the boiling heat transfer sur- faces. The steam-free water is recirculated with the feedwater to the heat absorbing surfaces for further steam generation. The saturated steam is discharged through a number of outlet nozzles for direct use or further heating. The steam drum also serves to: 1. mix the feedwater with the saturated water re- maining after steam separation, 2. mix the corrosion control and water treatment chemicals (if used), 3. purify the steam to remove contaminants and re- sidual moisture, 4. remove part of the water (blowdown) to control the boiler water chemistry (solids content), and 5. provide limited water storage to accommodate rapid changes in boiler load. However, the primary function of the steam drum is to permit the effective separation of steam and wa- ter. This may be accomplished by providing a large steam-water surface for natural gravity-driven sepa- ration or by having sufficient space for mechanical separation equipment. High efficiency separation is critical in most boiler applications in order to: 1. prevent water droplet carryover into the super- heater where thermal damage may occur, 2. minimize steam carryunder in the water leaving the drum where residual steam can reduce the effective hydraulic pumping head, and 3. preventthecarryoverofsolidsdissolvedinthesteam- entrained water droplets into the superheater and turbine where damaging deposits may form. The last item is of particular importance. Boiler wa- ter may contain contaminants, principally in solution. These arise from impurities in the makeup water, treatment chemicals and condensate system leaks, as well as from the reaction of the water and contami- nants with the boiler and preboiler equipment mate- rials. Even low levels of these solids in the steam (less than 0.6 ppm) can damage the superheater and tur- bine. Because the solubility of these solids is typically several orders of magnitude less in steam than in wa- ter (see Chapter 42),smallamountsofwaterdropletcar- ryover(greaterthan0.25%byweight)mayresultindra- matically increased solids carryover and unacceptable deposition in the superheater and turbine. The deposits havecausedturbinedamageaswellassuperheatertube temperature increases, distortion and burnout. A cross-section of a horizontal steam drum found on a modern high capacity fossil fuel boiler is shown in Fig. 19. This illustrates the general arrangement of the baffle plates, primary cyclone separators, sec- ondary separator elements (scrubbers), water dis- charger (downcomer) and feedwater inlets. The blow- down (water removal) connections are not shown. The steam-water separation typically takes place in two stages. The primary separation removes nearly all the steam from the water so that very little steam is recir- culated from the bottom of the drum through the out- let connection (downcomer) towards the heated tubes. The steam leaving the primary separators in high pressure boilers still typically contains too much liq- uid in the form of contaminant-containing droplets for satisfactory superheater and turbine performance. Therefore, the steam is passed through a secondary set of separators, or scrubber elements (usually closely spaced, corrugated parallel plates) for final water droplet removal. The steam is then exhausted through several connections. As this figure indicates, success- ful steam-water separation involves the integrated operation of primary separators, secondary scrubbers and general drum arrangement. Factors affecting steam separation Effective steam separation from the steam-water mixture relies on certain design and operating factors. The design factors include: 1. pressure, 2. drum length and diameter, 3. rate of steam generation, 4. average inlet steam quality, 5. type and arrangement of mechanical separators, 6. feedwater supply and steam discharge equipment arrangement, and 7. arrangement of downcomer and riser connections to the steam drum.
- 154. 5-14 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company The operating factors include: 1. pressure, 2. boiler load (steam flow), 3. type of steam load, 4. chemical analysis of boiler water, and 5. water level. Primary separation equipment generally takes one of three forms: 1. natural gravity-driven separation, 2. baffle-assisted separation, and 3. high capacity mechanical separation. Natural gravity-driven separation While simple in concept, natural steam-water sepa- ration is quite complex. It is strongly dependent upon inlet velocities and inlet locations, average inlet steam quality, water and steam outlet locations, and disen- gagement of liquid and steam above the nominal wa- tersurface.SomeoftheseeffectsareillustratedinFigs. 20 and 21. For a low rate of steam generation, up to about 3 ft/s (0.9 m/s) velocity of steam leaving the water sur- face, there is sufficient time for the steam bubbles to separate from the mixture by gravity without being drawn into the discharge connections and without carrying entrained water droplets into the steam out- let (Fig. 20a). However, for the same arrangement at a higher rate of steam generation (Fig. 20b), there is insufficient time to attain either of these desirable results. Moreover, the dense upward traffic of steam bubbles in the mixture may also cause a false water level indication, as shown. The effect of the riser or inlet connection locations in relation to the water level is illustrated in diagrams a and b of Fig. 21. Neither arrangement is likely to yield desirable results in a drum where gravity alone is used for separation. From an economic standpoint, the diameter of a single drum may become prohibitive. To overcome this limitation, several smaller steam drums may be used, as shown in Fig. 22a, although this is no longer com- mon. However, in most boiler applications, natural gravity-driven separation alone is generally uneco- nomical, leading to the need for separation assistance. Baffle-assisted primary separation Simple screens and baffle arrangements may be used to greatly improve the steam-water separation process. Three relatively common baffle arrangements are illustrated in Fig. 22. In each case, the baffles provide: 1) changes in direction, 2) more even distri- Fig. 19 Steam drum with three rows of primary cyclone separators.
- 155. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-15 The Babcock & Wilcox Company bution of the steam-water mixture, 3) added flow re- sistance, and 4) the maximum steam flow travel length to enhance the gravity-driven separation process. Various combinations of perforated plates have also been used. The performance of these devices must be determined by experimental evaluations and they are typically limited to smaller, low capacity boilers. Mechanical primary separators Centrifugal force or radial acceleration is used al- most universally for modern steam-water separators. Three types of separators are shown in Fig. 23: the conical cyclone, the curved arm and the horizontal cyclone. The B&W vertical cyclone steam separator is shown in more detail in Fig. 24. Vertical cyclones are arranged internally in rows along the length of the drum and the steam-water mixture is admitted tan- gentially as shown in Fig. 19. The water forms a layer against the cylinder walls and the steam moves to the core of the cylinder then upward. The water flows downward in the cylinder and is discharged through an annulus at the bottom, below the drum water level. With the water returning from drum storage to the Fig. 20 Effect of rate of steam generation on steam separation in a boiler drum without separation devices. Fig. 21 Effect of location of discharge from risers on steam separation in a boiler drum without separation devices. downcomers virtually free of steam bubbles, the maxi- mum net pumping head is available for producing flow in the circuits. The steam moving upward from the cylinder passes through a small primary corrugated scrubber at the top of the cyclone (see Fig. 24) for ad- ditional separation. Under many operating conditions, no further separation is required. When wide load fluctuations and water analysis variations are expected, large corrugated secondary scrubbers may be installed at the top of the drum (see Fig. 19) to provide very high steam separation. These scrubbers are also termed secondary separators. They provide a large surface which intercepts water drop- lets as the steam flows sinuously between closely fit- ted plates. Steam velocity through the corrugated plate assembly is very low, so that water re-entrainment is avoided. The collected water is drained from the bot- tom of the assembly to the water below. One to four rows of cyclone separators are installed in boiler drums, with ample room for access. For smaller boilers at lower pressures [100 psig (0.7 MPa gauge)], the separation rate of clean steam by single and double rows of cyclone separators is approximately Fig. 22 Simple types of primary steam separators in boiler drums: a) deflector baffle, b) alternate deflector baffle, and c) compartment baffle.
- 156. 5-16 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company 4000 and 6000 lb, respectively, per hour per foot of drum length (1.7 and 2.5 kg/s m). At pressures near 1050 psig (7.24 MPa gauge), these values increase to 9000 and 15,000 lb/h ft (3.7 and 6.2 kg/s m), respec- tively. For large utility boilers operating at 2800 psig (19.3 MPa gauge), separation can be as high as 67,000 lb/h ft (28 kg/s m) of steam with four rows of cyclone separators. This combination of cyclone separators and scrub- bers provides a steam purity of less than 1.0 ppm sol- ids content under a wide variety of operating condi- tions. This purity is generally adequate in commer- cial practice. However, further refinement in steam purification is required where it is necessary to remove boiler water salts, such as silica, which are entrained in the steam by a vaporization or solution mechanism. Washing the steam with condensate or feedwater of acceptable purity may be used for this purpose. Specialized vertical steam-water separators can be used in once-through fossil fueled boiler systems which are designed for part-load recirculation of wa- ter during startup and low-load operation. These are basically vertical cylindrical pressure vessels (see Fig. 25) where the steam-water mixture enters through multiple tangential inlets in the vertical vessel wall. Theresultingcentrifugalaccelerationcreatesacyclone action similar to that in the primary cyclone separa- tors (Fig. 24) which separates the water from the steam. Water is returned to the boiler circuitry for further heating and steam generation while the steam is sent to the superheating circuits. Mechanical separator performance The overall performance of mechanical separators is defined by: 1) the maximum steam flow rate at a specified average inlet quality per cyclone which meets droplet carryover limits, and 2) the predicted pressure loss. In addition, the maximum expected steam car- ryunder (% steam by weight) should also be known. These parameters are influenced by total flow rate, pressure, separator length, aperture sizes, drum wa- ter level, inlet steam quality, interior separator finish and overall drum arrangement. Performance charac- teristics are highly hardware-specific. The general trends are listed in Table 2. Steam separator evaluation To date, theoretical analyses alone do not satisfactorily predict separation performance. Therefore, extensive experimental in- vestigations are performed to characterize individual steam-water primary separator designs. Fig. 23 Typical primary steam-water separators. (a) Conical Cyclone Long Tangential Steam-Water Inlet Steam Out Diverging Body Baseplate with Swirl Vanes (b) Curved Arm Water Out Steam- Water Inlet Water Out Curved Arm Injector Shroud Cylinder Steam Out Steam-Water Inlet Water Out (c) Horizontal Cyclone Separator Steam Out Fig. 24 Vertical cyclone separator.
- 157. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-17 The Babcock & Wilcox Company Pressure drop of two-phase flow through a separa- tor is extremely complex. An approximation involves using the homogeneous model two-phase multiplier, Φ, and a dimensionless loss coefficient, Kss, as follows: ∆ ΦP K G g ss f c separator = 2 2 υ (20) where Φ = + − 1 0. υ υ υ g f f x The variable Kss is a unique function of pressure for each steam separator design. The other variables are defined after Equation 16. The maximum steam flow per primary separator defines the minimum number of standard units re- quired, while the ∆P is used in the circulation calcu- lations. Given the unique design of each separator, B&W has acquired extensive experimental perfor- mance data under full-scale, full-flow and full-pres- sure conditions for its equipment. Steam drum capacity Given the flow capabilities of standardized steam- water separation equipment, the boiler drum is sized to accommodate the number of separators necessary for the largest expected boiler load (maximum steam flowrate)andtoaccommodatethechangesinwaterlevel that occur during the expected load changes. The drum diameter, in incremental steps, and length are adjusted to meet the space requirements at a minimum cost. An evaluation limit in steam drum design is the maximum steam carryunder into the downcomer. Carryunder, or transport of steam into the downcom- ers, is not desirable because it reduces the available thermal pumping force by reducing the density at the top of the downcomer. Carryunder performance is a function of physical arrangement, operating pressure, feedwater enthalpy, free-water surface area, drum water level and separator efficiency. Empirical correc- tion factors for specific designs are developed and used in the circulation calculations to account for the steam entering the downcomers. The steam is eventually completely condensed after it travels a short distance into the downcomer. However, the average density in the top portion of the downcomer is still lower than thermal equilibrium would indicate. A rapid increase in steam demand is usually accom- panied by a temporary drop in pressure until the fir- ing rate can be sufficiently increased. During this in- terval, the volume of steam throughout the boiler is increased and the resulting swell raises the water level in the drum. The rise depends on the rate and mag- nitude of the load change and the rate at which the heat and feed inputs can be changed to meet the load demand. Steam drums are designed to provide the nec- essary volume, in combination with the controls and firing equipment, to prevent excessive water rise into the steam separators. This, in turn, prevents water carryover with the steam. Circulation The purpose of the steam-water flow circuitry is to provide the desired steam output at the specified tem- perature and pressure. The circuitry flow also ensures effective cooling of the tube walls under expected op- erating conditions, provided the unit is properly op- erated and maintained. A number of methods have been developed. Four of the most common systems are illustrated in Fig. 26. These systems are typically clas- sified as either recirculating or once-through. In recirculating systems, water is only partially evaporated into steam in the boiler tubes. The residual water plus the makeup water supply are then recir- culated to the boiler tube inlet for further heating and steam generation. A steam drum provides the space required for effective steam-water separation. Once- through systems provide for continuous evaporation of slightly subcooled water to 100% steam without steam-water separation. Steam drums are not re- quired. These designs use forced circulation for the necessary water and steam-water flow. In some cases, a combination of these approaches is used. At low loads, recirculation maintains adequate tube wall cool- Table 2 Mechanical Separator Performance Trends Moisture carryover with steam 1. increases gradually with steam flow rate until a breakaway point is reached where a sudden rise in carryover occurs, 2. increases with water level until flooding occurs, and 3. increases with steam quality. Carryunder of steam with water 1. declines with increasing water level, and 2. declines with decreasing inlet steam quality. Pressure drop (Pin − Pdrum ) 1. increases with mass flow and steam quality. Fig. 25 Vertical steam-water separator in a spiral wound universal pressure (SWUP™) boiler startup system.
- 158. 5-18 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company ing while at high loads, high pressure once-through operation enhances cycle efficiency. Natural circulation In natural circulation, gravity acting on the den- sity difference between the subcooled water in the downcomer and the steam-water mixture in the tube circuits produces the driving force or pumping head to drive the flow. As shown in Fig. 27, a simplified boiler circuit consists of an unheated leg or downcomer and heated boiler tubes. The water in the downcomer is subcooled through the mixing of the low tempera- ture feedwater from the economizer with the satura- tion-temperature water discharged from the steam- water separators. Steam-water, two-phase flow is cre- ated in the boiler tubes as a result of the heat input. Because the steam-water mixture has a lower average density than the single-phase downcomer flow, a pres- sure differential or pumping pressure is created by the action of gravity and the water flows around the cir- cuit. The flow increases or decreases until the pressure losses in all boiler circuits are balanced by the avail- able pumping pressure. For steady-state, incompress- ible flow conditions, this balance takes the form: Z z dz g g P P P d Z c ρ ρ− ∫ ( )( ) = + + 0 ∆ ∆ ∆friction acceleration local(( ) (21) where Z = total vertical elevation, ft (m) z = incremental vertical elevations, ft (m) ρ(z) = heated tube local fluid density, lb/ft3 (kg/m3 ) ρd = average downcomer fluid density, lb/ft3 (kg/ m3 ) g = acceleration of gravity, ft/s2 (m/s2 ) gc = 32.17 lbm ft/lbf s2 (l kg m/N s2 ) ∆P = circuitry pressure loss due to friction, fluid acceleration and local losses, lb/ft2 (Pa) As the heat input increases, circulation rate in- creases until a maximum flow rate is reached (Fig. 28). If higher heat inputs occur, they will result in larger pressurelossesintheheatedtubeswithoutcorrespond- ing increases in pressure differential. As a result, the flow rate declines. Natural circulation boilers are designed to operate in the region where increased heat input results in an increase in flow for all specified operating conditions. In this mode, a natural circulation system tends to be self compensating for numerous variations in heat absorption. These can include sudden changes in load, Fig. 28 Typical relationship between circulation at a given pressure and steam production (arbitrary scale). Fig. 27 Simple furnace circulation diagram. Fig. 26 Common fossil fuel boiler circulation systems. Superheater (SH) Drum Economizer (Econ) Furnace Walls (Furn) (a) Natural Recirculation (c) Once-Through SH Furn Econ SH DrumEcon Furn (b) Forced Recirculation Circ Pump Orifices (d) Once-Through with Part-Load Recirculation SH Sep Econ FurnCirc Pump
- 159. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-19 The Babcock & Wilcox Company changes in heating surface cleanliness and changes in burner operation. Natural circulation is most effective where there is a considerable difference in density between steam and water phases. As shown in Fig. 29, the potential for natural circulation flow remains very high even at pressures of 3100 psi (21.4 MPa). Forced circulation In recirculating or once-through forced circulation systems, mechanical pumps provide the driving head to overcome the pressure losses in the flow circuitry. Unlike natural circulation, forced circulation does not enjoy an inherent flow-compensating effect when heat input changes, i.e., flow does not increase signifi- cantly with increasing heat input. This is because a large portion of the total flow resistance in the boiler tubes arises from the flow distribution devices (usually orifices) used to balance flow at the circuit inlets. The large resistance of the flow distributors prevents signifi- cant increases in flow when heat absorption is increased. Forced circulation is, however, used where the boil- ers are designed to operate near or above the critical pressure [3200 psi (22.1 MPa)]. There are instances in the process and waste heat fields and in some spe- cialized boiler designs where the use of circulating pumps and forced circulation can be economically at- tractive. Atpressuresabove3100psi(21.4MPa)anatu- ral circulation system becomes increasingly large and costly and a pump can be more economical. In addition, the forced circulation principle can work effectively in both the supercritical and subcritical pressure ranges. In forced recirculation there is a net thermal loss because of the separate circulating pump. While prac- tically all the energy required to drive the pumps re- appears in the water as added enthalpy, this energy originally came from the fuel at a conversion to use- ful energy factor of less than 1.0. If an electric motor drive is used, the net energy lost is about twice the energy supplied to the pump motor for typical fossil fuel systems. Circulation design and evaluation The furnace wall enclosure circuits are very impor- tant areas in a boiler. High constant heat flux condi- tions make uninterrupted cooling of furnace tubes essential. Inadequate cooling can result in rapid over- heating, cycling thermal stress failure, or material failures from differential tube expansion. Sufficient conservatism must be engineered into the system to provide adequate cooling even during transient up- set conditions. Simultaneously, the rated steam flow conditions must be maintained at the drum outlet.Any of the circulation methods discussed may be used to cool the furnace waterwall tubes. In evaluating the circulation method selected for a particular situation, the following general procedure can be used: 1. The furnace geometry is set by the fuel and combus- tion system selected. (SeeChapters11,14,19and21.) 2. Standardized components (furnace walls, headers, drums, etc.) are selected to enclose the furnace ar- rangement as needed. (See Chapters 19 and 21.) 3. The local heat absorption is evaluated based upon the furnace geometry, fuel and firing method. Lo- cal upset factors are evaluated based upon past field experience. (See Chapter 4.) 4. Circulation calculations are performed using the pressure drop relationships. 5. Thecalculatedcirculationresults(velocities,steam qualities, etc.) are compared to the design criteria. 6. The flow circuitry is modified and the circulation re-evaluated until all of the design criteria are met. Some of the design criteria include: 1. Critical heat flux limits For recirculating systems, CHF conditions are generally avoided. For once- through systems, the temperature excursions at CHF are accommodated as part of the design. 2. Stability limits These limits generally indicate acceptablepressuredropversusmassflowrelation- ships to ensure positive flow in all circuits and to avoid oscillating flow behavior. 3. Steam separator and steam drum limits These indicate maximum steam and water flow rates to individual steam-water separators and maximum water flow to the drum downcomer locations to ensure that steam carryunder and water carryover will not be problems. 4. Minimum velocity limits Minimum circuit satu- rated velocities assure that solids deposition, po- tentially detrimental chemistry interactions, and selected operating problems are minimized. 5. Sensitivity The system flow characteristic is checked to ensure that flow increases with heat input for all expected operating conditions. Circulation is analyzed by dividing the boiler into individual simple circuits – groups of tubes or circuits with common end points and similar geometry and heat absorption characteristics. The balanced flow condition is the simultaneous solution of the flow char- acteristics of all boiler circuits. At the heart of a B&W circulation evaluation is a circulation computer program that incorporates tech-Fig. 29 Effect of pressure on pumping head.
- 160. 5-20 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company niques for calculating the single- and two-phase heat transfer and flow parameters discussed above and in Chapters 3 and 4. With this program, a circulation model of the entire boiler is developed. Input into the program is a geometric description of each boiler cir- cuit including descriptions of downcomers, supplies, risers, orifices, bends and swages, as well as individual tubes. Each of the circuits within the boiler is subjected to the local variation in heat transfer through inputs based upon the furnace heat flux distribution. (See Chapter 4.) Given the geometry description and heat absorption profile, the computer program determines the balanced steam-water flow to each circuit by solv- ing the energy, mass and momentum equations for the model. The results of the program provide the detailed information on fluid properties, pressure drop and flow rates for each circuit so that they can be compared to the design criteria. Adjustments frequently made to improve the individual circuit circulation rates can include: changing the number of riser and supply connections, changing the number or type of steam separators in the drum, adding orifices to the inlets to individual tubes, changing the drum internal baffling, changing the operating pressure (if possible) and low- ering the feedwater temperature entering the drum. Oncethesteam-watercircuitryisfinalized,thedetailed mechanical design proceeds. Fig. 30 Moody critical flow model for maximum steam-water flow rate.17 Critical flow Atwo-phaseflowparameterofparticularimportance in nuclear reactor safety analysis and in the operation of valves in many two-phase flow systems is the criti- cal flow rate. This is the maximum possible flow rate through an opening when the flow becomes choked and further changes in upstream pressure no longer affect the rate. For single-phase flows, the critical flow rate is set by the sonic velocity. The analysis is based upon the assumption that the flow is one dimensional, homogeneous, at equilibrium and isentropic. These as- sumptions result in the following relationships: Sonic velocity = = C dP d g s c ρ (22) Critical flow max= = G dP d gcρ ρ (23) where C = velocity, ft/s (m/s) P = pressure, lb/ft2 (Pa) ρ = fluid density, lb/ft3 (kg/m3 ) gc = 32.17 lbm ft/lbf s2 (1 kg m/N s2 ) Gmax = mass flux, lb/s ft2 (kg/m2 s) However, when saturated water or a two-phase steam-water mixture is present, these simplifying as- sumptions are no longer valid. The flow is heteroge- neous and nonisentropic with strong interfacial trans- port and highly unstable conditions. Moody’sanalysis17 ofsteam-watercriticalflowisper- haps the most frequently used. It is based upon an annular flow model with uniform axial velocities of each phase and equilibrium between the two phases. A key element of the analysis involves maximizing the flow rate with respect to the slip ratio and the pres- sure. The results are presented in Fig. 30. The critical steam-water flow rate is presented as a function of the stagnation condition. Compared to experimental ob- servations, this correlation slightly overpredicts the maximum discharge at low qualities (x < 0.1) and pre- dicts reasonably accurately at moderate qualities (0.2 < x < 0.6), but tends to underpredict at higher quali- ties (x > 0.6). References 1. Collier, J.G., and Thome, J.R., Convective Boiling & Con- densation, Third Ed., Oxford University Press, Oxford, United Kingdom, 1994. 2. Jens, W.H., and Lottes, P.A., “Analysis of heat trans- fer, burnout, pressure drop, and density data for high pres- sure water,” Argonne National Laboratory Report ANL- 4627, May, 1951. 3. Thom, J.R.S., et al., “Boiling in subcooled water dur- ing flow up heated tubes or annuli,” Proceedings of Insti- tute of Mechanical Engineers, Vol. 180, pp. 226-246, 1966. 4. Chen, J.C., “Correlation for boiling heat transfer to satu- rated liquids in convective flow,” Industrial & Engineer- ing Chemistry Process & Design Development, Vol. 5, pp. 322-329, 1966. 5. Kitto, J.B., and Albrecht, M.J., “Elements of two-phase flow in fossil boilers,” Two-Phase Flow Heat Exchangers, Kakaç, S., Bergles,A.E. and Fernandes, E.O., Eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 495-552, 1988.
- 161. Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation 5-21 The Babcock & Wilcox Company Bergles, A.E., et al., Two-Phase Flow and Heat Transfer in the Power and Process Industries, Hemisphere, Wash- ington, D.C., August, 1981. Butterworth, D., and Hewitt, G.F., Eds., Two-Phase Flow and Heat Transfer, Oxford University Press, Oxford, England, United Kingdom, 1977. Chen, J.C., Ed., Flow Boiling, Taylor and Francis Group, New York, New York, 1996. Hsu, Y-Y, and Graham, R.W., Transport Processes in Boiling and Two-Phase Systems, Hemisphere, Washing- ton, D.C., 1976. Kakaç, S., Boilers, Evaporators and Condensers, John Wiley & Sons, New York, New York, 1991. Bibliography Kitto, J.B., “Steam Generators,” Standard Handbook of Powerplant Engineering, Second Ed., Elliot, T.C., Chen, K., and Swanekamp, R.C., McGraw-Hill, New York, New York, 1998. Lahey, R.T., and Moody, F.J., Thermal-Hydraulics of a Boiling Water Nuclear Reactor, Second Ed., American Nuclear Society (ANS), Hinsdale, Illinois, 1993. Lokshin, V.A., Peterson, D.F., and Schwarz, A.L., Stan- dard Methods of Hydraulic Design for Power Boilers, Hemisphere Publishing, New York, New York, 1988. Tong, L.S., Boiling Heat Transfer and Two-Phase Flow, John Wiley & Sons, New York, New York, 1965. Wallis, G.B., One-Dimension Two-Phase Flow, McGraw- Hill, New York, New York, 1969. 6. Watson, G.B., Lee, R.A., and Wiener, M., “Critical heat flux in inclined and vertical smooth and ribbed tubes,” Pro- ceedings of The Fifth International Heat Transfer Con- ference, Vol. 4, Japan Society of Mechanical Engineers, To- kyo, Japan, pp. 275-279, 1974. 7. Gellerstedt, J.S., et al., “Correlation of critical heat flux in a bundle cooled by pressurized water,” Two-Phase Flow and Heat Transfer in Rod Bundles, Schock, V.E., Ed., American Society of Mechanical Engineers (ASME), New York, New York, pp. 63-71, 1969. 8. Wiener, M., “The latest developments in natural cir- culation boiler design,” Proceedings of The American Power Conference, Vol. 39, pp. 336-348, 1977. 9. Swenson, H.S., Carver, J.R., and Kakarala, C.R., “Heat transfer to supercritical water in smooth-bore tubes,” Journal of Heat Transfer, Vol. 87, pp. 477-484, 1965. 10. Ackerman, J.W., “Pseudoboiling heat transfer to su- percritical pressure water in smooth and ribbed tubes,” Journal of Heat Transfer, Vol. 92, pp. 490-498, 1970. 11. Hewitt, G.F., and Roberts, D.W., “Studies of two-phase flow patterns by simultaneous x-ray and flash photogra- phy,” Atomic Energy Research Establishment Report M2159, HMSO, London, England, United Kingdom, 1969. 12. Thom, J.R.S., “Prediction of pressure drop during forced circulation boiling of water,” International Journal of Heat and Mass Transfer, Vol. 7, pp. 709-724, 1964. 13. Martinelli, R.C., and Nelson, D.B., “Prediction of pres- sure drop during forced-circulation boiling of water,” Trans- actions of the American Society of Mechanical Engineers (ASME), pp. 695-702, 1948. 14. Zuber, N., and Findlay, J.A., “Average volumetric con- centration in two-phase flow systems,” Journal of Heat Transfer, Vol. 87, pp. 453-468, 1965. 15. Chexal, B.J., Horowitz, J., and Lellouche, G.S., “An assessment of eight void fraction models for vertical flows,” Electric Power Research Institute Report NSAC-107, De- cember, 1986. 16. Ledinegg, M., “Instability of flow during natural and forced circulation,” Die Wärme, Vol. 61, No. 48, pp. 891- 898, 1938 (AEC-tr-1861, 1954). 17. Moody, F.J., “Maximum flow rate of a single compo- nent, two-phase mixture,” Journal of Heat Transfer, Vol. 87, pp. 134-142, 1965.
- 162. 5-22 Steam 41 / Boiling Heat Transfer, Two-Phase Flow and Circulation The Babcock & Wilcox Company Two-phase flow void fraction measurements.
- 163. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-1 Chapter 6 Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion Numerical modeling – an overview Continuous and steady advances in computer tech- nology have changed the way engineering design and analyses are performed. These advances allow engi- neers to deal with larger-scale problems and more com- plex systems, or to look in more detail at a specific process. Indeed, through the use of advanced com- puter technology to perform engineering analysis, nu- merical modeling has emerged as an important field in engineering. While this chapter focuses on fluid flow and heat transfer, Chapter 8 provides a brief dis- cussion of numerical modeling for structural analysis. In general, the term numerical method describes solving a mathematical description of a physical pro- cess using a numerical rather than an analytical ap- proach. This may be done for a number of reasons, including the following: 1. An analytical means of solving the equations that describe the system may not exist. 2. Even though an analytical method is available, it may be necessary to repeat the calculation many times, and a numerical method can be used to ac- celerate the overall process. A small-scale replica of an apparatus is considered a physical model because it describes the full-size ap- paratus on a smaller scale. This model can incorpo- rate varying levels of detail depending on need and circumstances. A mathematical description of a physi- cal system (referred to as a mathematical model) can also incorporate varying levels of detail. Similar to a physical model, the amount of detail is often deter- mined by the accuracy required and the resources available to use the model. This creates a need to strike a balance between accuracy, complexity and efficiency. There are two basic approaches to mathematical modeling. 1. Model the behavior of a system. Network flow mod- els and heat exchanger heat transfer correlations are examples of a system model. 2. Model the fundamental physics of a system to de- termine the behavior. Computational fluid dynam- ics (CFD) and chemical reaction models fall into this category. The term numerical modeling usually refers to the use of numerical methods on high-powered computers tosolveacomplexsystemofmathematicalmodelsbased on the fundamental physics of the system. In this re- spect,itdescribesthesecondapproachidentifiedabove. As an example, consider analysis of hot air moving through a length of duct composed of several differ- ent components all in a cold environment. The first type of analysis would involve a network model. This model would describe the pressure drop and heat loss along the duct based on the length, shape, number of turns, etc. This model is based on extensive flow measurements taken on the individual components (i.e., straight sections, turns, reductions, etc.) that make up the duct. Aset of empirical and fun- damental correlations is used to analyze the flow rate throughtheduct.Thecomputationcanbesetupquickly andwithminimaleffort.Resultsandmultiplevariations can be rapidly obtained. While results are reasonably accurate, they are limited to the components for which a flow correlation already exists. A unique component design that has not been described by a correlation may not be accurately evaluated with this type of model. The second type of analysis would involve a CFD model of the same duct. The detailed behavior of the flow through the entire duct is modeled. From this information, pressure drop and heat loss along the length of the duct may be determined. However, un- like the first analysis, this type of model provides ad- ditional details. For example, the first model does not consider how the flow through a bend differs if it is followed by another bend or a straight section; the first model may result in the same pressure drop regard- less of how the components are arranged. The second analysis would account for these differences. In addi- tion, variation in heat loss from one side of the duct to the other can be determined. Most importantly, this model is not restricted to duct components where ex- tensive experimental data is available. New concepts can easily be evaluated. These two approaches have both benefits and limi- tations. The appropriate use of each is determined by the information needed and the information available. Whilebothapproachesareimportantengineeringtools, the remaining discussion here will focus on the second, specifically on CFD and combustion modeling, and how theyrelatetofurnaces,boilersandaccessory equipment.
- 164. The Babcock & Wilcox Company 6-2 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion Benefits There are numerous benefits to using a sophisti- cated tool such as a numerical model for engineering analysis. These tools can often provide information that can only be obtained through expensive experi- ments or may not be available any other way. Numeri- cal modeling may often be used to obtain needed in- formation quickly and at a reduced cost. While it is important to understand the advantages of using numerical modeling, it is equally important to understand that it is only one means of obtaining the required information. Engineering has long relied on theory and experiments for design and analysis. Numerical modeling adds a third approach. Each ap- proach offers different insights with different benefits. Increased understanding The primary purpose of using numerical modeling is to increase understanding of a physical process. As such, it is often used in addition to or in conjunction with other available tools. Consider the duct example described above. It is possible to use a network model on a large number of duct designs to narrow the pos- sibilities to a few candidate designs. A full CFD model could then be used to analyze each of the candidate designs to gain a better understanding of the strengths and weaknesses of each design. Exploration of unfamiliar conditions As previously described, it is possible that a compo- nent of the duct can not be accurately described within the context of a flow network model. A conservative approximation can be used but may result in an overly conservative solution. A CFD model of the new com- ponent can provide the missing information, or a CFD model of the entire system can be performed. The model allows the exploration and analysis of new equipment and systems. Design validation/examination of interactions Traditional methods of analysis and design are of- ten focused on individual system components such as the burners, air system, or heat transfer surfaces in a furnace. A full accounting of the complex interaction between the components is often not given. Numeri- cal modeling provides a vehicle to evaluate the inter- actions and validate the system design. Troubleshooting Engineering analysis often investigates the behav- ior of existing systems. This is particularly true when the behavior does not agree with the expectations. Nu- merical modeling can play a vital role in determining the nature of the problem and suggesting solutions. Flexibility A distinct feature of numerical modeling is that it is a flexible method of analysis. Modeling can be used to look at any number of different geometries or oper- ating conditions. In addition, the level of detail used in the model can vary from use to use. A high level of detail may be required to model flow near a fuel inlet to a burner, but the same level of detail may not be necessary for flow in a duct. The complexity is often dictated by the problem. Historical perspectives In many ways, the history of numerical modeling in the context of CFD has followed the development of computational capabilities. Early efforts in CFD started in the 1960s, when computers first became commercially available, and when many of the con- cepts and ideas that form the basis of current tech- niques in CFD were first developed. One example is the way much of the turbulent flow is modeled today. Early efforts were often limited to simple two-dimen- sional laminar flows. The resolution of the geometry was also very limited. It was not until the 1970s that CFD saw substan- tial successes. It was during this time that CFD be- gan to be used for general engineering problems. Progress included turbulence modeling, two-dimen- sional reacting flows and three-dimensional flows. As further advances were made in computational technology, more sophisticated and detailed numeri- cal models, as well as increased resolution, became possible. This increased the acceptance of CFD as a useful engineering tool and gave it a much wider ap- plication base. Soon, large comprehensive combustion CFD models were developed. These were fully three- dimensionalturbulent-reactingflowmodels.Sub-mod- els of detailed physics for specific applications were included, such as pulverized coal combustion and ra- diation heat transfer models. Improvements continue to be made today that promise to increase the utility of combustion CFD modeling. Modeling process In its simplest terms, a numerical model is provided with input data that is used to fix specific operating parameters and return results. Without further un- derstanding, this simplistic view of modeling can lead to unsatisfactory results. More appropriately, a multi- step process is used: 1. Obtain a complete situational description includ- ing physical geometry, process flow, physical prop- erty data and the level of detail needed. It is im- portant to obtain detailed information because seemingly small differences can have a significant effect on numerical solutions. 2. Define the modeling assumptions appropriate for the specific flow system and computer model se- lected while making appropriate tradeoffs; cost and time are balanced against level of detail and information required. 3. Prepare the input data by converting the general technical information obtained in step 1 into the detailed inputs required by the computational model selected. Much of this is accomplished with the use of various computer programs such as com- puter assisted drafting (CAD) software and mesh generation software. Verification of the input data is an important part of this process.
- 165. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-3 4. Run the numerical computational model until an acceptable solution is obtained. 5. Analyze the results to verify the initial model as- sumptions, to check the results against known trends, to benchmark the output with known field data, and to present the results in a usable form. In application, the computer programs or software used to perform the modeling function are broken down into three general groups that work together to complete the analysis: 1. Pre-processing: generation of the calculational mesh or grid representing all boundary conditions (part of step 3 above and discussed later under Mesh generation), 2. Solution: execution of the numerical model to de- rive an acceptable solution (step 4 above), and 3. Post-processing: generation of typically graphical or tabular key results from the numerical model to permit interpretation and evaluation of the re- sults (part of step 5 above). Limitations Despite recent advances in technology, increased understanding of physics, and improvements in de- scribing input conditions, limitations remain in apply- ing numerical modeling to engineering problems. Nu- merical modeling can only be applied where there is an adequate understanding of the physics involved. In situations where there is not an appropriate math- ematical description of the physics, numerical model- ing is not possible. Even when a description exists, it may be too complex to be readily used in a model and a simplified approach is required. In this case, results will reflect the simplifying assumptions of the model. Computer technology continues to limit the level of detail that can be modeled with numerical methods. Our understanding of the physics of systems that are routinely modeled with CFD far exceeds the compu- tational resources (size and speed) that are available to model them. A considerable amount of effort is ex- pended on developing simplified descriptions of the physics to make the problem manageable with current computer technology. The precision and accuracy of the input data also represents a significant limitation to numerical mod- eling. Sources where this may be significant include the level at which the geometry is described and rep- resented, the accuracy of imposing an inlet condition, and the assumptions made in specifying other bound- ary conditions and modeling parameters. Despite these limitations, numerical modeling can be used in conjunction with other engineering analy- ses. When applied appropriately, numerical modeling can provide invaluable information. Uses Many applications for CFD and combustion mod- eling exist within the design and evaluation of steam generators (or boilers) and related equipment. Nu- merical models of the flue gas and steam-water flows are used to predict boiler behavior, evaluate design modifications, or investigate localized phenomena. Ex- amples of flue gas applications include predicting tem- perature distributions within a furnace, evaluating fluid mixing due to the retrofit of systems to control nitrogen oxides (NOx) emissions, and improving air heater flow distributions to increase heat absorption. Water-sideapplicationsincludedeterminingflowrates for boiler furnace circulation systems and evaluating system stability, among others. Many of the uses are summarized in Table 1. Theory The foundation of numerical modeling is the devel- opment of a mathematical description of the physical system to be modeled. Whether this is as simple as heat transfer through a wall or as complex as a pul- Table 1 Sample Numerical Model Applications Application Purpose Windboxes Evaluate flow field within windbox, determine expected air distribution to combustion equipment, and determine pressure losses throughout system Burners Accurately determine boundary conditions for furnace models, evaluate flame and burner flow characteristics Overfire air ports Accurately determine boundary conditions for furnace models, determine flow characteristics and pressure losses through port Pulverized Examine combustion characteristics coal-fired boilers throughout the entire furnace; evaluate fuel/air mixing, furnace performance, heat transfer, emissions and flow characteristics Recovery boilers Examine combustion characteristics throughout the entire furnace; evaluate fuel/air mixing, furnace performance, heat transfer, emissions, carryover and flow characteristics within the furnace Waste-to-energy Examine combustion characteristics boilers of the entire furnace; evaluate fuel/air mixing, furnace performance, heat transfer, emissions and flow characteristics Selective catalytic Determine inlet flow and reduction systems temperature distributions; evaluate flow correction devices to meet specified velocity and temperature criteria Wet scrubbers Determine flow and pressure drop conditions, evaluate scrubber emission removal performance
- 166. The Babcock & Wilcox Company 6-4 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion verized coal flame, the first step is to adequately de- fine the mathematical description. The description is derived from first principles and physical laws and is primarily based on a set of con- servation relationships that result in a series of ordi- nary and partial differential equations (ODE and PDE). The PDEs describe such things as the conser- vation of mass, momentum, energy, and others. In addition,fundamentalrelationshipsareusedtocomplete the description of the system. The complete description is made up of these PDEs and algebraic relationships. Combustion modeling results in a particularly com- plex mathematical description of the overall process. Each physical process involved in a combustion sys- tem is described individually; however, they interact with other physical processes. This interaction creates a coupling between all the descriptions of the indi- vidual processes. To demonstrate this coupling, consider a simple dif- fusion flame. Fluid dynamics describe the process of mixing two streams of reactants. The resulting reac- tion alters the constituents of the fluid, and heat re- lease from the reaction increases the local tempera- ture. The change in temperature and chemical compo- sition has a strong effect on local density. This change in density, in turn, has a strong effect on the fluid flow. The system of processes, equations and interrela- tionships in a coal-fired boiler is far more complex, as shown in Fig. 1. Five fundamental processes must be addressed while providing for all key interactions: 1. Fluid transport: fluid motion, component mass and energy transport in a turbulent mixing envi- ronment. 2. Particle transport: particle (in this case coal) or dis- crete phase motion in a fluid. 3. Homogeneous chemical reactions: gaseous species combustion. 4. Heterogeneouschemicalreactions:particlecombustion. 5. Radiative heat transfer: radiative heat transfer in a particle-laden participating media. The second step to modeling the system is to use an appropriate technique to solve the set of equations that hasbeenchosentodescribethephysicalsystem.Itisnot possibletoanalyticallysolvethepartialdifferentialequa- tionstypicallyencounteredinmodelingcombustionsys- tems. Thus, the differential equations are discretized to obtain a set of non-linear algebraic equations that can be solved with known numerical techniques. The last step in the process is to obtain the final solution. Following is a more detailed description of each of these processes. Number and Velocity of Particles Particle Velocities Gas Velocities Particle Size and Density Gas Velocities Number and Location of Particles Gas Properties Gas Velocities and Pressure Complex Coupling Phenomena Between Subprocess Modules Change in Gas Composition and Enthalpy Gas Composition and Temperature Gas Composition and Temperature Radiation Heat Transfer Particle Size, Temperature, and Composition Radiative Heat Transfer Module Fluid Transport Module Heterogeneous Chemical Reaction Module Homogeneous Chemical Reaction Module O2 NOX CO2CHX Particle Transport Module Fig. 1 Model for the evaluation of pulverized coal-fired combustion based upon five fundamental processes.
- 167. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-5 Fundamental equations Combustion systems involve a complex interaction of many different physical processes. This includes fluid flow, heat transfer, chemical reactions, and po- tentially fluid-solid interactions. Some of the funda- mental equations that describe these processes are introduced in Chapters 3 and 4. Each of these pro- cesses is briefly described below in the context of nu- merical modeling. Representation of turbulence Large-scale combustion systems are typically char- acterized by turbulent, reacting flow conditions. The effect of turbulent flow (turbulence) on combustion processes is significant and must be considered to ac- count for this effect. As yet, it is not practical to model the full detail of the temporal and spatial fluctuations that are associated with turbulence. As computing resources become more powerful and our ability to handle the enormous amount of information that will be generated increases, it may one day be possible to model the details of turbulent flow on industrial com- bustion systems. Until that day, a simplified model representation of turbulence must be used. Often, dealing with turbulence involves time-aver- aging the fundamental equations to eliminate the tur- bulent fluctuations and utilizing a separate turbulence model to account for the influence of turbulent fluc- tuations on the flow. The fundamental equations can then be solved for the mean quantities. Alternatively, large scale turbulent fluctuations can be directly solved while utilizing a turbulence model for the small scale fluctuations. This technique, called large eddy simulation (LES), is an important advancement in tur- bulence modeling but requires large computational re- sources compared to time-averaging. Time-averaging is typically done either with Reynolds averaging, the conventional time-averaging, or with Favre averaging, a density-weighted averag- ing. The latter is better suited to handle the large den- sityvariationsexperiencedincombustionapplications. Averaging of the conservation equations is accom- plished by first assuming that instantaneous quanti- ties are represented by mean and fluctuating portions as shown in Equation 1. By allowing φ to represent the dependant variable, this can be expressed as: φ φ φ= + ′ (1) where φ is the instantaneous value, φ is the mean portion and ′φ is the fluctuating portion. Density- weighted averaging offers advantages over conven- tional time-averaging for combustion-related flows since it simplifies the treatment of large density changes. The density-weighted mean value, φ , is de- fined as: φ ρφ ρ = (2) where ρφ is the time-averaged product of the instan- taneous density (ρ) and instantaneous value (φ ) and ρ is the time-averaged density. The instantaneous value may then be written as the sum of the density- weighted average and the fluctuating value ′′φ : φ φ φ= + ′′ (3) Equation 3 can be substituted into the transport equation and then time-averaged to derive equations in terms of the mean quantities. While it is not impor- tant to detail the process here, it is important to note that the results produce additional terms in the result- ing equations. These extra terms are known as Reynolds stresses in the equations of motion and tur- bulent fluxes in the other conservation equations. Tur- bulence models are generally required to model these extra terms, closing the system of equations. Fluid flow and heat transfer Gas-phase transport in combustion systems is gov- erned by PDEs that describe the conservation of mass, momentum, component mass and energy. The conser- vation of mass or continuity equation is discussed in Chapter 3. The conservation of momentum is repre- sented by the Navier-Stokes equations that are also briefly discussed in Chapter 3. The Cartesian form of Navier-Stokes equations, as well as the continuity equation, can be found in the first four equations in Table 2. In these four equations, ρ is the density, u, v, and w are the velocity components, and x, y, and z are the coordinate directions, µ is the dynamic viscosity, P is the pressure, and g is the body force due to gravity. The remaining conservation equations used to de- scribe the gas-phase transport are the energy and com- ponent mass equations, expressed in Table 2 in terms of specific enthalpy and component mass fraction. The energy source terms are on a volumetric basis and rep- resent the contribution from radiative heat trans- fer,−∇iqr ,energyexchangewiththediscretephasepar- ticles, SH part , and viscous dissipation, SH. The component mass source terms include the mean production rate due to gas-phase reactions, Ri, and the net species pro- duction rate from heterogeneous reactions, Si part . Turbulence model As previously mentioned, the process of time-aver- aging the conservation equations introduces extra terms into the equations. Numerous turbulence mod- els have been developed over the years to determine the values of these extra terms. One of the most com- mon and widely accepted approaches, known as the Boussinesq hypothesis, is to assume that the Reynolds stresses are analogous to viscous dissipation stresses. This approach introduces the turbulent viscosity µand a turbulent transport coefficient σ into each equation. Most of the turbulence models currently used for fluid flow and combustion are focused on determin- ing µ. In the k-epsilon model (one of the most widely used and accepted), the turbulent viscosity is given as: µ ρ ε µ t C k = 2 (4)
- 168. The Babcock & Wilcox Company 6-6 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion Table 2 Summary of Fundamental Differential Equations General form of the transport equation: Physical Transport Source Equation Parameter Coefficient Term Γ S Continuity 1 0 Sm part X-Momentum ~u Y-Momentum ~v Z-Momentum w~ Enthalpy H ~ H Turbulent k Energy k Dissipation ε Rate Species Y ~ i i Other terms appearing in general form: Nomenclature Subscripts/Superscripts S part = source term accounting for exchange between e = effective discrete phase particles and gas phase t = turbulent u, v, w = velocity components x, y, z = directional component H = enthalpy i = ith chemical specie k = turbulent kinetic energy ~ = Favre (density weighted) average ε = turbulent kinetic energy dissipation − = time-average = effective viscosity part = discrete phase particle component = turbulent viscosity g = gravitational vector (x, y, z) = density c1, c2 = model constants Ri = reaction rate Yi = species mass fraction
- 169. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-7 where Cµ is a model parameter, k is the turbulent ki- netic energy, and ε is the turbulent kinetic energy dissipation. The turbulent kinetic energy and the dis- sipation are determined by solving an additional par- tial differential equation for each quantity as given in Table 2. Discrete phase transport Manycombustionapplications,includingpulverized coal, oil, black liquor and even wood involve small solid or liquid particles moving through the combustion gases. The combustion gases are described by assuming that they represent a continuum, whereas a description of the solid and liquid fuel involves discrete particles. Describing the motion of this discrete phase presents unique modeling challenges. There are two basic refer- ence frames that can be used to model the transport of the discrete phase particles, Eulerian and Lagrangian. The Eulerian reference frame describes a control volume centered at a fixed point in space. Conserva- tion equations similar to the ones used for gas trans- port are used to describe the transport mass and en- ergy of particles passing through this control volume. The interaction of the particle phase and the gas phase is accomplished through source terms in the respec- tive transport equations. The Lagrangian reference frame considers a con- trol volume centered on a single particle. This ap- proach tracks the particle on its trajectory as it trav- els through space and interacts with the surrounding gases. The motion of a particle can be described by: m du dt F Fpart part D g= + (5) wherempart representsthemassoftheparticle, upart isthe particle vector velocity, t is time, and FD and Fg represent drag and gravitational forces. Aerodynamic drag is a function of the relative differences between particle and gas velocities, Reynolds number and turbulent fluctua- tionsinthegas.Considerationisalsogivenformassloss from the particle due to combustion.1,2,3 Turbulence has the effect of dispersing or diffus- ing the particles. This dispersion effect has been iden- tified with the ratio of the particle diameter to turbu- lence integral scale. For large particle sizes, particle migration will be negligible, while at small sizes par- ticles will follow the motion of the gas phase. This ef- fect can be modeled using the Lagrangian stochastic deterministic (LSD) model.4 The LSD model computes an instantaneous gas velocity which is the sum of the mean gas velocity and a fluctuating component. The instantaneous gas velocity is used in computing the right-hand side of Equation 5. From the particle velocity the particle position, xpart, is expressed as: dx dt upart part= (6) This equation, along with appropriate initial condi- tions, describes the particle trajectory within the com- putational domain. Combustion Homogeneous chemical reactions Homogeneous or gas-phase combustion involves the transport and chemical reaction of various gas species. During this process, heat is released and combustion product spe- cies are formed. As mentioned, a transport equation for each of the chemical species involved is solved. The main objective of a gas-phase combustion model is to determine the mean production rate, Ri for turbulent combustion. Various methods can be used to determine the pro- duction rate. One common method known as the Eddy Dissipation Combustion Model (EDM) was developed by Magnussen and Hjertager5 and is based on the eddy break-up model.6 This model assumes that the rate of combustion is controlled by the rate of mixing of the reactants on a molecular scale. The reaction rate is given by: W v v C k Y W v k RCTi ij ij j=1 N A k k kj j rc ( ) min :′′ − ′ ′ ∈ ∑ ε ρ Term 1 Term 2 Term 3 R W i i i = = ω ρ (7) where Wi is the component molecular weight, ′vij and ′′vij are the reactant and product stoichiometric coeffi- cients for the ith species and the jth reaction, ε is the turbulent dissipation, kis the turbulent kinetic energy, CA is the model dependent mixing constant and RCTj denotes the set of species that are reactants for the jth reaction. Term 1 represents the stoichiometric coeffi- cients in the particular reaction, Term 2 represents the molecular mixing rate, and Term 3 limits the reaction to the availability of individual reactants. Magnussen7 later proposed the eddy dissipation con- cept (EDC) to overcome some limitations of other mod- els. Specifically, the EDC model is applicable to non- premixed and premixed combustion and can be used with simplified or detailed chemistry to describe the reaction process. A detailed description of the EDC model can be found in Magnussen,7 Lilleheie et al.,8 Magnussen9 and Lilleheie et al.10 Magnussen’s premise is that chemical reactions oc- cur in the fine structures of turbulence where the tur- bulent energy is being dissipated. Within these struc- tures, molecular mixing occurs and the reactions can be treated at the molecular level. The EDC model is based on the concept of a reactor defined by a reaction zone in these fine turbulence structures. The length and time scales from the turbulence model are used to characterize these fine turbulence structures. The re- action rates within these fine structures can be defined with the specification of an appropriate chemical kinet- ics mechanism. These reaction rates are then related to the average reaction rates in the bulk fluid and then applied to the time-averaged transport equations.
- 170. The Babcock & Wilcox Company 6-8 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion While some of the simpler models mentioned above have been utilized extensively, the EDC provides a means of more accurately treating the complexities of coal combustion and modern combustion systems. This is particularly important as the sophistication of the heterogeneous combustion models improves. Heterogeneouschemicalreactions Simulationofcoal combustion must account for a complex set of physical processes including drying, devolatilization, and char oxidation. When a coal particle enters the combustion zone, the rapid heatup causes moisture to evaporate. Coal Dry Coal + Water Vapor→ (8) Evaporation is followed by devolatilization to produce volatiles and char. Dry Coal Gaseous Fuel + Char→ (9) The volatiles consist of light gases (primarily hydro- gen, carbon monoxide, carbon dioxide, and methane), tars and other residues. The devolatilization rate can not be adequately represented with a single first-or- der kinetic expression. Ubhayaker et al.11 suggested a two first-order kinetic rate expression: Dry Coal Gaseous Fuel Char K 1 i i d i i i i → + −( ) = α α 1 2, (10) where Ki d isthekineticrateofreactionand ai isthevola- tiles’massfraction.Thekineticratesarefirst-orderinthe massofcoalremainingandareexpressedinanArrhenius form. The total devolatilization rate becomes: d i i i d K K= ∑ α (11) A more advanced model known as the Chemical Percolation Devolatilization (CPD)12,13,14 has been de- veloped and is described elsewhere. Unlike the empiri- cal formulation of Ubhayaker et al.,11 the CPD model is based on characteristics of the chemical structure of the parent coal. Following devolatilization the remaining particle consists of char residue and inert ash. Char is assumed to react heterogeneously with the oxidizer: Char + Oxidant Gaseous Products + Ash→ (12) A basic approach to char oxidation was described by Field.15 The effective char oxidation rate is a func- tion of the kinetic rate of the chemical reaction and the diffusion rate of the oxidizer to the particle.15,16 Char + Oxidant Gaseous Products + Ash i i i ch K i → = 1,22 (13) where Ki ch is the effective char oxidation rate. The to- tal char oxidation rate is expressed as: ch i i ch K K= ∑ (14) The Carbon Burnout Kinetic (CBK) model has been developed by Hurt et al.17 specifically to model the details of carbon burnout. The model has a quantita- tive description of thermal annealing, statistical kinet- ics, statistical densities, and ash inhibition in the late stages of combustion. Radiative heat transfer Radiative heat transfer in combustion systems is an important mode of heat transfer and is described by the radiative transfer equation (RTE): iΩ Ω Ω Φ Ω Ω ∇( ) ( ) = − +( ) ( ) + ( ) + ′ → I r I r I r Ib λ λ λ λ λ λ λ κ σ κ σ π , , ( ) 4 r d, ′( ) ′∫ Ω Ω Ω (15) where κλ is the spectral absorption coefficient, σλ is the scattering coefficient, and Ibλ is the black body ra- diant intensity. This equation describes the change in radiant in- tensity, I rλ ,Ω( ), at location r in direction Ω. Thethree terms on the right-hand side represent the decrease in intensity due to absorption and out-scattering, the increase in intensity due to emission, and the increase in intensity due to in-scattering. Radiative heat transfer information is obtained by solving the RTE (Equation 15) which is coupled with the thermal energy equation by the divergence of the radiant flux vector −∇ ℑi . The divergence can be ob- tained from: ∇ ℑ = − ∫∫∫ ∞∞ i 4 0 4 00 κ λ κ λλ λ λ λ π E T d I d db ( ) ( )Ω Ω (16) The two terms on the right-hand side account for emission and absorption, respectively. Discretization of equations In the preceding sections, a mathematical descrip- tion of combustion modeling, consisting of a fundamen- tal set of algebraic relations and differential equations of various forms, has been described. This includes fluid transport, particle transport, combustion and ra- diative heat transfer. Because this system of equations istoocomplextosolvewithanalyticmethods,anumeri- cal method must be employed. The methods of discretizing the fluid transport and radiative heat trans- fer are of particular interest and are presented here. Finite volume approach It should be recognized that many of the partial dif- ferential equations are of a single general form as pro- vided in Table 2 and can be expressed as: ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ ∂ ∂ + ∂ ∂ t x u y v z w x x y ( ) ( ) ( ) ( )ρφ ρ φ ρ φ ρ φ φ φΓ Γφφ φ φ φ φ∂ ∂ + ∂ ∂ ∂ ∂ + y z z SΓ (17)
- 171. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-9 Since many of the equations share this form, a single method can be used to solve all of the associ- ated equations. Most of these methods involve divid- ing the physical domain into small sub-domains and obtaining a solution only at discrete locations, or grid points, throughout the domain. The well-known finite difference method is one such method. Another very powerful method, that is particularly suited for use in combustion modeling, is the finite volume approach. The basic idea of the finite volume approach is very straightforward and is detailed in Patankar.18 The entire domain is divided into non-overlapping control volumes with a grid point at the center of each. The differential equation in the form of Equation 17 is in- tegrated over the entire control volume and after some rearrangement becomes: (18) Carrying out the integrations, the resulting equation is: ∂ ∂ ( ) ∆ + −( ) = ∆∑t V C D S Vf f f f ρφ φ φ φ( ) (19) where ∆V is the volume of the control volume, Cf is the mass flow rate out of the control volume, Df is the diffusive flux into the control volume, and the sum- mation is made over all the control volume faces, f. The temporal derivative in the first term of Equation 19 can be expressed using a first-order backward differ- ence scheme: ∂ ∂ ( ) = − ∆ +∆ t t t t t t ρφ ρ φ φ (20) The mass flow rate Cf is determined from the solu- tion of the mass and momentum equations while the diffusive flux Df is based on the effective diffusivity and the gradient at the control volume face. Combin- ing Equations 19 and 20 with the definitions of Cf and Df and an interpolated value for φf results in an alge- braic expression in terms of the dependant variable φi at grid point i and the neighboring grid points. This is expressed as: a a bi i n n n iφ φ= +∑ (21) where ai and an are coefficients for the control volume and its neighbors respectively and bi represents the remaining terms. The number of neighboring values that appear in Equation 21 is a function of the mesh, the method used to interpolate the dependant vari- able to the control volume face, and the method used to determine gradients at the control volume face. Following this procedure for each grid point in the entire domain produces a coupled set of algebraic equations. This set of equations can be solved with an appropriate method from linear algebra. Many differ- ent techniques are possible and can be found in a ref- erence on numerical methods. There are two advantages to the finite volume ap- proach. First, the dependant variable in the resultant discretized equation is a quantity of fundamental in- terest such as enthalpy, velocity or species mass frac- tion, and the physical significance of the individual terms is maintained. Second, this approach expresses the conservation principle for the dependant variable over a finite control volume in the same way the con- servation equation expresses it for an infinitesimal control volume. By so doing, conservation is main- tained over any collection of control volumes and is enforced over the entire domain. Discrete ordinates method Several radiative heat transfer models have been developed and many are described by Brewster19 and Modest.20 A recent review of radiative heat transfer models21 states that the discrete ordinates method coupled with an appropriate spectral model provide the necessary detail to accurately model radiative heat transfer in combustion systems. This is one of the most common methods currently used to model radiative heat transfer. The discrete ordinates method (DOM)22,23 solves the radiative transport equation for a number of ordinate directions. The integrals over direction are replaced by a quadrature and a spectral model is used to de- termine radiative properties of κ and σ. This results in a set of partial differential equations given by: µ η ξ κ σ κ σ π m m m m m m m b m I x I y I z I I S ∂ ∂ + ∂ ∂ + ∂ ∂ = − +( ) + + 4 (22) where µ η ξm m m, , are the direction cosines of the cho- sen intensity Im and Sm is the angular integral. This set of equations is solved by a method outlined by Fiveland22 to find the radiative intensities throughout the combustion space. The source term for the energy equation can be found by summing over all directions: ∇ = − ′ ′ ′ ∑i q T w Ir m m m 4 4 κ σ κ (23) Mesh generation Once discretized, the transport equations must be solved at individual points throughout the domain. This requires that the individual points be specified and the relationship between other points be identi- fied. Displaying the points along with the connections between them creates a pattern that looks something like a woven mesh. The process of creating the mesh is therefore known as mesh generation. Mesh generation is an important and often chal- lenging step in the overall modeling effort. The first criterion in mesh generation is to accurately represent the geometry being modeled. Secondly, adequate de- tail must be placed throughout the domain to obtain
- 172. The Babcock & Wilcox Company 6-10 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion an accurate solution. Other criteria include mesh quality and total mesh size. A discussion on these cri- teria can be found elsewhere.24 Cell types The basic unit in a mesh is the control volume or cell. The cells are arranged such that they cover the entire domain without overlapping. Common cell types are shown in Fig. 2. The mesh may be made of a single cell type (homogeneous mesh) or possibly a combina- tion of different types (hybrid mesh). Structured mesh Structured meshes consist of cells placed in a regu- lar arrangement such that adjacent cells can be iden- tified simply by their order in a list. Fig. 3 shows how the neighboring cells are identifiable simply by incrementing an index that is typically aligned with the coordinate directions. This greatly simplifies the task of retrieving information from neighboring cells. Forsimplegeometries,astructuredmeshisbothsimple to generate and efficient when solving the problem. However, complex geometries highlight particular challenges with this approach. This is illustrated in Fig. 4. Two common techniques of dealing with irregu- larities in geometry are 1) a cartesian stair-stepped mesh and 2) body-fitted mesh. The stair-stepped mesh can place cells in areas outside of the domain and approximates boundaries by stair-stepping the mesh (Fig. 4a). The cells outside of the domain are main- tained as part of the mesh structure but are unused during the computation. The body-fitted mesh follows geometric features and the cell shape changes to ac- commodate these physical features (Fig. 4b). Slight variations of the simple structured mesh can be used. Block structured meshes provide more geo- metric flexibility since the entire mesh is a composite of smaller structured meshes. Unstructured mesh An unstructured mesh provides the maximum flex- ibility for complex geometries. While the ease of ob- taining neighboring cell information has been lost, the ability to place cells anywhere in the computational domain increases the ease by which the geometry can be accurately represented. Fig. 4 compares an un- structured mesh with two structured mesh ap- proaches. With an unstructured mesh approach there is greater control over the level of detail in the mesh for different parts of the domain. Embedding and adaption More detail can be obtained in portions of the do- main through increasing the mesh resolution by em- bedding more cells. This is accomplished by splitting an existing cell in some fashion to create additional cells. By splitting a cell in each of the cell’s parametric coordinatedirections,asinglehexahedronwouldbecome eight.Thisgreatlyincreasestheresolutioninthisregion. Often it is not possible to know where resolution is needed a priori. The process of adaption can be used to increase the resolution based on the actual solution. For example, high discretization error may often be related to high solution gradients across cells. In this case the velocity gradient from the solution can be used to dis- cover where more cells are needed. This is an especially powerfultoolwhencomputationalresourcesarelimited. Example applications Wet scrubbers Situation The two-phase flow in a wet flue gas des- ulfurization (WFGD) scrubber tower is a complex pro- cess involving spray atomization, liquid entrainment, droplet disengagement and phase separation. The physical arrangement of a basic WFGD scrubber mod- ule is shown in Chapter 35, Fig. 2. With a tray, there is a bubbly froth due to countercurrent flow of liquid and gas with holdup of liquid on the tray. The vari- ous two-phase flow regimes complicate the calculation of pressure drop and gas velocity distribution in a wet scrubber.Predictionoftwo-phaseflowisessentialsince liquid residence time and total interfacial liquid/gas area are important factors in determining the amount of SO2 absorption. Therefore, The Babcock & Wilcox Company (B&W) has implemented a multi-dimen- sional two-phase flow model for wet scrubbers based on CFD analysis. A multi-dimensional hydraulic model solves sepa- rate equations for mass and momentum for both the liquid and gas phases. An interfacial drag law calcu- lates the resistance of liquid to the gas flow and vice versa. These interfacial drag laws depend primarily on droplet diameter. However, alternate drag equa- tions can be implemented in the multi-dimensional model for the various two-phase flow regimes. By us- ing the fundamental relations for interfacial drag, the model can calculate separate three-dimensional veloc- ity fields for the liquid and gas phases. Both liquid and gas momentum equations share a common static pres- sure field. Fig. 2 Cell or control volume types used in numerical modeling grids or meshes. Triangle Tetrahedron Pyramid Quadrilateral Hexahedron Prism or Wedge Two-Dimensional Elements Three-Dimensional Elements
- 173. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-11 The numerical model is used as an analysis tool to compare and contrast various design configurations for wet scrubbers. The design features considered by the model include: 1. an overall cylindrical geometry, 2. a tray model with baffles and porous plates, 3. nozzles located at various elevations, 4. conventional or interspatial headers, 5. separate air and water outlets, 6. multiple mist eliminator heights and elevations, 7. conical or straight inlets with or without inlet aw- nings, and 8. cylindrical or conical outlet ducts. These design features are adjustable, thereby permit- ting a wide range of scrubber configurations for util- ity boiler applications. The boundary conditions at the gas inlet and spray nozzles can be adjusted to cover all scrubber gas velocities and liquid mass fluxes. Analysis The model was initially validated against hydraulic data from a one-eighth scale laboratory wet scrubber. By comparing model predictions to scale model pressure drop data, confidence was built in the two-phase flow modeling capability. Once validated, the model was tested for full-scale application by com- paring results to company design standards. Although the model compared favorably to data and standards, absolute prediction of wet scrubber performance is not the primary purpose. Instead, comparative studies are done to predict relative performance of various design options. The numerical model excels at looking at new design configurations that fall outside of existing de- sign standards. Results As discussed in Chapter 35, Sulfur Diox- ide (SO2) Control, the flue gas enters the side of the scrubber tower and turns upward to flow through the tower while the reagent slurry flows countercurrent downward, removing SO2. A uniform gas velocity pro- file across the tower diameter maximizes removal ef- ficiency as the reagent slurry and flue gas flow are uniformly mixed. Fig. 5 shows the CFD modeling re- sults as vertical velocity profiles at several plains through the tower, and illustrates the impact of the B&W tray design in producing uniform flue gas flow i, j+1 i, j i, j-1 i-1, j i+1, j i-1, j+1 i+1, j+1 i-1, j-1 i+1, j-1 Fig. 3 Unit cell identification in a rectangular arrangement. Fig. 4 How mesh or grid structure approximates geometric features. b) Body Fitted c) Unstructured a) Stair-Stepped
- 174. The Babcock & Wilcox Company 6-12 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion through the unit. Fig. 5a shows the case without the tray. The lowest profile shows how non-uniform flow develops as the high velocity flue gas is introduced into the tower, is decelerated, and makes a sharp right- angle turn to flow up the tower. In the absence of a tray, the high velocity (red) and low velocity (blue) regions persist as the flue gas moves through the middle of the tower (middle velocity profile) entering the first level of spray headers. Some of the non-uni- formity persists even up to the mist eliminators. With the addition of the tray (Fig. 5b), the large high and low velocity regions are effectively eliminated. The re- sulting more-uniform velocity profile and the gas/re- agent mixing on top of the tray permit higher levels of SO2 control at reduced slurry recirculation rates. This model has also been used to explore design changes to meet site-specific new and retrofit require- ments.25 These have included alternate flue gas exit geometries, flue gas inlet conditions, tower diameter transitions,headerlocations,slurryrecirculationrates or other factors while still achieving the desired per- formance. It has also been used to investigate inter- nal design alternatives to boost performance and re- duce pressure drop. Popcorn ash Situation Popcorn, or large particle, ash forms un- der certain conditions from the combustion of coal and is light, porous, irregularly shaped, and often forms in the upper boiler furnace or on the convective heat transfer surface. This ash can plug the top catalyst layer in selective catalyst reduction (SCR) NOx con- trol systems, increasing pressure drop and decreasing catalyst performance. Modifications to both the econo- mizer outlet hoppers and the ash removal systems can increase ash capture to address this situation. Accurately predicting how the popcorn ash behaves within the economizer gas outlet requires detailed knowledge of the aerodynamic properties of the ash particles and sophisticated modeling techniques. Key ash properties include the particle density, drag coef- ficient, coefficients of restitution, and its coefficient of friction with a steel plate. CFD models involve solv- ing the gas flow solution, then calculating the particle trajectories using B&W’s proprietary CFD software. Analysis Most CFD programs that handle particle- to-wall interactions are not adequate to accurately predict the complex behavior seen in the popcorn ash physical experiments. These deficiencies have been remedied by adding capabilities to B&W’s proprietary CFD software. First, the coefficient of restitution is separated into its normal and tangential components. Next, a particle-to-wall friction model is used for par- ticles sliding along the wall and experiencing a fric- tion force proportional to the coefficient of friction measured in the physical tests. Also, the ability to set Fig. 5 Effect of B&W’s tray design on gas velocities through a wet flue gas desulfurization system – numerical model results on a 650 MW absorber.
- 175. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-13 up user-defined planes through which flue gas could flow, but off which particles would reflect, has been developed to accurately model particle interaction with wire mesh screens. Results The numerical models used in popcorn ash analysis normally extend from just above the bottom of the economizer (providing a reasonably uniform inlet flow distribution) to just beyond the opening of the economizer gas outlet flue (see Fig. 6). For this samplegeometry,thebaselineparticletrajectoriesfrom the numerical model are shown in Fig. 7. Over the ash particle size range typical of this application, 20 to 50 % of the particles (Fig. 8) pass through the economizer hopper into the downstream equipment depending on particle size, potentially causing the plugging prob- lems in the SCR or air heater. Several solutions were evaluated for this sample geometry including a design that relies on the aerodynamic separation of the par- ticles from the flue gas and another design that in- volves physical barriers to the particles using a wire mesh screen. The aerodynamic solution was selected and a baffle was designed and installed. The general baffle location and the particle trajectories from the numerical model are shown in Fig. 9. The fully three- dimensional model predicted a dramatic improvement in the particle collection efficiency with more than 90% of particles collected for the range of particle sizes evaluated and virtually 100% above a certain cut size Gas Outlet Flue Economizer Hoppers Economizer Gas Outlet Gas and Particle Inlet Surfaces for Ash Removal Fig. 6 Profile of popcorn ash evaluation numerical model. PercentofAshParticlesCaptured 100 90 80 70 60 50 40 Increasing Density Baffle Arrangement Baseline Fig. 8 Comparison of sensitivity to particle density between base case and baffled numerical models. Fig. 7 Base case particle trajectories from popcorn ash evaluation. Fig. 9 Particle trajectories from popcorn ash evaluation numerical model with baffle.
- 176. The Babcock & Wilcox Company 6-14 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion (see Fig. 8). Using numerical models also permitted an optimization of the baffle position to achieve the great- est capture rate while minimizing the pressure drop. In other cases, where an aerodynamic solution is not obtainable,barriersmadefromwiremeshscreenshave beenrecommended.Inthesecases,thescreenopenings would be smaller than the openings in the catalyst.26 Kraft recovery boilers Situation A kraft process recovery boiler, as its name implies, recovers energy and chemicals from black liquor, a byproduct of the papermaking process (see Chapter 28). Air and liquor delivery systems con- trol several complex and interacting combustion pro- cesses (black liquor spray, deposition and burning on furnace walls, char bed burning, smelt flow) that af- fectboilerperformance(capacity,reliability,emissions, chemical recovery, and energy efficiency). Good air jet penetration and effective mixing of secondary and ter- tiary air are desirable for complete combustion and re- duced emissions of carbon monoxide (CO) and hydro- gen sulfide. Distribution of air to three or more air in- jection levels produces fuel-rich conditions in the lower furnace that are desirable for smelt reduction and re- duced emissions of NOx. Flow and temperature unifor- mity in the furnace minimize carryover of inorganic salts, provide an even heat load, and minimize deposi- tiononconvectionsurfacesatthefurnaceexit.Uniform distribution of liquor spray ensures adequate drying of liquor spray, minimum carryover, and stable char bed combustion. Analysis Detailed combustion models for black li- quor have been developed27,28 and are used in conjunc- tion with CFD modeling. Black liquor combustion is simulated for individual droplets as they heat up and burn in suspension. Stages of combustion along a single trajectory include drying, devolatilization, char burning, smelt oxidation, and molten salt formation. The trajectories of thousands of particles determine the distribution of liquor spray in the furnace as shown in Fig. 10 for a range of droplet sizes. Combus- tion processes on the walls and char bed are also simu- lated with particle deposition, char burning, smelt flow and char accumulation. These capabilities are useful for evaluating the effect of air and liquor delivery sys- tems on combustion processes in the furnace and for predicting the quantity and composition of particulate that leaves the furnace. Results Fig. 11 shows gas velocity vectors at selected planes that cross-sect the furnace. The char bed shape is approximated so its impact on flow in the lower fur- nace can be evaluated with the model. Jets of air pen- etrate across the furnace to produce uniform upward flow and effective mixing with combustion gases. Three-dimensional computer-generated images can be examined interactively to help visualize air jet pen- etration and the interaction of jets from neighboring air ports. Gas temperature distribution predictions, shown in Fig. 12, are used to analyze heat transfer in the furnace and convection pass. Other informa- tion such as char bed surface temperature and burn- ing rates, gas species concentrations (i.e., O2, CO, NOx), and wall heat flux distribution are also gener- ated. Results are used by boiler designers and opera- tors to evaluate air system designs, liquor spraying systems, liquor firing capacity, char bed combustion instabilities, convection pass fouling, furnace wall corrosion, and CO and NOx emissions. The results shownwerecreatedbyB&W’sproprietaryCFDsoftware. Wall-fired pulverized-coal boiler furnaces Situation Within a staged, wall-fired furnace, the mixing between the upward-flowing partially-reacted fuel and the jets from the overfire air (OFA) ports is a complex, three-dimensional process. This mixing pro- cess can have a significant impact on the distribution and magnitude of CO emissions. While proprietary technology standards can initially be used to set ef- fective OFA port arrangements for a staged combus- tion system, numerical modeling is often used to con- firm this design and suggest alternatives to improve performance. Modeling is especially useful when there are physical obstructions that prevent OFA port place- ment in the optimal locations. In these circumstances, compromises must be made and determining the best available port layout may not be obvious. Analysis In this example, a numerical model has been used to predict the steady-state flow, heat trans- fer, and combustion processes within a wall-fired pul- verized-coal boiler being upgraded with low NOx burn- ers and OFA ports. As part of the design process, many Fig. 10 Liquor spray distribution in the lower furnace of a recovery boiler.
- 177. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-15 configurations (number and location) of OFA ports were modeled, and the results were compared to de- termine the best port configuration. Boiler geometry, including a portion of the convection tube banks, was approximated using a collection of control volumes, also called a computational grid or mesh, for one of the configurations considered (see Fig. 13). Local re- finement of the mesh was used as needed to better resolve the solution, such as within the OFA region. The coal analysis and boiler operating conditions in- cluding burner and OFA port settings were used to set inlet and boundary conditions for the model. Results The model produces tabular (integrated species concentrations, gas temperatures, gas flow rates, emissions) and graphical (color contour plots of gas speed, gas temperature, or species; coal particle trajectories; gas streamlines) output that are used to evaluate each configuration. As an example, Fig. 14 compares contours of CO concentration throughout the boiler for two different OFA arrangements for a 775 MW wall-fired pulverized coal boiler. Arrange- ment 1 has the OFA ports directly above the burner openings and directly across from the ports on the opposing wall, while arrangement 2 uses horizontally offset ports which provide better mixing and cross-sec- tional coverage. As shown in the figure, OFA arrange- ment 2 results in lower CO concentrations in the up- per furnace than the OFA arrangement 1 (15% lower at the arch, and 23% lower at the furnace exit). The results for this example were created by the B&W- developed computer software. The numerical model described above also provides Fig. 11 Velocity vectors at selected planes that cross-sect a recovery furnace – horizontal planes at primary, secondary and tertiary levels (left); vertical planes at center of furnace (center and right).
- 178. The Babcock & Wilcox Company 6-16 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion a wealth of other information for the boiler designer. Fig. 15 provides a flue gas temperature profile through the center of the furnace and a horizontal section profile across the furnace exit gas pass. As noted in Chapter 19, the average or integrated fur- nace exit gas temperature (FEGT) is a critical design parameter in boiler sizing for performance while miti- gating slagging and fouling. Flow areas with exces- sively high local temperatures identified by such nu- merical models may be more prone to slagging in the furnace or fouling in the convection pass. Additional parameters of interest provided by the numerical models include, but are not limited to, local velocity profiles for performance enhancement and erosion evaluation, furnace heat flux profiles for steam-wa- ter circulation evaluation,29 variation in local chemi- cal constituents such as oxygen for studying combus- tion optimization, and many others. Numerical boiler furnace models continue to evolve and more closely simulate field conditions. While current models as of this publication are not sufficient alone for final boiler design, they offer an additional tool to: 1) aid in de- sign optimization, 2) address non-standard conditions, 3) evaluate the relative impact of fuel changes, 4) highlight areas for design improvement, 5) help in- vestigate the root causes of unusual field observations, and 6) screen potential approaches to address design issues. Numerical modeling will become an increas- ingly important tool in boiler engineering. Windbox Situation The problems encountered in a windbox analysis deal with air flow imbalance and/or excess system pressure loss. Difficulties in tuning burner combustion performance can be frequently attributed to the flow distribution within the windbox. Therefore, creating a uniform flow distribution to each burner is highly desirable to obtain optimum emissions perfor- mance. The flow imbalance problem can be between the front and rear walls of a furnace, compartments in a Fig. 12 Gas temperature contours at vertical planes at the center of a recovery boiler furnace.
- 179. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-17 windbox,orindividualburnersand/orports.Anyimbal- anceormaldistributioncausesnon-uniformairintroduc- tion into the furnace. This imbalance can lead to poor furnace combustion and potentially higher gas emis- sions. The system can be modeled to reduce air flow im- balance and reduce system pressure loss, which allows more flexibility in combustion tuning of a single burner. Analysis A computer model that describes the de- tails of the windbox (walls, bends, etc.) must first be built (see Fig. 16). This requires both flow and geo- metric design information. Care must be taken to en- sure accurate representation of the entire air flow path includinganysignificantly-sizedinternalobstructions. The inlet of the model is usually the outlet of the air heater. This is done for two reasons. An accurate and simple air flow distribution is usually known at this location, and it is far enough upstream to capture all the resulting flow disturbances. The burners and ports must also be modeled accurately to ensure precise flow results. Boundary conditions are the final and very important step, to be placed accurately in the model to exactly represent the windbox/duct flow conditions. Results Once the model has been built, it is checked to make sure grid characteristics are acceptable. This step ensures that there is enough grid resolution to ac- curately represent the flow conditions in any area (i.e., turns,ducts,plenums)andaroundanyobjects(i.e.,turn- ingvanes,perforatedplates,airfoils).Themodelisthen run using CFD software. These calculations yield an accurate representation of the air flowing in the space inside the ducts and windbox. Fig. 17 shows the plan view of the secondary air Fig. 13 Computational mesh on wall-fired boiler surface – full mesh (left) and enlarged view of upper burners and OFA ports (right).
- 180. The Babcock & Wilcox Company 6-18 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion ducts and the windbox with the velocity-vector flow field at the middle of the duct system. Each arrow pro- vides the direction and the magnitude (arrow length) of the local air flow. Fig. 18 is Section A-A through the windbox plan view of Fig. 17, looking into the fur- nace. Fig. 18a shows the original design which in- cluded a simple windbox with a large horizontal per- forated plate intended to provide uniform flow to the bottom three burner rows. The numerical model re- sults indicated a very high velocity zone (large red arrows) in the upper windbox which forced much of the air to bypass the upper burner row and over-sup- ply the bottom two rows. The 30% flow variation be- tween highest and lowest flow burners was too high and could lead to poor emissions performance and in- complete combustion. Several numerical modeling it- erations using CFD computer software suggested the optimized solution shown in Fig. 18b. Eliminating the original large horizontal perforated plate plus adding two turning vanes, a vertical solid plate in the top of the windbox, and ten short vertical perforated plates dramatically improved the burner-to-burner flow dis- tribution to within normal design tolerances. The numerical model permitted testing of ten alter- natives prior to selecting the low-cost solution which would also achieve the desired performance results. SCR systems with economizer bypass Situation A selective catalyst reduction (SCR) sys- tem with an economizer bypass is designed to reduce NOx emissionsbyachemicalreactionbetweenNOx and added ammonia in the presence of a catalyst. (See Chapter 34.) To optimize the chemical reaction at low and intermediate loads, an economizer bypass is needed to increase the temperature of the economizer exit flue gas. The ammonia injection grid (AIG) dis- tributes ammonia uniformly into the exit gas for the correct molar ratio of ammonia to NOx. Finally, the catalyst is used to aid in the chemical reaction. CFD modeling of the SCR system includes full-scale representation, multiple temperature gas paths, heat absorption modeling capability, multi-point testing Fig. 14 Carbon monoxide concentration contours at various elevations – comparison between two OFA arrangements.
- 181. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-19 over an entire grid plane or discrete point testing, chemical species tracking, and rapid flow device test- ing for proper mixing, flow distribution, and minimal pressure drop. Analysis The numerical model is constructed and tuned for actual conditions of an unmodified system according to existing economizer exit flue gas condi- tions. Drawings of future construction and design of the flue work, AIG, and information supplied by the catalyst vendor are used to establish a base operat- ing condition. The chemical species are tracked for ac- curate mixing of ammonia and NOx reagents. The data collected at specific planes in the grid are evaluated against established criteria for efficient NOx removal such as velocity distribution, ammonia-to-NOx ratio, and average temperature entering the catalyst. Inter- nal corrective devices such as turning vanes, flow dis- tributiondiverters,staticmixersandporousplates,are used to precondition the flue gas to meet the criteria for NOx reduction. Grid refinement may be necessary to accurately predict the physical characteristics of in- ternal objects, flue bends and flow distribution devices. Results One such design involves a unit operating at three loads with an economizer bypass taken off the reheat side of the back wall convection pass to achieve adequate remix temperatures for the chemical reac- tion. For bypass operation, three gas paths are con- sidered in the design process: superheat, reheat, and economizer bypass. Because of physical constraints and potential changes in the economizer outlet tem- perature with reheater or superheater bypass ar- rangements, a bypass around the economizer surface was selected. Fig. 19 shows the velocity flow field for the numerical evaluation from the superheater through the exit of the SCR. Fig. 20 shows the detailed velocity field and physical geometry at the bypass lo- cation. A key issue was the complete mixing of the high temperature bypass flow with the main flue gas flow exiting the economizer in order to provide an accept- ably uniform flue gas temperature entering the SCR catalyst. To achieve the desired mixing, a series of turning vanes and mixing devices for the economizer Fig. 15 Numerical modeling results of furnace temperature profiles for a typical 775 MW bituminous coal-fired boiler.
- 182. The Babcock & Wilcox Company 6-20 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion Fig. 17 Plan view of secondary air system flow model results – velocity vectors. Fig. 16 Numerical model of 1100 MW coal-fired boiler windbox and secondary air system.
- 183. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-21 outlet hopper were developed with the aid of the nu- merical model to provide the high velocity bypass jet that would adequately penetrate the main economizer outlet flue gas flow. Success in the design iteration pro- cess was achieved when the velocity profile entering the AIG and the temperature profile entering the SCR achieved the specified uniformity. Waste-to-energy systems Situation Effective combustion of municipal solid waste (MSW) and biomass fuels has become more chal- lenging over time as emissions regulations have been tightened and the variation of fuel characteristics has increased. As part of the process to meet these more demanding requirements, numerical modeling has become a routine engineering tool used in the instal- lation of emissions control systems such as selective non-catalytic reduction (SNCR) NOx control systems (see Chapter 34), refinement of the design and opera- tion of the stoker/grate combustion system with aux- iliary burners (Chapter 16) and overall design of the boiler (Chapters 29 and 30). Control of the flue gas in thefurnaceintermsofchemicalspecies,particles,tem- perature and flow is important where a good furnace design results in more uniform velocity profiles. High velocity regions can cause: 1) increased wall deterio- ration from the hot corrosive flue gas with premature component replacement, 2) sub-optimal emissions con- trol without adequate residence time at temperature, and 3) incomplete burnout of the fuel. Analysis A numerical evaluation of the furnace was conducted as part of the design of a 132 ton per day (120 tm/d) mass burn MSW stoker-fired system. Fig. 21 shows the sectional side view of a European waste- to-energy plant design supplied by B&W. A complete flow field evaluation of the furnace design using nu- merical modeling was conducted to determine the physical furnace modifications necessary to minimize high velocity areas. Results Fig. 22 shows the numerically evaluated velocity vector flow field before (a) and after (b) the design changes. The flow field is represented by ar- rows that show the local velocity direction and mag- nitude (arrow length). In Fig. 22a, a high velocity jet region impinges on the top of the grate, and high ve- locity regions exist along the first (up) and second (down) pass furnace walls. The addition of noses at the bottom of the first pass and the top of the second pass walls as shown in Fig. 22b significantly reduce the ve- locities throughout the furnace and reduce the peak velocity regions near the grate and along the furnace walls. The more moderate velocity in the first pass results in less particle impingement and longer over- all residence time. The maximum velocity in the sec- ond pass is reduced from 13 m/s to 9 m/s (42.6 to 29.5 ft/s), which reduced the thermal load on the back wall of the second pass. Advanced burner development Situation Advanced burner and combustion system development are increasingly relying on the use of numerical modeling as an integral tool in the quest for new hardware and concepts to improve the NOx reduction performance of coal-fired burners. While tra- ditional experimental methods of burner development have been able to dramatically reduce NOx emission levels from bituminous pulverized coal burners below 0.4 lb/106 Btu (492 mg/Nm3 ), increasingly more strin- gent emission reduction regulations are pushing speci- fied combustion emission limits to well below 0.15 lb/ 106 Btu (184 mg/Nm3 ). To develop such equipment, it is becoming even more necessary to understand not only what is happening at the macro-level (which can be observed and tested) but also with small-scale in- teractions deep within the flame and initial ignition zone. Numerical modeling studies of detailed burner designs offer a valuable tool by combining fundamen- tal knowledge of combustion with complex fluid and thermal dynamics to better understand how to further reduce NOx emissions and improve combustion effi- ciency. When combined with small-scale and large- scale tests with advanced test instrumentation, nu- Fig. 18b After – removal of the large horizontal perforated plate plus the addition of two turning vanes and 10 small vertical perforated plates provides more uniform flow to the burners. Fig. 18a Before – high velocity zone in upper windbox (red arrows) under-supplies top row of burners and over-supplies other rows.
- 184. The Babcock & Wilcox Company 6-22 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion Fig. 20 SCR detail at the bypass flue location – turning vanes and mixing devices provide adequate bypass flow penetration for optimal mixing. Fig. 19 Velocity field numerical model output – SCR system from the boiler convection pass to SCR outlet. The high velocity, high temperature bypass flow is visible as high jet penetration is needed to achieve good thermal mixing by the SCR inlet. See also Fig. 20.
- 185. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-23 Fuel Feed Hopper Flue Gas Outlet Grates Fig. 21 Sectional view of a 132 t/d (120 tm/d) mass burn municipal solid waste (MSW) boiler for European application. merical modeling is helping identify techniques to burn fuels more cleanly. Analysis Numerical models, with enhanced resolu- tion (see Fig. 23), have been developed that accurately represent the critical details of physical burners. Ex- perimental studies provide inlet flow boundary con- ditions that can offer the starting point for the analy- sis. These are combined with the results from funda- mental studies of fuel devolatilization, burning of gas- eous species, gaseous diffusion, combustion of solid material and other factors to develop numerical mod- els that begin to simulate the complex combustion pro- cess in commercial coal-fired burners. Physical test- ing, validation and adjustments to the model can pro- duce numerical tools that can be used for advanced burner development. Results Fig. 24 shows detailed gas velocity fields for an advanced burner design. In this case, analysis of the numerical model predictions helped identify the value of an additional burner air supply zone to in- duce recirculation of nitrogen oxide (NO) formed in the outer oxygen-rich portions of the flame into the fuel-rich internal recirculation zone where NO is re- duced. See Chapter 14 for further discussion of coal- fired burners and combustion systems. Fig. 22 MSW boiler from Fig. 21 showing flow field before and after the addition of guide noses in the furnace wall. a) Before design changes b) After guide nose additions
- 186. The Babcock & Wilcox Company 6-24 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion Fig. 23 Detailed numerical model evaluation grid for an advanced coal burner. Fig. 24 Gas velocity model for the coal burner shown in Fig. 23.
- 187. The Babcock & Wilcox Company Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion 6-25 References 1. Wallis, G.B., One-Dimensional Two-Phase Funda- mental, McGraw-Hill Company, New York, New York, 1969. 2. Crowe, C.T., Smoot, L.D., Pratt, D.T., Eds., “Gas Par- ticle Flow,” Pulverized Coal Combustion and Gasification, Plenum Press, New York, New York, 1979. 3. Bailey, G.H., Slater, I.W., Eisenblam, P., “Dynamics Equations and Solutions for Particles Undergoing Mass Transfer,” British Chemical Engineering, Vol. 15, p. 912, 1970. 4. Milojevic, D., “Lagrangian Stochastic-Deterministic (LSD) Predictions of Particle Dispersion in Turbulence,” Journal of Particles and Particle Systems Characteriza- tion, Vol. 7, pp. 181-190, 1990. 5. Magnussen, B. F., and Hjertager, B. H., “On math- ematical modeling of turbulent combustion with empha- sis on soot formation and combustion,” Proceedings of the 16th International Symposium on Combustion, 719-729, The Combustion Institute, Pittsburgh, Pennsylvania, 1976. 6. Spalding, D. B., “Mixing and Chemical Reaction in Steady Confined Turbulent Flames,” Proceedings of the 13th International Symposium on Combustion. The Com- bustion Institute, Pittsburgh, Pennsylvania, 1971. 7. Magnussen, B. F., “On the structure of turbulence and the generalized Eddy Dissipation Concept for turbulent reactive flows,” Proceedings of the 19th American Insti- tute of Aeronautics and Astronautics Aerospace Science Meeting, St. Louis, Missouri, 1981. 8. Lilleheie, N. I., Ertesvåg, I., Bjosrge, T., et al., “Mod- eling and Chemical Reactions,” SINTEF Report STF1s- A89024, 1989. 9. Magnussen, B. F., “The Eddy Dissipation Concept,” XI Task Leaders Meeting: Energy Conservation in Com- bustion, IEA, 1989. 10. Lilleheie, N. I., Byggstøyl, B., Magnussen, B. F., et al., “Modeling Natural Gas Turbulent Jet Diffusion Flames with Full and Reduced Chemistry,” Proceedings from the 1992 International Gas Research Conference, Orlando, Florida, November 2-5, 1992. 11. Ubhayakar, S.K., Stickler, D.B., Von Rosenburg, C.W., et al., “Rapid Devolatilization of Pulverized Coal in Hot Combustion Gases,” 16th International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pennsylvania, 1975. 12. Grant, D. M., Pugmire, R. J., Fletcher, T. H., et al., “A Chemical Model of Coal Devolatilization Using Perco- lation Lattice Statistics,” Energy and Fuels, Vol. 3, p. 175, 1989. 13. Fletcher, T. H., Kerstein, A. R., Pugmire, R. J., et al., “A Chemical Percolation Model for Devolatilization: Mile- stone Report,” Sandia report SAND92-8207, available Na- tional Technical Information Service, May, 1992. 14. Perry, S., “A Global Free-Radical Mechanism for Ni- trogen Release During Devolatilization Based on Coal Chemical Structure,” Ph.D. dissertation for the Depart- ment of Chemical Engineering, Brigham Young Univer- sity, Provo, Utah, United States, 1999. 15. Field, M.A., Grill, D.W., Morgan, B.B., et al., Com- bustion of Pulverized Coal, The British Coal Utilization Research Association, Leatherhead, Surrey, England, United Kingdom, 1967. 16. Fiveland, W.A., Jamaluddin, A.S., “An Efficient Method for Predicting Unburned Carbon in Boilers,” Com- bustion Science and Technology, Vol. 81, pp. 147-167, 1992. 17. Hurt, R., Sun, J.K., Lunden, L., “A Kinetic Model of Carbon Burnout in Pulverized Coal Combustion,” Com- bustion and Flame, Vol. 113, pp. 181-197, 1998. 18. Patakanar, S., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York, New York, 1980. 19. Brewster, M. Q., Thermal Radiative Transfer and Properties, John Wiley & Sons, Inc. New York, New York, 1992. 20. Modest, M. F., Radiative Heat Transfer, McGraw-Hill, Inc., New York, New York, 1993. 21. Viskanta, R., “Overview of computational radiation transfer methods for combustion systems,” Proceedings of the Third International Conference on Computational Heat and Mass Transfer, Banff, Alberta, Canada, 2003. 22. Fiveland, W. A., “Discrete-ordinates solutions of the radiative transport equations for rectangular enclosures,” Transactions of American Society of Mechanical Engi- neers Journal of Heat Transfer, 106, pp. 699-706, 1984. 23. Jessee, J.P. and Fiveland, W.A., “Bounded, High-Reso- lution Differencing Schemes Applied to the Discrete Ordi- nates Method,” Journal of Thermophysics and Heat Transfer, Vol.11, No. 4. October-December, 1997. 24. Thompson, J.F., Soni, B., Weatherhill, N., Eds., Hand- book of Grid Generation, CRC Press, New York, New York, 1999. 25. Dudek, S.A., Rodgers, J.A. and Gohara, W.F., “Com- putational Fluid Dynamics (CFD) Model for Predicting Two-Phase Flow in a Flue-Gas-Desulfurization Wet Scrub- ber,” EPRI-DOE-EPA Combined Utility Air Pollution Con- trol Symposium, Atlanta, Georgia, United States, August 16-20, 1999 (BR-1688). 26. Ryan, A. and St. John B., “SCR System Design Con- siderations for ‘Popcorn’ Ash,” EPRI-DOE-EPA-AWMA Combined Power Plant Air Pollutant Control Mega Sym- posium, Washington, D.C., May 19-22, 2003 (BR-1741). 27. Verrill, C.L., Wessel, R.A., “Detailed Black Liquor Drop Combustion Model for Predicting Fume in Kraft Recov- ery Boilers,” TAPPI Journal, 81(9):139, 1998. 28. Wessel, R.A., Parker, K.L., Verrill, C.L., “Three-Di- mensional Kraft Recovery Furnace Model: Implementa- tion and Results of Improved Black Liquor Combustion Models,” TAPPI Journal, 80(10):207, 1997. 29. Albrecht, M.J., “Enhancing the Circulation Analysis of a Recovery Boiler through the Incorporation of 3-D Fur- nace Heat Transfer Results from COMO™,” TAPPI Fall Technical Conference, San Diego, California, September 8-12, 2002.
- 188. The Babcock & Wilcox Company 6-26 Steam 41 / Numerical Modeling for Fluid Flow, Heat Transfer, and Combustion Advanced computational numerical modeling of a pulverized coal burner.
- 189. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-1 Chapter 7 Metallurgy, Materials and Mechanical Properties Boilers, pressure vessels and their associated com- ponents are primarily made of metals. Most of these are various types of steels. Less common, but still im- portant, are cast irons and nickel base alloys. Finally, ceramics and refractories, coatings, and engineered combinations are used in special applications. Metallurgy Crystal structure The smallest unit of a metal is its atom. In solid structures, the atoms of metals follow an orderly ar- rangement, called a lattice. An example of a simple point lattice is shown in Fig. 1a and the unit cell is emphasized. The lengths of the unit cell axes are de- fined by a, b and c, and the angles between them are defined by α, β and γ in Fig. 1b. The steels used in boilers and pressure vessels are mainly limited to two different lattice types: body-centered cubic (BCC) and face-centered cubic (FCC). (See Fig. 2.) Where changes in the structure or interruptions occur within a crys- tal, these are referred to as defects. Crystal (or grain) boundaries are a type of crystal defect. A few useful structures are composed of a single crystal in which all the unit cells have the same relationship to one another and have few defects. Some high performance jet engine turbine blades have been made of single crystals. These structures are difficult to make, but are worthwhile; their strength is very high as it is deter- mined by close interactions of the atomic bonds in their optimum arrangement. The behavior of all other me- tallic structures, which make up the huge majority of engineering metallic materials, is determined by the nature and extent of the defects in their structures. Structures are made of imperfect assemblies of imper- fect crystals, and their strengths are orders of magni- tude lower than the theoretical strengths of perfect single crystals. Defects in crystals Perfect crystals do not exist in nature. The imper- fections found in metal crystals and their interactions control their material properties. Point defects Point defects include missing atoms (vacancies), atoms of a different element occurring on crystal lattice points (substitutionals), and atoms of a different element occurring in the spaces between crystal lattice points (interstitials). Thermally created vacancies are always present, because they reduce the free energy of the crystal structure by raising its en- tropy. There is an equilibrium number of vacancies present;thisnumbervarieswiththetemperatureofthe crystal. The presence of such vacancies permits diffu- sion(thetransportofonespeciesofmetalatomthrough the lattice of another) and helps facilitate some forms of time dependent deformation, such as creep. Vacancies can also be created by irradiation dam- age and plastic deformations, and the thermodynami- cally controlled processes of diffusion and creep can also be affected by these other processes.Fig. 1 Simple point lattice and unit cell (courtesy of Addison-Wesley).1 Fig. 2 Two Bravais lattices.1
- 190. The Babcock & Wilcox Company 7-2 Steam 41 / Metallurgy, Materials and Mechanical Properties When atoms of two metals are mixed in the molten state and then cooled to solidification, the atoms of one metal may take positions in the lattice of the other, forming a substitutional alloy. Because the atoms may be different sizes and because the bond strength be- tween unlike atoms is different from that of like at- oms, the properties of the alloy can be quite different from those of either pure metal. Atoms of carbon, oxygen, nitrogen and boron are much smaller than metal atoms and they can fit in the spaces, or interstices, between the metal atoms in the lattice structure. The diffusion of an interstitial in a metal lattice is also affected by temperature, and is much more rapid at higher temperatures. Interstitial elements are often only partly soluble in metal lattices. Certainatomssuchascarboninironarenearlyinsoluble, so their presence in a lattice produces major effects. Several crystal defects are illustrated in Fig. 3. This is a two-dimensional schematic of a cubic iron lattice containing point defects (vacancies, substitutional foreign atoms, interstitial atoms), linear and planar defects (dislocations, sub-boundaries, grain bound- aries), and volume defects (voids, and inclusions or precipitates of a totally different structure).2 Disloca- tions are linear defects formed by a deformation pro- cess called slip, the sliding of two close-packed crystal structure planes over one another. Grain boundaries Grain boundaries are more com- plex interfaces between crystals (grains) of signifi- cantly different orientations in a metal. They are ar- rays of dislocations between misoriented crystals. Be- cause the atomic bonds at grain boundaries and at other planar crystal defects are different from those in the body of the more perfect crystal, they react dif- ferently to heat and chemical reagents. This difference appears as grain boundaries on polished and etched metal surfaces under a microscope. Grain size can have positive or negative effects on metal properties. At lower temperatures, a steel with very small grains (fine grain size) may be stronger than the same steel with fewer large grains (coarse grain size) because the grain boundaries act as barriers to deformation due to slip.At higher temperatures, where thermally acti- vated deformation such as creep can occur, a fine grain structure material may be weaker because the irregular structure at the grain boundaries promotes local creep due to a mechanism known as grain bound- ary sliding. Volume defects Volume defects can be voids formed by coalescence of vacancies or separation of grain boundaries. More common volume defects are inclu- sions of oxides, sulfides and other compounds, or other phases that form during solidification from the mol- ten state. Physical metallurgy of steel Phases A phase is a homogeneous body of matter existing in a prescribed physical form. Metallurgists use a graph, called a phase diagram, to plot the stable phasesattemperatureversuscompositionofanymetal composed of two or more elements. When more than one element is involved, even for binary alloys, a variety of phases can result. One type is the binary isomorphous system, typified by only a few combinations: copper-nickel (Cu-Ni), gold-silver (Au-Ag), gold-platinum (Au-Pt) and antimony-bis- muth (Sb-Bi). The phase diagram for one of these simplesystemsillustratestwocharacteristicsofallsolid solutions: 1) a range of composition can coexist in liq- uid/solid solutions, and 2) the change of phase (in these systems, from liquid to solid) takes place over a range of temperatures (unlike water and pure metals which freeze and change structure at a single tem- perature). Fig. 4 is a portion of the phase diagram for Cu-Ni, which shows what species precipitate out of solution when the liquid is slowly cooled.4 (In the re- mainder of this chapter, chemical symbols are often used to represent the elements. See Periodic Table, Appendix 1.) Alloy systems in which both species are infinitely soluble in each other are rare. More often the species are only partly soluble and mixtures of phases pre- cipitate on cooling. Also common is the situation in which the species attract each other in a particular ratio and form a chemical compound. These interme- tallic compounds may still have a range of composi- tions, but it is much narrower than that for solid so- lutions. Two systems that form such intermetallic com- pounds are chromium-iron (Cr-Fe) and iron-carbon (Fe-C). Iron-carbon phase diagram Steel is an iron base al- loy containing manganese (Mn), carbon and other alloying elements. Virtually all metals used in boilers and pressure vessels are steels. Mn, usually present at about 1% in carbon steels, is a substitutional solid solutionelement.Becauseitsatomicsizeandelectronic structure are similar to those of Fe, it has little effect on the Fe lattice or phase diagram in these low con- centrations. Carbon, on the other hand, has signifi- cant effects; by varying the carbon content and heat treatment of Fe, an enormous range of mechanical properties can be obtained. These effects can best be understood using the Fe-C equilibrium phase diagram, shown in Fig. 5. This shows that the maximum solu- Fig. 3 Some important defects and defect complexes in metals (courtesy of Wiley).3
- 191. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-3 bility of carbon in α (BCC) iron is only about 0.025%, while its solubility in γ (FCC) iron is slightly above 2.0%. Alloys of Fe-C up to 2% C are malleable and are considered steels. Iron alloys containing more than 2% C are decidedly inferior to steels in malleability, strength, toughness and ductility. They are usually used in cast form and are called cast irons. Carbon atoms are substantially smaller than iron atoms, and in BCC iron, they fit at the midpoints of the cube edges and face centers. This structure is called ferrite. In FCC iron, the carbon atoms fit at the mid- points of the cube edges at the cube center. This struc- ture is called austenite. In both structures, the inter- stitial spaces are smaller than the carbon atom, lead- ing to local distortion of the lattice and resulting in limited carbon solubility in iron. The interstices are larger in austenite than in ferrite, partly accounting for the higher solubility of carbon in austenite. If aus- tenite containing more than 0.025% C cools slowly and transforms to ferrite, the carbon in excess of 0.025% precipitates from the solid solution. However, it is not precipitated as pure carbon (graphite) but as the intermetallic compound Fe3C, cementite. As with most metallic carbides, this is a hard substance. There- fore, the hardness of steel generally increases with carbon content even without heat treatment. Critical transformation temperatures The melting point of iron is reduced by the addition of carbon up to about 4.3% C.At the higher temperatures, solid and liquid coexist. The BCC δ iron range is restricted and finally eliminated as a single phase when the carbon content reaches about 0.1%. Some δ iron remains up to about 0.5% C but is in combination with other phases. Below the δ iron region, austenite exists and absorbs carbon up to the composition limits (Fig. 5), the limiting solid-solution solubility. The temperature at which only austenite exists decreases as the car- bon increases (line G-S) to the eutectoid point: 0.80% C at 1333F (723C). Then, the temperature increases along line S-E with the carbon content because the Fig. 4 The copper-nickel equilibrium diagram (courtesy of Hodder and Staughton).4 Fig. 5 Carbon-iron equilibrium diagram showing phase solubility limits.
- 192. The Babcock & Wilcox Company 7-4 Steam 41 / Metallurgy, Materials and Mechanical Properties austenite is unable to absorb additional carbon, ex- cept at higher temperatures. Any transformation in which a single solid phase decomposes into two new phases on cooling, and in which the reverse reaction takes place on heating, is called a eutectoid reaction. At the eutectoid composi- tion of 0.80% C, only austenite exists above 1333F (723C) and only ferrite and Fe3C carbide exist below that temperature. This is the lower critical transfor- mation temperature, A1. At lower carbon contents, in the hypoeutectoid region, as austenite cools and reachesA3, the upper critical transformation tempera- ture, ferrite precipitates first. As the temperature is further reduced to 1333F (723C) at A1, the remaining austenite is transformed to ferrite and carbide. In the hypereutectoid region, above 0.80% C, cementite pre- cipitates first when austenite cools to the thermal ar- rest line (Acm). Again, the remaining austenite trans- forms to ferrite and carbide when it cools to 1333F (723C). For a given steel composition, A3, A1 and Acm represent the critical transformation temperatures, or critical points. A2 is the Curie point, the temperature at which iron loses its ferromagnetism. At the A1 temperature, on cooling, all the remain- ing austenite must transform to ferrite and carbide. Because there is not time for the carbon to go very far as it is rejected from the forming ferrite matrix, the resulting structure is one of alternating thin plates, or lamellae, of ferrite and carbide. This lamellar struc- ture is typical of all eutectoid decomposition reactions. In steel, this structure is called pearlite, which always has the eutectoid composition of 0.8% C. When pearlite is held at a moderately high tempera- ture, such as 950F (510C), for a long time (years), the metastable cementite eventually decomposes to ferrite and graphite. First, the Fe3C lamellae agglomerate into spheres. The resulting structure is considered spheroidized. Later, the iron atoms are rejected from the spheres, leaving a graphitized structure. Graphi- tized structures are shown in Fig. 6. Isothermal transformation diagrams The transfor- mation lines on the equilibrium diagram, Fig. 5, are subject to displacement when the austenite is rapidly cooled or when the pearlite and ferrite, or pearlite and cementite, are rapidly heated. This has led to the re- finement of A1 and A3 into Ac1 and Ac3 on heating (c, from the French chauffage, heating) and into Ar1 and Ar3 for the displacement on cooling (r, from refroidissement, cooling). Because these are descrip- tions of dynamic effects, they distort the meaning of an equilibrium diagram which represents prevailing conditions given an infinite time for reactions to oc- cur. Because fabrication processes involve times rang- ing from seconds (laser welding) to several days (heat treatment of large vessels), the effect of time is impor- tant. Isothermal transformation experiments are used to determine phase transformation times when the steel is cooled very rapidly to a particular temperature. The data are plotted on time-temperature-transforma- tion (TTT) diagrams. The isothermal transformation diagram in Fig. 7, for a hypoeutectoid steel, shows the time required for transformation from austenite to other constituents at the various temperature levels. The steel is heated to about 1600F (871C) and it becomes completely aus- tenitic. It is then quickly transferred to and held in a furnace or bath at 700F (371C). Fig. 5 shows that ferrite and carbides should eventually exist at this temperature and Fig. 7 indicates how long this reac- tion takes. By projecting the time intervals during the transformation, as indicated in the lower portion of Fig. 7, to the top portion of the diagram, the austen- ite is predicted to exist for about three seconds before transformation. Then, at about 100 s, the transforma- tion is 50% complete. At 700 s, the austenite is entirely replaced by an agglomerate of fine carbides and ferrite. For this particular steel, at temperatures below about 600F (316C) austenite transforms to martensite, the hardest constituent of heat treated steels. The tem- perature at which martensite starts to form is denoted Ms. It decreases with increasing carbon content of the austenite. The nose of the left curve in Fig. 7, at about 900F (482C), is of prime significance because the transformation at this temperature is very rapid.Also, if this steel is to be quenched to form martensite (for maximum hardness), it must pass through about 900F (482C) very rapidly to prevent some of the austenite from transforming to pearlite (F + C), which is much softer. Martensite is therefore a supercooled metastable structure that has the same composition as the auste- nite from which it forms. It is a solution of carbon in iron, having a body-centered tetragonal (BCT) crys- tal structure. (See Reference 1.) Because martensite forms with no change of composition, diffusion is not required for the transformation to occur. It is for this reason that martensite can form at such low tempera- tures. Its hardness is due to the high, supersaturated carbon content, to the great lattice distortion caused by trapping excess carbon, and to the volume change of the transformation. The specific volume of marten- site is greater than that of the austenite. Fig. 6 Chain graphitization (black areas) in carbon-molybdenum steel, 200 X magnification.
- 193. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-5 The formation of martensite does not occur by nucleation and growth. It can not be suppressed by quenching and it is athermal.Austenite begins to form martensite at a temperature Ms. As the temperature is lowered, the relative amount of martensite in the structure increases. Eventually, a temperature (Mf) is reachedwherethetransformationtomartensiteiscom- plete.At any intermediate temperature, the amount of martensite characteristic of that temperature forms instantly and holding at that temperature results in no further transformation. The Ms and Mf temperatures, therefore, are shown on the isothermal transformation diagram (Fig. 8) as horizontal lines. Under the micro- scope, martensite has the appearance of acicular needles. Each needle is a martensite crystal. Bainite is produced when the eutectoid (0.8% C) transformation takes place at a lower temperature (but above the Ms temperature for the alloy). The tem- perature regions of the TTT curve in which pearlite, bainite and martensite form are shown in Fig. 8. In the pearlite transformation, the cementite and the ferrite form in a fine lamellar pattern of alternating layers of ferrite and cementite. EffectsofalloyingelementsontheFe-Fe3Cphasedia- gram Adding one or more elements to the Fe-C alloy can have significant effects on the relative size of the phase fields in the Fe-Fe3C phase diagram. The ele- ments Ni, Mn, Cu and cobalt (Co) are called austenite formers because their addition to the Fe-C alloy sys- tem raises the temperature at which austenite trans- forms to δ ferrite and lowers A3 in Fig. 5. Adding a sufficient amount of these elements increases the size of the austenite field and the FCC structure may be- come stable at room temperature. Because most of these elements do not form carbides, the carbon stays in solution in the austenite. Many useful material propertiesresult,includinghighstability,strengthand ductility, even at high temperatures. The elements Cr, molybdenum (Mo), tungsten (W), vanadium (V), alu- minum (Al) and silicon (Si) have the opposite effect and are considered ferrite formers. They raise the A3 temperature and some of them form very stable car- bides, promoting the stability of BCC ferrite, even at very high temperatures. Specific effect of alloying elements Steel alloys are the chief structural materials of modern engineering because their wide range in prop- erties suits so many applications. These properties are affected directly not only by the characteristics and the amounts of the elements which, either alone or in combination, enter into the composition of the steel, but also by their reaction as constituents under vari- ous conditions of temperature and time during fabri- cation and use. For example, Cr increases resistance to corrosion and scaling, Mo increases creep strength at elevated temperatures, and Ni (in adequate amounts) renders the steel austenitic. The specific effects of the most important elements found in steel are as follows. Carbon (C) is the most important alloying element in steel. In general, an increase in carbon content pro- duces higher ultimate strength and hardness but low- ers the ductility and toughness of steel alloys. The curves in Fig. 9 indicate the general effect of carbon on the mechanical properties of hot rolled carbon steel. Carbon also increases air hardening tendencies and Fig. 8 Time-temperature-transformation curves for a 0.8% plain carbon steel.4 Fig. 7 Typical isothermal transformation diagram. Time required in a specific steel at 700F (371C) taken as an example.
- 194. The Babcock & Wilcox Company 7-6 Steam 41 / Metallurgy, Materials and Mechanical Properties weld hardness, especially in the presence of Cr. In low alloy steel for high temperature applications, the car- bon content is usually restricted to a maximum of about 0.15% to ensure optimum ductility for welding, expanding and bending operations, but it should be no lower than 0.07% for optimum creep strength. To minimize intergranular corrosion caused by carbide precipitation, the carbon content of austenitic stain- lesssteelalloysislimitedto0.10%.Thismaximummay be reduced to 0.03% in extremely low carbon grades used in certain corrosion resistant applications. How- ever, at least 0.04% C is required for acceptable creep strength. In plain, normalized carbon steels, the creep resistance at temperatures below 825F (441C) in- creases with carbon content up to 0.4% C; at higher temperatures, there is little variation of creep proper- ties with carbon content. An increase in carbon con- tent also lessens the thermal and electrical conductivi- ties of steel and increases its hardness on quenching. Manganese (Mn) is infinitely soluble in austenite and up to about 10% soluble in ferrite. It combines with residual sulfur while the steel is molten to form manganese sulfides, which have a much higher melt- ing point than iron sulfides. Without the Mn, iron sul- fides, which melt at about 1800F (982C), would form. This would lead to hot-shortness, a brittle-failure mechanism, during hot forming operations. The Mn therefore produces the malleability that differentiates steel from cast iron. Mn is a good solid solution strengthener, better than Ni and about as good as Cr. In alloy steels, manga- nese decreases the critical cooling rate to cause mar- tensitic structure and thus contributes to deep hard- ening. It can also be used in austenitic stainless steels to replace Ni as the austenite stabilizer at lower cost.5 Molybdenum (Mo), when added to steel, increases its strength, elastic limit, resistance to wear, impact qualities and hardenability. Mo contributes to high temperature strength and permits heating steel to a red hot condition without loss of hardness. It also in- creases the resistance to softening on tempering and restrainsgraingrowth.Momakeschromiumsteelsless susceptible to temper embrittlement and it is the most effective single additive that increases high tempera- ture creep strength. An important use of Mo is for corrosion resistance improvement in austenitic stainless steels. It enhances the inherent corrosion resistance of these steels in reducing chemical media and it increases their pas- sivity under mildly oxidizing conditions. Under cer- tain conditions, molybdenum reduces the susceptibil- ity of stainless steels to pitting. Chromium (Cr) is the essential constituent of stain- lesssteel.Whileotherelementsarestrongeroxideform- ers, Cr is the only one that is highly soluble in iron (about 20% in austenite and infinite in ferrite) and forms a stable, tightly adherent oxide. It is virtually irreplace- able in resisting oxidation at elevated temperatures. Cr raises the yield and ultimate strength, hardness, and toughness of ferritic steel at room temperature. It also contributes to high temperature strength. The optimum chromium content for creep strength in an- nealed low alloy steels is about 2.25%. A steady improvement in resistance to atmospheric corrosion and to attack by many reagents is also noted when the chromium content is increased. A steel with 12% or more Cr is considered stainless, i.e., the Cr2O3 film is sufficient to prevent surface rust (hydrated iron oxide) formation. The chemical properties of the steel, however, are affected by the carbon content. Higher chromium and lower carbon levels generally promote increased corrosion resistance. Adding more than 1% of chromium may cause ap- preciable air hardening in the steel. Up to about 13.5% Cr, air hardening is a direct function of chromium and carbon content. Low carbon alloy steels containing more than 12% Cr can become nonhardening, but the impact strength is reduced and the ductility is poor. Cr lessens thermal and electrical conductivities. The ad- dition of sufficient Cr prevents graphitization during long-term high temperature service of ferritic steels. Nickel (Ni) increases toughness when added to steel, particularly in amounts over 1%. Improved re- sistance to corrosion by some media is attained with Ni contents over 5%. Ni dissolves in the iron matrix in all proportions and, therefore, raises the ultimate strength without impairing the ductility of the steel. Ni is particularly effective in improving impact prop- erties, especially at low temperature. The most important use of nickel as an alloying el- ement in steel is its combination with chromium in amounts of 8% Ni or more. Ni is such a strong auste- nite former that the high chromium Fe-Ni-C alloys are austenitic at room temperature. The various combi- nations of chromium and nickel in iron produce alloy properties that can not be obtained with equivalent amounts of a single element. Common combinations are 18% Cr - 8% Ni, 25% Cr - 12% Ni, 25% Cr - 20% Ni, and 20% Cr - 30% Ni. These steels are resistant to atmospheric corrosion and to oxidation at high tem- peratures. In addition, they offer greatly enhanced creep strength. Ni is only slightly beneficial to creep properties of Fig. 9 General effect of carbon on the mechanical properties of hot- rolled carbon steel.
- 195. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-7 low alloy ferritic steels. It reduces the coefficient of thermal expansion and diminishes the electrical and thermal conductivities. It is attacked by sulfur com- pounds at elevated temperatures. Cobalt(Co) suppresses hardenability in steels. How- ever, when added to austenite, it is a strong solution strengthener and a carbide former. It also significantly improves creep strength. Binary Fe-Co alloys have the highest magnetic saturation induction of any known materials. Therefore, such alloys are often used in permanent magnets. Tungsten (W) acts similarly to molybdenum. It is a very strong carbide former and solid solution strengthener. It forms hard, abrasion resisting car- bides in tool steels, develops high temperature hard- ness in quenched and tempered steels, and contrib- utes to creep strength in some high temperature alloys.5 Vanadium (V) is a degasifying and deoxidizing agent, but it is seldom used in that capacity because of high cost. It is applied chiefly as an alloying ele- ment in steel to increase strength, toughness and hardness. It is essentially a carbide forming element which stabilizes the structure, especially at high tem- peratures. Vanadium minimizes grain growth tenden- cies,therebypermittingmuchhigherheattreatingtem- peratures. It also intensifies the properties of other ele- ments in alloy steels. Small additions of vanadium (0.1 to 0.5%), accompanied by proper heat treatment, give steels containing 0.5 to 1.0% molybdenum pronounced improvement in high temperature creep properties. Titanium (Ti) and columbium (Cb) (also known as niobium) are the most potent carbide forming ele- ments. Ti is also a good deoxidizer and denitrider. These elements are most effective in the Cr-Ni auste- nitic alloys, where they react more readily with car- bon than does Cr. This allows the Cr to remain in solid solution and in the concentrations necessary to main- tain corrosion resistance. Ti and Cb [or Cb plus tan- talum (Ta)] are used to reduce air hardening tenden- cies and to increase oxidation resistance in steel containing up to 14% Cr. These elements have a ben- eficial effect on the long term, high temperature proper- ties of Cr-Ni stainless steels because of the stability of theircarbides,nitridesandcarbonitrides.CbandTihave also been used in some of the super alloys to improve high temperature properties. Ti forms an intermetallic compound with Ni in these alloys, Ni3Ti, called gamma prime ′( )γ , which is a potent strengthening phase. Copper (Cu), when added to steel in small amounts, improves its resistance to atmospheric corrosion and lowers the attack rate in reducing acids. Cu, like Ni, is not resistant to sulfur compounds at elevated tem- peratures. Consequently, it is not ordinarily used in low alloy steels intended for high temperature service where sulfur is a major component of the environ- ment, as in combustion gases. Cu is added (up to 1%) in low alloy constructional steels to improve yield strength and resistance to atmospheric corrosion. Its presence in some of the high alloy steels increases corrosion resistance to sulfuric acid. Boron (B) is usually added to steel to improve hardenability, that is, to increase the depth of hard- ening during quenching of alloy steels. When com- bined with Mo, it is a strong bainite stabilizer. Small amounts of boron in the presence of Mo suppress the formation of martensite, leading to the complete trans- formation to bainite before the Ms temperature is reached. This substantially improves the strength and stability of Cr-Mo pressure vessel steels. The B-10 iso- tope of boron has a very high neutron-capture cross- section,soitisaddedtosteelsusedforcontainmentand storage vessels of nuclear fuels and waste products. Nitrogen (N) has two primary functions as an al- loying agent in steels. In carbon and low alloy steels, it is used in case hardening, in which nascent nitro- gen is diffused into the steel surface. Nitrogen and car- bon are interstitial solid solution strengtheners. In the presence of Al or Ti, additional strengthening results by precipitate formations of the respective nitrides or carbonitrides. In austenitic stainless steels, nitrogen provides the same interstitial strengthening as car- bon, but does not deplete the austenite of chromium as does carbon by the formation of carbides. The strength of nitrogen-containing stainless steels is therefore equivalent to that of the carbon-containing stainlesses. This strength is achieved without the sus- ceptibility to corrosive attack that results from local carbide formation at grain boundaries of these steels. Oxygen (O) is not normally considered to be an al- loying element. It is present in steel as a residual of the steel making process.6,7 However, a few oxides are so hard and stable, notably those ofAl, Ti and thorium (Th),thattheyarepotentstrengthenerswhendispersed as fine particles throughout an alloy. This can be accom- plished by internal oxidation in an oxygen-containing atmosphere or by powder metallurgical techniques. Aluminum (Al) is an important minor constituent of low alloy steels. It is an efficient deoxidizer and grain refiner, and is widely used in producing killed steel. When added to steel in appreciable quantities, Al forms tightly adhering refractory oxide scales and therefore, increases resistance to scaling. It is difficult, however, to add appreciable amounts of this element without producing undesirable effects. In the amounts customarily added (0.015 to 0.080%), Al does not in- crease resistance to ordinary forms of corrosion. Be- cause of their affinity for oxygen, high-aluminum steels generally contain numerous alumina inclusions which can promote pitting corrosion. The refined grain size does improve room temperature toughness and ductility of carbon steels. An excessive quantity of aluminum has a detrimen- tal effect on creep properties, particularly in plain carbon steel. This is attributable to its grain refining effect and to its acceleration of graphitization of the carbide phase. Silicon (Si) greatly contributes to steel quality be- cause of its deoxidizing and degasifying properties. When added in amounts up to 2.5%, the ultimate strength of steel is increased without loss in ductility. Si in excess of 2.5% causes brittleness and amounts higher than 5% make the steel nonmalleable. Resistance to oxidation of steel is increased by add- ing silicon. Si increases the electrical conductivity of steel and decreases hysteresis losses. Si steels are, therefore, widely used in electrical apparatus.
- 196. The Babcock & Wilcox Company 7-8 Steam 41 / Metallurgy, Materials and Mechanical Properties Killing agents, such as Si and Al, are added to steel for deoxidation; the latter is used for grain size con- trol. Calcium and rare earth metals, when added to the melt, have the same effects. Additionally, these elements form complex oxides or oxysulfides and can significantly improve formability by controlling the sulfide shape. Phosphorus (P) is a surprisingly effective hardener when dissolved in quantities of up to 0.20%.5 However, a high phosphorus content can notably decrease the resistance of carbon steel to brittle fracture and reduce ductilitywhenthemetaliscoldworked.Thisembrittling effect is referred to as cold-shortness. The detrimental effect of phosphorus increases with carbon content. Phosphorus is effective in improving the machin- ability of free-cutting steels. This is related to its embrittling effect, which permits easier chip formation on machining. In alloy steels intended for boiler ap- plications, the permissible phosphorus content is less than that for machining steels and its presence is ob- jectionable for welding. Phosphorus is used as an al- loying element (up to 0.15%) in proprietary low alloy, high strength steels, where increased yield strength and atmospheric corrosion resistance are primary re- quirements. In the presence of certain acids, however, a highphosphoruscontentmayincreasethecorrosionrate. Sulfur (S) is generally undesirable in steel and many processes have been developed to minimize its presence. However, sulfur is sometimes added to steel to improve its machinability, as are phosphorus and other free-machining additives: calcium, lead, bis- muth, selenium and tellurium. Several of these ele- ments are virtually insoluble in steel and have low melting points, or they form low melting temperature compounds. These compounds can lead to cracking due to liquid metal embrittlement or hot-shortness at evenmoderatelyelevatedtemperatures.Hot-shortness occurs when liquid iron sulfide forms at grain bound- aries during hot-working and heat treatment of steels.6 Because the fastener industry favors free machining steels due to their beneficial production effects, boiler and pressure vessel manufacturers must exercise care in applying threaded fasteners containing these ele- ments at high temperatures. Heat treating practices Steel can be altered by modifying its microstructure through heat treatment. Various heat treatments may be used to meet hardness or ductility requirements, improve machinability, refine grain structure, remove internal stresses, or obtain high strength levels or impact properties. The more common heat treatments, annealing, normalizing, spheroidizing, hardening (quenching) and tempering, are briefly described. Annealing is a general term applied to several dis- tinctly different methods of heat treatment. These are full, solution, stabilization, intercritical, isothermal, and process annealing. Full annealing is done by heating a ferritic steel above the upper critical transformation temperature (A3 in Fig. 5), holding it there long enough to fully transform the steel to austenite, and then cooling it at a controlled rate in the furnace to below 600F (316C). A full anneal refines grain structure and pro- vides a relatively soft, ductile material that is free of internal stresses. Solution annealing is done by heating an austen- itic stainless steel to a temperature that puts most of the carbides into solution. The steel is held at this tem- perature long enough to achieve grain growth. It is then quenched in water or another liquid for fast cool- ing, which prevents most of the carbides from reprecipitating. This process achieves optimum creep strength and corrosion resistance. For many boiler applications,austeniticstainlesssteelsrequirethehigh creep strength of a coarse grain structure but do not require aqueous corrosion resistance, because they are only exposed to dry steam and flue gases. Solution treatment,usedtoachievegraingrowth,isrequiredforthese applications, but the quenching step is not required. Stabilization annealing is performed on austenitic stainless steels used in severe aqueous corrosion en- vironments. The steel is first solution annealed, then reheated to about 1600F (871C) and held there. Ini- tially, chromium carbides precipitate at the grain boundaries in the steel. Because these are mostly of the complex M23C6 type, which are very high in Cr, the austenite adjacent to the grain boundaries is depleted of chromium. This would normally leave the steel sus- ceptibletocorrosiveattack,butholdingitat1600F(871C) permitstheCrremainingintheaustenitesolutiontore- distribute within the grains, restoring corrosion resis- tance, even adjacent to the grain boundaries. Intercritical annealing and isothermal annealing are similar. They involve heating a hypoeutectoid fer- ritic steel above the lower critical transformation tem- perature (A1 in Fig. 5) but below the upper critical temperature,A3.Thisdissolvesalltheironcarbidesbut does not transform all the ferrite to austenite. Cool- ing slowly from this temperature throughA1 produces a structure of ferrite and pearlite that is free of inter- nal stresses. In intercritical annealing, the steel con- tinues to cool slowly in the furnace, similarly to full annealing. In isothermal annealing, cooling is stopped just below A1, assuring complete transformation to ferrite and pearlite, and eliminating the potential for bainite formation. Process annealing, sometimes called subcritical an- nealing or stress relieving, is performed at tempera- tures just below the lower critical temperatureA1, usu- ally between 950 and 1300F (510 and 704C). Process annealing neither refines grains nor redissolves ce- mentite, but it improves the ductility and decreases residual stresses in work hardened steel. Normalizing is a variation of full annealing. Once it has been heated above the upper critical tempera- ture, normalized steel is cooled in air rather than in a controlled furnace atmosphere. Normalizing is some- times used as a homogenization procedure; it assures that any prior fabrication or heat treatment history of the material is eliminated. Normalizing relieves the internal stressescausedbypreviousworkingand,while itproducessufficientsoftnessandductilityformanypur- poses, it leaves the steel harder and with higher tensile strengththanfullannealing.Toremovecoolingstresses, normalizing is often followed by tempering.
- 197. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-9 Spheroidizing is a type of subcritical annealing used to soften the steel and to improve its machinability. Heating fine pearlite just below the lower critical tem- perature of the steel, followed by very slow cooling, causes spheroidization. Hardening (quenching) occurs when steels of the higher carbon grades are heated to produce austen- ite and then cooled rapidly (quenched) in a liquid such as water or oil. Upon hardening, the austenite trans- forms into martensite. Martensite is formed at tem- peratures below about 400F (204C), depending on the carbon content and the type and amount of alloying elements in the steel. It is the hardest form of heat treated steels and has high strength and abrasion resistance. Tempering is applied after normalizing or quench- ingsomeairhardeningsteels.Thesepreliminarytreat- ments impart a degree of hardness to the steel but also make it brittle. The object of tempering, a secondary treatment, is to remove some of that brittleness by allowing certain transformations to proceed in the hardened steel. It involves heating to a predetermined point below the lower critical temperature, A1, and is followed by any desired rate of cooling. Some hard- ness is lost by tempering, but toughness is increased, and stresses induced by quenching are reduced or eliminated. Higher tempering temperatures promote softer and tougher steels. Some steels may become embrittled on slow cooling from certain tempering tem- peratures. These steels are said to be temper brittle. To overcome this difficulty, they are quenched from the tempering temperature. Post fabrication heat treatments are often applied to restore more stable, stress free conditions. These in- clude post weld and post forming heat treatments and solution treatment. Fabrication processes Any mechanical work applied to the metal below its recrystallization temperature is cold work. Mechani- cal work performed above the recrystallization tem- perature is hot work and the simultaneous annealing that occurs at that temperature retards work-harden- ing. The recrystallization temperature is dependent on the amount of deformation. If a material is formed at a temperaturesignificantlyaboveroomtemperature,but below its recrystallization temperature, the process is sometimes referred to as warm working. The temperature at which steel is mechanically worked has a profound effect on its properties. Cold workincreasesthehardness,tensilestrengthandyield strength of steel, but its indices of ductility – elonga- tion and reduction of area – are decreased. The ex- tent of the work-hardening, with progressive elonga- tion of the grains in the direction of working, depends on the amount of cold work and on the material. If the work-hardening caused by the necessary shaping operation becomes excessive, the ductility may be ex- hausted and further work can cause fracture. Hot working variations include forging, rolling, pressing, extruding, piercing, upsetting and bending. Most of these are largely compressive operations, in which the metal is squeezed into a desired shape. They introduce some degree of orientation to the internal structure. Even if the metal experiences phase trans- formations or other recrystallization processes, some degree of orientation is maintained in the pattern re- tained by the oxides, sulfides, and other inclusions that do not dissolve during hot working or heat treat- ment. Depending on the application, the resultant orientation may have no effect, be useful, or be harm- ful. Rolled plates, for instance, often have inferior properties in the through-thickness direction due to retention of mid-plane segregated inclusions and to the predominant grain orientation in the longitudinal and transverse directions. This can result in a failure mode known as lamellar tearing if not addressed. Hot rolling of carbon steel and low alloy steel into drum or pressure vessel sections is often done at tem- peratures above A3. Temperatures and times of heat- ing before forming need to be controlled to ensure that the resulting product retains the desired fine grain size and consequent good toughness, and to ensure that excessive plate surface oxidation does not occur. Cold working operations used in manufacturing boiler components are rolling, forging, bending and swaging. Detailed information about these processes and their effects on materials can be found elsewhere. (See References 6 and 7.) Cold rolling of plate to make shells for drums is lim- ited only by the capacity and diameter of available rolling equipment and the inherent ductility of the steel. This process is most often applied to carbon steel, and any post forming heat treatment performed is usually combined with post weld heat treatment of the completed drum. In some low pressure applications, tube-to-header or tube-to-drum connections may be made by roll expanding the tube into an internally grooved socket in the shell. The strength of the con- nection depends on the mechanical interference be- tween the roll expanded tube, which generally de- forms plastically, and the hole in the shell, which mostly deforms elastically. Cold forging of boiler components is usually lim- ited to final size forming of shells. Threaded fasten- ers used in boilers may have been cold headed or may have had their threads cold rolled. Effects of such forming operations are normally mitigated by heat treatments required by the specification, but occasion- ally this heat treatment does not eliminate microstruc- tural differences between the cold formed portion and the remainder of the part. This is particularly true of austenitic stainless steel or nickel alloy bolts, which do not transform during heat treatment. These bolts may be susceptible to cracking at the interface between the cold formed head and the shank in certain aque- ous environments. Cold bending is performed on many configurations of tubes and pipes for boilers. Boiler designers consider the effects of this process on the geometry and prop- erties of the finished product. Austenitic stainless steels and nickel alloys used in high pressure boilers are often exposed to tempera- tures at which the strain energy of the cold bending is sufficient to cause polygonization and recrystalli- zation to a fine grain size during service. The service
- 198. The Babcock & Wilcox Company 7-10 Steam 41 / Metallurgy, Materials and Mechanical Properties temperature is insufficient to produce grain growth and the fine grain size material has lower high tem- perature (creep) strength. To prevent this from hap- pening, cold bends in these alloys are given a high temperature (solution) heat treatment to stabilize the coarse grain structure. Mostcarbonandlowalloyferriticsteeltubeandpipe alloys may be used in the cold bent condition, unless theamountofcoldstrainimpartedisveryhigh.Ifstrain in excess of about 30% is developed in bending, the re- sulting structure and low residual ductility can render the bends susceptible to strain aging and breakage during subsequent handling and service. Cold working of carbon steels has also been shown to render them susceptible to creep crack growth of minor surface flaws and imperfections when these steels are operating at temperatures where the crack- ing mechanism is operative. Certain Cr-Mo high strength ferritic steels can also experience significant degradation of creep strength if they are cold worked to levels near and above about 20% strain. In all of these cases, post fabrication heat treatments must be applied to recover acceptable prop- erties. This most often requires re-annealing, normal- ization, or normalizing and tempering as is appropri- ate for the given alloy. In some cases, simple subcriti- cal tempering or stress relief heat treatment may be sufficient. Welding Joining of boiler pressure parts and of nonpressure parts to pressure parts is almost always accomplished by welding. This is particularly true of high tempera- ture, high pressure boilers, whose service conditions are too severe for most mechanical joints (bolted flanges with gaskets) and brazed joints. Welding is the joining of two or more pieces of metal by applying heat or pressure, or both, with or with- out the addition of filler metal, to produce a localized union through fusion across the interface.8 There are many welding processes, but the most widely used for joining pressure parts is fusion welding with the ad- dition of filler metal, using little or no pressure. Fig. 10 indicates the variety of processes. Weld morphology Because of the heat distribution characteristics of the welding process, the weld joint is usually a chemically and mechanically heteroge- neous composite consisting of up to six metallurgically distinct regions: a composite zone, the unmixed zone, the weld interface, the partially melted zone, the heat- affected zone (HAZ) and the unaffected base metal. These zones are shown in Fig. 11. The composite zone is the completely melted mixture of filler metal and melted base metal. The narrow region surrounding the composite zone is the unmixed zone, which is a bound- ary layer of melted base metal that solidifies before mixing in the composite zone. This layer is at the edges of the weld pool, with a composition essentially iden- tical to the base metal. The composite zone and the unmixed zone together make up what is commonly referred to as the fusion zone. The third region is the weld interface, or the boundary between the unmelted base metal on one side and the solidified weld metal on the other. The partially melted zone occurs in the base metal immediately adjacent to the weld interface, where some localized melting of lower melting tem- perature constituents, inclusions or impurities may have occurred. Liquation, for instance, of manganese sulfide inclusions can result in hot cracking or microfissuring. The heat-affected zone is that portion of the base material in the weld joint that has been subjected to peak temperatures high enough to pro- duce solid state microstructural changes, but not high Fig. 10 Classification of welding processes.4 Welding Processes Fusion Pressure Gas Welding Arc Welding Thermit Process Smith Friction Cold Resistance Welding Electron Beam Spot Seam Butt Flash Laser Beam Energy Beam Oxyacetylene Brazing Metallic Arc Submerged Arc Gas Shielded Electro- slag Shielded Metal Arc Flux Cored Arc Gas Metal Arc Gas Tungsten Arc
- 199. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-11 enough to cause melting. Finally, the last part of the work piece that has not undergone a metallurgical change is the unaffected base metal. Weld quality issues The general subject of welding and weldability is a very broad subject, addressed by a large number of excellent references.10,10a The following addresses only a few issues that are particularly unique and impor- tant to boilers and pressure vessels. Ferrite content Austenitic stainless steel weld met- als are susceptible to hot cracking or microfissuring as they cool from the solidus to about 1800F (982C). The microfissuring can be minimized by providing a small percentage of ferrite in the as-deposited welds. Graphitization The shrinkage of the weld on freez- ing results in plastic deformation and high residual stresses in the weld joint. In carbon and carbon-mo- lybdenum steels containing no stronger carbide-form- ing elements, the areas of localized strain adjacent to the heat-affected weld zones provide sites where the volume increase of the cementite to graphite decom- position can be more readily accommodated. At about 900F (482C), graphite nodules can precipitate on these planes of deformation. When samples of such materi- als are viewed in cross-section, the nodules appear to be arranged in rows or chains, and this condition has been termed chain graphitization (Fig. 6). The inter- facial bond between the graphite and the ferrite ma- trix in such weldments is very low, much lower than that between ferrite and pearlite or ferrite and cement- ite. In the early 1950s, several failures of carbon- molybdenum main steam piping weldments occurred due to this phenomenon. The ruptures occurred with little warning because they were not preceded by swelling of the joints and, as a result, significant dam- age resulted. In consequence, the use of carbon-mo- lybdenum main steam piping has been essentially eliminated and the maximum use temperature of car- bon steel piping has been significantly restricted. Post weld heat treatment When cooling is com- plete, the welded joint contains residual stresses com- parable to the yield strength of the base metal at its final temperature. The thermal relief of residual stresses by post weld heat treatment (PWHT) is ac- complished by heating the welded structure to a tem- perature high enough to reduce the yield strength of the steel to a fraction of its magnitude at ambient tem- perature. Because the steel can no longer sustain the residual stress level, it undergoes plastic deformation until the stresses are reduced to the at-temperature yield strength. Fig. 12 shows the effect of stress relief on several steels. The temperature reached during the treatment has a far greater effect in relieving stresses than the length of time the weldment is held at tem- perature. The closer the temperature is to the critical or recrystallization temperature, the more effective it is in removing residual stresses, provided the proper heating and cooling cycles are used.10 Lamellar tearing Weld defect causes and inspec- tion procedures are covered more extensively in Ref- erences 9 and 11. However, one metallurgical effect of residual stresses should be mentioned in the con- text of boilers and pressure vessels: lamellar tearing. Lamellar tearing may result when an attachment is welded to a plate in the T-shaped orientation shown in Fig. 13, particularly if the plate contains shrink- age voids, inclusions, or other internal segregation parallel to the plate surface. In such an instance, the residual shrinkage stresses may be sufficient to open a tear or tears parallel to the plate surface to which the T-portion is welded. Joining dissimilar metals It may be necessary to join austenitic and ferritic steels. Weld failures have oc- curred in these welds since the introduction of auste- nitic stainless steel superheater tubing materials. Nickel base filler metals have long been used to miti- gate these problems, but these do not offer a perma- nent solution.Additional system stresses from compo- nent location, system expansion and bending can in- crease the potential for such failures. Fig. 11 Metallurgical zones developed in a typical weld (courtesy of ASM).9 Fig. 12 Effect of temperature and time on stress relief in carbon steel (upper graph) and steels with varying as-welded strengths (courtesy of AWS).11
- 200. The Babcock & Wilcox Company 7-12 Steam 41 / Metallurgy, Materials and Mechanical Properties Research is continuing toward the development of filler metals less likely to permit failures but none has become commercially available. The best alternative is toavoiddissimilarmetalweldsbyusinghigherstrength ferriticalloymaterials,suchasmodified9Cr-1Mo-Vtub- ing and piping, when design conditions permit. Materials Almost all of the materials used in constructing boilers and pressure vessels are steels and the vast majority of components are made of carbon steels. Carbon steels are used for most types of pressure and nonpressure parts: drums, headers, piping, tubes, structural steel, flues and ducts, and lagging. Carbon steels may be defined by the amount of car- bon retained in the steel or by the steelmaking prac- tice. These steels are commonly divided into four classes by carbon content: low carbon, 0.15% C maxi- mum; medium-low carbon, between 0.15 and 0.23% C; medium-high carbon, between 0.23 and 0.44% C; and high carbon, more than 0.44% C. However, from a design viewpoint, high carbon steels are those over 0.35%, because these can not be used as welded pres- sure parts. Low carbon steels see extensive use as pres- sure parts, particularly in low pressure applications where strength is not a significant design issue. For most structural applications and the majority of pres- sureparts,mediumcarbonsteels,withcarboncontents between 0.20 and 0.35%, predominate. Carbon steels are also referred to as killed, semi- killed, rimmed and capped, depending on how the carbon-oxygen reaction of the steel refining process was treated. During the steelmaking process, oxygen, introduced to refine the steel, combines with carbon to form carbon monoxide or carbon dioxide, and also exists as excess oxygen. If the oxygen introduced is not removed or combined prior to or during casting by the addition of Si,Al, or some other deoxidizing agent, the gaseous products are trapped during solidification of the metal in the mold. The amount of gas evolved during solidification determines the type of steel and the amount of carbon left in the steel. If no gas is evolved and the liquid lies quietly in the mold, it is known as killed steel. With increasing degrees of gas evolution, the products are known as semi-killed and rimmed steels. Virtually all steels used in boilers to- day are fully killed. Microalloyed steels are carbon steels to which small amounts (typically less than 1%) of alloying elements have been added to achieve higher strength. Common additions are vanadium and boron. Such steels are seldom used in pressure part applications, but they are gaining acceptance as structural steels. Residual elements are present in steels in small amounts and are elements other than those deliber- ately added as alloying or killing agents during the steelmaking process. Their source is the scrap or pig iron used in the furnace charge. Cu, Ni, Cr, V and B are typical examples of residuals often found in car- bon steels. S and P, also considered to be residual ele- ments, usually are reported in chemical analyses of steels, and their concentrations are limited by specifi- cation because they degrade ductility. The residual elements S, P, Sb and tin (Sn) are also important con- tributors to temper embrittlement in steels. Historically,residualelementsotherthanSandPwere neitherlimitednorreported.Thispracticeischanging,how- ever, and several residuals have established limits. Low and medium alloy steels are the next most im- portant category of steels used in boilers. These are characterizedbyCrcontentslessthan11.5%andlesser amounts of other elements. The most common alloy combinations in this group encountered in boilers are: C-1/2Mo, 1/2Cr-1/2Mo, 1Cr-1/2Mo, 1-1/4Cr-1/2Mo-Si, 2-1/4Cr-1Mo, and 9Cr-1Mo-V. Other less common al- loysinthisgroupare3Cr-1Mo,5Cr-1/2Moand9Cr-1Mo. Because of the exceptional strength-enhancing ca- pability of Mo in carbon steel, it is not surprising that C-1/2Mo steel has many applications for pressure parts, particularly in the temperature range of about 700 to 975F (371 to 524C). C-Mo steels, however, are particularly prone to graphitization at temperatures above about 875F (468C). Inside the boiler, where graphitization failures do not present a safety hazard, C-Mo tubing has many uses up to 975F (524C), its oxidation limit. Because Al content promotes graphi- tization, C-Mo steel is usually Si-killed and it has a coarse grain structure as a consequence. Therefore, C-Mo components are somewhat prone to brittle fail- ures at low temperatures. This is not a problem in service, because the design application range of this alloy is at high temperature. The oxidation resistance of low alloy steels increases with Cr content. The first common alloy in the Cr-Mo family is 1/2Cr-1/2Mo. This steel was developed in response to the graphitization failures of C-Mo pip- ing. It was found that the addition of about 0.25% Cr was sufficient to make the alloy immune to graphiti- zation. Furthermore, 1/2Cr-1/2Mo has essentially the same strength as C-Mo and has therefore displaced it in many applications. Because the application of 1/2Cr- 1/2Moisvirtuallyuniquetotheboilerindustry,itisless readily available in certain sizes and product forms. Fig. 13 Lamellar tearing.
- 201. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-13 The next alloys in this series are the nearly identi- cal 1Cr-1/2Mo and 1-1/4Cr-1/2Mo-Si; the Si-contain- ing version is slightly more oxidation resistant. How- ever, extensive analyses of the databases indicate that the 1Cr-1/2Mo version is stronger over the tempera- ture range of 800 to 1050F (427 to 566C). As a result, this alloy is rapidly displacing 1-1/4Cr-1/2Mo-Si in most applications in this temperature regime. Absent the addition of other alloying elements, the 2-1/4Cr-1Mo composition is the optimum alloy for high temperature strength. Where the need for strength at temperatures between 975 and 1115F (524 and 602C) is the dominant design requirement, 2-1/4Cr- 1Mo is the industry workhorse alloy. The 3Cr through 9Cr alloys are less strong, but they have application where improved oxidation resistance is desired and lower strength can be tolerated. The increasing air- hardenability of these alloys with increasing Cr con- tent makes fabrication processes more complex and their use is somewhat more costly as a result. Mn-Mo and Mn-Mo-Ni alloys have limited use in fossil-fueled boilers. Their slightly higher strength compared to carbon steels promotes their application in very large components, where the strength to weight ratio is an important consideration. Their gen- erally superior toughness has made them a popular choice for nuclear pressure vessels. The heat treatable low alloy steels, typified by the AISI-SAE 4340 grade (nominally 0.40C-0.80Cr-1.8Ni- 0.25Mo), are used for relatively low temperature struc- tural applications in boilers and nuclear pressure ves- sels. The instability of their microstructures and there- fore, of their strength, with long exposure at elevated temperatures,haseliminatedthemfromconsideration for boiler pressure parts. Higher Cr-Mo alloys Because of their tendency to- ward embrittlement, the martensitic 9Cr-1Mo and 12Cr-1Mo steels have not been widely used for pres- sure vessel and piping applications in North America prior to the 1980s. However, in the early 1970s, the United States (U.S.) Department of Energy (DOE) sponsored research to develop a 9Cr-1Mo steel with improved strength, toughness and weldability12 for tubing in steam generators for liquid metal fast breeder nuclear reactors.13 The alloy is 9Cr-1Mo-V, commonly called Grade 91. It has exceptional strength, toughness and stability at temperatures up to 1150F (621C). Because it is nearly twice as strong as 2-1/4Cr- 1Mo at 1000F (538C), it is displacing that alloy in high pressure header applications. The resultant thinner vessels have significantly reduced thermal stresses and associated creep-fatigue failures compared to 2- 1/4Cr-1Mo and 1-1/4Cr-1/2Mo-Si headers.14,15 Because Grade 91 is stronger than austenitic stainless steel up to about 1125F (607C), it is also displacing that alloy class in high pressure tubing applications. It has the added advantage of being a ferritic alloy, eliminating the need for many dissimilar metal welds between pressure parts. The Grade 91 gains its strength, tough- ness, and stability from its alloy additions and features the fully bainitic microstructure resulting from care- ful normalizing and tempering. While not popular in North America because of the care necessary in handling very air-hardenable alloys during fabrication, the 12Cr-Mo and 12Cr-Mo-V al- loys have had wide use in the European boiler indus- try. In addition, the experience being gained with Grade 91 may eventually enhance the acceptance of the 12Cr group. Austenitic stainless steel Every attempt is made to minimize the use of stainless steels in boilers because of their high cost, but the combination of strength and corrosion resistance they provide makes them the fa- vored choices in certain applications. They are virtu- ally the only choices for service above 1150F (621C). At lower temperatures, down to about 1050F (566C), they often displace the Cr-Mo ferritic steels, where the lower pressure drop afforded by the thinner stainless steel component wall is important. The common alloys of stainless steels used in boiler pressure parts are 18Cr-8Ni, 18Cr-8Ni-Ti, 18Cr-8Ni- Cb, 16Cr-12Ni-2Mo, 25Cr-12Ni, 25Cr-20Ni, and 20Cr- 30Ni. The last alloy in this group is technically a non- ferrous alloy, because it has less than 50% Fe when its other minor alloying constituents are considered. However, because it is so similar to the other austen- itic stainless steels, it may be considered one of them. These alloys are commonly designated the 300 series: 304, 321, 347, 316, 309 and 310 stainless steels, re- spectively. The 20Cr-30Ni alloy is commonly known as Alloy 800. Because the strength of these materials at high temperature is dependent on a moderate car- bon content and usually on a coarse grain size, mate- rials with those qualities are often specified for high temperature service. They carry the added designa- tion of the letter H, e.g., 304H or 800H. Of these alloys, 304H is the most commonly used. It provides an excellent balance of strength and oxi- dation resistance at the lowest cost of any alloy in this group. However, if severe aqueous corrosive conditions may exist either before or during service, especially in solutions containing halogens, other stainless steel alloys should be substituted. The 304H alloy is sus- ceptible to sensitization at grain boundaries and, thus, may suffer stress corrosion cracking or intergranular attack in that environment. In these cases, a stabi- lized stainless steel composition such as 347H should be used. Further details on how theAmerican Society of Mechanical Engineers (ASME) Code establishes allowable design stresses for materials can be found in the Appendix to ASME Section II, Part D. All of the 300 series alloys are susceptible to sigma phase formation after long exposure at temperatures of 1050 to 1700F (566 to 927C). Those with some ini- tial ferrite, such as 309, can form the sigma phase earlier, but all eventually do so. This phase formation decreases toughness and ductility but has no effect on strength or corrosion resistance. It has been a prob- lem in heavy-section piping components made of 316 stainless steels, but it is not a design consideration for smaller (tubing) components. The 321 type is not as strong as the others in this series. While it is a stabilized grade and has impor- tant low temperature applications, the stability of the titanium carbide makes it extremely difficult to heat treat type 321 in one thermal treatment and obtain a
- 202. The Babcock & Wilcox Company 7-14 Steam 41 / Metallurgy, Materials and Mechanical Properties resulting structure that is both coarse grained, for high temperature creep strength, and has stabilized carbides for sensitization resistance. It is possible to apply a lower temperature stabilizing heat treatment, at about 1300F (704C), following the solution treat- ment to achieve a stabilized condition and good creep strength. The stability of the columbium (niobium) carbidesintype347isbetter,andthisgradecanbeheat treated to obtain creep strength and sensitization re- sistance. This 18Cr-8Ni-Cb alloy is widely used at high temperatures because of its superior creep strength. The Mo content of the 316 type increases its pitting resistance at lower temperatures. While this alloy has good creep strength, it is not often used because of its higher cost. Thesealloysaresusceptibletostresscorrosioncrack- ing in certain aqueous environments. The 300 series alloys are particularly sensitive to the presence of halide ions.As a result, their use in water-wetted ser- vice is usually prohibited. The stress corrosion crack- ing experience with Alloy 800 has been mixed and, while this grade is permitted in water-wetted service, it is not common practice. Types 309, 25Cr-12Ni, and 310, 25Cr-20Ni, have virtually identical strengths and corrosion resistance. They are not as strong as 304 or 347 but are more oxidation resistant. The high Ni alloys, likeAlloy 800, are somewhat more affected by sulfidation attack. They have been used as nonpressure fluidized-bed boiler components designed to remove particulate from hot gas streams. Most of these alloys are available in a multiplicity of minor variations: H grades, with 0.04 to 0.10% C and a required high temperature anneal and coarse grain size for creep strength; L grades, with 0.035% maximum C for sensitization resistance; N grades, with 0.010% minimum N added for strength; LN grades, with 0.035% maximum C and 0.010% mini- mum N for sensitization resistance and strength; and straight (no suffix) grades, with 0.08% maximum C. Ferritic stainless steels contain at least 10% Cr and have a ferrite-plus-carbide structure. Martensitic stainless steels are ferritic in the annealed condition but are martensitic after rapid cooling from above the critical temperature. They usually contain less than 14% Cr.16 Precipitation hardened stainless steels are more highly alloyed and are strengthened by precipi- tation of a finely dispersed phase from a supersatu- rated solution on cooling. None of these steels are used for pressure parts or load carrying components in boil- ers because, at the high temperatures at which their oxidation resistance is useful, they are subject to a vari- etyofembrittling,phaseprecipitationreactions,includ- ing 885F (474C) embrittlement and sigma phase forma- tion. They are used as studs for holding refractories and heatabsorbingprojectionsandasthermalshields.These alloys are also difficult to weld without cracking. Duplex alloys, with mixed austenitic-ferritic struc- tures, have been developed. They are useful in corro- sive lower temperature applications such as those found in wet desulfurization equipment used as boiler flue gas scrubbers. Bimetallic materials Weld cladding of one alloy with another has been available for many years. A more recent development has been the proliferation of bi- metallic components, such as tubes and plate contain- ing a load carrying alloy for their major constituent covered with a layer of a corrosion resistant alloy. The first bimetallic tubes to see wide use in boilers were made from Alloy 800H clad with a 50Cr-50Ni alloy (Alloy 671) for coal ash corrosion resistance. The com- bination in widest use today is carbon steel clad with 304L, used in pulp and paper process recovery (PR) boilers. One of the latest to be developed is carbon steel or 1/2Cr-1/2Mo clad withAlloy 825 (42Ni-21.5Cr-5Mo- 2.3Cu) used in PR and refuse-fired boilers.17 Other combinations that have been used are 1/2Cr-1/2Mo and 2-1/4Cr-1Mo clad with 309. Cast irons Cast irons and cast steels (containing more than 2% or less than 2% C, respectively) have long had wide acceptance as wear resistant and struc- tural components in boilers. Cast steels are also used for boiler pressure parts. The three types of cast iron used in boilers are white, gray and ductile iron. White iron White cast iron is so known because of the silvery luster of its fracture surface. In this alloy, the carbon is present in combined form as the iron carbide cementite (Fe3C). This carbide is chiefly re- sponsible for the hardness, brittleness and poor ma- chinability of white cast iron. Chilled iron differs from white cast iron only in its method of manufacture and it behaves similarly. This type of iron is cast against metal blocks, or chills, that cause rapid cooling at the adjacent areas, promoting the formation of cement- ite. Consequently, a white or mottled structure, which is characterized by high resistance to wear and abra- sion, is obtained. Elverite® alloys, a series of white iron, Ni-enriched cast materials developed by The Babcock & Wilcox Company (B&W) for use in pulverizers and other wear resistant parts, have long been noted for their uniformity and high quality. VAM 20, a more recent development, is a 20% Cr white iron with a carbide-in-martensite matrix, very high hardness and good toughness (compared to other white irons). The hardness and wear resistance of VAM 20 are superior to those of the Elverites and simi- lar alloys. It is always used in the heat treated condi- tion, which accounts for its good toughness and uni- formity. VAM 20 is used in grinding elements of coal pulverizers. Malleable cast iron is white cast iron that has been heat treated to change its combined carbon (cement- ite) into free, or temper carbon (nodules of graphite). The iron becomes malleable because, in this condition, the carbon no longer forms planes of weakness. Gray iron Gray cast iron is by far the most widely used cast metal. In this alloy, the carbon is predomi- nantly in the free state in the form of graphite flakes, which form a multitude of notches and discontinuities in the iron matrix. The fracture appearance of this iron is gray because the graphite flakes are exposed. Gray iron’s strength depends on the size of the graphite crystals and the amount of cementite formed with the graphite. The strength of the iron increases as the graphite crystal size decreases and the amount of ce- mentite increases. Gray cast iron is easily machinable
- 203. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-15 because the graphite acts as a lubricant. It also pro- vides discontinuities that break the chips as they are formed. Modern gray iron having a wide range of ten- sile strength, from 20,000 to 90,000 psi (138 to 621 MPa), can be made by suitable alloying with Ni, Cr, Mo, V and Cu. Ductile iron Another member of the cast iron family is ductile cast iron. It is a high carbon, Mg-treated ferrous product containing graphite in the form of spheroids or impacted particles. Ductile cast iron is similar to gray cast iron in melting point, fluidity and machinability, but it possesses superior mechanical properties. This alloy is especially suited for pressure castings.Byspecialprocedures(castingagainstachill), it is possible to obtain a carbide-containing abrasion resistant surface with an interior of good ductility. Cast iron was used extensively in early steam boil- ers for tubes and headers. This material is no longer used in the pressure parts of modern power boilers but is used in related equipment such as stoker parts and the grinding elements of coal pulverizers. Cast alloys Cast steels and non-ferrous alloys are used for many support and alignment applications in boilers, and for some pressure parts having complex shapes. The alloys range from carbon steel and 2-1/ 4Cr-1Mo to 25Cr-12Ni and 50Cr-50Ni. Ceramics and refractory materials Ceramics and refractory materials are used for their insulating and erosion resisting properties. Brick furnace walls have mostly been replaced by steel membrane panels. (See Chapter 23.) However, in many applications, these walls may still have a rammed, troweled or cast re- fractory protection applied. Refractory linings are still importantfeaturesofsomefurnaces,particularlythose exposed to molten slag. In Cyclone furnaces (see Chap- ter 15) and other wet-bottom boilers, gunned and troweled alumina and silicon carbide refractory prod- ucts are generally used. Chromium-containing refrac- tories are no longer in general use since being classi- fied as a hazardous material. Cera-VAM is a high density alumina ceramic used as an erosion liner in coal-air pipeline elbows, coal pulverizer internals, and pulverizer swing valves to reduce erosion and the associated maintenance costs. (See Chapter 13.) Structural ceramics have also been introduced as hot gas filters. These filters remove par- ticulates from the flue gas of fluidized-bed boilers be- fore the gas enters the high temperature gas turbine of combined cycle plants. (See Chapter 17.) Coatings Many types of coatings are applied to boiler metal parts. In addition to the cast, gunned and troweled types mentioned above, thinner carbide-con- taining, metallic matrix coatings are sprayed onto surfaces in boilers exposed to high velocity particulate erosion. Metallic coatings are sprayed on boiler parts exposed to erosion and corrosion wastage by the flame spraying,twin-wireelectricarc,plasmaandhighvelocity oxy-fuel processes. These are shop- and field-applied maintenance processes that protect and repair compo- nents that experience wastage. Proper surface prepa- ration and process control must be exercised to ensure thatthesecoatingsadhere,havetheproperdensity,and achieve the recommended thickness on all surfaces. Chromizing In the mid 1970s, B&W pioneered the use of chemical vapor deposition (CVD) coatings for boiler components. Chromizing, a process previously applied to aircraft jet engine components, is applied to large surfaces on the interior of tubing and piping. The purpose of this process is to develop a high Cr- containing surface that is resistant to oxidation and subsequent exfoliation. High temperature steam car- rying pressure parts suffer from oxidation on their internal surfaces. When the oxide layer becomes thick enough, it spalls off the surface and the particles are carried to the steam turbine, where the resulting ero- sion damage causes loss of efficiency and creates a risk of mechanical damage. Perfect coverage of tube inside diameter (ID) surfaces is not necessary to reduce this condition. If 95% of the susceptible tube surface is chromized, a twenty-fold reduction in exfoliate par- ticles will result. In CVD processes, such as chromizing, the surfaces to be coated are usually covered with or embedded in a mixture containing powdered metal of the coating element, e.g., Cr, a halide salt, and a refractory pow- der, often alumina. When the parts and the mixture are heated to a sufficiently high temperature, the salt decomposes and the metal powder reacts with the halide ion to form a gas, e.g., CrCl2 or CrBr2. At the surface of the part being coated, an exchange reac- tion takes place.An Fe atom replaces the Cr in the gas and the Cr atom is deposited on the surface. The pro- cess is conducted at sufficient time and temperature to permit the Cr to diffuse into the base material. At the chromizing temperature, 2-1/4Cr-1Mo, for ex- ample, is fully austenitic. However, as Cr atoms are deposited on the surface, the Cr increases the stabil- ity of the ferrite phase. As a result, the diffusion front advances into the matrix concurrently with the phase transformation front. This results in a diffusion zone with a nearly constant Cr content. (See Fig. 14.) Typi- cal depths of this zone range from 0.002 to 0.025 in. (0.051 to 0.64 mm). The diffusion layer on a 2-1/4Cr- 1Mo substrate has a Cr content range of 30 to 13%. Chromizing, though first developed to reduce solid particle erosion of turbines, is now being applied to external surfaces of boiler pressure parts to reduce or prevent corrosion and corrosion-fatigue damage. In these applications, near perfect continuity and integ- rity of the coating is required. A thicker coating is necessary to resist the more hostile external environ- ments. Improvements in chromized coating composi- tion and processing have been achieved. Co-diffusion of Cr and Si, or Cr and Al, is now possible, improving the corrosion resistance of the coating. Process im- provements have allowed for shorter times at diffus- ing temperature, thus resulting in less undercoating decarburization and better material properties. Aluminizing Aluminizing, a similar CVD process, has been used for many years to protect components in petrochemical process pressure vessels. However, alumina, as silica, is soluble in high temperature, high pressure steam and it can be carried to the turbine, where pressure and temperature drops cause it to precipitate on the turbine components; this is unde- sirable. Aluminizing, either with diffusion processes
- 204. The Babcock & Wilcox Company 7-16 Steam 41 / Metallurgy, Materials and Mechanical Properties or spray metallizing, has also seen some use as an external, fireside surface protective coating. The dif- fusion coating over iron-based alloys does create a brittle iron aluminide phase that can lead to prema- ture loss of the coating, but it has had long term suc- cess in a number of petrochemical applications, espe- cially sulfuric acid service, and where carburization (metal dusting) must be avoided. Fusedcoatings Tungstencarbide/chromiumcarbide fused metallic coatings are also used for erosion pro- tection of tube membrane panels, for example, in ba- sic oxygen furnace steelmaking furnace hoods. Fused coatings differ from sprayed coatings in possessing higher density and achieving better bond strength due to the brazing-type action of the application process, which includes a high temperature heat treatment following the coating application using a conventional metallizing process. Galvanizing More mundane coatings, such as gal- vanizing, painting and organic rust prevention coat- ings, are also used on boiler components. Galvanizing, a zinc coating usually applied by dip- ping in molten metal or by electroplating, is usually used on structural components external to the boiler, when erection is near a seashore or a petrochemical complex.18 Galvanized components must be kept out of hightemperatureareastoavoidstructuraldamagedue to zinc grain boundary embrittlement, generally be- lieved to occur at temperatures above 450F (232C). Mechanical properties Low temperature properties Steels of different properties are used in boilers, each selected for one or more specific purposes. Each steel must have properties for both manufacturing and satisfactory service life. Each particular type, or grade, of steel must be consistent in its properties, and tests are normally run on each lot to demonstrate that the desired properties have been achieved. Specifications standardizing all the conditions re- lating to test specimens, methods and test frequency have been formulated by the American Society for Testing and Materials (ASTM) and other authorities. Tensile test In the tensile test, a gradually applied unidirec- tional pull determines the maximum load that a ma- terial can sustain before breaking. The relationship between the stress (load per unit area) and the corre- sponding strain (change of length as a percent of the original length) in the test piece is illustrated in the stress-strain diagrams of Figs. 15 and 16. The metal begins to stretch as soon as the load is applied and, for somerangeofincreasingload,thestrainisproportional tothestress.Thisistheelasticregionofthestress-strain curve,inwhichthematerialverycloselyfollowsHooke’s Law: strain, ε, is proportional to stress, σ. The propor- tionality constant may be considered as a spring con- stant and is called Young’s modulus, E. Young’s modu- lus is a true material property, characteristic of each alloy. Young’s modulus for steel is approximately 30 × 106 psi (206.8 × 106 kPa) at room temperature. If the stress is released at any point in this region, the test specimen will return to very nearly its initial dimensions. However, if the stress is increased beyond a certain point, the metal will no longer behave elas- tically; it will have a permanent (plastic) elongation, and the linear relationship between stress and strain ceases. This value is known as the proportional limit of the material and, in this discussion, may be consid- ered practically the same as the elastic limit, which may be defined as the maximum stress that can be developed just before permanent elongation occurs. Fig. 15 Engineering stress-strain curve for 1030 carbon steel (courtesy of Wiley).19 Fig. 14 Chromized 2-1/4Cr-1Mo at 400 X magnification.
- 205. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-17 When a material has a well defined point at which it continues to elongate without further increase in load, this point is called the yield point. Many steels do not have a yield point and even in those that do, neither it nor the proportional or elastic limits can be determined with accuracy. By convention, therefore, engineers have adopted an arbitrary but readily mea- surable concept: the yield strength of a metal. This is defined as the stress at which the strain reaches 0.2% of the gauge length of the test specimen. This is illus- trated in Fig. 16. (Other values, 0.1% or 0.5% are oc- casionally used, but 0.2% is most common.) If the loading is continued after yielding begins, a test specimen of a ductile material with homogeneous composition and uniform cross-section will be elon- gated uniformly over its length, with a corresponding reduction in area. Eventually, a constriction or neck- ing may occur. In some materials, localized necking may not occur, but the cross-section may reduce more or less uniformly along the full gauge length to the instant of rupture. In all ductile materials, however, an appreciable increase in elongation occurs in the reduced area of the specimen. The more ductile the steel, the greater is the elongation before rupture. The maximum applied load required to pull the specimen apart, divided by the area of the original cross-section, is known as the ultimate tensile strength. Brittle ma- terials do not exhibit yielding or plastic deformation, and their yield point and ultimate tensile strength are nearly coincident. The ductility of the metal is determined by measur- ing the increase in length (total elongation) and the final area at the plane of rupture after the specimen has broken, and is expressed as percent elongation or percent reduction of area. Hardness test Hardness may be defined as resistance to indenta- tion under static or dynamic loads and also as resis- tance to scratching, abrasion, cutting or drilling. To the metallurgist, hardness is important as an indica- tor of the effect of heat treatment, fabrication pro- cesses, or service exposure. Hardness values are roughly indicative of the ultimate tensile strength of steels. Hardness tests are also used as easy acceptance tests and to explore local variations in properties. Hardness is usually determined by using specially designed and standardized machines: Rockwell, Brinell, Vickers (diamond pyramid), or Tukon. These all measure resistance to indentation under static loads. The pressure is applied using a fixed load and for a specified time, and the indentation is measured eitherwithamicroscopeorautomatically.Itisexpressed as a hardness number, by reference to tables. Hardness can also be determined by a scleroscope test, in which the loss in kinetic energy of a falling metal weight, ab- sorbed by indentation upon impact of the metal being tested, is indicated by the height of the rebound. Toughness tests Toughness is a property that represents the ability of a material to absorb local stresses by plastic defor- mation and thereby redistribute the stresses over a larger volume of material, before the material fails locally. It is therefore dependent on the rate of appli- cation of the load and the degree of concentration of the local stresses. In most steels, it is also temperature dependent, increasing with increasing temperature (although not linearly). Toughness tests are of two types, relative and absolute. Notched bar impact tests are an example of the rela- tive type. The most common is the Charpy test, in which a simple horizontal beam, supported at both ends, is struck in the center, opposite a V-shaped notch, by a single blow of a swinging pendulum. A Charpy specimen is illustrated in Fig. 17a. The energy ab- sorbed by the breaking specimen can be read directly on a calibrated scale and is expressed in ft lb units. The specimen is also examined to determine how much it has spread laterally and how much of its frac- ture surface deformed in shear versus cleavage. The toughness is expressed in units of absorbed energy (ft lb or J), mils (thousandths of an inch or mm) lateral expansion and percent shear. The values are charac- teristic of not only the material and temperature, but also of the specimen size. Therefore, comparison be- tween materials and tests have meaning only when specimengeometriesandothertestconditionsareiden- tical. Specimens are inexpensive and the test is easy to do. Often, vessel designers are interested in the variation of toughness with temperature. Fig. 18 il- lustrates the variation in toughness with temperature of 22 heats of a fine grained carbon steel, SA-299, as determined by Charpy testing. This material displays a gradual transition from higher to lower toughness. Another toughness test, and one that provides a more sharply defined transition, is the drop-weight test. The specimen for this test is shown in Fig. 17b. A known weight is dropped from a fixed height and im- pacts the specimen. This is a pass or fail test and is performed on a series of specimens at varying tem- peratures, selected to bracket the break versus no- break temperature within 10F (6C). If the impact causes a crack to propagate to either edge of the speci- men from the crack-starter notch in the brittle weld bead deposited on the face of the specimen, the speci- men is considered to have broken at that temperature. The lowest temperature at which a specimen fails determines the nil-ductility transition temperature Fig. 16 Engineering stress-strain diagram for polycrystalline copper. Left, complete diagram. Right, elastic region and initial plastic region showing 0.2% offset yield strength.19
- 206. The Babcock & Wilcox Company 7-18 Steam 41 / Metallurgy, Materials and Mechanical Properties (NDTT). Fig. 19 shows a histogram of NDTTs from 20 heats of fine grained SA-299. Fracture toughness tests measure true character- istics of a given metal. They are more complex and specimens are more costly. However, they produce values that can be used in analytical stress calcula- tions to determine critical flaw sizes above which flaws or cracks may propagate with little or no increase in load. A typical fracture toughness specimen is shown in Fig. 17c. Variations of fracture toughness tests in- volve testing under cyclic rather than monotonically increasing load (fatigue crack growth testing) and test- ing in various environments to determine crack growth rates as a function of concurrent corrosion processes. The same specimen is used to determine fatigue crack growth behavior. Fig. 20 illustrates the difference in crack growth rate in air and in a salt solution for 4340 steel tempered to two strength levels. Formability tests Several different types of deformation tests are used to determine the potential behavior of a material in fab- rication. These include bending, flattening, flaring and cupping tests. They furnish visual evidence of the capa- bility of the material to withstand various forming op- erations. They are only a rough guide and are no substi- tute for full scale testing on production machinery. High temperature properties Tensile or yield strength data determined at ambi- ent temperatures can not be used as a guide to the mechanical properties of metals at higher tempera- tures. Even though such tests are made at the higher temperatures, the data are inadequate for designing equipment for long term service at these temperatures. This is true because, at elevated temperatures, contin- ued application of load produces a very slow continu- ous deformation, which can be significant and measur- able over a period of time and may eventually lead to fracture, depending on the stress and temperatures involved. This slow deformation (creep) occurs for tem- peratures exceeding about 700F (371C) for ferritic steels and about 1000F (538C) for austenitic steels. Tensile strength Although the design of high temperature equipment generally requires use of creep and creep-rupture test data, the short time tensile test does indicate the strength properties of metals up to the creep range of the material. This test also provides information on ductility characteristics helpful in fabrication. The ultimate strength of plain carbon steel and a number of alloy steels, as determined by short time tensile tests over a temperature range of 100F (38C) to 1300 to 1500F (704 to 816C), is shown in Fig. 21. In general, the results of these tests indicate that strength decreases with increase in temperature, al- though there is a region for the austenitic alloys be- tween 400 and 900F (204 and 482C) where strength is fairly constant. An exception to the general rule is Fig. 17 (a) Charpy specimen, (b) nil ductility transition temperature (drop weight) test specimen, (c) compact tension specimen (courtesy of Prentice-Hall).20 Fig. 19 Drop weight nil-ductility transition temperature (NDTT) frequency distribution for 20 heats of fine grained SA-299 plate material. Fig. 18 Charpy V-notch impact energy versus test temperature for fine grained SA-299 plate material.
- 207. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-19 the increase in strength over that at room tempera- ture of carbon and many low alloy steels (with corre- sponding decrease in ductility) over the temperature range of 100 to 600F (38 to 316C). As the tempera- ture is increased beyond 600 to 750F (316 to 399C), the strength of the carbon and most of the low alloy steels falls off from that at room temperature with a corresponding increase in ductility. Creep and creep-rupture test It has long been known that certain nonmetallic materials, such as glass, undergo slow and continu- ous deformation with time when subjected to stress. The concept of creep in metallic materials, however, did not attract serious attention until the early 1920s. Results of several investigations at that time demon- strated that rupture of a metallic material could oc- cur when it is subjected to a stress at elevated tem- peratures for a sufficiently long time, even though the load applied is considerably lower than that necessary to cause rupture in the short time tensile test at the same temperature. The earliest investigations of creep in the U.S. were sponsored by B&W in 1926. Many steels now used successfully in power generating units and in the pe- troleum refining and chemical industries were tested and proved in the course of these investigations, us- ing the best equipment available at the time. The creep-rupture test is used to determine both the rate of deformation and the time to rupture at a given temperature. The test piece, maintained at constant temperature, is subjected to a fixed static tensile load. The deformation of the test sample is measured dur- ing the test and the time to rupture is determined. The duration of the test may range from 1000 to 10,000 h, or even longer.Adiagrammatic plot of the observed length of the specimen against elapsed time is often of the form illustrated in Fig. 22. Thecurverepresentingclassicalcreepisdividedinto three stages. It begins after the initial extension (0- A), which is simply the measure of deformation of the specimen caused by the loading. The magnitude of this initial extension depends on test conditions, varying with load and temperature and normally increasing with increases in temperature and load. The first stage of creep (A-B), referred to as primary creep, is char- acterized by a decreasing rate of deformation during the period. The second stage (B-C), referred to as sec- ondary creep, is usually characterized by extremely small variations in rate of deformation; this period is essentially one of constant rate of creep. The third stage (C-D), referred to as tertiary creep, is charac- terized by an accelerating rate of deformation lead- ing to fracture. Some alloys, however, display a very limited (or no) secondary creep and spend most of their test life in tertiary creep. To simplify the practical application of creep data it is customary to establish two values of stress (for a material at a temperature) that will produce two cor- responding rates of creep (elongation): 1.0% per 10,000 h and 100,000 h, respectively. For any specified temperature, several creep-rup- ture tests must be run under different loads. The creep rate during the period of secondary creep is deter- mined from these curves and is plotted against the stress. When these data are plotted on logarithmic scales, the points for each specimen often lie on a line Fig. 20 Corrosion fatigue crack growth rates for 4340 steel.20 Fig. 21 Tensile strength of various steels at temperatures to 1500F (816C).
- 208. The Babcock & Wilcox Company 7-20 Steam 41 / Metallurgy, Materials and Mechanical Properties with a slight curvature. The minimum creep rate for any stress level can be obtained from this graph, and the curve can also be extrapolated to obtain creep rates for stresses beyond those for which data are obtained. Fig. 23 presents such creep rate curves for 2-1/4Cr- 1Mo steel at 1000, 1100 and 1200F (538, 593 and 649C). The shape of the creep curve depends on the chemical composition and microstructure of the metal as well as the applied load and test temperature. Creep-rupture strength is the stress (initial load divided by initial area) at which rupture occurs in some specified time, in an air atmosphere, in the tempera- ture range in which creep takes place. The time for rupture at any temperature is a function of the ap- pliedload.Alogarithmic-scaleplotofstressversustime for fracture of specimens generally takes the form of the curves shown for 2-1/4Cr-1Mo steel in Fig. 24. In general, rapid rates of elongation indicate a transgranular (ductile) fracture and slow rates of elon- gation indicate an intergranular (brittle) fracture. As a rule, surface oxidation is present when the fracture is transgranular, while visible intercrystalline oxida- tion may or may not be present when the fracture is intergranular. Because of the discontinuities produced by the presence of intercrystalline oxides, the time to rupture at a given temperature-load relationship may be appreciably reduced. In Fig. 24, the slope of the data at 1200F (649C) is steeper than those for lower temperatures. This is to be expected, because 1200F (649C) is above the usual temperature limit for maxi- mum resistance to oxidation of 2-1/4Cr-1Mo. There- fore, excessive scaling occurs in the long time rupture tests conducted at 1200F (649C). A complete creep-rupture test program for a given steel actually consists of a series of tests at constant temperature with each specimen loaded at a different level. Because tests are not normally conducted for more than 10,000 h, the values for rupture times longer than this are determined by extrapolation. The ASME Boiler and Pressure Vessel Code Committee uses several methods of extrapolation, depending on the behavior of the particular alloy for which design values are being established and on the extent and quality of the database that is available. Several in- formative discussions on these methods may be found in ASME publications. (See Appendix 2.) Material applications in boilers ASME specifications and allowable stresses The ASME Boiler and Pressure Vessel Code Sub- committee on Materials is responsible for identifying and approving material specifications for those met- als deemed suitable for boiler and pressure vessel con- struction and for developing the allowable design values for metals as a function of temperature. Most industrial and all utility boilers are designed to Sec- tion I of the Code, Power Boilers, which lists those material specifications approved for boiler construc- tion. The specifications themselves are listed in Sec- tion II, PartA, Ferrous Materials, and Section II, Part B, Non-Ferrous Materials. The design values are listed in Section II, Part D, Properties. (Section II, Part C, Specifications for Welding Rods, Electrodes, and Filler Metals, contains approved welding materials.) For many years, there were relatively few changes in either specifications or design values. Over the last five or ten years, however, many new alloys have been introduced and much new data have become avail- able. The restructuring of the North American steel industry and the globalization of sources of supply and markets are partly responsible for this rapid rate of change. As a result, detailed tables of design values in a text such as this become obsolete much more rap- idly than was once the case. A few examples of cur- rent allowable stresses are presented below for illus- trative purposes. However, the reader is encouraged to consult Section II for an exposure to material speci- fications and the latest design values. The maximum allowable working stresses for ma- terials in power boilers, set by the American Society of Mechanical Engineers (ASME), are based on both time-independent and time-dependent properties. The ASME Boiler and Pressure Vessel Code, Sec- tion I, Power Boilers, has established the maximum Fig. 22 Classic (diagrammatic) creep test at constant load and temperature. Fig. 23 Creep rate curves for 2-1/4Cr-1Mo steel.
- 209. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-21 allowable design stress values for pressure parts to be no higher than the lowest of: 1. 1 / 3.5 × the minimum specified ultimate tensile strength, 2. 1.1 / 3.5 × the tensile strength at temperature, 3. 67% of the specified minimum yield strength at room temperature, 4. 67% of the yield strength at temperature, for fer- ritic steels; or 90% of the yield strength at tempera- ture of austenitic steels and nickel base alloys, 5. a conservative average of the stress to give a creep rate of 0.01% in 1000 hours (1% in 100,000 hours), or 6. 67% of the average or 80% of the minimum stress to produce rupture in 100,000 hours. Furthermore, the allowable stress at a higher tem- perature can not exceed that at a lower temperature, so no advantage is taken of strain aging behavior. The allowable stress is therefore the lower bound envelope of all these criteria. The tensile and yield strengths at temperature have a particular meaning in Code usage. For austenitic materials that possess allowable de- sign properties above 1500F (816C), the ASME Code has recently adopted an additional criterion applied to creep rupture data of the specific alloy. The crite- rion involves a statistical evaluation of the data and ensures that a consistent safety factor exists at the very high temperatures. Pressure part applications The metal product forms used in boiler pressure parts are tubes and pipe (often used interchangeably), plate, forgings and castings. Tubular products com- pose the greatest part of the weight. The matrix in Table 1 shows the common pressure part material specifications used in fossil fuel fired boilers today, their minimum specified properties, recommended maximum use temperatures, and their applications. This list is not meant to be all inclusive, as there are many other specifications permitted by Section I and several of them see occasional use. Neither is it meant to be exclusive, as several of these specifications are used occasionally for components not checked in Table 1. Finally, the recommended maximum use tempera- tures represent one or more of a variety of limits. The temperature listed may be the highest for which stresses are listed in Section I, the oxidation limit for long-term service, a temperature at which graphiti- zation may be expected, or current commercial prac- tice, whichever is least. Boiler, furnace waterwall, convection pass enclosures and economizers Boiler, furnace waterwall, and convection pass en- closure surfaces are generally made of carbon steel, C-Mo,and1/2Cr-1/2Moseamlessorelectric-resistance- welded (ERW) tubes. Lower carbon grades and 1/2Cr- 1/2Mo alloy are used in high heat input regions to avoid the risk of graphitization in this region where tube metal temperatures may be subject to more fluc- tuation and uncertainty. Higher carbon grades and C-Mo are used in furnace floors, upper furnace walls, convection pass enclosures, and economizers. The boiler industry is seeing increasing use of higher Cr-Mo grades in these applications, especially as temperatures and pressures increase with the lat- est designs. 1Cr-1/2Mo, 1-1/4 Cr-1/2Mo-Si, and even 2-1/4 Cr-1Mo will see increased use. Even higher al- loys present formidable manufacturing challenges that will likely restrict these applications to alloys pos- sessing less than 3% Cr. Superheaters and reheaters The highest metal temperatures of pressure parts in the steam generating unit occur in the superheater and reheater. Consequently, these tubes are made of material having superior high temperature properties and resistance to oxidation. Carbon steel is a suitable and economical material to about 850 to 950F (454 to 510C) metal temperature, depending on pressure. Above this range, alloy and stainless steels are re- quired because of the low oxidation resistance and the low allowable stresses of carbon steel. Usually two or more alloys are used in the construction of the super- heater. The lower alloys, such as carbon and C-Mo steels, are used toward the inlet section, while the low and intermediate alloy Cr-Mo steels are used toward the outlet, where the steam and metal temperatures are higher. (See Chapter 19.) Stainless steel tubes have been required in the hottest sections of the superheater. However, stainless steels are being replaced in many applications by 9Cr- 1Mo-V. This high strength ferritic steel was developed initially by The Oak Ridge National Laboratory for fast breeder nuclear reactor components. However, it has found many applications in fossil fuel-fired boil- ers because of its high strength and excellent tough- ness. Because it is ferritic, its use in place of stainless steel eliminates dissimilar metal weld failures. New alloys, both ferritic and austenitic, are con- stantly being developed and are appearing in boilers around the world. The most promising ferritic alloys use alloying additions of elements such as V, Cb (Nb), W and N which, when combined with controlled nor- malizing and tempering heat treatment, result in materials possessing creep strength far superior to the traditional Cr-Mo alloy grades in the 2.25 to 12% Cr range. Newer austenitic alloys use modified alloying with elements such as Cu, Cb (Nb) and N, sometimes combined with special thermal mechanical processing, Fig. 24 Typical creep rupture curves for 2-1/4Cr-1Mo steel.
- 210. The Babcock & Wilcox Company 7-22 Steam 41 / Metallurgy, Materials and Mechanical Properties to enhance creep strength. A new family of Ni and Ni- Cr-Co alloys is also available, specifically for advanced supercriticalandadvanced supercriticalboilerdesigns. Fuel ash corrosion considerations might dictate the use of higher alloys at lower temperatures. This is common in process recovery and refuse-fired boilers with very corrosive flue gas and ash. For example, SB- 407-825 (42Ni-21.5Cr-3Mo-2.25Cu-0.9Ti-bal Fe) is used in the highly corrosive regions of refuse boiler superheaters, even at temperatures below 1000F (538C). In extreme cases, bimetallic tubes, with a core of a Code material for pressure retention and a clad- ding of a corrosion resistant alloy, are used for both furnace wall and superheater applications. Some com- mon combinations are SA-210A1/304L, SA-210A1/ Alloy 825, and SB-407-800H/50Cr-50Ni. Selection factors Many factors influence material selection in a su- perheater. These include cost as well as performance factors (heat transfer surface area required, final steam temperature, total mass flow through the tubes, Table 1 Boiler Materials and Typical Applications (English Units) Min Min High Heat Other Furn SH Unheated Headers Recomm Nominal Product Tensile, Yield, Input Furn Walls and RH Conn Pipe and Pipe Max Use Specification Composition Form ksi ksi Walls Enclosures Econ <10.75 in. OD >10.75 in. OD Drums Temp, F Notes SA-178A C-Steel ERW tube (47.0) (26.0) X X X 950 1,2 SA-192 C-Steel Seamless tube (47.0) (26.0) X X X X 950 1 SA-178C C-Steel ERW tube 60.0 37.0 X X 950 2 SA-210A1 C-Steel Seamless tube 60.0 37.0 X X X X 950 SA-106B C-Steel Seamless pipe 60.0 35.0 X X 950 3 SA-178D C-Steel ERW tube 70.0 40.0 X X X 950 2 SA-210C C-Steel Seamless tube 70.0 40.0 X X X 950 SA-106C C-Steel Seamless pipe 70.0 40.0 X X 950 3 SA-216WCB C-Steel Casting 70.0 36.0 X X X X 950 SA-105 C-Steel Forging 70.0 36.0 X X X X 950 3 SA-181-70 C-Steel Forging 70.0 36.0 X X X X 950 3 SA-266Cl2 C-Steel Forging 70.0 36.0 X 800 SA-516-70 C-Steel Plate 70.0 38.0 X X 800 SA-266Cl3 C-Steel Forging 75.0 37.5 X 800 SA-299 C-Steel Plate 75.0 40.0 X 800 SA-250T1a C-Mo ERW tube 60.0 32.0 X X 975 4,5 SA-209T1a C-Mo Seamless tube 60.0 32.0 X X X 975 4 SA-250T2 1/2Cr-1/2Mo ERW tube 60.0 30.0 X X X 1025 6 SA-213T2 1/2Cr-1/2Mo Seamless tube 60.0 30.0 X X X 1025 6 SA-250T12 1Cr-1/2Mo ERW tube 60.0 32.0 X X 1050 5 SA-213T12 1Cr-1/2Mo Seamless tube 60.0 32.0 X X X 1050 SA-335P12 1/2Cr-1/2Mo Seamless pipe 60.0 32.0 X 1050 SA-250T11 1-1/4Cr-1/2Mo-Si ERW tube 60.0 30.0 X X 1050 5 SA-213T11 1-1/4Cr-1/2Mo-Si Seamless tube 60.0 30.0 X X X 1050 SA-335P11 1-1/4Cr-1/2Mo-Si Seamless pipe 60.0 30.0 X X 1050 SA-217WC6 1-1/4Cr-1/2Mo Casting 70.0 40.0 X X X X 1100 SA-250T22 2-1/4Cr-1Mo ERW tube 60.0 30.0 X 1115 5 SA-213T22 2-1/4Cr-1Mo Seamless tube 60.0 30.0 X 1115 SA-213T23 2-1/4Cr-W-V Seamless tube 74.0 58.0 X X 1115 SA-335P22 2-1/4Cr-1Mo Seamless pipe 60.0 30.0 X X 1100 SA-217WC9 2-1/4Cr-1Mo Casting 70.0 40.0 X X X 1115 SA-182F22Cl1 2-1/4Cr-1Mo Forging 60.0 30.0 X X 1115 SA-336F22Cl1 2-1/4Cr-1Mo Forging 60.0 30.0 X 1100 SA-213T91 9Cr-1Mo-V Seamless tube 85.0 60.0 X 1150 SA-335P91 9Cr-1Mo-V Seamless pipe 85.0 60.0 X X 1150 SA-217C12A 9Cr-1Mo-V Casting 85.0 60.0 X X 1200 SA-182F91 9Cr-1Mo-V Forging 85.0 60.0 X 1150 SA-336F91 9Cr-1Mo-V Forging 85.0 60.0 X 1150 SA-213T92 9Cr-2W Seamless tube 90.0 64.0 X X 1200 SA-213TP304H 18Cr-8Ni Seamless tube 75.0 30.0 X 1400 SA-213TP347H 18Cr-10Ni-Cb Seamless tube 75.0 30.0 X 1400 SA-213TP310H 25Cr-20Ni Seamless tube 75.0 30.0 X 1500 SB-407-800H Ni-Cr-Fe Seamless tube 65.0 25.0 X 1500 SB-423-825 Ni-Fe-Cr-Mo-Cu Seamless tube 85.0 35.0 X 1000 Notes: 1. Values in parentheses are not required minimums, but are expected minimums. 2. Requires special inspection if used at 100% efficiency above 850F. 3. Limited to 800F maximum for piping 10.75 in. OD and larger and outside the boiler setting. 4. Limited to 875F maximum for applications outside the boiler setting. 5. Requires special inspection if used at 100% efficiency. 6. Maximum OD temperature is 1025F. Maximum mean metal temperature for Code calculations is l000F.
- 211. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-23 and flow balancing among circuits); mechanical fac- tors (internal pressure, design temperature, support systems and relative thermal expansion stresses); environmental factors (resistance to steam oxidation and out of service pitting corrosion on the ID, and oxi- dation, fuel ash corrosion, and erosion on the outside diameter/OD); and manufacturing process and equip- mentlimitationsandconsiderations,suchasweldability. Cost Material cost is usually the single largest factor affecting material selection when more than one ma- terial candidate exists for a given set of boiler appli- cation conditions. Raw material cost is established by taking into account each material’s allowable design stress, at design temperature and pressure, and re- quired mass flow requirements for the water or steam. Pressure part sizes are established, average weight determined, and material cost is estimated when knowing the raw material cost offered by the selected raw material supplier. Other factors are also consid- ered such as required corrosion allowance, if any, and unique manufacturing costs and risks. Once this evaluationisaccomplishedandcomparisonofmaterials is completed, it is quite common to find that stronger, higher alloys become economically attractive over lower strength, less costly steels at operating conditions usu- ally acceptable and appropriate for the lower alloy steel. Headers and piping Specifications for most of the commonly used pipe materials are listed in Table 1. As these components are usually not in the gas stream and are unheated, the major design factor, other than strength at tem- perature, is steam oxidation resistance. Carbon steels are not used above 800F (427C) outside the boiler set- ting, and C-Mo is limited to applications of small sizes [less than 10.75 in. (273 mm) OD] and below 875F (468C) to avoid graphitization. 9Cr-1Mo-V has replaced 2-1/4Cr-1Mo for many superheater outlet header applications (see Fig. 25). This material is not operating in the creep range even at the 1000 to 1050F (538 to 566C) design tempera- tures of most such components. This factor and its very high strength allow thinner components which are much less susceptible to the creep-fatigue failures observed in older 1-1/4Cr-1/2Mo-Si and 2-1/4Cr-1Mo headers. The use of forged outlet nozzle tee sections in place of welded nozzles has also reduced the poten- tial for failure of these large piping connections. Drums Carbon steel plate is the primary material used in drums. SA-299, a 75,000 psi (517.1 MPa) tensile strength material, ordered to fine grain melting prac- tice for improved toughness, is used for heavy section Fig. 25 The 9Cr-1Mo-V superheater outlet header features high strength and thin material less susceptible to creep-fatigue failure.
- 212. The Babcock & Wilcox Company 7-24 Steam 41 / Metallurgy, Materials and Mechanical Properties drums, those more than about 4 in. (101.6 mm) in thickness. SA-516 Gr 70, a fine grained 70,000 psi (482.7 MPa) tensile strength steel, is used for appli- cations below this thickness, down to 1.5 in. (38.1 mm) thick shells. SA-515 Gr 70, a coarse grain melting practice steel, is used for thinner shells. Steel grades of 80,000 psi (552 MPa) and higher are available. However, only in rare cases, where crane lifting ca- pacity or long distance shipping costs are important considerations, are higher strength steels used due to increased manufacturing difficulties with the higher strength steels. Heat resistant alloys for nonpressure parts High alloy heat resistant materials must be used for certain boiler parts that are exposed to high tem- perature and can not be water or steam cooled. These parts are made from alloys of the oxidation resistant, relatively high strength Cr-Ni-Fe type, many of them cast to shape as baffles, supports and hanger fittings. Oil burner impellers, sootblower clamps and hangers are also made of such heat resisting alloy steels. Deterioration of these parts may occur through con- version of the surface layers to oxides, sulfides and sulfates. Experience indicates that 25Cr-12Ni and 25Cr-20Ni steels give reasonably good service life, depending on the location of the part in the flue gas stream and on the characteristics of the fuel. Tempera- tures to which these metal parts are exposed may range from 1000 to 2800F (538 to 1538C). Welding of such austenitic castings to ferritic alloy tubes presents a dissimilar metal weld that is susceptible to failure. Normal practice is to use a nickel-base filler metal that better matches the thermal expansion properties of the ferritic tube than would an austenitic stainless weld composition. If possible, a ferritic alloy weld rod should be used to further reduce stresses against the ferritic pressure part, provided there is adequate weldability and operating conditions at the weld location are ac- ceptable. Special patented nonwelded constructions are also used where such combinations are required. Life may be shortened if these steels are exposed to flue gases from fuel oil containing vanadium com- pounds. Sulfur compounds formed from combustion of high sulfur fuels are also detrimental and act to reduce life. These may react in the presence of V and cause greatly accelerated rates of attack, especially when the temperature of the metal part exceeds 1200F (649C). Combinations of Na, S and V compounds are reported to melt at as low as 1050F (566C). Such de- posits are extremely corrosive when molten because of their slagging action. In these circumstances, 50Cr- 50Nior60Cr-40Nicastingsareusedtoresistcorrosion. 1. Cullity, B.D., Elements of X-Ray Diffraction, Second Ed., Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1978. 2. Darken, L.S., The Physical Chemistry of Metallic So- lutions and Intermetallic Compounds, Her Majesty’s Sta- tionery Office, London, England, United Kingdom, 1958. 3. Swalin, R.A., Thermodynamics of Solids, Wiley & Sons, New York, New York, 1972. 4. Higgins, R.A., Properties of Engineering Materials, Hodder and Staughton, London, England, United King- dom, 1979. 5. Bain, E.C., and Paxton, H.W., Alloying Elements in Steel, Second Ed., American Society for Metals, Metals Park, Ohio, 1966. 6. McGannon, H.E., Ed., The Making, Shaping and Treat- ing of Steel, Ninth Ed., United States Steel, Pittsburgh, Pennsylvania, 1970. 7. Lankford, W.T., Jr., et al., The Making, Shaping and Treating of Steel, Tenth Ed., Association of Iron and Steel Engineers, Pittsburgh, Pennsylvania, 1985. 8. Long, C.J., and DeLong, W.T., “The ferrite content of austenitic stainless steel weld metal,” Welding Journal, Research Supplement, pp. 281S-297S, Vol. 52 (7), 1973. 9. Boyer, H.E., and Gall, T.L., Eds., Metals Handbook: Desk Edition, American Society for Metals, Metals Park, Ohio, 1985. 10. Connor, L., Ed., Welding Handbook, Eighth Ed., American Welding Society, Vol. 1, Miami, Florida, 1987. 10a. Weisman, C., Ed., Welding Handbook, Seventh Ed., American Welding Society, p. 272, Vol. 1, Miami, Florida, l981. 11. Weisman, C., Ed., Welding Handbook, Seventh Ed., American Welding Society, p. 229, Vol. 1, Miami, Florida, l981. 12. Sikka, V.K., et al., “Modified 9Cr-1Mo steel: an im- proved alloy for steam generator application,” Ferritic Steels for High Temperature Applications, Proceedings of the ASM International Conference on Production, Fabri- cation, Properties and Application of Ferritic Steels for High Temperature Service, pp. 65-84, Warren, Pennsyl- vania, October 6-8, 1981, Khare, A.K., Ed., American So- ciety for Metals, Metals Park, Ohio, 1963. 13. Swindeman, R.W., and Gold, M., “Developments in fer- rous alloy technology for high temperature service,” Widera, G.E.O., Ed., Transactions of the ASME: J. Pressure Vessel Technology, p. 135, American Society of Mechanical Engi- neers (ASME), New York, New York, May, 1991. 14. Rudd, A.H., and Tanzosh, J.M., “Developments appli- cable to improved coal-fired power plants,” presented at the First EPRI International Conference on Improved Coal- Fired Power Plants, Palo Alto, California, November 19- 21, 1986. References
- 213. The Babcock & Wilcox Company Steam 41 / Metallurgy, Materials and Mechanical Properties 7-25 15. Viswanathan, R., et al., “Ligament cracking and the use of modified 9Cr-1Mo alloy steel (P91) for boiler head- ers,” presented at the 1990 American Society of Mechani- cal Engineers (ASME) Pressure Vessels and Piping Confer- ence, Nashville, Tennessee, June 17-21, 1990, Prager, M., and Cantzlereds, C., New Alloys for Pressure Vessels and Piping, pp. 97-104, ASME, New York, New York, 1990. 16. Benjamin, D., et al., “Properties and selection: stain- less steels, tool materials and special purpose metals,” Metals Handbook, Ninth Ed., Vol. 3, American Society for Metals, Metals Park, Ohio, p. 17, 1980. 17. Barna, J.L., et al., “Furnace wall corrosion in refuse- fired boilers,” presented to the ASME 12th Biennial Na- tional Waste Processing Conference, Denver, Colorado, June l-4, 1986. 18. Morro, H., III, “Zinc,” Metals Handbook, Desk Edi- tion, pp. 11-l to 11-3, Boyer, H.E., and Gall, T.L., Eds., American Society for Metals, Metals Park, Ohio. 19. Hayden, H.W., et al., The Structure and Properties of Materials, Vol. III, Mechanical Behavior, Wiley & Sons, New York, New York, 1965. 20. Barsom, J.M., and Rolfe, S.T., Fracture and Fatigue Control in Structures, Second Ed., Prentice-Hall, Englewood Cliffs, New Jersey, 1987.
- 214. The Babcock & Wilcox Company 7-26 Steam 41 / Metallurgy, Materials and Mechanical Properties Application of protective coating to boiler tubes.
- 215. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-1 Chapter 8 Structural Analysis and Design Equipment used in the power, chemical, petroleum and cryogenic fields often includes large steel vessels. These vessels may require tons of structural steel for their support. Steam generating and emissions con- trol equipment, for example, may be comprised of pres- sure parts ranging from small diameter tubing to ves- sels weighing more than 1000 t (907 tm). A large fossil fuel boiler may extend 300 ft (91.4 m) above the ground, requiring a steel support structure compa- rable to a 30 story building. To assure reliability, a thorough design analysis of pressure parts and their supporting structural components is required. Pressure vessel design and analysis Steam generating units require pressure vessel components that operate at internal pressures of up to 4000 psi (27.6 MPa) and at steam temperatures up to 1100F (566C). Even higher temperature and pres- sure conditions are possible in advanced system de- signs. Maximum reliability can be assured only with a thorough stress analysis of the components. There- fore, considerable attention is given to the design and stress analysis of steam drums, superheater headers, heat exchangers, pressurizers and nuclear reactors. In designing these vessels, the basic approach is to account for all unknown factors such as local yield- ing and stress redistribution, variability in material properties, inexact knowledge of loadings, and inex- act stress evaluations by using allowable working stresses that include appropriate factors of safety. The analysis and design of complex pressure ves- sels and components such as the reactor closure head, shown in Fig. 1, and the fossil boiler steam drum, shown in Fig. 2, requires sophisticated principles and methods. Mathematical equations based on the theory of elasticity are applied to regions of discontinuities, nozzle openings and supports. Advanced computerized structuralmechanicsmethods,suchasthefiniteelement method, are used to determine complex vessel stresses. In the United States (U.S.), pressure vessel con- struction codes adopted by state, federal and munici- pal authorities establish safety requirements for ves- sel construction. The most widely used code is the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code. Key sections include Sections I, Rules for Construction of Power Boilers; III, Rules for Construction of Nuclear Power Plant Com- ponents; and VIII, Rules for Construction of Pressure Vessels. A further introduction to the ASME Code is presented in Appendix 2. Stress significance Stress is defined as the internal force between two adjacent elements of a body, divided by the area over which it is applied. The main significance of a stress is its magnitude; however, the nature of the applied Fig. 1 Head of nuclear reactor vessel.
- 216. The Babcock & Wilcox Company 8-2 Steam 41 / Structural Analysis and Design load and the resulting stress distribution are also im- portant. The designer must consider whether the load- ing is mechanical or thermal,whetheritissteady-state or transient, and whether the stress pattern is uniform. Stress distribution depends on the material prop- erties. For example, yielding or strain readjustment can cause redistribution of stresses. Steady-state conditions An excessive steady-state stress due to applied pressure results in vessel mate- rial distortion, progresses to leakage at fittings and ultimately causes failure in a ductile vessel. To pre- vent this type of failure a safety factor is applied to the material properties. The two predominant prop- erties considered are yield strength, which establishes the pressure at which permanent distortion occurs, and tensile strength, which determines the vessel bursting pressure. ASME Codes establish pressure vessel design safety factors based on the sophistica- tion of quality assurance, manufacturing control, and design analysis techniques. Transient conditions When the applied stresses are repetitive, such as those occurring during testing and transient operation, they may limit the fatigue life of the vessel. The designer must consider transient con- ditions causing fatigue stresses in addition to those caused by steady-state forces. Although vessels must have nozzles, supports and flanges in order to be useful, these features often em- body abrupt changes in cross-section. These changes can introduce irregularities in the overall stress pat- tern called local or peak stresses. Other construction details can also promote stress concentrations which, in turn, affect the vessel’s fatigue life. Strength theories Several material strength theories are used to de- termine when failure will occur under the action of multi-axial stresses on the basis of data obtained from uni-axial tension or compression tests. The three most commonly applied theories which are used to estab- lish elastic design stress limits are the maximum (prin- cipal) stress theory, the maximum shear stress theory, and the distortion energy theory. Maximum stress theory Themaximumstresstheory considers failure to occur when one of the three prin- cipal stresses (σ) reaches the material yield point (σy.p.) in tension: σ σ= y.p. (1) This theory is the simplest to apply and, with an adequate safety factor, it results in safe, reliable pres- sure vessel designs. This is the theory of strength used in the ASME Code, Section I, Section VIII Division 1, and Section III Division 1 (design by formula Subsec- tions NC-3300, ND-3300 and NE-3300). Maximum shear stress theory The maximum shear stress theory, also known as the Tresca theory,1 con- siders failure to occur when the maximum shear stress reaches the maximum shear stress at the yield strength of the material in tension. Noting that the maximum shear stress (τ) is equal to half the differ- ence of the maximum and minimum principal stresses, and that the maximum shear stress in a tension test specimen is half the axial principal stress, the condi- tion for yielding becomes: τ σ σ σ τ σ σ σ = − = = − = max min y.p. max min y.p. 2 2 2 (2) The value 2τ is called the shear stress intensity. The maximum shear stress theory predicts ductile mate- rial yielding more accurately than the maximum stress theory. This is the theory of strength used in the ASME Code, Section VIII Division 2, and Section III Division 1, Subsection NB, and design by analysis, Subsections NC-3200 and NE-3200. Distortion energy theory The distortion energy theory (also known as the Mises criterion1 ) considers yielding to occur when the distortion energy at a point in a stressed element is equal to the distortion energy in a uni-axial test specimenatthepointitbeginstoyield. While the distortion energy theory is the most accurate for ductile materials, it is cumbersome to use and is not routinely applied in pressure vessel design codes. Design criteria1 To determine the allowable stresses in a pressure vessel, one must consider the nature of the loading and the vessel response to the loading. Stress interpreta- tion determines the required stress analyses and the allowable stress magnitudes. Current design codes establish the criteria for safe design and operation of pressure vessels. Stress classifications Stresses in pressure vessels have three major classifications: primary, secondary and peak. Primary stresses (P) are caused by loadings which are necessary to satisfy the laws of equilibrium with applied pressure and other loads. These stresses are further divided into general primary membrane (Pm), local primary membrane (PL) and primary bending (Pb) stresses. A primary stress is not self-limiting, i.e., if the materialyieldsorisdeformed,thestressisnotreduced. A good example of this type of stress is that produced Fig. 2 Fossil fuel boiler steam drum.
- 217. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-3 by internal pressure such as in a steam drum. When it exceeds the vessel material yield strength, perma- nent distortion appears and failure may occur. Secondary stresses (Q), due to mechanical loads or differential thermal expansion, are developed by the constraint of adjacent material or adjacent compo- nents. They are self-limiting and are usually confined to local areas of the vessel. Local yielding or minor distortion can reduce secondary stresses. Although they do not affect the static bursting strength of a vessel, secondary stresses must be considered in es- tablishing its fatigue life. Peak stresses (F) are concentrated in highly local- ized areas at abrupt geometry changes. Although no appreciable vessel deformations are associated with them, peak stresses are particularly important in evaluating the fatigue life of a vessel. Codedesign/analysisrequirements Allowablestress limits and design analysis requirements vary with pressure vessel design codes. According to ASME Code, Section I, the minimum vessel wall thickness is determined by evaluating the general primary membrane stress. This stress, limited to the allowable material tension stress S, is calculated at the vessel design temperature. The Section I regu- lations have been established to ensure that second- ary and peak stresses are minimized; a detailed analy- sis of these stresses is normally not required. The design criteria of ASME Code, Sections VIII Division 1, and Section III Division 1 (design by for- mula Subsections NC-3300, ND-3300 and NE-3300), are similar to those of Section I. However, they require cylindrical shell thickness calculations in the circum- ferential and longitudinal directions. The minimum required pressure vessel wall thickness is set by the maximum stress in either direction. Section III Divi- sion 1 and Subsections NC-3300 and ND-3300 per- mit the combination of primary membrane and pri- mary bending stresses to be up to 1.5 S at design tem- perature. Section VIII Division 1 permits the combi- nation of primary membrane and primary bending stresses to be 1.5 S at temperatures where tensile or yield strength sets the allowable stress S, and a value smaller than 1.5 S at temperatures where creep gov- erns the allowable stress. ASME Code, Section VIII Division 2 provides for- mulas and rules for common configurations of shells and formed heads. It also requires detailed stress analysis of complex geometries with unusual or cyclic loadingconditions.Thecalculatedstressintensitiesare assigned to specific categories. The allowable stress intensity of each category is based on a multiplier of the Code allowable stress intensity value. The Code allowable stress intensity, Sm, is based on the material yield strength, Sy, or tensile strength, Su. (See Table 1.) The factor k varies with the type of loading: k Loading 1.0 sustained 1.2 sustained and transient 1.25 hydrostatic test 1.5 pneumatic test The design criteria for ASME Code, Section III Divi- sion 1, Subsection NB and design by analysis Subsec- tions NC-3200 and NE-3200 are similar to those for Section VIII Division 2 except there is less use of design formulas, curves, and tables, and greater use of design by analysis in Section III. The categories of stresses and stress intensity limits are the same in both sections. Stress analysis methods Stress analysis of pressure vessels can be performed by analytical or experimental methods. An analytical method, involving a rigorous mathematical solution based on the theory of elasticity and plasticity, is the most direct and inexpensive approach when the prob- lem is adaptable to such a solution. When the prob- lem is too complex for this method, approximate ana- lytical structural mechanics methods, such as finite element analysis, are applied. If the problem is beyond analytical solutions, experimental methods must be used. Mathematical formulas2 Pressure vessels are com- monly spheres, cylinders, ellipsoids, tori or composites of these. When the wall thickness is small compared to other dimensions, vessels are referred to as membrane shells. Stresses acting over the thickness of the vessel wall and tangential to its surface can be represented by mathematical formulas for the common shell forms. Pressurestressesareclassifiedasprimarymembrane stresses since they remain as long as the pressure is applied to the vessel. The basic equation for the lon- gitudinal stress σ1 and hoop stress σ2 in a vessel of thickness h, longitudinal radius r1, and circumferen- tial radius r2, which is subject to a pressure P, shown in Fig. 3 is: σ σ1 1 2 2r r P h + = (3) From this equation, and by equating the total pres- sure load with the longitudinal forces acting on a trans- versesectionofthevessel,thestressesinthecommonly used shells of revolution can be found. Table 1 Code-Allowable Stress Intensity Basis for Allowable Stress Intensity Allowable Value at k = 1.0 Category Value (Lesser Value) General primary kSm 2/3 Sy or 1/3 Su membrane (Pm ) Local primary 3/2 kSm Sy or 1/2 Su membrane (PL ) Primary membrane 3/2 kSm Sy or 1/2 Su plus primary bending (Pm + Pb) Range of primary plus 3 Sm 2 Sy or Su secondary (Pm + Pb + Q)
- 218. The Babcock & Wilcox Company 8-4 Steam 41 / Structural Analysis and Design 1. Cylindrical vessel – in this case, r1 = ∞, r2 = r, and σ1 2 = Pr h (4) σ2 = Pr h (5) 2. Spherical vessel – in this case, r1 = r2 = r, and σ1 2 = Pr h (6) σ2 2 = Pr h (7) 3. Conical vessel – in this case, r1 = ∞, r2 = r/cos α where α is half the cone apex angle, and σ α1 2 = Pr cosh (8) σ α2 = Pr cosh (9) 4. Ellipsoidal vessel – in this case (Fig. 4), the instan- taneous radius of curvature varies with each po- sition on the ellipsoid, whose major axis is a and minor axis is b, and the stresses are given by: σ1 2 2 = Pr h (10) σ2 2 2 2 12 = − P h r r r (11) At the equator, the longitudinal stress is the same as the longitudinal stress in a cylinder, namely: σ1 2 = Pa h (12) and the hoop stress is: σ2 2 2 1 2 = − Pa h a b (13) When the ratio of major to minor axis is 2:1, the hoop stress is the same as that in a cylinder of the same mating diameter, but the stress is compres- sive rather than tensile. The hoop stress rises rap- idly when the ratio of major to minor axis exceeds 2:1 and, because this stress is compressive, buck- ling instability becomes a major concern. For this reason, ratios greater than 2:1 are seldom used. 5. Torus – in this case (Fig. 5), Ro is the radius of the bend centerline, θ is the angular hoop location from this centerline and: σ1 2 = Pr h (14) σ θ θ2 2 2 = + + Pr h R r sin R r sin o o (15) The longitudinal stress remains uniform around the circumference and is the same as that for a straight cylinder. The hoop stress, however, varies for differ- ent points in the torus cross-section. At the bend centerline, it is the same as that in a straight cylin- der. At the outside of the bend, it is less than this and is at its minimum. At the inside of the bend, or crotch, the value is at its maximum. Hoop stresses are depen- Fig. 3 Membrane stress in vessels (courtesy Van Nostrand Reinhold).2 Fig. 4 Stress in an ellipsoid.2
- 219. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-5 dent on the sharpness of the bend and are inversely proportional to bend radii. In pipe bending operations, the material thins at the outside and becomes thicker at the crotch of the bend. This is an offsetting factor for the higher hoop stresses that form with smaller bend radii. Thermal stresses result when a member is re- strained as it attempts to expand or contract due to a temperature change, ∆T. They are classified as sec- ondary stresses because they are self-limiting. If the material is restricted in only one direction, the stress developed is: σ α= ± E T∆ (16) where E is the modulus of elasticity and α is the coef- ficient of thermal expansion. If the member is re- stricted from expanding or contracting in two direc- ASME Code calculations In most U.S. states and Canadian provinces laws have been established requiring that boilers and pres- sure vessels comply with the rules for the design and construction of boilers and pressure vessels in the ASME Code. The complexity of these rules and the amount of analysis required are inversely related to the factors of safety which are applied to the material properties used to establish the allowable stresses. That is, when the stress analysis is simplified, the factor of safety is larger. When the stress analysis is more complex, the factory of safety is smaller. Thus, overall safety is maintained even though the factor of safety is smaller. For condi- tions when material tensile strength establishes the allowable stress, ASME Code, Section IV, Rules for Con- struction of Heating Boilers, requires only a simple thickness calculation with a safety factor on tensile strength of 5. ASME Code, Section I, Rules for Construc- tion of Power Boilers and Section VIII, Division 1, Rules for Construction of Pressure Vessels, require a more complex analysis with additional items to be considered. However, the factor of safety on tensile strength is re- duced to 3.5. Section III, Rules for Construction of Nuclear Components and Section VIII, Division 2, Rules for Construction of Pressure Vessels require extensive analyses which are required to be certified by a regis- tered professional engineer. In return, the factor of safety on tensile strength is reduced even further to 3.0. When the wall thickness is small compared to the di- ameter, membrane formulas (Equations 4 and 5) may be used with adequate accuracy. However, when the wall thickness is large relative to the vessel diameter, usually to accommodate higher internal design pressure, the mem- brane formulas are modified for ASME Code applications. Basically the minimum wall thickness of a cylindri- cal shell is initially set by solving the circumferential or hoop stress equation assuming there are no additional loadings other than internal pressure. Other loadings may then be considered to determine if the initial mini- mum required wall thickness has to be increased to keep calculated stresses below allowable stress values. As an example, consider a Section VIII, Division 1, pressure vessel with no unreinforced openings and no additional loadings other than an internal design pres- sure of 1200 psi at 500F. The inside diameter is 10 in. and the material is SA-516, Grade 70 carbon steel. There is no corrosion allowance required by this application and the butt weld joints are 100% radiographed. What is the minimum required wall thickness needed? The equation for setting the minimum required wall thick- ness in Section VIII, Division 1, of the Code (paragraph UG-27(c)(l), 2001 Edition) is: t PR SE P = − 0 6. where t = minimum required wall thickness, in. P = internal design pressure, psi R = inside radius, in. S = allowable stress at design temperature, psi (Sec- tion II, Part D) = 20,000 psi E = lower of weld joint efficiency or ligament efficiency (fully radiographed with manual penetrations) = 1.0 For the pressure vessel described above: P = 1200 psi R = 5 in. S = 20,000 psi E = 1.0 t = ( ) − ( ) = ( ) ( ) ( , ) . ( . ) . 1200 in. 5 20 000 1 0 0 6 1200 0 311 Using commercial sizes, this plate thickness probably would be ordered at 0.375 in. If Equation 5 for simple hoop stress (see Figure be- low) is used alone to calculate the plate thickness using the specified minimum tensile strength of SA-516, Grade 70 of 70,000 psi, the thickness h would be evaluated to be: h = = 1200 5 70 000 0 0857 ( ) , . Therefore, the factor of safety (FS) based on tensile strength is: FS 0.311 0.0857 .6= = 3
- 220. The Babcock & Wilcox Company 8-6 Steam 41 / Structural Analysis and Design tions, as is the case in pressure vessels, the resulting stress is: σ α µ = ± − E T∆ 1 (17) where µ is Poisson’s ratio. These thermal stress equations consider full re- straint, and therefore are the maximum that can be created. When the temperature varies within a mem- ber, the natural growth of one fiber is influenced by the differential growth of adjacent fibers. As a result, fibers at high temperatures are compressed and those at lower temperatures are stretched. The general equations for radial (σr), tangential (σt), and axial (σz) thermal stresses in a cylindrical vessel subject to a radial thermal gradient are: σ α µr a b a rE r r a b a Trdr Trdr= −( ) − − − ∫ ∫1 2 2 2 2 2 (18) σ α µt a b a rE r r a b a Trdr Trdr Tr= −( ) + − + − ∫ ∫1 2 2 2 2 2 2 (19) σ α µz a bE b a Trdr T= −( ) − − ∫1 2 2 2 (20) where E = modulus of elasticity µ = Poisson’s ratio r = radius at any location a = inside radius b = outside radius T = temperature For a cylindrical vessel in which heat is flowing radially through the walls under steady-state condi- tions, the maximum thermal stresses are: σ α µ ta a inside ET n b a b b a n b a ( ) = −( ) − − 2 1 1 2 2 2 2 (21) σ α µ tb a outside ET n b a a b a n b a ( ) = −( ) − − 2 1 1 2 2 2 2 (22) For relatively thin tubes and Ta > Tb, this can be sim- plified to: σ α µta E T = − −( ) ∆ 2 1 (23) σ α µtb E T = −( ) ∆ 2 1 (24) To summarize, the maximum thermal stress for a thin cylinder with a logarithmic wall temperature gradient is one half the thermal stress of an element restrained in two directions and subjected to a tem- perature change ∆T (Equation 17). For a radial ther- mal gradient of different shape, the thermal stress can be represented by: σ α µ = − K E T∆ 1 (25) where K ranges between 0.5 and 1.0. Alternating stresses resulting from cyclic pressure vessel operation may lead to fatigue cracks at high stress concentrations. Fatigue life is evaluated by com- paring the alternating stress amplitude with design fatigue curves (allowable stress versus number of cycles or σ-N curves) experimentally established for the material at temperature. A typical σ-N design curve for carbon steel is shown in Fig. 6 and can be expressed by the equation: σa a a E N n d TS d= − + 4 100 100 01. ( ) (26) where σa = allowable alternating stress amplitude E = modulus of elasticity at temperature N = number of cycles da = percent reduction in area TS = tensile strength at temperature The two controlling parameters are tensile strength and reduction in area. Tensile strength is controlling in the high cycle fatigue region, while reduction in area is controlling in low cycle fatigue. The usual di- Fig. 5 Hoop stress variation in a bend.2 Fig. 6 Design fatigue curve. N, Number of Allowed Cycles (6,890) (689) (68.9) (6.90) 700F (371C) 800F (427C) 900F (482C) 1000F (538C) Valuesof AlternatingStressIntensity,,psi(MPa)a
- 221. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-7 vision between low and high cycle fatigue is 105 cycles. Pressure vessels often fall into the low cycle fatigue category, thereby demonstrating the importance of the material’s ability to deform in the plastic range with- out fracturing. Lower strength materials, with their greater ductility, have better low cycle fatigue resis- tance than do higher strength materials. Practical operating service conditions subject many vessels to the random occurrence of a number of stress cycles at different magnitudes. One method of ap- praising the damage from repetitive stresses to a ves- sel is the criterion that the cumulative damage from fatigue will occur when the summation of the incre- ments of damage at the various stress levels exceeds unity. That is: n N =∑ 1 (27) where n = number of cycles at stress σ, and N = num- ber of cycles to failure at the same stress σ. The ratio n/N is called the cycle damage ratio since it represents the fraction of the total life which is expended by the cycles that occur at a particular stress value. The value N is determined from σ-N curves for the mate- rial. If the sum of these cycle ratios is less than unity, the vessel is considered safe. This is particularly im- portant in designing an economic and safe structure which experiences only a relatively few cycles at a high stress level and the major number at a relatively low stress level. Discontinuity analysis method At geometrical discontinuities in axisymmetric structures, such as the intersection of a hemispherical shell element and a cylindrical shell element (Fig. 7a), the magnitude and characteristic of the stress are considerably different than those in elements remote from the discontinu- ity. A linear elastic analysis method is used to evalu- ate these local stresses. Discontinuity stresses that occur in pressure ves- sels,particularlyaxisymmetricvessels,aredetermined by a discontinuity analysis method. A discontinuity stress results from displacement and rotation incom- patibilities at the intersection of two elements. The forces and moments at the intersection (Fig. 7c) are redundant and self-limiting. They develop solely to ensure compatibility at the intersection. As a conse- quence, a discontinuity stress can not cause failure in ductile materials in one load application even if the maximum stress exceeds the material yield strength. Such stresses must be considered in cyclic load appli- cations or in special cases where materials can not safely redistribute stresses. The ASME Code refers to discontinuity stresses as secondary stresses. The ap- plication to the shell of revolution shown in Fig. 7 outlines the major steps involved in the method used to determine discontinuity stresses. Under internal pressure, a sphere radially expands approximately one half that of a cylindrical shell (Fig. 7b). The difference in free body displacement results in redundant loadings at the intersection if Elements (1) and (2) are joined (Fig. 7c). The final displacement and rotation of the cylindrical shell are equal to the free body displacement plus the displacements due to the redundant shear force Vo and redundant bending moment Mo (Fig. 7d). The direction of the redundant loading is unknown and must be assumed. A consistent sign convention must be followed. In addition, the direction of loading on the two elements must be set up consistently be- cause Element (1) reacts Element (2) loading and vice versa. If Mo or Vo as calculated is negative, the correct direction is opposite to that assumed. In equation form then, for Element (1): δ δ β βδ δFINAL 1 FREE1= − +V o M oV M1 1 (28) γ γ β βγ γFINAL 1 FREE1= + −V o M oV M1 1 (29) Similarly for Element (2): δ δ β βδ δFINAL2 FREE2= + +V o M oV M2 2 (30) γ γ β βγ γFINAL2 FREE2= + +V o M oV M2 2 (31) where δ µ FREE1 2 PR = − Et 1 2 (32) δ µ γ γ FREE 2 FREE1 FREE 2 PR in this case = −( ) = = 2 2 1 0 Et (33) The constants β are the deflections or rotations due to loading per unit of perimeter, and are referred to as influence coefficients. These constants can be deter- mined for a variety of geometries, including rings and thin shells of revolution, using standard handbook solutions. For example: βδV1 = radial displacement of Element (1) due to unit shear load Fig. 7 Discontinuity analysis.
- 222. The Babcock & Wilcox Company 8-8 Steam 41 / Structural Analysis and Design βδM1 = radial displacement of Element (1) due to unit moment load βγV1 = rotation of Element (1) due to unit shear load βγM1 = rotation of Element (1) due to unit moment load Because δFINAL 1 = δFINAL 2 and γFINAL 1 = γFINAL 2 from com- patibility requirements, Equations 28 through 31 can be reduced to two equations for two unknowns, Vo and Mo, which are solved simultaneously. Note that the number of equations reduces to the number of redun- dant loadings and that the force F can be determined by static equilibrium requirements. Once Vo and Mo have been calculated, handbook solutions can be applied to determine the resulting membrane and bending stresses. The discontinuity stress must then be added to the free body stress to obtain the total stress at the intersection. Although the example demonstrates internal pres- sure loading, the same method applies to determin- ing thermally induced discontinuity stress. For more complicated geometries involving four or more un- known redundant loadings, commercially available computer programs should be considered for solution. Finite element analysis Whenthegeometryofacom- ponent or vessel is too complex for classical formulas or closed form solutions, finite element analysis (FEA) can often provide the required results. FEA is a pow- erful numerical technique that can evaluate structural deformations and stresses, heat flows and tempera- tures, and dynamic responses of a structure. Because FEA is usually more economical than experimental stress analysis, scale modeling, or other numerical methods, it has become the dominant sophisticated stress analysis method. During product development, FEA is used to pre- dict performance of a new product or concept before building an expensive prototype. For example, a de- sign idea to protect the inside of a burner could be ana- lyzed to find out if it will have adequate cooling and fa- tigue life. FEA is also used to investigate field problems. To apply FEA, the structure is modeled as an as- sembly of discrete building blocks called elements. The elements canbelinear(onedimensionaltrussorbeam), plane (representing two dimensional behavior), or solid (three dimensional bricks). Elements are connected at their boundaries by nodes as illustrated in Fig. 8. Except for analyses using truss or beam elements, the accuracy of FEA is dependent on the mesh den- sity. This refers to the number of nodes per modeled volume. As mesh density increases, the result accu- racy also increases. Alternatively, in p-method analy- sis, the mesh density remains constant while increased accuracy is attained through mathematical changes to the solution process. Acomputersolutionisessentialbecauseofthenumer- ous calculations involved. A medium sized FEA may re- quire the simultaneous solution of thousands of equa- tions, but taking merely seconds of computer time. FEA is one of the most demanding computer applications. FEA theory is illustrated by considering a simple structural analysis with applied loads and specified node displacements. The mathematical theory is es- sentially as follows. For each element, a stiffness matrix satisfying the following relationship is found: k d r { } = { } (34) where [k] = an element stiffness matrix. It is square and defines the element stiffness in each direction (degree of freedom) {d} = a column of nodal displacements for one element {r} = a column of nodal loads for one element The determination of [k] can be very complex and its theory is not outlined here. Modeling the whole struc- ture requires that: K D R { } = { } (35) where [K] = structure stiffness matrix; each member of [K] is an assembly of the individual stiffness contributions surrounding a given node {D} = column of nodal displacements for the struc- ture {R} = column of nodal loads on the structure In general, neither {D} nor {R} is completely known. Therefore, Equation 35 must be partitioned (rear- ranged) to separate known and unknown quantities. Equation 35 then becomes: K K K K D D R R s o o s 11 12 21 22 = (36) where Ds = unknown displacements Do = known displacements Rs = unknown loads Ro = known loads Equation 36 represents the two following equations: K D K D Rs o o11 12 { } + { } = { } (37) K D K D Rs o s21 22 { } + { } = { } (38) Equation 37 can be solved for Ds and Equation 38 can then be solved for Rs. Using the calculated displacements {D}, {d} can be Fig. 8 Finite element model composed of brick elements.
- 223. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-9 found for each element and the stress can be calcu- lated by: σ{ } = { }E B d (39) where {σ} are element stresses [E] and [B] relate stresses to strains and strains to displacements respectively FEA theory may also be used to determine tempera- tures throughout complex geometric components. (See also Chapter 4.) Considering conduction alone, the governing relationship for thermal analysis is: C T K T Q { }+ { } = { } (40) where [C] = system heat capacity matrix {T } = column of rate of change of nodal temperatures [K ] = system thermal conductivity matrix {T} = column of nodal temperatures {Q} = column of nodal rates of heat transfer In many respects, the solution for thermal analy- sis is similar to that of the structural analysis. One im- portant difference, however, is that the thermal solu- tion is iterative and nonlinear. Three aspects of a ther- mal analysis require an iterative solution. First, thermal material properties are temperature dependent. Because they are primary unknowns, tem- perature assumptions must be made to establish the initial material properties. Each node is first given an assumed temperature. The first thermal distribution is then obtained, and the calculated temperatures are used in a second iteration. Convergence is attained when the calculated temperature distributions from two successive iterations are nearly the same. Second, when convective heat transfer is accounted for, heat transfer at a fluid boundary is dependent on the material surface temperature. Again, because tem- peratures are the primary unknowns, the solution must be iterative. Third, in a transient analysis, the input parameters, including boundary conditions, may change with time, and the analysis must be broken into discrete steps. Within each time step, the input parameters are held constant. For this reason, transient thermal analysis is sometimes termed quasi-static. FEA applied to dynamic problems is based upon the differential equation of motion: M D C D K D R { }+ { }+ { } = { } (41) where [M ] = structure lumped mass matrix [C] = structure damping matrix [K ] = structure stiffness matrix {R} = column of nodal forcing functions { }, { } { }D D Dand are columns of nodal displacements, velocities, and accelerations, respectively. Variations on Equation 41 can be used to solve for the natural frequencies, mode shapes, and responses due to a forcing function (periodic or nonperiodic), or to do a dynamic seismic analysis. Limitations of FEA involve computer and human resources. The user must have substantial experience and, among other abilities, he must be skilled in se- lecting element types and in geometry modeling. In FEA, result accuracy increases with the num- ber of nodes and elements. However, computation time also increases and handling the mass of data can be cumbersome. In most finite element analyses, large scale yield- ing (plastic strain) and deformations (including buck- ling instability), and creep are not accounted for; the material is considered to be linear elastic. In a linear structural analysis, the response (stress, strain, etc.) is proportional to the load. For example, if the applied load is doubled, the stress response would also double. For nonlinear analysis, FEA can also be beneficial. Recent advancements in computer hardware and soft- ware have enabled increased use of nonlinear analy- sis techniques. AlthoughmostFEAsoftwarehaswelldevelopedthree dimensionalcapabilities,somepressurevesselanalyses are imprecise due to a lack of acceptance criteria. Computer software consists of commercially avail- able and proprietary FEA programs. This software can be categorized into three groups: 1) preprocessors, 2) finite element solvers, and 3) postprocessors. A preprocessor builds a model geometry and applies boundary conditions, then verifies and optimizes the model. The output of a finite element solver consists of displacements, stresses, temperatures, or dynamic response data. Postprocessors manipulate the output from the fi- nite element solver for comparison to acceptance cri- teria or to make contour map plots. Application of FEA Because classical formulas and shell analysis solutions are limited to simple shapes, FEA fills a technical void and is applied in response to ASME Code requirements. A large portion of The Babcock & Wilcox Company’s (B&W) FEA supports pressure vessel design. Stresses can be calculated near nozzles and other abrupt geometry changes. In addi- tion, temperature changes and the resulting thermal stresses can be predicted using FEA. The raw output from a finite element solver can not be directly applied to the ASME Code criteria. The stressesorstrainsmustfirstbeclassifiedasmembrane, bending, or peak (Fig. 9). B&W pioneered the classi- fication of finite element stresses and these procedures are now used throughout the industry. Piping flexibility, for example, is an ideal FEA ap- plication. In addition, structural steel designers rely on FEA to analyze complex frame systems that sup- portsteamgenerationandemissionscontrolequipment. Finite element analysis is often used for preliminary review of new product designs. For example, Fig. 10 shows the deflected shape of two economizer fin con- figurations modeled using FEA.
- 224. The Babcock & Wilcox Company 8-10 Steam 41 / Structural Analysis and Design Fracture mechanics methods Fracture mechanics provides analysis methods to account for the presence of flaws such as voids or cracks. This is in contrast to the stress analysis meth- ods discussed above in which the structure was con- sidered to be free of those kinds of defects. Flaws may be found by nondestructive examination (NDE) or they may be hypothesized prior to fabrication. Frac- ture mechanics is particularly useful to design or evalu- atecomponentsfabricatedusingmaterialsthataremore sensitive to flaws. Additionally, it is well suited to the prediction of the remaining life of components under cyclic fatigue and high temperature creep conditions. During component design, the flaw size is hypoth- esized. Allowable design stresses can be determined knowing the lower bound material toughness from accepted design procedures in conjunction with a fac- tor of safety. Fracture mechanics can be used to evaluate the integrity of a flawed existing structure. The defect, usually found by NDE, is idealized according to ac- cepted ASME practices. An analysis uses design or calculatedstressesbasedonrealorhypothesizedloads, and material properties are found from testing a speci- men of similar material. Determining allowable flaw sizesstronglyreliesonaccuratematerialpropertiesand the best estimates of structural stresses. Appropriate safety factors are then added to the calculations. During inspection of power plant components, mi- nor cracks or flaws may be discovered. However, the flaws may propagate by creep or fatigue and become significant. The remaining life of components can not be accurately predicted from stress/cycles to failure (σ/N) curves alone. These predictions become possible using fracture mechanics. Linear elastic fracture mechanics The basic concept of linear elastic fracture mechanics (LEFM) was origi- nally developed to quantitatively evaluate sudden structural failure. LEFM, based on an analysis of the stresses near a sharp crack, assumes elastic behavior throughout the structure. The stress distribution near the crack tip depends on a single quantity, termed the stress intensity factor, KI. LEFM assumes that un- stable propagation of existing flaws occurs when the stress intensity factor becomes critical; this critical value is the fracture toughness of the material KIC. The theory of linear elastic fracture mechanics, LEFM, is based on the assumption that, at fracture, stress σ and defect size a are related to the fracture toughness KIC, as follows: K C aI = σ π (42a) and K KI IC≥ at failure (42b) The critical material property, KIC, is compared to the stress intensity factor of the cracked structure, KI, to identify failure potential. KI should not be confused with the stress intensity used elsewhere in ASME design codes for analysis of unflawed structures. The term C, accounting for the geometry of the crack and structure, is a function of the crack size and relevant structure dimensions such as width or thickness. C is exactly 1.0 for an infinitely wide center cracked panel with a through-wall crack length 2a, loaded in tension by a uniform remote stress σ. The factor C varies for other crack geometries illustrated in Fig. 11. Defects in a structure due to manufacture, in-service environment, or in-service cyclic fatigue are usually assumed to be flat, sharp, planar discontinuities where the planar area is normal to the applied stress. ASME Code procedures for fracture mechanics de- sign/analysis are presently given in Sections III and XI which are used for component thicknesses of at least 4 in. (102 mm) for ferritic materials with yield strengths less than 50,000 psi (344.7 MPa) and for simple geometries and stress distributions. The basic concepts of the Code may be extended to other ferritic materials (including clad ferritic materials) and more complex geometries; however, it does not apply to austenitic or high nickel alloys. These procedures pro- vide methods for designing against brittle fractures in structures and for evaluating the significance of flaws found during in-service inspections. Fig. 9 Classification of finite element stress results on a vessel cross- section for comparison to code criteria.3 Fig. 10 Economizer tube and fin (quarter symmetry model) deformed shape plots before (upper) and after (lower) design modifications.
- 225. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-11 The ASME Code, Section III uses the principles of linear elastic fracture mechanics to determine allow- able loadings in ferritic pressure vessels with an as- sumed defect. The stress intensity factors (KI) are cal- culated separately for membrane, bending, and ther- mal gradient stresses. They are further subdivided into primary and secondary stresses before summing and comparison to the allowable toughness, KIR. KIR is the reference critical stress intensity factor (tough- ness). It accounts for temperature and irradiation embrittlement effects on toughness. A safety factor of 2 is applied to the primary stress components and a factor of 1 is applied to the secondary components. To determine an operating pressure that is below the brittle fracture point, the following approach is used: 1. A maximum flaw size is assumed. This is a semi- elliptical surface flaw one fourth the pressure ves- sel wall thickness in depth and 1.5 times the thick- ness in length. 2. Knowing the specific material’s nil ductility tem- perature, and the design temperature KIR can be found from the Code. 3. The stress intensity factor is determined based on the membrane and bending stresses, and the ap- propriate correction factors. Additional determi- nants include the wall thickness and normal stress to yield strength ratio of the material. 4. The calculated stress intensity is compared to KIR. The ASME Code, Section XI provides a procedure to evaluate flaw indications found during in-service inspection of nuclear reactor coolant systems. If an indication is smaller than certain limits set by Section XI, it is considered acceptable without further analy- sis. If the indication is larger than these limits, Sec- tion XI provides information that enables the follow- ing procedure for further evaluation: 1. Determine the size, location and orientation of the flaw by NDE. 2. Determine the applied stresses at the flaw location (calculated without the flaw present) for all normal (includingupset),emergencyandfaultedconditions. 3. Calculate the stress intensity factors for each of the loading conditions. 4. Determine the necessary material properties, in- cluding the effects of irradiation. A reference tem- perature shift procedure is used to normalize the lower bound toughness versus temperature curves. These curves are based on crack arrest and staticinitiationvaluesfromfracturetoughnesstests. The temperature shift procedure accounts for heat to heat variation in material toughness properties. 5. Using the procedures above, as well as a procedure for calculating cumulative fatigue crack growth, three critical flaw parameters are determined: af = maximum size to which the detected flaw can grow during the remaining service of the component acrit = maximum critical size of the detected flaw under normal conditions ainit = maximum critical size for nonarresting growth initiation of the observed flaw un- der emergency and faulted conditions 6. Using these critical flaw parameters, determine if the detected flaw meets the following conditions for continued operation: a a a a f crit f init < < 0 1 0 5 . . (43) Elastic-plastic fracture mechanics (EPFM) LEFM provides a one parameter failure criterion in terms of the crack tip stress intensity factor (KI), but is limited to analyses where the plastic region surrounding the crack tip is small compared to the overall component di- mensions.Asthematerialbecomesmoreductileandthe structural response becomes nonlinear, the LEFM ap- proachlosesitsaccuracyandeventuallybecomesinvalid. A direct extension of LEFM to EPFM is possible by using a parameter to characterize the crack tip region that is not dependent on the crack tip stress. This parameter, the path independent J-integral, can char- acterize LEFM, EPFM, and fully plastic fracture me- chanics. It is capable of characterizing crack initiation, growth, and instability. The J-integral is a measure of the potential energy rate of change for nonlinear elastic structures containing defects. The J-integral can be calculated from stresses around a crack tip using nonlinear finite element analysis. An alternate approach is to use previously calculated deformation plasticity solutions in terms of the J-integral from the Electric Power Research In- stitute (EPRI) Elastic-Plastic Fracture Analysis Handbook.4 The onset of crack growth is predicted when: J JI IC≥ (44) The material property JIC is obtained using American Society for Testing and Materials (ASTM) test E813- 89, and JI is the calculated structural response. Stable crack growth occurs when: J a P J aI R,( ) = ( )∆ Fig. 11 Types of cracks.
- 226. The Babcock & Wilcox Company 8-12 Steam 41 / Structural Analysis and Design and a a ao= + ∆ (45) where a = current crack size P = applied remote load JR(∆a) = material crack growth resistance (ASTM test standard E1152-87) ∆a = change in crack size ao = initial crack size For crack instability, an additional criterion is: ∂ ∂ ≥ ∂ ∂J a J aR/ / (46) Failure assessment diagrams Failure assessment dia- grams are tools for the determination of safety mar- gins, prediction of failure or plastic instability and leak-before-break analysis of flawed structures. These diagrams recognize both brittle fracture and net sec- tion collapse mechanisms. The failure diagram (see Fig. 12) is a safety/failure plane defined by the stress intensity factor/toughness ratio (Kr) as the ordinate andtheappliedstress/netsectionplasticcollapsestress ratio (Sr) as the abscissa. For a fixed applied stress and defect size, the coordinates Kr, Sr are readily calcu- lable. If the assessment point denoted by these coor- dinates lies inside the failure assessment curve, no crack growth can occur. If the assessment point lies outside the curve, unstable crack growth is predicted. The distance of the assessment point from the failure assessment curve is a measure of failure potential of the flawed structure. In a leak-before-break analysis, a through-wall crack is postulated. If the resulting assessment point lies inside the failure assessment curve, the crack will leak before an unstable crack growth occurs. The deformation plasticity failure assessment dia- gram (DPFAD)5 is a specific variation of a failure as- sessmentdiagram.DPFADfollowstheBritishPD6493 R-66 format, and incorporates EPFM deformation plas- ticity J-integral solutions. The DPFAD curve is deter- mined by normalizing the deformation plasticity J- integral response of the flawed structure by its elastic response. The square root of this ratio is denoted by Kr. The Sr coordinate is the ratio of the applied stress to the net section plastic collapse stress. Various com- puter programs are available which automate this process for application purposes. Subcritical crack growth Subcritical crack growth refers to crack propagation due to cyclic fatigue, stress corrosion cracking, creep crack growth or a combina- tion of the three. Stress corrosion cracking and creep crack growth are time based while fatigue crack growth is based on the number of stress cycles. Fatigue crack growth Metal fatigue, although stud- ied for more than 100 years, continues to plague struc- tures subjected to cyclic stresses. The traditional ap- proach to prevent fatigue failures is to base the allow- able fatigue stresses on test results of carefully made laboratoryspecimensorrepresentativestructuralcom- ponents. These results are usually presented in cyclic stress versus cycles to failure, or σ/N, curves. The significant events of metal fatigue are crack initiation and subsequent growth until the net section yields or until the stress intensity factor of the struc- ture exceeds the material resistance to fracture. Tra- ditional analysis assumes that a structure is initially crack free. However, a structure can have cracks that originate during fabrication or during operation. Therefore, fatigue crack growth calculations are re- quired to predict the service life of a structure. Fatigue crack growth calculations can 1) determine the service life of a flawed structure that (during its lifetime) undergoes significant in-service cyclic load- ing, or 2) determine the initial flaw size that can be tolerated prior to or during a specified operating pe- riod of the structure. The most useful way of presenting fatigue crack growth rates is to consider them as a function of the stressintensity difference,∆K,whichisthedifferencebe- tweenthemaximumandminimumstressintensityfactors. To calculate fatigue crack growth, an experimen- tally determined curve such as Fig. 13 is used. The vertical axis, da/dN, is the crack growth per cycle. ASME Code, Section XI contains similar growth rate curves for pressure vessel steels. Creep crack growth Predicting the remaining life of fossil power plant components from creep rupture data alone is not reliable. Cracks can develop at critical lo- cations and these cracks can then propagate by creep crack growth. At temperatures above 800F (427C), creep crack growth can cause structural components to fail. Op- erating temperatures for certain fossil power plant components range from 900 to 1100F (482 to 593C). At these temperatures, creep deformation and crack growth become dependent on strain rate and time exposure. Macroscopic crack growth in a creeping material occurs by nucleation and joining of microcavities in the highly strained region ahead of the crack tip. In time dependent fracture mechanics (TDFM), the energy release rate (power) parameter Ct correlates7 creepcrackgrowththroughtherelationship: da dt bC t q / = (47) Fig. 12 Deformation plasticity failure assessment diagram in terms of stable crack growth.
- 227. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-13 By using the energy rate definition, Ct can be de- terminedexperimentallyfromtestspecimens.Thecon- stants b and q are determined by a curve fit technique. Under steady-state creep where the crack tip stresses no longer change with time, the crack growth can be characterized solely by the path independent energy rate line integral C*, analogous to the J-integral. C* and Ct can both be interpreted as the difference in energy rates (power) between two bodies with in- crementally differing crack lengths. Furthermore, C* characterizes the strength of the crack tip stress sin- gularity in the same manner as the J-integral char- acterizes the elastic-plastic stress singularity. The fully plastic deformation solutions from the EPRI Elastic-Plastic Fracture Handbook can then be used to estimate the creep crack tip steady-state pa- rameter, C*. Significant data support Ct as a parameter for corre- latingcreepcrackgrowthbehaviorrepresentedbyEqua- tion 47. An approximate expression8 for Ct is as follows: C C t tt T n n = ( ) + − − * / 3 1 1 (48) where tT is the transition time given by: t K n EC T I = −( ) +( ) 1 1 2 2 µ * (49) and µ is Poisson’s ratio, and n is the secondary creep rate exponent. For continuous operation, Equation 48 is integrated over the time covering crack growth from the initial flaw size to the final flaw size. The limiting final flaw size is chosen based on fracture toughness or insta- bility considerations, possibly governed by cold startup conditions. For this calculation, fracture toughness data such as KIC, JIC or the JR curve would be used in a failure assessment diagram approach to determine the limiting final flaw size. Construction features All pressure vessels require construction features such as fluid inlets and outlets, access openings, and structural attachments at support locations. These shell areas must have adequate reinforcement and gradualgeometrictransitionswhichlimitlocalstresses to acceptable levels. Openings Openings are the most prevalent con- struction features on a vessel. They can become ar- eas of weakness and may lead to unacceptable local distortion, known as bell mouthing, when the vessel is pressurized. Such distortions are associated with high local membrane stresses around the opening. Analytical studies have shown that these high stresses are confined to a distance of approximately one hole diameter, d, along the shell from the axis of the open- ing and are limited to a distance of 0.37 (dtnozzle)1/2 nor- mal to the shell. Reinforcement to reduce the membrane stress near an opening can be provided by increasing the vessel wall thickness. An alternate, more economical stress reduction method is to thicken the vessel locally around the nozzle axis of symmetry. The reinforcing material must be within the area of high local stress to be effective. The ASME Code provides guidelines for reinforc- ing openings. The reinforcement must meet require- ments for the amount and distribution of the added material. A relatively small opening [approximately d<0.2 (Rts)1/2 where R is mean radius of shell and ts is thickness of shell] remote from other locally stressed areas does not require reinforcement. Larger openings are normally reinforced as illus- trated in Figs. 14a and 14b. It is important to avoid excessive reinforcement that may result in high sec- ondary stresses. Fig. 14c shows an opening with over reinforcement and Fig. 14a shows one with well pro- portionedreinforcement.Fig.14balsoshowsabalanced design that minimizes secondary stresses at the nozzle/ shell juncture. Designs a and b, combined with gener- ous radii r, are most suitable for cyclic load applications. The ligament efficiency method is also used to com- pensate for metal removed at shell openings. This method considers the load carrying ability of an area between two points in relation to the load carrying ability of the remaining ligament when the two points become the centers of two openings. The ASME Code guidelines used in this method only apply to cylindri- Fig. 13 Relationship between da/dN and ∆K as plotted on logarithmic coordinates.
- 228. The Babcock & Wilcox Company 8-14 Steam 41 / Structural Analysis and Design cal pressure vessels wherethecircumferentialstressis twice the longitudinal stress. In determining the thick- ness of such vessels, the allowable stress in the thick- nesscalculationismultipliedbytheligamentefficiency. Nozzle and attachment loadings When external load- ings are applied to nozzles or attachment components, local stresses are generated in the shell. Several types of loading may be applied, such as sustained, tran- sient and thermal expansion flexibility loadings. The local membrane stresses produced by such loadings must be limited to avoid unacceptable distortion due to a single load application. The combination of local membrane and bending stresses must also be limited to avoid incremental distortion under cyclic loading. Finally, to prevent cyclic load fatigue failures, the nozzle or attachment should include gradual transi- tions which minimize stress concentrations. Pressure vessels may require local thickening at nozzles and attachments to avoid yielding or incre- mental distortion due to the combined effects of ex- ternal loading, internal pressure, and thermal load- ing. Simple procedures to determine such reinforce- ment are not available, however FEA methods can be used. The Welding Research Council (WRC) Bulletin No. 107 also provides a procedure for determining lo- cal stresses adjacent to nozzles and rectangular at- tachments on cylindrical and spherical shells. The external loadings considered by the WRC are longitudinal moment, transverse moment, torsional moment, and axial force. Stresses at various inside and outside shell surfaces are obtained by combining the stresses from the various applied loads. These ex- ternalloadstressesarethencombinedwithinternalpres- surestressesandcomparedwithallowablestresslimits. Use of the WRC procedure is restricted by limitations on shell and attachment parameters; however, experi- mental and theoretical work continues in this area. Structural support components Pressure vessels are normally supported by saddles, cylindrical support skirts, hanger lugs and brackets, ring girders, or integral support legs. A vessel has concentrated loads imposed on its shell where these supports are located. Therefore, it is important that the support arrangements minimize local stresses in the vessel. In addition, the components must provide support for the specified loading conditions and with- stand corresponding temperature requirements. Design criteria Structural elements that provide support, stiffen- ing, and/or stabilization of pressure vessels or compo- nents may be directly attached by welding or bolting. They can also be indirectly attached by clips, pins, or clamps, or may be completelyunattachedtherebytrans- ferring load through surface bearing and friction. Loading conditions In general, loads applied to structural components are categorized as dead, live, or transient loads. Dead loads are due to the force of gravity on the equipment and supports. Live loads vary in magnitude and are applied to produce the maximum design conditions. Transient loads are time dependent and are expected to occur randomly for the life of the structural components. Specific loadings that are considered in designing a pressure component support include: 1. weight of the component and its contents during operating and test conditions, including loads due to static and dynamic head and fluid flow, 2. weight of the support components, 3. superimposed static and thermal loads induced by the supported components, 4. environmental loads such as wind and snow, 5. dynamic loads including those caused by earth- quake, vibration, or rapid pressure change, 6. loads from piping thermal expansion,Fig. 14 Nozzle opening reinforcements.
- 229. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-15 7. loads from expansion or contraction due to pres- sure, and 8. loads due to anchor settlement. Code design/analysis requirements Code require- ments for designing pressure part structural supports vary. The ASME Code, Section I, only covers pressure part attaching lugs, hangers or brackets. These must be properly fitted and must be made of weldable and comparable quality material. Only the weld attach- ing the structural member to the pressure part is con- sidered within the scope of Section I. Prudent design of all other support hardware is the manufacturer’s responsibility. The ASME Code, Section VIII, Division 1, does not contain design requirements for vessel supports; how- ever, suggested rules of good practice are presented. These rules primarily address support details which prevent excessive local shell stresses at the attach- ments. For example, horizontal pressure vessel sup- port saddles are recommended to support at least one third of the shell circumference. Rules for the saddle design are not covered. However, the Code refers the designer to the Manual of Steel Construction, pub- lished by the American Institute of Steel Construction (AISC). This reference details the allowable stress design (ASD) method for structural steel building de- signs. When adjustments are made for elevated tem- peratures, this specification can be used for design- ing pressure vessel support components. Similarly, Section VIII, Division 2, does not contain design meth- ods for vessel support components. However, materi- als for structural attachments welded to pressure com- ponents and details of permissible attachment welds are covered. Section III of the ASME Code contains rules for the material, design, fabrication, examination, and instal- lation of certain pressure component and piping sup- ports. The supports are placed within three categories: 1. plate and shell type supports, such as vessel skirts and saddles, which are fabricated from plate and shell elements, 2. linear supports which include axially loaded struts, beams and columns, subjected to bending, and trusses, frames, rings, arches and cables, and 3. standard supports (catalog items) such as constant and variable type spring hangers, shock arrest- ers, sway braces, vibration dampers, clevises, etc. The design procedures for each of these support types are: 1. designbyanalysisincludingmethodsbasedonmaxi- mum shear stress and maximum stress theories, 2. experimental stress analysis, and 3. load rating by testing full size prototypes. The analysis required for each type of support de- pends on the class of the pressure component being supported. Typical support design considerations Designbyanalysisinvolvesdeterminingthestresses in the structural components and their connections by accepted analysis methods. Unless specified in an applicable code, choosing the analysis method is the designer’s prerogative. Linear elastic analysis (covered in depth here), using the maximum stress or maximum shear stress theory, is commonly applied to plate, shell type and linear type supports. As an alternate, the method of limit (plastic) analysis can be used for framed linear structures when appropriate load ad- justment factors are applied. Plateandshelltypesupports Cylindricalshellskirts are commonly used to support vertical pressure ves- sels. They are attached to the vessel with a minimum offset in order to reduce local bending stresses at the vessel skirt junction. This construction also permits radial pressure and thermal growth of the supported vessel through bending of the skirt. The length of the support is chosen to permit this bending to occur safely. See Fig. 15 for typical shell type support skirt details. In designing the skirt, the magnitudes of the loads that must be supported are determined. These nor- mally include the vessel weight, the contents of the vessel, the imposed loads of any equipment supported from the vessel, and loads from piping or other attach- ments. Next a skirt height is set and the forces and moments at the skirt base, due to the loads applied, are determined. Treating the cylindrical shell as a beam, the axial stress in the skirt is then determined from: σ = − ± P A Mc I v (50) where σ = axial stress in skirt Pv = total vertical design load A = cross-sectional area M = moment at base due to design loads c = radial distance from centerline of skirt I = moment of inertia For thin shells (R/t > 10), the equation for the axial stress becomes: σ π π = − ± P Rt M R t v 2 2 (51) where R = mean radius of skirt t = thickness of skirt Because the compressive stress is larger than the ten- sile stress, it usually controls the skirt design. Using the maximum stress theory for this example, the skirt thickness is obtained by: t P RF M R F v A A = + 2 2 π π (52) where FA = allowable axial compressive stress The designer must also consider stresses caused by transient loadings such as wind or earthquakes. Fi- nally, skirt connections at the vessel and support base must be checked for local primary and secondary
- 230. The Babcock & Wilcox Company 8-16 Steam 41 / Structural Analysis and Design bending stresses. The consideration of overall stress levels provides the most accurate design. Local thermal bending stresses often occur because of a temperature difference between the skirt and sup- port base. The magnitudes of these bending stresses are dependent upon the severity of this axial thermal gradient; steeper gradients promote higher stresses. To minimize these stresses, the thermal gradient at the junction can be reduced by full penetration welds at the skirt to shell junction, which permit maximum conduction heat flow through the metal at that point, and by selective use of insulation in the crotch region to permit heat flow by convection and radiation. De- pending on the complexity of the attachment detail, the discontinuity stress analysis or the linear elastic finite element method is used to solve for the thermal bending stresses. Linear type supports Utility fossil fuel-fired steam generators contain many linear components that sup- port and reinforce the boiler pressure parts. For ex- ample, the furnace enclosure walls, which are con- structed of welded membraned tube panels, must be reinforced by external structural members (buckstays) to resist furnace gas pressure as well as wind and seis- mic forces. (See Chapter 23.) Similarly, chambers, such as the burner equipment enclosure (windbox), require internal systems to support the enclosure and its con- tents as well as to reinforce the furnace walls. The design of these structural systems is based on linear elastic methods using maximum stress theory allow- able limits. The buckstay system is typically comprised of hori- zontally oriented beams or trusses which are attached to the outside of the furnace membraned vertical tube walls. As shown in Fig. 16, the buckstay ends are con- nected to tie bars that link them to opposing wall buckstays thereby forming a self-equilibrating struc- tural system. The furnace enclosure walls are continu- ously welded at the corners creating a water-cooled, orthotropic plate, rectangular pressure vessel. The strength of the walls in the horizontal direction is con- siderably less than in the vertical direction, therefore thebuckstaysystemmembersarehorizontallyoriented. The buckstay spacing is based on the ability of the enclosure walls to resist the following loads: 1. internal tube design pressure (P), 2. axial dead loads (DL), 3. sustained furnace gas pressure (PLs), 4. transient furnace gas pressure (PLT), 5. wind loads (WL), and 6. seismic loads (EQ). The buckstay elevations are initially established based on wall stress checks and on the location of nec- essary equipment such as sootblowers, burners, access doors, and observation ports. These established buckstay elevations are considered as horizontal sup- ports for the continuous vertical tube wall. The wall is then analyzed for the following load combinations using a linear elastic analysis method: 1. DL + PLs + P, 2. DL + PLs + WL + P, 3. DL + PLs + EQ + P, and 4. DL + PLT + P. Buckstay spacings are varied to assure that the wall stresses are within allowable design limits. Addition- ally, their locations are designed to make full use of the structural capability of the membraned walls. The buckstay system members, their end connec- tions, and the wall attachments are designed for the maximum loads obtained from the wall analysis. They are designed as pinned end bending members accord- ing to the latest AISC ASD specification. This specifi- cation is modified for use at elevated temperatures and uses safety factors consistent with ASME Code, Sec- tions I and VIII. The most important design consider- ations for the buckstay system include: 1. stabilization of the outboard beam flanges or truss chords to prevent lateral buckling when subjected to compression stress, 2. the development of buckstay to tie bar end con- nections and buckstay to wall attachments that provide load transfer but allow differential expan- sion between connected elements, and 3. providing adequate buckstay spacing and stiffness to prevent resonance due to low frequency com- bustion gas pressure pulsations common in fossil fuel-fired boilers. Fig. 15 Support skirt details.2
- 231. The Babcock & Wilcox Company Steam 41 / Structural Analysis and Design 8-17 References 1. Farr, J.R., and Jawad, M.H., Structural Analysis and Design of Process Equipment, Second Ed., John Wiley and Sons, Inc., New York, New York, January, 1989. 2. Harvey, J.F., Theory and Design of Pressure Vessels, Van Nostrand Reinhold Company, New York, New York, 1985. 3. Kroenke, W.C., “Classification of Finite Element StressesAccording toASME Section III Stress Categories,” Pressure Vessels and Piping, Analysis and Computers, American Society of Mechanical Engineers (ASME), June, 1974. 4. Kumar, V., et al., “An Engineering Approach for Elas- tic-Plastic FractureAnalysis,” Report EPRI NP-1931, Elec- tric Power Research Institute (EPRI), Palo Alto, Califor- nia, July, 1981. 5. Bloom, J.M., “Deformation Plasticity Failure Assess- ment Diagram,” Elastic Plastic Fracture Mechanics Tech- nology, ASTM STGP 896, American Society for Testing and Materials, Philadelphia, Pennsylvania, 1985. 6. “Guidance on Methods for Assessing the Acceptability of Flaws in Fusion Welded Structure,” PD 6493:1991 Weld- ing Standards Committee, London, England, United King- dom, August 30, 1991. 7. Saxena, A., “Creep Crack Growth Under Non-Steady- State Conditions,” Fracture Mechanics, Vol. 17, ASTM STP 905, Philadelphia, Pennsylvania, 1986. 8. Bassani, J.L., Hawk, D.E., and Saxena, A., “Evalua- tion of the Ct Parameter for Characterizing Creep Crack Growth Rate in the Transient Region,” Third International Symposium on Nonlinear Fracture Mechanics, ASTM STP 995, Philadelphia, Pennsylvania, 1989. Bibliography Manual of Steel Construction (M016): Includes Code of Standard Practice, Simple Shears, and Specification for Structural Joints Using ASTM A325 or A490 Bolts, Ninth Ed.,American Institute of Steel Construction, July 1, 1989. Cook, R.D. et al., Concepts and Applications of Finite Element Analysis, Fourth Ed., Wiley Publishers, New York, New York, October, 2001. Harvey, J.F., Theory and Design of Pressure Vessels, Second Ed., Chapman and Hall, London, England, United Kingdom, December, 1991. Mershon, J.L., et al., “Local Stresses in Cylindrical Shells Due to External Loadings on Nozzles,” Welding Research Council (WRC) Bulletin No. 297, Supplement to WRC Bulle- tin No. 107(Revision1),August,1984,revisedSeptember,1987. Thornton, W.A., Manual of Steel Construction: Load and Resistance Factor Design (Manual of Steel Construction), Third Ed., American Institute of Steel Construction (AISC), November 1, 2001. Wichman, K.R., Hopper, A.G., and Mershon, J.L., “Local Stresses in Spherical and Cylindrical Shells Due to Ex- ternal Loadings,” Welding Research Council (WRC), Bul- letin No. 107, August, 1965, revised March, 1979, updated October, 2002. Fig. 16 Typical buckstay elevation, plan view.
- 232. The Babcock & Wilcox Company 8-18 Steam 41 / Structural Analysis and Design A large steam drum is being lifted within power plant structural steel.
- 233. The Babcock & Wilcox Company Steam 41 Section II Steam Generation from Chemical Energy This section containing 17 chapters applies the fundamentals of steam gen- eration to the design of boilers, superheaters, economizers and air heaters for steam generation from chemical or fossil fuels (coal, oil and natural gas). As discussed in Chapter 1, the fuel and method of combustion have a dramatic impact on the size and configuration of the steam producing system. There- fore, Chapters 9 and 10 begin the section by exploring the variety and charac- teristics of chemical and fossil fuels, and summarize the combustion calcula- tions that are the basis for system design. The variety of combustion systems available to handle these fuels and the supporting fuel handling and preparation equipment are then described in Chapters 11 through 18. These range from the venerable stoker in its newest configurations to circular burners used for pulverized coal, oil and gas, to flu- idized-bed combustion and coal gasification. A key element in all of these sys- tems is the control of atmospheric emissions, in particular oxides of nitrogen (NOx) which are byproducts of the combustion process. Combustion NOx con- trol is discussed as an integral part of each system. It is also discussed in Sec- tion IV, Chapter 34. Based upon these combustion systems, Chapters 19 through 22 address the design and performance evaluation of the major steam generator heat trans- fer components: boiler, superheater, reheater, economizer and air heater. These are configured around the combustion system selected with special attention to properly handling the high temperature, often particle-laden flue gas. The fundamentals of heat transfer, fluid dynamics, materials science and struc- tural analysis are combined to provide the tradeoffs necessary for an economi- cal steam generating system design. The boiler setting and auxiliary equip- ment, such as sootblowers, ash handling systems and fans, which are key ele- ments in completing the overall steam system, conclude this section in Chap- ters 23 through 25.
- 234. Steam 41 / Sources of Chemical Energy 9-1 The Babcock & Wilcox Company Chapter 9 Sources of Chemical Energy World energy consumption continues to grow with the primary resources being the fossil fuels. Between 1991 and 2000, world production of primary energy increased at an annual rate of 1.4%. Production of pri- mary energy increased from 351 × 1015 Btu (370 × 1018 J) in 1991 to 397 × 1015 Btu (419 × 1018 J) in 2000. The trend in energy production by source from 1970 to 2000 is shown in Fig. 1. World energy production and fossil fuel reserves by region are shown in Figs. 2 and 3. The United States (U.S.), former Soviet Union (FSU) and China were the leading producers and con- sumers of world energy in 2000. They produced 38% and consumed 41% of the world’s energy. Energy use in the developing world is expected to continue to in- crease with demand in developing Asia and Central and SouthAmerica more than doubling between 1999 and 2020. Projected world energy consumption through the year 2025 is shown in Fig. 4. Annual energy production in the U.S. rose to 71.6 × 1015 Btu (75.5 × 1018 J) in 2000, which is about 18% of world production.Approximately 81% of this energy is in the form of fossil fuels. U.S. energy production by source is given in Fig. 5. The relative U.S. production of coal compared to other fossil fuels has increased since 1976, when 26% was coal, 29% was crude oil and 33% was natural gas. In 1999, coal production accounted for 32%, crude oil was 17% and natural gas was 28%. Coal production for 1999 and 2000 represented the first time in forty years that production declined for two consecutive years. On an annual basis, the average utility price per ton of coal delivered to utilities dropped by 1.8% in 2000, continuing a downward trend started in 1978. Overall energy consumption in the U.S. was ap- proximately 99 × 1015 Btu (104 × 1018 J) in 2000.About 28% of this energy was consumed by electric utilities in the form of fossil fuels. Overall U.S. fossil fuel consumption continues to increase and grew to 84 × 1015 Btu (88.6 × 1018 J) in 2000. In spite of the decline in the cost of crude oil in the 1980s, it continues to be the most dominant and costly fuel in the fossil fuel mix. The trends in coal, oil and natural gas prices are given in Fig. 6. World availability of coal Coal is the second leading source of fuel, supplying 23% of the world’s primary energy in 2000. It is also the mostusedfossilfuelforutilityandindustrialpowergen- QuadrillionBtu 180 160 140 120 100 80 60 40 20 0 Crude Oil and NGL Natural Gas (Dry) Coal Hydroelectric Power Nuclear Power 101 133 136 37 55 76 63 73 94 12 18 23 1 8 20 1970 1980 1990 2000 155 91 93 28 26 Fig. 1 Trends in world energy production by source (NGL = natural gas liquids). Eastern Europe and FSU 16% Far East and Oceania 21% North America 25% Western Europe 11% Central/South America 6% Middle East 14% Africa 7% Fig. 2 World primary energy production by region, 2001.
- 235. 9-2 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company eration. Major reserves by coal type and location are lig- nite in the U.S. and the former Soviet Union (FSU); sub- bituminous in China, the FSU, Australia and Germany; and bituminous in China, the U.S. and the FSU. Reserves of coal by regions of the world are given in Fig. 3. Of those regions, China consumed the most (25%) in 2000, followed by the U.S. (21%) and the FSU (9%). Because of its worldwide availability and low price, the demand for coal has grown and world coal trade has expanded by about 40% since 1980. The largest coal exporters are Australia, China, Indonesia, South Africa, the U.S., Canada, the FSU and Poland.1 U.S. availability of coal The coal reserves of the U.S. constitute a vast en- ergy resource, accounting for about 25% of the world’s total recoverable coal.2 According to the Energy Infor- mationAdministration (EIA), the national estimate of theDemonstratedReserveBasecoalresourcesremain- ing as of 2002, is 498 billion short tons. Reserves that are likely to be mined are estimated at 275 ×109 t (249 ×109 tm ).3 The U.S. produced 1.074 × 109 t (0.974 × 109 tm) of coal in 2000. Fig. 7 summarizes U.S. pro- duction from 1978 to 2000. U.S. coal consumption has steadily increased from 0.7 billion short tons in 1980 to 1.05 billion in 1999. The states with the largest coal reserves in the ground as of January, 2000, are shown in Table 1.4 States with large reserves, such as Mon- tana and Illinois, do not necessarily rank as high in pro- duction as Wyoming, Kentucky or West Virginia. Because of the resulting sulfur dioxide (SO2) emis- sions, coal sulfur levels are important production cri- teria and have been a factor in the growth of produc- tion from the western region, particularly the Powder River Basin. Table 2 shows the distribution of coal reserves by state at various sulfur levels. Coal fields in the U.S. are shown in Fig. 8. The two largest producing regions are the western region con- sisting of Arizona, Colorado, Montana, New Mexico, North Dakota, Utah, Washington, and Wyoming and theAppalachian region including Pennsylvania, West Virginia, Ohio, western Maryland, eastern Kentucky, Virginia, Tennessee and Alabama. In 2000, these re- gions produced 510.7 × 106 t (463 × 106 tm ) and 419 × 106 t (380 × 106 tm ), respectively. Two-thirds of the re- Crude Oil End of Year 1999 1018 Billion Barrels Western Europe Middle East Far East and Oceania Africa Eastern Europe and FSU North, South and Central America Natural Gas End of Year 1999 5150 Trillion ft Middle East Africa Far East and Oceania Eastern Europe and FSU Western Europe North, South and Central America Coal End of Year 1999 1082 Billion Short Tons Eastern Europe and FSU Middle East, Far East and Oceania Africa Western Europe North, South and Central America Fig. 3 Fossil fuel reserves by world region. Fig. 5 U.S. energy production by source, 2002. Crude Oil 17% Coal 31% Natural Gas 28% Wood, Waste, Other 5% Hydroelectric Power 4% Nuclear Power 11% Natural Gas Plant Liquids 4% Fig. 4 World primary energy consumption by fuel.1 QuadrillionBtu 250 200 150 100 50 0 2025 Year 20102000199019801970 History Projections Oil Natural Gas Coal Renewables Nuclear
- 236. Steam 41 / Sources of Chemical Energy 9-3 The Babcock & Wilcox Company serves lie in the Great Plains, the Rocky Mountains and the western states. These coals are mostly subbi- tuminous and lignitic, which have low sulfur content. Therefore, these fields have been rapidly developed to meet the increasing demands of electric utilities. The low sulfur coal permits more economical conform- ancetotheFederalCleanAirAct,itsAmendments,and acid rain legislation. (See Chapter 32.) U.S. electric utilities used coal to generate 51% of the net electrical power in 2000, and remain the larg- est coal consumers. Continuing the downward trend since 1982, the average delivered cost of coal decreased 27% in current dollars per million Btu. Environmental concerns about SO2, nitrogen oxides (NOx), carbon dioxide (CO2) and mercury (Hg) emis- sions could limit the growth of coal consumption. How- ever, the U.S., as well as Japan and several European countries, is researching clean coal technologies to reduce these emissions while boosting power produc- tion efficiency. These technologies are rapidly ap- proaching commercialization in the U.S. They are expected to be integrated into current and future power plants. How coal is formed Coal is formed from plants by chemical and geologi- cal processes that occur over millions of years. Layers of plant debris are deposited in wet or swampy regions under conditions that prevent exposure to air and com- plete decay as the debris accumulates. Bacterial ac- tion, pressure and temperature act on the organic matter over time to form coal. The geochemical pro- cess that transforms plant debris to coal is called coali- fication. The first product of this process, peat, often contains partially decomposed stems, twigs, and bark Table 2 Sulfur Content and Demonstrated Total Underground and Surface Coal Reserve Base of the U.S. (Million tons) Sulfur Range, % State <1.0 1.1 to 3.0 >3.0 Unknown Total* Alabama 624.7 1,099.9 16.4 1,239.4 2,981.8 Alaska 11,458.4 184.2 0.0 0.0 11,645.4 Arizona 173.3 176.7 0.0 0.0 350.0 Arkansas 81.2 463.1 46.3 74.3 665.7 Colorado 7,475.5 786.2 47.3 6,547.3 14,869.2 Georgia 0.3 0.0 0.0 0.2 0.5 Illinois 1,095.1 7,341.4 42,968.9 14,256.2 65,664.8 Indiana 548.8 3,305.8 5,262.4 1,504.1 10,622.6 Iowa 1.5 226.7 2,105.9 549.2 2,884.9 Kansas 0.0 309.2 695.6 383.2 1,388.1 Kentucky-East 6,558.4 3,321.8 299.5 2,729.3 12,916.7 Kentucky-West 0.2 564.4 9,243.9 2,815.9 12,623.9 Maryland 135.1 690.5 187.4 34.6 1,048.2 Michigan 4.6 85.4 20.9 7.0 118.2 Missouri 0.0 182.0 5,226.0 4,080.5 9,487.3 Montana 101,646.6 4,115.0 502.6 2,116.7 108,396.2 New Mexico 3,575.3 793.4 0.9 27.5 4,394.8 North Carolina 0.0 0.0 0.0 31.7 31.7 North Dakota 5,389.0 10,325.4 268.7 15.0 16,003.0 Ohio 134.4 6,440.9 12,534.3 1,872.0 21,077.2 Oklahoma 275.0 326.6 241.4 450.5 1,294.2 Oregon 1.5 0.3 0.0 0.0 1.8 Pennsylvania 7,318.3 16,913.6 3,799.6 2,954.2 31,000.6 South Dakota 103.1 287.9 35.9 1.0 428.0 Tennessee 204.8 533.2 156.6 88.0 986.7 Texas 659.8 1,884.6 284.1 444.0 3,271.9 Utah 1,968.5 1,546.7 49.4 478.3 4,042.5 Virginia 2,140.1 1,163.5 14.1 330.0 3,649.9 Washington 603.5 1,265.5 39.0 45.1 1,954.0 West Virginia 14,092.1 14,006.2 6,823.3 4,652.5 39,589.8 Wyoming 33,912.3 14,657.4 1,701.1 3,060.3 53,336.1 Total* 200,181.4 92,997.5 92,571.5 50,788.0 436,725.7 *Data may not add to totals shown due to independent rounding. Source, Bureau of Mines Bulletin, CoalBituminous and Lignite, 1974. Table 1 U.S. Energy Information Administration States with Largest Demonstrated Coal Reserves (x 109 t)* Total Underground Surface % Total State Reserves Reserves Reserves U.S. t (tm) t (tm) t (tm) Montana 120 109 71 64 49 44 23.9 Illinois 105 95 88 80 17 15 20.9 Wyoming 67 61 43 39 24 22 13.3 West Virginia 35 32 30 27 4 3.6 7.0 Kentucky 31 28 18 16 14 13 6.2 Pennsylvania 28 25 24 22 4 3.6 5.5 Ohio 24 22 18 16 6 5 4.8 Colorado 17 15 12 11 5 4.5 3.4 Texas 13 12 0 0 13 11.8 2.6 New Mexico 12 11 6 5 6 5 2.4 Indiana 10 9 9 8 1 0.9 2.0 All others 41 37 20 18 21 19 8.2 Total U.S. 503 456 339 306 164 147 100.0 * Figures are rounded and include anthracite. Chained(1996)DollarsperMillionBtu 10 8 6 4 2 0 2000 Year 19951990198519801975 Crude Oil Natural Gas Coal Fossil Fuel Composite Fig. 6 Trends in U.S. fossil fuel prices. MillionShortTons 700 600 500 400 300 200 100 0 1978 1989 2000 Bituminous Coal Subbituminous Coal Lignite 657 534 549 434 231 97 34 87 89 Fig. 7 U.S. coal production trends.
- 237. 9-4 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company and is not classified as coal. However, peat is progres- sively transformed to lignite that eventually can be- come anthracite, given the proper progression of geo- logical changes. Various physical and chemical processes occur dur- ing coalification. The heat and pressure to which the organic material is exposed cause chemical and struc- tural changes. These changes include an increase in carbon content; loss of water, oxygen and hydrogen; and resistance to solvents. The coalification process is shown schematically in Fig. 9. Coal is very heterogeneous and can vary in chemi- cal composition by location. In addition to the major organic ingredients (carbon, hydrogen and oxygen), coal also contains impurities. The impurities that are of major concern are ash and sulfur. The ash results from mineral or inorganic material introduced during coalification. Ash sources include inorganic sub- stances, such as silica, that are part of the chemical structure of the plants. Dissolved inorganic ions and mineral grains found in swampy water are also cap- tured by the organic matter during early coalification. Mud,shaleandpyritearedepositedinporesandcracks of the coal seams. Sulfur occurs in coal in three forms: 1) organic sul- fur, which is part of the coal’s molecular structure, 2) pyritic sulfur, which occurs as the mineral pyrite, and 3) sulfate sulfur, primarily from iron sulfate. The prin- cipal sulfur source is sulfate ion, found in water. Fresh water has a low sulfate concentration while salt wa- ter has a high sulfate content. Therefore, bituminous coal, deposited in the interior of the U.S. when seas covered this region, are high in sulfur. Some Iowa coals contain as much as 8% sulfur. Although coal is a complex, heterogeneous mixture and not a polymer or biological molecule, it is some- times useful for chemists to draw an idealized struc- tural formula. These formulas can serve as models that illustrate coal reactions. This can aid the further de- velopment of coal processes such as gasification, com- bustion and liquefaction. Fig. 9 The coalification process (DAF = dry ash-free). Fig. 8 U.S. coal reserves.
- 238. Steam 41 / Sources of Chemical Energy 9-5 The Babcock & Wilcox Company Classifying coal A coal classification system is needed because coal is a heterogeneous substance with a wide range of com- position and properties. Coals are typically classified by rank. This indicates the progressive alteration in the coalification process from lignite to subbituminous, bituminous and anthracite coals. The rank indicates a coal’s geological history and broad characteristics. ASTM classification by rank ThesystemusedintheU.S.forclassifyingcoalbyrank wasestablishedbytheAmericanSocietyforTestingand Materials(ASTM).5 ASTMclassificationisasystemthat uses the volatile matter (VM) and fixed carbon (FC) re- sultsfromtheproximateanalysisandtheheatingvalue of the coal as ranking criteria. This system aids in iden- tifying commercial uses of coals and provides basic in- formation regarding combustion characteristics. The classification system is given in Table 3 and described in section D 388 of the ASTM standards. Proximate analysis is based on the laboratory proce- dure described in ASTM D 3172. In this procedure, moisture content, ash remaining after complete burn- ing, amount of gases released when heated to a pre- scribed temperature, and fixed carbon remaining af- ter volatilization are determined. Table 4 gives a typical as-received proximate analy- sis of a West Virginia coal.An as-received analysis in- cludes the total moisture content of the coal as it is received at the power plant. For older or higher rank coals, FC and VM are used astheclassifyingcriteria.Thesecriteriaaredetermined on a dry, mineral-matter-free basis using formulas de- veloped by S.W. Parr in 1906 (shown in Equations 1 through 6).6 The younger or low rank coals are classi- fied by Btu content on a moist, mineral-matter-free ba- sis. Agglomerating or weathering indices, as described in ASTM D 388, are used to differentiate adjacent groups. Parr Formulas Dry, mineral-free S S FC FC M A = − − + +( ) × 0 15 100 1 08 0 55 100 . . . , % (1) Table 3 Classification of Coals by Ranka (ASTM D 388) Fixed Carbon Volatile Matter Calorific Value Limits, % Limits, % Limits, Btu/lb (Dry, Mineral- (Dry, Mineral- (Moist,b Matter-Free Matter-Free Mineral-Matter- Basis) Basis) Free Basis) Equal or Equal Equal or Greater Less Greater or Less Greater Less Agglomerating Class Group Than Than Than Than Than Than Character 1. Meta-anthracite 98 − − 2 − − I. Anthracitic 2. Anthracite 92 98 2 8 − − Nonagglomerating 3. Semianthracitec 86 92 8 14 − − 1. Low volatile bituminous coal 78 86 14 22 − − 2. Medium volatile bituminous coal 69 78 22 31 − − II. Bituminous 3. High volatile A bituminous coal − 69 31 − 14,000d − Commonly 4. High volatile B bituminous coal − − − − 13,000d 14,000 agglomeratinge 5. High volatile C bituminous coal − − − − 11,500 13,000 10,500e 11,500 Agglomerating 1. Subbituminous A coal − − − − 10,500 11,500 III. Subbituminous 2. Subbituminous B coal − − − − 9,500 10,500 3. Subbituminous C coal − − − − 8,300 9,500 Nonagglomerating 1. Lignite A − − − − 6,300 8,300IV. Lignitic 2. Lignite B − − − − − 6,300 a This classification does not include a few coals, principally nonbanded varieties, which have unusual physical and chemical properties and which come within the limits of fixed carbon or calorific value of the high volatile bituminous and subbituminous ranks. All of these coals either contain less than 48% dry, mineral-matter-free fixed carbon or have more than 15,500 moist, mineral-matter-free Btu/lb. b Moist refers to coal containing its natural inherent moisture but not including visible water on the surface of the coal. c If agglomerating, classify in low volatile group of the bituminous class. d Coals having 69% or more fixed carbon on the dry, mineral- matter-free basis shall be classified according to fixed carbon, regardless of calorific value. e It is recognized that there may be nonagglomerating varieties in these groups of the bituminous class, and there are notable exceptions in high volatile C bituminous group.
- 239. 9-6 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company Dry, mineral-free Dry, mineral-free VM FC = −100 , % (2) Moist, mineral-free Btu Btu S S , per l = − − +( ) × 50 100 1 08 0 55 100 . .A bb (3) Approximation Formulas Dry, mineral-free S FC FC M A = − + +( ) × 100 1 1 0 1 100 . . , % (4) Dry, mineral-free Dry, mineral-free VM FC = −100 , % (5) Moist, mineral-free Btu Btu S , per lb = − +( ) × 100 1 1 0 1 100 . .A (6) where Btu = heating value per lb (kJ/kg = 2.326 × Btu/lb) FC = fixed carbon, % VM = volatile matter, % M = bed moisture, A = ash, % S = sulfur, % all for coal on a moist basis. Table 5 lists 16 selected U.S. coals, arranged in order ofASTMclassification.Thefollowingdescriptionsbriefly summarize the characteristics of each coal rank. Peat Peat, the first product in the formation of coal, is a heterogeneous material consisting of partially de- composed plant and mineral matter. Its color ranges from yellow to brownish-black, depending on its geo- logic age. Peat has a moisture content up to 70% and a heating value as low as 3000 Btu/lb (6978 kJ/kg). Lignite Lignite is the lowest rank coal. Lignites are relatively soft and brown to black in color with heat- ing values of less than 8300 Btu/lb (19,306 kJ/kg). The deposits are geologically young and can contain rec- ognizable remains of plant debris. The moisture con- tent of lignites is as high as 30% but the volatile con- tent is also high; consequently, they ignite easily. Lig- nite coal dries when exposed to air and spontaneous combustion during storage is a concern. Long distance shipment of these coals is usually not economical be- cause of their high moisture and low Btu content. The largest lignite deposit in the world spreads over the regions of North and South Dakota, Wyoming, and Montana in the U.S. and parts of Saskatchewan and Manitoba in Canada. Subbituminous Subbituminous coals are black, having little of the plant-like texture and none of the brown color associated with the lower rank lignite coal. Subbituminous coals are non-coking (undergo little swelling upon heating) and have a relatively high moisture content which averages from 15 to 30%. They also display a tendency toward spontaneous combus- tion when drying. Although they are high in VM content and ignite easily, subbituminous coals generally have less ash and are cleaner burning than lignite coals. Subbitu- minous coals in the U.S. in general have a very low sulfur content, often less than 1%. Because they have reasonably high heating values [8300 to 11,500 Btu/ lb (19,306 to 26,749 kJ/kg)] and low sulfur content, switching to subbituminous coal has become an attrac- tiveoptionformanypowerplantstolimitSO2 emissions. Bituminous Bituminous coal is the rank most com- monly burned in electric utility boilers. In general, it appears black with banded layers of glossy and dull black. Typical bituminous coals have heating values of 10,500 to 14,000 Btu/lb (24,423 to 32,564 kJ/kg) and a fixed carbon content of 69 to 86%. The heating value is higher, but moisture and volatile content are lower than the subbituminous and lignite coals. Bi- tuminous coals rarely experience spontaneous com- bustion in storage. Furthermore, the high heating value and fairly high volatile content enable bitumi- nous coals to burn easily when pulverized to a fine powder. Some types of bituminous coal, when heated in the absence of air, soften and release volatiles to form the porous, hard, black product known as coke. Coke is used as fuel in blast furnaces to make iron. Anthracite Anthracite, the highest rank of coal, is shiny black, hard and brittle, with little appearance of layers. It has the highest content of fixed carbon, 86 to 98%. However, its low volatile content makes it a slow burning fuel. Most anthracites have a very low moisture content of about 3%; heating values of 15,000 Btu/lb (34,890 kJ/kg) are slightly lower than the best quality bituminous coals.Anthracite is low in sulfur and volatiles and burns with a hot, clean flame. These qualities make it a premium fuel used mostly for domestic heating. Other classification systems There are other classifications of coal that are cur- rently in limited use in Europe. These are the Inter- national Classification of Hard Coals by Type and the Table 4 Coal Analyses on As-Received Basis (Pittsburgh Seam Coal, West Virginia) Proximate Analysis Ultimate Analysis Component % by wt Component % by wt Moisture 2.5 Moisture 2.5 Volatile matter 37.6 Carbon 75.0 Fixed carbon 52.9 Hydrogen 5.0 Ash 7.0 Sulfur 2.3 Total 100.0 Nitrogen 1.5 Oxygen 6.7 Heating value, Ash 7.0 Btu/lb 13,000 Total 100.0 (kJ/kg) (30,238)
- 240. Steam 41 / Sources of Chemical Energy 9-7 The Babcock & Wilcox Company InternationalClassificationofBrownCoals.Thesesys- tems were developed by the Coal Committee of the Economic Commission for Europe in 1949. Coal characterization As previously described, the criteria for ranking coal are based on its proximate analysis. In addition to pro- viding classifications, coal analysis provides other use- ful information. This includes assistance in selecting coal for steam generation, evaluation of existing han- dling and combustion equipment, and input for de- sign. The analyses consist of standard ASTM proce- dures and special tests developed by The Babcock & Wilcox Company (B&W). The following briefly sum- marizes some of these tests. Standard ASTM analyses5,7 Bases for analyses Because of the variability of moisture and ash content in coals, the composition determined by proximate analysis can be reported on several bases. The most common include as-received, moisture-free or dry, and mineral-matter-free. The as- received analysis reports the percentage by weight of each constituent in the coal as it is received at the labo- ratory. As-received samples contain varying levels of moisture. For analysis on a dry basis, the moisture of the sample is determined and then used to correct each constituent to a common dry level. As previously men- tioned, the ash in coal as determined by proximate analysis is different than the mineral matter in coal. This can cause problems when ranking coals by the ASTM method. Formulas used to correct for the min- eral matter and to determine volatile matter, fixed carbon and heating value on a mineral-matter-free basis are provided in Equations 1 to 6 above. Moisture determination Coal received at an electric power plant contains varying amounts of moisture in several forms. There is inherent and surface moisture in coal. Inherent moisture is that which is a naturally combined part of the coal deposit. It is held tightly within the coal structure and can not be removed eas- ily when the coal is dried in air. The surface moisture is not part of the coal deposit and has been added ex- ternally. Surface moisture is more easily removed from coal when exposed to air. It is not possible to distin- guish, by analysis, inherent and surface moisture. There are many other moistures that arise when characterizing coal including equilibrium, free and air dry moisture. Their definitions and use depend on the application. Equilibrium moisture is sometimes used as an estimate of bed moisture. The ASTM standard terminology of coal and coke, D 121, defines the total coal moisture as the loss in weight of a sample under controlled conditions of temperature, time and air flow. Using ASTM D 3302, the total moisture is calculated Table 5 Sixteen Selected U.S. Coals Arranged in Order of ASTM Classification Coal Rank Coal Analysis, Bed Moisture Basis Rank Rank No. Class Group State County M VM FC A S Btu FC Btu 1 I 1 Pa. Schuylkill 4.5 1.7 84.1 9.7 0.77 12,745 99.2 14,280 2 I 2 Pa. Lackawanna 2.5 6.2 79.4 11.9 0.60 12,925 94.1 14,880 3 I 3 Va. Montgomery 2.0 10.6 67.2 20.2 0.62 11,925 88.7 15,340 4 II 1 W.Va. McDowell 1.0 16.6 77.3 5.1 0.74 14,715 82.8 15,600 5 II 1 Pa. Cambria 1.3 17.5 70.9 10.3 1.68 13,800 81.3 15,595 6 II 2 Pa. Somerset 1.5 20.8 67.5 10.2 1.68 13,720 77.5 15,485 7 II 2 Pa. Indiana 1.5 23.4 64.9 10.2 2.20 13,800 74.5 15,580 8 II 3 Pa. Westmoreland 1.5 30.7 56.6 11.2 1.82 13,325 65.8 15,230 9 II 3 Ky. Pike 2.5 36.7 57.5 3.3 0.70 14,480 61.3 15,040 10 II 3 Ohio Belmont 3.6 40.0 47.3 9.1 4.00 12,850 55.4 14,380 11 II 4 Ill. Williamson 5.8 36.2 46.3 11.7 2.70 11,910 57.3 13,710 12 II 4 Utah Emery 5.2 38.2 50.2 6.4 0.90 12,600 57.3 13,560 13 II 5 Ill. Vermilion 12.2 38.8 40.0 9.0 3.20 11,340 51.8 12,630 14 III 2 Wyo. Sheridan 25.0 30.5 40.8 3.7 0.30 9,345 57.5 9,745 15 III 3 Wyo. Campbell 31.0 31.4 32.8 4.8 0.55 8,320 51.5 8,790 16 IV 1 N.D. Mercer 37.0 26.6 32.2 4.2 0.40 7,255 55.2 7,610 Notes: For definition of Rank Classification according to ASTM requirements, see Table 3. Data on Coal (Bed Moisture Basis) M = equilibrium moisture, %; VM = volatile matter, %; Rank FC = dry, mineral-matter-free fixed carbon, %; FC = fixed carbon, %; A = ash, %; S = sulfur, %; Rank Btu = moist, mineral-matter-free Btu/lb. Btu = Btu/lb, higher heating value. Calculations by Parr formulas.
- 241. 9-8 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company from the moisture lost or gained in air drying and the residualmoisture.Theresidualmoistureisdetermined by oven drying the air dried sample. Because subse- quent ASTM analyses (such as proximate and ulti- mate) are performed on an air dried sample, the re- sidual moisture value is required to convert these re- sults to a dry basis. In addition, the moisture lost on air drying provides an indication of the drying re- quired in the handling and pulverization portions of the boiler coal feed system. Proximateanalysis Proximateanalysis,ASTMD3172, includes the determination of volatile matter, fixed car- bon and ash. Volatile matter and fixed carbon, exclusive of the ash, are two indicators of coal rank. The amount of volatile matter in a coal indicates ease of ignition and whethersupplementalflamestabilizingfuelisrequired. The ash content indicates the load under which the ash collectionsystemmustoperate.Italsopermitsassessing related shipping and handling costs. Ultimate analysis Ultimate analysis, described in ASTM D 3176, includes measurements of carbon, hy- drogen, nitrogen and sulfur content, and the calcula- tion of oxygen content. Used with the heating value of the coal, combustion calculations can be performed to determine coal feed rates, combustion air require- ments, heat release rates, boiler performance, and sulfur emissions from the power plant. (See Table 4.) Heating value The gross calorific value of coal, de- termined using an adiabatic bomb calorimeter as de- scribed in ASTM D 2015, is expressed in Btu/lb (kJ/ kg) on various bases (dry, moisture and ash free, etc.). Thisvaluedeterminesthemaximumtheoreticalfuel energy available for the production of steam. Conse- quently, it is used to determine the quantity of fuel which must be handled, pulverized and fired. Gross (higher) heating value (HHV) is defined as the heat released from combustion of a unit fuel quan- tity (mass), with the products in the form of ash, gas- eous CO2, SO2, nitrogen and liquid water, exclusive of any water added as vapor. The net (lower) heating value (LHV) is calculated from the HHV. It is the heat produced by a unit quantity of fuel when all water in the products remains as vapor. This LHV calculation (ASTM Standard D 407) is made by deducting 1030 Btu/lb (2396 kJ/kg) of water derived from the fuel, including the water originally present as moisture and that formed by combustion. In the U.S., the gross calo- rific value is commonly used in heat balance calcula- tions, while in Europe the net value is generally used. Grindability The Hardgrove Grindability Test, de- veloped by B&W, is an empirical measure of the rela- tive ease with which coal can be pulverized. TheASTM D 409 method has been used for the past 30 years to evaluate the grindability of coals. The method involves grinding 50 g of air-dried 16 × 30 mesh (1.18 mm × 600 µm) test coal in a small ball-and-race mill. The mill is operated for 60 revolutions and the quantity of ma- terialthatpassesa200mesh(75micron)screenismea- sured. From a calibration curve relating –200 mesh (–75 micron) material to the grindability of standard samples supplied by the U.S. Department of Energy, the Hardgrove Grindability Index (HGI) is determined for the test coal. Pulverizer manufacturers have de- veloped correlations relating HGI to pulverizer capac- ity at desired levels of fineness. Sulfur forms The sulfur forms test, ASTM D 2492, measures the amounts of sulfate sulfur, pyritic sulfur and organically bound sulfur in a coal. This is accom- plished by measuring the total sulfur, sulfate, and py- ritic sulfur contents and obtaining the organic sulfur by difference. The quantity of pyritic sulfur is an in- dicator of potential coal abrasiveness. Free swelling index The free swelling index can be used to indicate caking characteristics. The index is determined by ASTM D 720 which consists of heat- ing a one gram coal sample for a specified time and temperature. The shape of the sample or button formed by the swelling coal is then compared to a set of standard buttons. Larger formed buttons indicate higher free swelling indices. Oxidized coals tend to have lower indices. The free swelling index can be used as a relative measurement of a coal’s caking proper- ties and extent of oxidation. Ash fusion temperatures Coal ash fusion tempera- tures are determined from cones of ash prepared and heated in accordance withASTM method D 1857. The temperatures at which the cones deform to specific shapes are determined in oxidizing and reducing at- mospheres. Fusion temperatures provide ash melting characteristics and are used for classifying the slag- ging potentials of the lignitic-type ashes. Ash composition Elemental ash analysis is con- ducted using a coal ash sample produced by theASTM D 3174 procedure. The elements present in the ash are determined and reported as oxides. Silicon diox- ide (SiO2), aluminum oxide (Al2O3), titanium dioxide (TiO2), ferric hydroxide (Fe2O3), calcium oxide (CaO), magnesium oxide (MgO), sodium oxide (Na2O) and potassium oxide (K2O) are measured using atomic absorption per ASTM D 3682. The results of the ash analyses permit calculations of fouling and slagging indices and slag viscosity versus temperature relation- ships. The nature, composition and properties of coal ash and their effects on boiler performance are de- scribed further in Chapter 21. Special B&W tests7 Burning profiles The burning profile technique was originated by B&W for predicting the relative combus- tion characteristics of fuels. The technique and appli- cation of results were described by Wagoner and Duzy,8 and are routinely applied to liquid and solid fuels. The test uses derivative thermogravimetry in which a sample of fuel is oxidized under controlled con- ditions.A300 mg sample of solid fuel with a particle size less than 60 mesh (250 microns) is heated at 27F/min (15C/min) in a stream of air. Weight change is measured continuouslyandtheburningprofileistheresultingplot of rate of weight loss versus furnace temperature. Coals with similar burning profiles would be ex- pected to behave similarly in large furnaces. By com- paring the burning profile of an unknown coal with that of a known sample, furnace design, residence time, excess air and burner settings can be predicted. In comparing profiles, key information is provided by
- 242. Steam 41 / Sources of Chemical Energy 9-9 The Babcock & Wilcox Company the start and completion temperatures of oxidation. The area under the temperature curve is proportional to the amount of combustible material in the sample; the height of the curve is a measure of the combus- tion intensity. Burning profiles are particularly use- ful for preliminary evaluations of new boiler fuels such as chars, coal-derived fuels and processed refuse. Fig. 10 shows burning profiles of coals of various ranks. Abrasiveness index The abrasiveness of coal affects pulverizer grinding element life, and quartz particles in the coal can significantly contribute to its abrasive- ness.Aprocedure for determining a coal’s quartz count has been developed at B&W. This procedure consists of burning the coal, collecting and washing the ash to remove acid soluble constituents, and screening to separate size fractions. In each size fraction, 1000 par- ticles are counted and the number of quartz particles is determined by a microscopic technique. From these data, the relative quartz value, an indicator of the coal’s relative abrasiveness, is calculated. Another abrasion index is determined using the Yancey-Geer Price apparatus. In this test, a sample of coal, sized 0.25 in. × 0 (6.35 mm × 0), is placed in contact with four metal test samples or coupons attached to a rotating shaft. The shaft is rotated at 1440 rpm (150.8 rad/s) for a total of 12,000 revolutions (75,400 rad). The weightlossofthemetalcouponsisthendetermined,from which a relative abrasion index is calculated. Indices from the test coals can be compared to those for other fuels. B&W has used the Yancey-Geer Price Index to determine wear in full scale pulverizers. The quartz count procedure and the Yancey-Geer Price procedures canprovidesomerelativeinformationandinsightwhen comparing the abrasiveness of different coals; however, they have limited value in predicting actual field wear rates. (See Chapter 13.) Erosiveness index Erosion occurs in boilers due to the impact of pulverized particles on burner lines and other components between the pulverizers and burn- ers. The erosiveness test, developed by B&W, subjects a steel coupon to a stream of pulverized coal under controlled conditions. The measured weight loss of the coupon indicates the erosiveness of the coal. Slag viscosity The viscosity of a coal ash slag is measured at various temperatures under oxidizing and reducing conditions using a high temperature ro- tational bob viscometer. This viscometer and its appli- cation are described in more detail in Chapter 21. The data obtained from slag viscosity measurements are used to predict a coal’s slagging behavior in pulver- ized coal-fired boiler applications. The results also in- dicate the suitability of a coal for use in B&W’s slag- ging and Cyclone furnaces. Properties of selected coals Table 6 gives basic fuel characteristics of typical U.S. coals. The coals are identified by state and rank, and the analytical data include proximate and ultimate analyses and HHVs. Table 7 provides similar fuel prop- erties of coals mined outside the U.S. The source of this information, B&W’s Fuels Catalogue, contains more than 10,000 fuel analyses performed and compiled since the 1950s. Fuels derived from coal Because of abundant supplies and low prices, the demand for coal as the prime or substitute fuel for utility boilers will most likely continue to increase. In addition, the future use of coal-derived fuels, such as coal refined liquids and gases, coal slurries, and chars, as inexpensive substitutes for oil and natural gas, is also possible. Therefore, methods to obtain clean and efficiently burning fuels derived from coal are continu- ally being investigated. A few of these fuels that ap- ply to steam generation are discussed below. Coke When coal is heated in the absence of air or with a large deficiency of air, the lighter constituents are volatilized and the heavier hydrocarbons crack, lib- erating gases and tars and leaving a residue of car- bon. Some of the volatilized portions crack on contact with the hot carbon, leaving an additional quantity of carbon. The carbonaceous residue containing the ash and some of the original coal sulfur is called coke. The amount of sulfur and ash in the coke mainly de- pends on the coal from which it is produced and the coking process used. The principal uses for coke are the production of pig iron in blast furnaces and the charging of iron foundry cupolas. Because it is smoke- less when burned, considerable quantities have been used for space heating. Undersized coke, called coke breeze, usually pass- ing a 0.625 in. (15.875 mm) screen, is unsuitable for charging blast furnaces and is often used for steam generation. A typical analysis of coke breeze appears in Table 8. Approximately 4.5% of the coal supplied to slot-type coke ovens is recovered as coke breeze. A portion of the coal tars produced as byproducts of the various coking processes may be burned in equipment similar to that used for heavy petroleum oil. Gaseous fuels from coal A number of gaseous fuels are derived from coal as process byproducts or from gasification processes. (See Fig. 10 Coal burning profiles.
- 243. 9-10 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company Chapter 18.) Table 9 lists selected analyses of these gases. They have currently been largely supplanted by natural gas and oil. However, improvements in coal gasification and wider use of coal in the chemical and liquid fuel industries could reverse this trend. Coke oven gas A considerable portion of coal is con- verted to gases in the production of coke. Valuable productsrecoveredfromthesegaseousportionsinclude ammonium sulfate, oils and tars. The non-condens- able portion is called coke oven gas. Constituents de- pend on the nature of the coal and the coking process used (Table 9). Part of the sulfur from coal may be present in coke oven gas as hydrogen sulfide and carbon disulfide. These may be removed by scrubbing. Coke oven gas often contains other impurities that deposit in pipe- lines and burners. The gas burns readily because of its high free hydrogen content and presents minimal problems when used as steam generation fuel. Blast furnace gas The gas discharged from steel mill blast furnaces is used at the mills in furnaces, in gas engines and for steam generation. Blast furnace gas has variable quality but generally has a high carbon monoxide (CO) content and low heating value (Table 9). This gas may be burned for steam generation. However, blast furnace gas deposits adhere firmly and provisions must be made for cleaning boiler heating surfaces. Water gas The gas produced by passing steam through a bed of hot coke is known as water gas. Car- bon in the coke combines with the steam to form H2 and CO. This is an endothermic reaction that cools the coke bed. Water gas is often enriched with oil by pass- ing the gas through a checkerwork of hot bricks sprayed with oil. The oil, in turn, is cracked to a gas by the heat. Refinery gas is also used for enrichment. It may be mixed with the steam and passed through the coke bed or may be mixed directly with the water gas. Such enriched gas is called carbureted water gas Table 6 Properties of U.S. Coals Upper Pittsburgh #8 Illinois #6 Freeport Spring Creek Decker HV HV MV Subbitu- Subbitu- Lignite Lignite Lignite Anthracite Bituminous Bituminous Bituminous minous minous Lignite (S.Hallsville) (Bryan) (San Miguel) State Ohio or Pa. Illinois Pennsylvania Wyoming Montana North Dakota Texas Texas Texas Proximate: Moisture 7.7 5.2 17.6 2.2 24.1 23.4 33.3 37.7 34.1 14.2 Volatile matter, dry 6.4 40.2 44.2 28.1 43.1 40.8 43.6 45.2 31.5 21.2 Fixed carbon, dry 83.1 50.7 45.0 58.5 51.2 54.0 45.3 44.4 18.1 10.0 Ash, dry 10.5 9.1 10.8 13.4 5.7 5.2 11.1 10.4 50.4 68.8 Heating value, Btu/lb: As-received 11,890 12,540 10,300 12,970 9,190 9,540 7,090 7,080 3,930 2,740 Dry 12,880 13,230 12,500 13,260 12,110 12,450 10,630 11,360 5,960 3,200 MAF 14,390 14,550 14,010 15,320 12,840 13,130 11,960 12,680 12,020 10,260 Ultimate: Carbon 83.7 74.0 69.0 74.9 70.3 72.0 63.3 66.3 33.8 18.4 Hydrogen 1.9 5.1 4.9 4.7 5.0 5.0 4.5 4.9 3.3 2.3 Nitrogen 0.9 1.6 1.0 1.27 0.96 0.95 1.0 1.0 0.4 0.29 Sulfur 0.7 2.3 4.3 0.76 0.35 0.44 1.1 1.2 1.0 1.2 Ash 10.5 9.1 10.8 13.4 5.7 5.2 11.1 10.4 50.4 68.8 Oxygen 2.3 7.9 10.0 4.97 17.69 16.41 19.0 16.2 11.1 9.01 Ash fusion temps, F Reducing/Oxidizing: Red Oxid Red Oxid Red Oxid Red Oxid Red Oxid ID 2220 2560 1930 2140 2750+ 2750+ 2100 2180 ST Sp. 2440 2640 2040 2330 2750+ 2750+ 2160 2300 ST Hsp. 2470 2650 2080 2400 2750+ 2750+ 2170 2320 FT 0.0625 in. 2570 2670 2420 2600 2750+ 2750+ 2190 2360 FT Flat 2750+ 2750+ 2490 2700 2750+ 2750+ 2370 2700 Ash analysis: SiO2 51.0 50.58 41.68 59.60 32.61 23.77 29.80 23.32 62.4 66.85 Al2O3 34.0 24.62 20.0 27.42 13.38 15.79 10.0 13.0 21.5 23.62 Fe2O3 3.5 17.16 19.0 4.67 7.53 6.41 9.0 22.0 3.0 1.18 TiO2 2.4 1.10 0.8 1.34 1.57 1.08 0.4 0.8 0.5 1.46 CaO 0.6 1.13 8.0 0.62 15.12 21.85 19.0 22.0 3.0 1.76 MgO 0.3 0.62 0.8 0.75 4.26 3.11 5.0 5.0 1.2 0.42 Na2O 0.74 0.39 1.62 0.42 7.41 6.20 5.80 1.05 0.59 1.67 K2O 2.65 1.99 1.63 2.47 0.87 0.57 0.49 0.27 0.92 1.57 P2O5 − 0.39 − 0.42 0.44 0.99 − − − − SO3 1.38 1.11 4.41 0.99 14.56 18.85 20.85 9.08 3.50 1.32 Note: HV = high volatile; MV = medium volatile; ID = initial deformation temp; ST = softening temp; FT = fluid temp; Sp. = spherical; Hsp. = hemispherical. Red Oxid Red Oxid Red Oxid Red Oxid Red Oxid 2120 2420 2030 2160 2000 2210 2370 2470 2730 2750+ 2250 2470 2130 2190 2060 2250 2580 2670 2750+ 2750+ 2270 2490 2170 2220 2090 2280 2690 2760 2750+ 2750+ 2310 2510 2210 2280 2220 2350 2900+ 2900+ 2750+ 2750+ 2380 2750+ 2300 2300 2330 2400 2900+ 2900+ 2750+ 2750+
- 244. Steam 41 / Sources of Chemical Energy 9-11 The Babcock & Wilcox Company (Table 9). In many areas, carbureted water gas has been replaced by natural gas. Producer gas When coal or coke is burned with a deficiency of air and a controlled amount of moisture (steam), a product known as producer gas is obtained. This gas, after removal of entrained ash and sulfur compounds, is used near its source because of its low heating value (Table 9). Byproduct gas from gasification Coal gasification processes are a source of synthetic natural gas. There are many processes under devel- opment. The effluent gas from steam-oxygen coal gas- ification consists principally of H2, CO, CH4, CO2 and unreacted steam. The gas will also be diluted with N2 if air is used as the oxygen source. Although the com- peting chemical reactions that coal undergoes during gasification are complex, they usually include the re- action of steam and carbon to produce H2 and CO. Some CH4 is produced by the reaction of carbon with H2 and by thermal cracking of the heavy hydrocar- bons in the coal. CO2 and heat needed for the process are produced by reaction of carbon with O2. Final gas composition is modified by reaction between CO and steam to produce H2 and CO2. The products of coal gasification are often classified as low, intermediate and high Btu gases. Low Btu gas has a heating value of 100 to 200 Btu/SCF (3.9 to 7.9 MJ/Nm3 ) and is produced by gasification with air rather than oxygen. Typically, the gas is used as a boiler fuel at the gasification plant site or as feed to a turbine in combined cycles. Intermediate Btu gas has a heating value of 300 to 450 Btu/SCF (11.8 to 17.7 MJ/Nm3 ) and is produced by gasification with oxygen or by a process that produces a nitrogen-free product. The applications of intermediate Btu gas are similar to low Btu gas. High Btu gas has a heating value greater than 900 Btu/SCF (35.4 MJ/Nm3 ) and is used as a fuel Table 7 Properties of Selected International Coals Source Australia China France S. Africa Indonesia Korea Spain Ultimate: Carbon 56.60 62.67 74.60 69.70 56.53 68.46 37.02 Hydrogen 3.50 3.86 4.86 4.50 4.13 0.90 2.75 Nitrogen 1.22 0.83 1.39 1.60 0.88 0.20 0.88 Sulfur 0.35 0.46 0.79 0.70 0.21 2.09 7.46 Ash 24.00 4.71 8.13 10.10 1.77 23.48 38.69 Oxygen 7.43 10.34 9.42 9.10 12.58 4.38 11.39 Proximate: Moisture 6.90 17.13 0.80 4.30 23.90 0.50 1.80 Volatile matter, dry 24.80 30.92 36.11 35.30 45.57 7.46 45.27 Fixed carbon, dry 44.30 47.24 54.96 50.30 28.76 68.56 14.24 Ash, dry 24.00 4.71 8.13 10.10 1.77 23.48 38.69 Higher heating value, Btu/lb 9660 10,740 13,144 12,170 9,840 9,443 6,098 Ash analysis: SiO2 57.90 22.70 44.60 44.00 71.37 55.00 14.50 Al2O3 32.80 9.00 29.90 32.70 13.32 17.00 8.20 Fe2O3 6.20 15.68 13.10 4.60 7.00 12.50 2.70 TiO2 1.00 0.43 0.60 1.20 0.57 1.40 0.30 CaO 0.60 28.88 − 5.70 2.88 0.10 45.00 MgO 0.80 2.00 3.50 1.30 0.53 0.10 1.20 Na2O 0.10 0.70 3.10 0.10 0.34 0.10 0.10 K2O 0.50 0.46 − 0.30 0.25 3.10 0.40 P2O5 − 0.09 − 2.20 0.16 − − SO3 0.80 20.23 2.80 4.60 3.90 − − Ash fusion temps, F Reducing/Oxidizing: Red Oxid Red Oxid Red Oxid Red Oxid Red Oxid Red Oxid Red Oxid ID 2740 2750+ 2200 2220 2190 2300 2620 2670 2140 2410 2350 2600 2530 2520 ST Sp. 2750+ 2750+ 2240 2270 2310 2500 2750 2750+ 2400 2490 2630 2730 2700 2670 ST Hsp. 2750+ 2750+ 2250 2280 − − 2750+ 2750+ 2450 2540 − − − − FT 0.0625 in. 2750+ 2750+ 2280 2290 2670 2820 2750+ 2750+ 2630 2680 2900 2900 2730 2740 FT Flat 2750+ 2750+ 2340 2320 − − 2750+ 2750+ 2750 2750+ − − − −
- 245. 9-12 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company in place of natural gas. High Btu gas is produced by the same gasification process as intermediate Btu gas and then upgraded by methanation. (See also Chapter 18.) Fuel oil One of the most widely accepted theories explain- ing the origin of oil is the organic theory. Over mil- lions of years, rivers carried mud and sand that de- posited and ultimately became sedimentary rock for- mations. Along with this inorganic material, tiny marine organisms were buried with the silt. Over time, in an airless and high pressure environment, the or- ganic material containing carbon and hydrogen was converted to the hydrocarbon molecules of petroleum (oil). Because of the porosity of sedimentary rock for- mations, the oil flowed and collected in traps, or loca- tionswherecrudeoilisconcentrated.Thisphenomenon greatly assists the economic recovery of crude oil. Fuel oil consumption for steam generation accounts for a minor share of U.S. domestic petroleum fuel us- age. Industrial users, excluding transportation, ac- count for about 25% of all petroleum use; electric utili- ties consume about 2% of the total.2 The end users of petroleum products for the years 1975 to 2000 are shown in Fig. 11. Crude oil reserves and world petro- leum consumption are shown in Figs. 12 and 13. Compared to coal, fuel oils are relatively easy to handle and burn. There is less bulk ash to dispose of and the ash discharged is correspondingly small. In most oil burners, the fuel is atomized and mixed with combustion air. In the atomized state, the characteris- ticsofoilapproachthoseofnaturalgas.(SeeChapter11.) Because of its relatively low cost, No. 6 fuel oil is the most widely used for steam generation. It can be considered a byproduct of the refining process. Its ash content ranges from 0.01 to 0.5% which is very low compared to coal. However, despite this low ash con- tent, compounds of vanadium, sodium and sulfur in the ash can pose operating problems. (See Chapter 21.) Fuel oil characterization Fuel oils include virtually all petroleum products that are less volatile than gasoline. They range from light oils, suitable for use in internal combustion or turbine engines, to heavy oils requiring heating. The MillionBarrelsperDay 20 15 10 5 0 Year 1975 1980 1985 1990 1995 2000 Fig. 11 U.S. petroleum end users. Table 9 Selected Analyses of Gaseous Fuels Derived from Coal Blast Coke Oven Furnace Carbureted Producer Gas Gas Water Gas Gas Analysis No. 1 2 3 4 Analyses, % by volume Hydrogen, H2 47.9 2.4 34.0 14.0 Methane, CH4 33.9 0.1 15.5 3.0 Ethylene, C2H4 5.2 4.7 Carbon monoxide, CO 6.1 23.3 32.0 27.0 Carbon dioxide, CO2 2.6 14.4 4.3 4.5 Nitrogen, N2 3.7 56.4 6.5 50.9 Oxygen, O2 0.6 0.7 0.6 Benzene, C6H6 2.3 Water, H2O 3.4 Specific gravity 0.413 1.015 0.666 0.857 (relative to air) HHV Btu/ft3 (kJ/m3 ) at 60F (16C) and 590 534 163 30 in. Hg (102 kPa) (21,983) (19,896) (6,073) at 80F (27C) and 83.8 30 in. Hg (102 kPa) (3,122) (3,122) Fig. 12 Major world crude oil reserves, 2000 (OPEC = Organization of Petroleum Exporting Countries). BillionsofBarrels 300 250 200 150 100 50 0 * Non-OPEC Country 261.7 112.5 97.8 96.5 89.7 76.9 57.1 28.3 2224 Saudi Arabia Iraq UnitedArab Emirates Kuwait Iran Venezuela FSU* Mexico* U.S.* China* Table 8 Analyses Bagasse and Coke Breeze Analyses (as-fired), Coke % by wt Bagasse Breeze Proximate Moisture 52.0 7.3 Volatile matter 40.2 2.3 Fixed carbon 6.1 79.4 Ash 1.7 11.0 Ultimate Hydrogen, H2 2.8 0.3 Carbon, C 23.4 80.0 Sulfur, S trace 0.6 Nitrogen, N2 0.1 0.3 Oxygen, O2 20.0 0.5 Moisture, H2O 52.0 7.3 Ash 1.7 11.0 Heating value, Btu/lb 4000 11,670 (kJ/kg) (9304) (27,144)
- 246. Steam 41 / Sources of Chemical Energy 9-13 The Babcock & Wilcox Company heavier fuels are primarily suited for steam genera- tion boilers. TheASTM specifications for fuel oil prop- erties are given in Table 10. Fuel oils can be divided into two classes: distillate and residual. Distillate fuels are those that are vapor- ized in a petroleum refining operation. They are typi- cally clean, essentially free of sediment and ash, and relatively low in viscosity. These fuels fall into the No. 1 or No. 2 category in ASTM D 396. Although No. 2 oil is sometimes used as a premium steam generation fuel, it best lends itself to applications where cleanli- ness and ease of handling outweigh its cost. Examples include home heating and industrial applications where low ash and/or sulfur are important. Steam generating applications are primarily limited to use as a startup or support fuel. Table 10 ASTM Standard Specifications for Fuel Oilsa No. 1 A distillate oil intended for vaporizing pot-type burners and other burners requiring this grade of fuel No. 2 A distillate oil for general purpose domestic heating for use in burners not requiring No. 1 fuel oil No. 4 Preheating not usually required for handling or burning No. 5 (Light) Preheating may be required depending on climate and equipment No. 5 (Heavy) Preheating may be required for burning and, in cold climates, may be required for handling No. 6 Preheating required for burning and handling Notes: a. Recognizing the necessity for low sulfur fuel oils used in connection with heat treatment, nonferrous metal, glass, and ceramic furnaces and other special uses, a sulfur requirement may be specified in accordance with the following table: Grade of Fuel Oil Sulfur, Max, % No. 1 . . . . . . . . . . . . . . . . . . 0.5 No. 2 . . . . . . . . . . . . . . . . . . 0.7 No. 4 . . . . . . . . . . . . . . . . . . no limit No. 5 . . . . . . . . . . . . . . . . . . no limit No. 6 . . . . . . . . . . . . . . . . . . no limit Other sulfur limits may be specified only by mutual agreement between the purchaser and the seller. b. It is the intent of these classifications that failure to meet any requirement of a given grade does not automatically place an oil in the next lower grade unless, in fact, it meets all requirements of the lower grade. c. Lower or higher pour points may be specified whenever required by conditions of storage or use. d. The 10% distillation temperature point may be specified at 440F (226C) maximum for use in other than atomizing burners. e. When pour point less than 0F is specified, the minimum viscosity shall be 1.8 cs (32.0 s, Saybolt Universal) and the minimum 90% point shall be waived. f. Viscosity values in parentheses are for information only and not necessarily limiting. g. The amount of water by distillation plus the sediment by extraction shall not exceed 2.00%. The amount of sediment by extraction shall not exceed 0.50%. A deduction in quantity shall be made for all water and sediment in excess of 1.0%. Source, ASTM D 396. Min Max Max Max Max Max Min Max Min Max No. 1 100 or 0 trace 0.15 420 550 legal (216) (288) (38) No. 2 100 or 20c 0.10 0.35 d 540c 640 (32.6)f (37.93) legal (-7) (282) (338) (38) No. 4 130 or 20 0.50 0.10 45 125 legal (-7) (55) No. 5 130 or 1.00 0.10 150 300 (Light) legal (55) No. 5 130 or 1.00 0.10 350 750 (Heavy) legal (55) No. 6 150 2.00g (900) (9000) (65) Min Max Min Max Min Max Min Max 1.4 2.2 35 Νο. 3 2.0e 3.6 30 (5.8) (26.4) (32) (65) (23) (40) (75) (162) (42) (81) 45 300 (92) (638) Distillation Water Carbon Temperatures, Kinematic Viscosity, Grade Flash Pour and Residue F (C) Saybolt Viscosity, s centistokes Copper of Point, Point, Sediment, on 10% Ash Gravity, Strip Fuel F F % by Bottoms, % by 10% 90% Universal at Furol at At 100F At 122F deg Cor- Oilb (C) (C) vol % wt Point Point 100F (38C) 122F (50C) (38C) (50C) API rosion The residual fuel oils are those that are not vapor- ized by heating. They contain virtually all the inor- ganic constituents present in the crude oil. Frequently, residual oils are black, high viscosity fluids that re- quire heating for proper handling and combustion. Fuel oils in grades No. 4 and 5 are less viscous and therefore more easily handled and burned than is No. 6 oil. Depending on the crude oil used, a fuel meeting the No. 4 specification may be a blend of residual oil and lighter distillate fractions. This oil does not usu- ally require heating for pumping and handling. No. 5 oils may require heating, depending on the firing equipment and the ambient temperature. No. 6 oils usually require heating for handling and burn- ing. (See Chapter 11 for oil storage, handling and use requirements.)
- 247. 9-14 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company Fuel analyses A typical analysis of a fuel oil or waste liquid con- tains the following information: 1. ultimate analysis 2. API gravity 3. heating value 4. viscosity 5. pour point 6. flash point 7. water and sediment Ultimate analysis The ultimate analysis for an oil is similar to that for a coal. The results indicate the quan- tities of sulfur, hydrogen, carbon, nitrogen, oxygen and ash. Ultimate analyses for various fuel oils are given in Table 11. The sulfur content of the oil is an indicator of its corrosiveness and is oxidized to sulfur oxides during combustion. These oxides can react with water vapor or ash constituents to form corrosive acids, salts, or boiler fouling potassium sulfate. When molten, these ash deposits are corrosive. Furthermore, vanadium can combine with the sulfur oxides to form a corro- sive product. (See Chapter 21.) API gravity The petroleum industry uses the API gravity scale to determine the relative density of oil. The scale was devised jointly by the American Petro- leum Institute (API) and the National Bureau of Stan- dards. The relationship between the API gravity and the specific gravity is given by the following formula: Deg API Gravity Specific gravity at 60/60F = − 141 5 131 5 . . Given this relationship, heavier liquid fuels are de- noted by lower API gravity values. Heating value The heating value of a liquid fuel in- dicates the heat released by the complete combustion of one unit of fuel [lb (kg)]. As for coal, there are two calculated heating values, higher (HHV) and lower (LHV). In computing the HHV, it is assumed that any water vapor formed by burning the hydrogen constitu- ent is condensed and cooled to its initial temperature. Therefore, the heat of vaporization of the water formed is included in the HHV. For the LHV, it is assumed that none of the water vapor condenses. Both heating values are determined by using an oxygen bomb calorimeter. Viscosity The viscosity of a liquid is the measure of its internal resistance to flow. Although there are nu- merous viscosity scales, those most commonly used in the U.S. are: 1. Saybolt Universal Seconds (SUS), 2. Saybolt Furol Seconds (SFS), 3. absolute viscosity (centipoise), and 4. kinematic viscosity (centistokes). The kinematic viscosity of oil is related to the abso- lute viscosity by the following formula: Kinematic viscosity (centistokes) Absolute viscosity (cen = ttipoise) Specific gravity Pour point The pour point is the lowest tempera- ture at which a liquid fuel flows under standardized conditions. Flash point The flash point is the temperature to which a liquid must be heated to produce vapors that flash but do not burn continuously when ignited. There are two instruments used to determine the flash point: the Pensky-Martens or closed cup flash tester, and the Cleveland or open cup tester. The closed cup tester indicates a lower flash point because it retains light vapors which are lost by the open cup unit. Water and sediment The water and sediment level, also called bottom sediment and water (BSW), is a measure of the contaminants in a liquid fuel. The sedi- mentnormallyconsistsofcalcium,sodium,magnesium and iron compounds. For heavy fuels, the sediment may also contain carbon. The basic analyses described are important in de- signing oil-fired boilers. The HHV determines the quantity of fuel required to reach a given heat input. The ultimate analysis determines the theoretical air required for complete combustion and therefore indi- cates the size of the burner throat.Also available from the ultimate analysis is the carbon/hydrogen ratio, which shows the ease with which a fuel burns. This ratio also indicates the expected level of carbon par- ticulate emissions. A carbon/hydrogen ratio in excess of 7.5 is usually indicative of troublesome burning. Considering the percentages of nitrogen and sul- fur in conjunction with the HHV, an estimate of NOx and SO2 emissions can be made. The ash percentage has a similar bearing on particulate emissions. The ash constituent analysis and ash content indicate fouling and corrosion tendencies. Additional information, which is often required when designing a boiler, includes: 1. carbon residue, 2. asphaltenes, 3. elemental ash analysis, 4. burning profile, and 5. distillation curve. ThousandBarrelsperDay 30,000 25,000 20,000 15,000 10,000 5,000 0 North America Central andSouth America Western Europe Eastern Europe andFSU Middle East Africa FarEast andOceania 1980 1989 2000 20,204 20,750 23,775 13,947 12,880 14,672 3,573 3,612 5,131 11,082 10,567 4,773 4,456 3,117 2,058 1,474 2,004 2,440 10,733 12,868 20,773 Fig. 13 Major petroleum consumption.
- 248. Steam 41 / Sources of Chemical Energy 9-15 The Babcock & Wilcox Company Properties of fuel oils Analytical results for various fuel oil properties are given in Table 11. Fuel oil heating values are closely related to their specific gravities. The relationships between the HHV of various fuel oils and their API gravities are shown in Fig. 14. A more accurate estimate of the heating value for an oil is obtained by correcting the HHV from Fig. 14 as follows: Apparent heating value S S = − + +( ) + HHV A M100 100 40 5. (7) where A = % weight of ash M = % weight of water S = % weight of sulfur The volume percentages of water and sediment can be used without appreciable error in place of their weight percentages. Fuel oils are generally sold on a volume basis us- ing 60F (16C) as the base temperature. Correction factors are given in Fig. 15 for converting volumes at Fig. 14 Relationship between HHV of various fuel oils and their API gravities. Table 11 Analyses of Fuel Oils Grade of Fuel Oil No. 1 No. 2 No. 4 No. 5 No. 6 % by weight: Sulfur 0.01 to 0.5 0.05 to 1.0 0.2 to 2.0 0.5 to 3.0 0.7 to 3.5 Hydrogen 13.3 to 14.1 11.8 to 13.9 (10.6 to 13.0)* (10.5 to 12.0)* (9.5 to 12.0)* Carbon 85.9 to 86.7 86.1 to 88.2 (86.5 to 89.2)* (86.5 to 89.2)* (86.5 to 90.2)* Nitrogen nil to 0.1 nil to 0.1 Oxygen Ash 0 to 0.1 0 to 0.1 0.01 to 0.5 Gravity: Deg API 40 to 44 28 to 40 15 to 30 14 to 22 7 to 22 Specific 0.825 to 0.806 0.887 to 0.825 0.966 to 0.876 0.972 to 0.922 1.022 to 0.922 lb/gal 6.87 to 6.71 7.39 to 6.87 8.04 to 7.30 8.10 to 7.68 8.51 to 7.68 Pour point, F 0 to −50 0 to −40 −10 to +50 −10 to +80 +15 to +85 Viscosity: Centistokes at 100F 1.4 to 2.2 1.9 to 3.0 10.5 to 65 65 to 200 260 to 750 SUS at 100F 32 to 38 60 to 300 SFS at 122F 20 to 40 45 to 300 Water and sediment, % by vol 0 to 0.1 tr to 1.0 0.05 to 1.0 0.05 to 2.0 Heating value, Btu/lb 19,670 to 19,860 19,170 to 19,750 18,280 to 19,400 18,100 to 19,020 17,410 to 18,990 gross (calculated) *Estimated
- 249. 9-16 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company other temperatures to this standard base. This correc- tion is also dependent on the API gravity range, as illustrated by the three lines of Fig. 15. Handling and burning equipment are usually de- signed for a maximum oil viscosity. If the viscosities of heavy oils are known at two temperatures, their viscosities at other temperatures can be closely pre- dicted by a linear interpolation between these two values on the standardASTM chart (Fig. 16). Viscosity- temperature variations for certain light oils can also be found using the ASTM chart. In this case, however, the designer only needs to know the viscosity at one tem- perature. For example, the viscosity of a light oil at a given temperature within the No. 2 fuel oil range can be found by drawing a line parallel to the No. 2 bound- ary lines through the point of known temperature. Natural gas Past consumption and availability Natural gas is found in porous rock in the earth’s crust. World natural gas production for 1999 is shown in Fig. 17. Electric power generation is the fastest growing seg- ment of U.S. natural gas consumption. By 2000, elec- tric generators had overtaken the residential segment as the second largest user of natural gas with a 22% share of U.S. consumption (Table 12). Environmen- tal regulations, higher efficiency gas turbines, and a large base of simple and combined cycle gas turbine plants installed in the late 1990s and early 2000s drove the annual usage of natural gas in the U.S., for elec- tricpowergeneration,from3.8trillioncubicfeetin1996 to 5.5 trillion cubic feet in 2002. The Department of Energy (DOE) expects that the volatile price of natural gas will hold growth to about 1.8% per year to 2025. Natural gas characteristics Natural gas can be found with petroleum reserves or in separate reservoirs. Methane is the principal com- ponent of natural gas; smaller components include ethane, propane and butane. Other hydrocarbons, such as pentane through decane, can also be found in natu- ralgas.Furthermore,othergasessuchasCO2, nitrogen, helium and hydrogen sulfide (H2S) may be present. Gas containing mostly methane is referred to as lean gas. Wet gas contains appreciable amountsofthehigher hydrocarbons (5 to 10% C). Gas containing H2S is sour gas; conversely, sweet gas contains little or no H2S. 40,000 35,000 30.000 25.000 20,000 15,000 10,000 5,000 0 North America Central andSouth America Western Europe Eastern Europe andFSU Middle East Africa FarEast andOceania 32,759 26,383 11,503 9,923 3,148 25,680 25,409 6,930 10,352 8,239 4,016 9,980 9,102 5,344 Gross Dry Production,Billionft Fig. 17 World natural gas production, 1999. Fig. 16 Approximate viscosity of fuel oil at various temperatures (courtesy of ASTM). Note: On the Y axis, find the SUS viscosity at 100F (standard test temperature) for the given oil; move horizontally to the ver- tical line for 100F. From this intersection, move parallel to the diagonal lines to the viscosity required for atomization; the tem- perature necessary to achieve this viscosity can be read on the X axis. The chart, based on U.S. Commercial Standard 12-48, has been developed from data for many fuels and should be sufficiently accurate for most applications. Fig. 15 Oil volume-temperature correction factors.
- 250. Steam 41 / Sources of Chemical Energy 9-17 The Babcock & Wilcox Company Of all chemical fuels, natural gas is considered to be the most desirable for steam generation. It is piped directly to the consumer, eliminating the need for stor- age. It is substantially free of ash and mixes easily with air, providing complete combustion without smoke. Although the total hydrogen content of natu- ral gas is high, its free hydrogen content is low. Be- cause of this, natural gas burns less easily than some manufactured gases with high free hydrogen content. The high hydrogen content of natural gas compared to that of oil or coal results in more water vapor being produced in the combustion gases. This results in a correspondingly lower efficiency of the steam gener- ating equipment. (See Chapter 10.) This can readily be taken into account when designing the equipment. Properties of natural gas Analyses of natural gas from several U.S. fields are given in Table 13. Other fuels While coal, oil and gas are the dominant fuel sources, other carbonaceous fuels being used for boiler applications include petroleum byproducts and heavy hydrocarbon emulsions; wood, its byproducts and wastes from wood processing industries; certain types of vegetation, particularly bagasse; and municipal solid waste. Coke from petroleum The heavy residuals from petroleum cracking pro- cesses are presently used to produce a higher yield of lighter hydrocarbons and a solid residue suitable for fuel. Characteristics of these residues vary widely and depend on the process used. Solid fuels from oil include delayed coke, fluid coke and petroleum pitch. Some selected analyses are given in Table 14. The delayed coking process uses residual oil that is heated and pumped to a reactor. Coke is deposited in the reactor as a solid mass and is subsequently stripped, mechanically or hydraulically, in the form of lumps and granular material. Some cokes are easy to pulverize and burn while others are difficult. Fluid coke is produced by spraying hot residual feed onto externally heated seed coke in a fluidized bed. The fluid coke is removed as small particles, which are built up in layers. This coke can be pulverized and burned, or it can be burned in a Cyclone furnace or in a fluidized bed. All three types of firing require supplemental fuel to aid ignition. The petroleum pitch process is an alternate to the coking process and yields fuels of various character- istics. Melting points vary considerably, and the physi- Table 13 Selected Samples of Natural Gas from U.S. Fields Sample No. 1 2 3 4 5 Source: Pa. S.C. Ohio La. Ok. Analyses: Constituents, % by vol H2, Hydrogen 1.82 CH4, Methane 83.40 84.00 93.33 90.00 84.10 C2H4, Ethylene 0.25 C2H6, Ethane 15.80 14.80 5.00 6.70 CO, Carbon monoxide 0.45 CO2, Carbon dioxide 0.70 0.22 0.80 N2, Nitrogen 0.80 0.50 3.40 5.00 8.40 O2, Oxygen 0.35 H2S, Hydrogen sulfide 0.18 Ultimate, % by wt S, Sulfur 0.34 H, Hydrogen 23.53 23.30 23.20 22.68 20.85 C, Carbon 75.25 74.72 69.12 69.26 64.84 N, Nitrogen 1.22 0.76 5.76 8.06 12.90 O, Oxygen 1.22 1.58 1.41 Specific gravity (rel to air) 0.636 0.636 0.567 0.600 0.630 HHV Btu/ft3 at 60F and 30 in. Hg 1,129 1,116 964 1,022 974 (kJ/m3 at 16C and 102 kPa) (42,065) (41,581) (35,918) (38,079) (36,290) Btu/lb(kJ/kg) 23,170 22,904 22,077 21,824 20,160 of fuel (53,893) (53,275) (51,351) (50,763) (46,892) Table 14 Selected Analyses of Solid Fuels Derived from Oil Analyses (dry basis) % by wt Delayed Coke Fluid Coke Proximate: VM 10.8 9.1 6.0 6.7 FC 88.5 90.8 93.7 93.2 Ash 0.7 0.1 0.3 0.1 Ultimate: Sulfur 9.9 1.5 4.7 5.7 Heating value, Btu/lb 14,700 15,700 14,160 14,290 (kJ/kg) (34,192) (36,518) (32,936) (33,239) Table 12 U.S. Natural Gas Consumption (Trillion ft3 ) Resi- Com- Indus- Elec. Transpor- Year dential mercial trial Power tation Total 1989 4.78 2.72 7.89 3.11 0.63 19.12 1990 4.39 2.62 8.26 3.25 0.66 19.17 1991 4.56 2.73 8.36 3.32 0.60 19.56 1992 4.69 2.80 8.70 3.45 0.59 20.23 1993 4.96 2.86 8.87 3.47 0.63 20.79 1994 4.85 2.90 8.91 3.90 0.69 21.25 1995 4.85 3.03 9.38 4.24 0.71 22.21 1996 5.24 3.16 9.69 3.81 0.72 22.61 1997 4.98 3.22 9.71 4.07 0.76 22.74 1998 4.52 3.00 9.49 4.57 0.65 22.25 1999 4.73 3.05 9.16 4.82 0.66 22.41 2000 5.00 3.22 9.29 5.21 0.66 23.37 2001 4.78 3.04 8.45 5.34 0.64 22.25 2002 4.91 3.11 8.23 5.55 0.65 22.46 Note: Total may not equal sum of components due to independent rounding. Source: Energy Information Administration, Annual Energy Review, 2003.
- 251. 9-18 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company cal properties vary from soft and gummy to hard and friable.Thelowmeltingpointpitchesmaybeheatedand burned like heavy oil, while those with higher melting points may be pulverized or crushed and burned. Oil emulsions With the discovery of large reserves of heavy hy- drocarbon and bitumen in Venezuela, considerable effort has been devoted to developing these sources as commercial fuels. This has led to the formulation of bitumen oil emulsions. Generically, these emulsions areliquidfuelscomposedofmicron-sizeoildropletsdis- persed in water. Droplet coalescence is prevented by adding a small amount of a proprietary chemical. The fuel is characterized by relatively high levels of sul- fur, asphaltenes and metals. The heating value, ash content and viscosity of the emulsions are similar to residual fuel oil as are their handling and combustion performancecharacteristics.Theemulsionscancontain vanadiumwhichformscorrosivecompoundsduringcom- bustion.VanadiumcanalsocatalyzetheoxidationofSO2 to SO3 and require the use of specific emission controls to avoid stack plumes of sulfuric acid aerosol. Orimulsion is the trade name of a proprietary bi- tumen emulsion produced by Bitor, a part of Petroleos de Venezuela SA (PDVSA), the Venezuelan national oil company. It is prepared from approximately 30% water and 70% bitumen from the Orinoco basin. Com- bined with other performance enhancing chemicals, a stableemulsifiedfuelforapplicationinboilersandother combustionequipmentisproduced.AtypicalOrimulsion composition compared to fuel oil is shown in Table 15. As of 2000, Orimulsion was being utilized world- wide at the rate of 6.2 million tons per year at boiler installations in Denmark, Japan, Italy and Canada. The fuel can offer cost advantage over No. 6 fuel oil. En- vironmentalcontrolequipmentisrequiredtoaddresssul- fur oxides, nitrogen oxides, and particulate emissions. Wood Selected analyses and heating values of wood and wood ash are given in Table 16. Wood is composed pri- marily of carbohydrates. Consequently, it has a rela- tively low heating value compared with bituminous coal and oil. Wood bark may pick up impurities during transpor- tation. It is common practice to drag the rough logs to central loading points and sand is often picked up. Where the logs are immersed in salt water, the bark can absorb the salt. Combustion temperatures from burning dry bark may be high enough for these im- purities to cause fluxing of refractory furnace walls and fouling of boiler heating surfaces, unless sufficient furnace cooling surface is provided. Sand passing through the boiler banks can cause erosion of the tubes, particularly if the flue gas sand loading is in- creased by returning collected material to the furnace. Such collectors may be required with some bark burn- ing equipment to reduce the stack discharge of incom- pletely burned bark. Wood or bark with a moisture content of 50% or less burns quite well; however, as the moisture increases above this amount, combustion becomes more difficult. With a moisture content above 65%, a large part of the heat is required to evaporate the inherent mois- ture and little remains for steam generation. Burn- ing this wet bark becomes a means of disposal rather than a source of energy. Table 16 Analyses of Wood and Wood Ash Wood analyses (dry Pine Oak Spruce Redwood basis), % by wt Bark Bark Bark* Bark* Proximate analysis, % Volatile matter 72.9 76.0 69.6 72.6 Fixed carbon 24.2 18.7 26.6 27.0 Ash 2.9 5.3 3.8 0.4 Ultimate analysis, % Hydrogen 5.6 5.4 5.7 5.1 Carbon 53.4 49.7 51.8 51.9 Sulfur 0.1 0.1 0.1 0.1 Nitrogen 0.1 0.2 0.2 0.1 Oxygen 37.9 39.3 38.4 42.4 Ash 2.9 5.3 3.8 0.4 Heating value, Btu/lb 9,030 8,370 8,740 8,350 (kJ/kg) (21,004) (19,469) (20,329) (19,422) Ash analysis, % by wt SiO2 39.0 11.1 32.0 14.3 Fe2O3 3.0 3.3 6.4 3.5 TiO2 0.2 0.1 0.8 0.3 Al2O3 14.0 0.1 11.0 4.0 Mn3O4 Trace Trace 1.5 0.1 CaO 25.5 64.5 25.3 6.0 MgO 6.5 1.2 4.1 6.6 Na2O 1.3 8.9 8.0 18.0 K2O 6.0 0.2 2.4 10.6 SO3 0.3 2.0 2.1 7.4 Cl Trace Trace Trace 18.4 Ash fusibility temp, F Reducing Initial deformation 2180 2690 Softening 2240 2720 Fluid 2310 2740 Oxidizing Initial deformation 2210 2680 Softening 2280 2730 Fluid 2350 2750 * Salt water stored. Table 15 Composition of Orimulsion 400 Orimulsion 400 No. 6 Fuel Oil Carbon (%) 60.20 85.71 Hydrogen (%) 7.20 10.14 Sulfur (%) 2.85 2.63 Oxygen (%) 0.18 0.92 Nitrogen (%) 0.50 0.51 Water (%) 29.00 0 Ash (%) 0.07 0.09 HHV (Btu/lb) 12,984 18,192
- 252. Steam 41 / Sources of Chemical Energy 9-19 The Babcock & Wilcox Company Hogged wood and bark are very bulky and require relatively large handling and storage equipment. Un- interrupted flow from bunkers or bins through chutes is difficult to maintain. (Also see Chapter 30.) Wood wastes There are several industries using wood as a raw material where combustible byproducts or wastes are available as fuels. The most important of these are the pulp and turpentine industries. The nature and methods of utilization of the combustible byproducts from the pulp industry are discussed in Chapter 28. The residue remaining after the steam distillation of coniferous woods for the production of turpentine is usable as a fuel. Some of the more easily burned constituents are removed in the distillation process; as aresult,theresidueissomewhatmoredifficulttoburn. Other than this, fuel properties are much the same as those of the raw wood and the problems involved in utilization are similar. Bagasse Mills grinding sugar cane commonly use bagasse for steam production. Bagasse is the dry pulp remain- ing after the juice has been extracted from sugar cane. The mills normally operate 24 hours per day during the grinding season. The supply of bagasse will eas- ily meet the plant steam demands in mills where the sugar is not refined. Consequently, where there is no other market for the bagasse, no particular effort is made to burn it efficiently, and burning equipment is provided that will burn the bagasse as-received from the grinders. In refining plants, supplemental fuels are required to provide the increased steam demands. Greater efforts to obtain higher efficiency are justi- fied in these plants. A selected analysis of bagasse is given in Table 8. Other vegetation wastes Food and related industries produce numerous veg- etable wastes that are usable as fuels. They include such materials as grain hulls, the residue from the Table 17 Analyses of MSW and RDF Compared to Bituminous Coal Analyses, % by wt Constituent MSW RDF Bituminous Coal Carbon 27.9 36.1 72.8 Hydrogen 3.7 5.1 4.8 Oxygen 20.7 31.6 6.2 Nitrogen 0.2 0.8 1.5 Sulfur 0.1 0.1 2.2 Chlorine 0.1 0.1 0 Water 31.3 20.2 3.5 Ash 16.0 6.0 9.0 HHV (wet), Btu/lb 5,100 6,200 13,000 (kJ/kg) (11,863) (14,421) (30,238) Orimulsion is a trademark of Bitumenes Orinoco, S.A. 1. International Energy Outlook 2003, Report DOE/EIA- 0484 (2003), United States (U.S.) Energy Information Ad- ministration, Washington, D.C., May, 2003. 2. Annual Energy Review 2001, Report DOE/EIA-0384 (2001), U.S. Energy Information Administration, Wash- ington, D.C., November, 2002. 3. 2001 Survey of Energy Resources, World Energy Con- gress, London, England, 2001. 4. Coal Industry Annual 2000, Report DOE/EIA-0584 (2000), U.S. Energy Information Administration, Wash- ington, D.C., 2001. 5. “Gaseous Fuels; Coal and Coke,” Vol. 05.05, Annual Book of ASTM Standards, American Society for Testing and Materials, West Conshohocken, Pennsylvania, 1999. 6. Parr, S.W., “The Classification of Coal,” Bulletin No. 180, Engineering Experiment Station, University of Illi- nois, Chicago, Illinois, 1928. 7. Vecci, S.J., Wagoner, C.L., and Olson, G.B., “Fuel and Ash Characterization and Its Effect on the Design of In- dustrial Boilers,” Proceedings of the American Power Con- ference, Vol. 40, pp. 850-864, 1978. 8. Wagoner, C.L., and Duzy, A.F., “Burning Profiles for Solid Fuels,” Technical Paper 67-WA-FU-4, American So- ciety of Mechanical Engineers, New York, New York, 1967. References production of furfural from corn cobs and grain hulls, coffee grounds from the production of instant coffee, and tobacco stems. Fuels of this type are available in such small quantities that they are relatively insig- nificant in total energy production. Municipal solid waste Municipal solid waste (MSW), or refuse, is an en- ergy source in the U.S., Europe and Japan. MSW is the combined residential and commercial waste gen- erated in a given municipality. It is burned as-re- ceived, called mass burning, or processed using size reduction and material recovery techniques to produce refuse-derived fuel (RDF). Much MSW continues to be landfilled, since siting and acceptance of waste-to- energy boilers have been greatly limited by the public’s concern over environmental issues. Table 17 shows a typical analysis of raw refuse and RDF compared to bituminous coal. The relatively low calorific value and high heterogeneous nature of MSW provide a challenge to the combustion system design engineer. The design of MSW handling and combus- tion systems is discussed in Chapter 29.
- 253. 9-20 Steam 41 / Sources of Chemical Energy The Babcock & Wilcox Company Coal remains the dominant fuel source for electric power generation worldwide.
- 254. Steam 41 / Principles of Combustion 10-1 The Babcock & Wilcox Company Chapter 10 Principles of Combustion A boiler requires a source of heat at a sufficient tem- perature to produce steam. Fossil fuel is generally burned directly in the boiler furnace to provide this heat although waste energy from another process may also be used. Combustion is defined as the rapid chemical com- bination of oxygen with the combustible elements of a fuel. There are just three combustible elements of significance in most fossil fuels: carbon, hydrogen and sulfur. Sulfur, usually of minor significance as a heat source, can be a major contributor to corrosion and pollution problems. (See Chapters 21 and 32.) The objective of good combustion is to release all of the energy in the fuel while minimizing losses from combustion imperfections and excess air. System re- quirement objectives include minimizing nitrogen oxides (NOx), carbon monoxide (CO), volatile organic compounds (VOC) and, for more difficult to burn fu- els, minimizing unburned carbon (UBC) and furnace corrosion. The combination of the combustible fuel el- ements and compounds in the fuel with all the oxy- gen requires temperatures high enough to ignite the constituents, mixing or turbulence to provide intimate oxygen-fuel contact, and sufficient time to complete the process, sometimes referred to as the three Ts of combustion. Table 1 lists the chemical elements and compounds found in fuels generally used in commercial steam generation. Concept of the mole The mass of a substance in pounds equal to its molecular weight is called a pound-mole (lb-mole) of the substance. The molecular weight is the sum of the atomic masses of a substance’s constituent atoms. For example,pureelementalcarbon(C)hasanatomicmass and molecular weight of 12 and therefore a lb-mole is equal to 12. In the case of carbon dioxide (CO2), car- bon still has an atomic mass of 12 and oxygen has an atomic mass of 16 giving CO2 a molecular weight and a lb-mole equal to (1 × 12) + (2 × 16) or 44. In SI, a similar system is based upon the molecular weight in kilograms expressed as kg-mole or kmole. In the United States (U.S.) power industry it is common prac- tice to replace lb-mole with mole. In the case of a gas, the volume occupied by one mole is called the molar volume. The volume of one mole of an ideal gas (a good approximation in most combustion calculations) is a constant regardless of its composition for a given temperature and pressure. Therefore, one lb-mole or mole of oxygen (O2) at 32 lb and one mole of CO2 at 44 lb will occupy the same volume equal to 394 ft3 at 80F and 14.7 psi. The vol- ume occupied by one mole of a gas can be corrected to other pressures and temperatures by the ideal gas law. Because substances combine on a molar basis dur- ing combustion but are usually measured in units of mass (pounds), the lb-mole and molar volume are important tools in combustion calculations. Fundamental laws Combustion calculations are based on several fun- damental physical laws. Conservation of matter This law states that matter can not be destroyed or created. There must be a mass balance between the sum of the components entering a process and the sum of those leaving: X pounds of fuel combined with Y pounds of air always results in X + Y pounds of prod- ucts (see Note below). Conservation of energy This law states that energy can not be destroyed or created. The sum of the energies (potential, kinetic, thermal,chemicalandelectrical)enteringaprocessmust equalthesumofthoseleaving,althoughtheproportions of each may change. In combustion, chemical energy is converted into thermal energy (see Note below). Note: While the laws of conservation of matter and energy are not rigorous from a nuclear physics standpoint (see Chap- ter 47), they are quite adequate for engineering combustion calculations. When a pound of a typical coal is burned re- leasing13,500Btu,theequivalentquantityofmassconverted to energy amounts to only 3.5 × 10–10 lb. For clarity, this chapter is provided in English units only. Appendix1providesacomprehensivelistofconversionfac- tors. Selected factors of particular interest here include: Btu/lb × 2.326 = kJ/kg; 5/9 (F-32) = C; lb × 0.4536 = kg. Selected SI constants include: universal gas constant = 8.3145 kJ/kmole K; one kmole at 0C and 1.01 bar = 22.4 m3 .
- 255. 10-2 Steam 41 / Principles of Combustion The Babcock & Wilcox Company 1CarbonC12.011014,09314,093 2HydrogenH22.01590.0053188.2450.0696324.2273.961,02951,558 3OxygenO231.99880.084411.8501.1053 4NitrogenN228.01340.073813.5430.9671 4Nitrogen(atm.)f N2a28.15800.074213.4740.9720 5CarbonMonoxideCO28.01040.073813.5420.9672320.6320.643424342 6CarbonDioxideCO244.00980.11668.5741.5277 ParafinseriesCnH2n+2 7MethaneCH416.04280.042423.6080.5548101291123,89121,511 8EthaneC2H630.06970.079912.5141.04661785163422,33420,429 9PropaneC3H844.09660.11838.4561.54892561235921,65319,921 10n-ButaneC4H1058.12350.15856.3102.07583376312421,29919,657 11IsobutaneC4H1058.12350.15806.3282.06993355310421,23119,589 12n-PentaneC5H1272.15040.20194.9522.64504258395621,08519,498 13IsopentaneC5H1272.15040.20014.9992.62024210390821,04319,455 14NeopentaneC5H1272.15040.1984g 5.040g 2.5989g 4159g 385720,958g 19,370 15n-HexaneC6H1486.17730.25083.9873.28495252490020,94319,392 OlefinseriesCnH2n 16EthyleneC2H428.05380.074413.4470.97401609150921,64320,282 17PropyleneC3H642.08070.11278.8741.47602371222021,03919,678 18n-Butene(Butylene)C4H856.10760.1524g 6.560g 1.9966g 3175g 297420,831g 19,470 19IsobuteneC4H856.10760.1524g 6.561g 1.9964g 3156g 295520,704g 19,343 20n-PenteneC5H1070.13450.1947h 5.135h 2.5508h 4032g 378120,704g 19,343 AromaticseriesCnH2n-6 21BenzeneC6H678.11370.22134.5182.89894024387318,17917,446 22TolueneC7H892.14060.2750h 3.637h 3.6016h 5068g 486718,430g 17,602 23XyleneC8H10106.16750.3480h 2.874h 4.5576h 6480g 622818,622g 17,723 Miscellaneous 24AcetyleneC2H226.03790.069114.4800.90461484143321,48220,749 25NaphthaleneC10H8128.17360.3384h 2.955h 4.4323h 5866566517,33516,739 26MethylalcoholCH3OH32.04220.0846h 11.820h 1.1081h 868g 76810,265g 9073 27EthylalcoholC2H5OH46.06910.1216h 8.224h 1.5927h 1602g 145113,172g 11,929 28AmmoniaNH317.03060.0454g 22.008g 0.5951g 440g 3649680g 7998 29SulfurS32.066039803980 30HydrogensulfideH2S34.08190.090711.0301.187564359370946534 31SulfurdioxideSO264.06480.1722g 5.806g 2.2558g 32WatervaporH2O18.01530.050319.8630.659450.3120.01059.80.0 33Airf 28.96250.076313.0981.0000 1.03.7734.7731.03.7732.6648.84611.5103.6648.8468.167 0.51.8872.3871.01.8877.93626.35334.2908.93726.3535.619 0.51.8872.3871.01.8870.5711.8972.4681.5711.8975.684 2.07.5479.5471.02.07.5473.98913.24617.2352.7432.24613.2467.214 3.513.20616.7062.03.013.2063.72412.36716.0922.9271.79712.3677.205 5.018.86623.8663.04.018.8663.62812.04715.6762.9941.63412.0477.239 6.524.52631.0264.05.024.5263.57811.88215.4603.0291.55011.8827.259 6.524.52631.0264.05.024.5263.57811.88215.4603.0291.55011.8827.282 8.030.18638.1865.06.030.1863.54811.78115.3293.0501.49811.7817.270 8.030.18638.1865.06.030.1863.54811.78115.3293.0501.49811.7817.284 8.030.18638.1865.06.030.1863.54811.78115.3293.0501.49811.7817.314 9.535.84645.3466.07.035.8463.52711.71315.2403.0641.46311.7137.277 3.011.32014.3202.02.011.3203.42211.36214.7843.1381.28411.3626.831 4.516.98021.4803.03.016.9803.42211.36214.7843.1381.28411.3627.027 6.022.64028.6404.04.022.6403.42211.36214.7843.1381.28411.3627.097 6.022.64028.6404.04.022.6403.42211.36214.7843.1381.28411.3627.141 7.528.30035.8005.05.028.3003.42211.36214.7843.1381.28411.3627.140 7.528.30035.8006.03.028.3003.07210.20113.2743.3800.69210.2017.302 9.033.95942.9597.04.033.9593.12510.37813.5043.3430.78210.3787.327 10.539.61950.1198.05.039.6193.16410.50813.6733.3160.84810.5087.342 2.59.43311.9332.01.09.4333.07210.20113.2743.3800.69210.2016.179 12.045.27957.27910.04.045.2792.9959.94712.9433.4340.5629.9477.467 1.55.6607.1601.02.05.6601.4984.9746.4721.3731.1244.9746.305 3.011.32014.3202.03.011.3202.0846.9199.0031.9111.1736.9196.835 0.752.8303.5801.53.3301.4094.6796.0881.5875.5026.290 SO2SO2 1.03.7734.7731.03.7731.0003.3204.3101.9983.32010.829 SO2SO2 1.55.6607.1601.01.05.6601.4104.6826.0931.8800.5294.6828.576 Allgasvolumescorrectedto60Fand14.696psidry. a1987AtomicWeights:C=12.011,H=1.00794,O=15.9994,N=14.0067,S=32.066. bDensitiescalculatedfromidealvaluesandcompressibilityfactorgiveninASTMD3588-98.Someofthematerialscannot existasgasesat60Fand14.696psi,inwhichcasethevaluesaretheoreticalones.Undertheactualconcentrationsin whichthesematerialsarepresent,theirpartialpressureislowenoughtokeepthemasgases. cForgasessaturatedwithwaterat60Fand14.696psi,1.74%oftheBtuvaluemustbededucted.Reference2. dReference2,ASTM3588-98. eCorrectionfromgrosstonetheatingvaluedeterminedbydeductingtheHVshownforwatervaportimesthemolesofH2. fReference3,Jones,F.E. gGasProcessorsSuppliersAssociation(GPSA)DataBook,Fig23-2,PhysicalConstants,1987. hEitherthedensityorthecompressibilityfactorhasbeenassumed. Table1CombustionConstantsReference1 HeatofCombustionc Specific Density,b Volumeb Specific Molecularlbperft3 GravitybBtuperft3 Btuperlb No.SubstanceFormulaWeighta ft3 perlb(air=1)Grossd Nete Grossd Nete ft3 perft3 ofCombustiblelbperlbofCombustible RequiredRequired forCombustionFlueProductsforCombustionFlueGasProducts O2N2aAirCO2H2ON2aO2N2aAirCO2H2ON2a Theor airlb/ 10,000 Btu
- 256. Steam 41 / Principles of Combustion 10-3 The Babcock & Wilcox Company Ideal gas law This law states that the volume of an ideal gas is directly proportional to its absolute temperature and inversely proportional to its absolute pressure. Theproportionalityconstantisthesameforonemole of any ideal gas, so this law may be expressed as: v P M = RT (1) where Mv = volume, ft3 /mole R = universal gas constant, 1545 ft lb/mole R T = absolute temperature, R = F + 460 P = absolute pressure, lb/ft2 Most gases involved in combustion calculations can be approximated as ideal gases. Law of combining weights This law states that all substances combine in ac- cordance with simple, definite weight relationships. These relationships are exactly proportional to the molecular weights of the constituents. For example, carbon (molecular weight = 12) combines with oxygen (molecular weight of O2 = 32) to form carbon dioxide (molecular weight = 44) so that 12 lb of C and 32 lb of O2 unite to form 44 lb of CO2. (See Application of fun- damental laws below.) Avogadro’s law Avogadro determined that equal volumes of differ- ent gases at the same pressure and temperature con- tain the same number of molecules. From the concept of the mole, a pound mole of any substance contains a mass equal to the molecular weight of the substance. Therefore, the ratio of mole weight to molecular weight is a constant and a mole of any chemically pure sub- stance contains the same number of molecules. Be- cause a mole of any ideal gas occupies the same volume at a given pressure and temperature (ideal gas law), equal volumes of different gases at the same pressure andtemperaturecontainthesamenumberofmolecules. Dalton’s law This law states that the total pressure of a mixture of gases is the sum of the partial pressures which would be exerted by each of the constituents if each gas were to occupy alone the same volume as the mix- ture. Consider equal volumes V of three gases (a, b and c), all at the same temperature T but at different pressures (Pa, Pb and Pc). When all three gases are placed in the space of the same volume V, then the resulting pressure P is equal to Pa + Pb + Pc. Each gas in a mixture fills the entire volume and exerts a pres- sure independent of the other gases. Amagat’s law Amagat determined that the total volume occupied by a mixture of gases is equal to the sum of the vol- umes which would be occupied by each of the constitu- ents when at the same pressure and temperature as the mixture. This law is related to Dalton’s law, but it considers the additive effects of volume instead of pres- sure. If all three gases are at pressure P and tempera- ture T but at volumes Va, Vb and Vc, then, when com- bined so that T and P are unchanged, the volume of the mixture V equals Va + Vb + Vc. Application of fundamental laws Table 2 summarizes the molecular and weight re- lationships between fuel and oxygen for constituents commonly involved in combustion. The heat of com- bustion for each constituent is also tabulated. Most of the weight and volume relationships in combustion cal- culations can be determined by using the information presented in Table 2 and the seven fundamental laws. The combustion process for C and H2 can be ex- pressed as follows: C + O2 = CO2 1 molecule + 1 molecule → 1 molecule 1 mole + 1 mole = 1 mole (See Note below) + 1 ft3 → 1 ft3 12 lb + 32 lb = 44 lb 2H2 + O2 = 2H2O 2 molecules + 1 molecule → 2 molecules 2 moles + 1 mole = 2 moles 2 ft3 + 1 ft3 → 2 ft3 4 lb + 32 lb = 36 lb Note: When 1 ft3 of oxygen (O2) combines with carbon (C), it forms 1 ft3 of carbon dioxide (CO2). If carbon were an ideal gas instead of a solid, 1 ft3 of carbon would be required. It is important to note that there is a mass or weight balance according to the law of combining weights but there is not necessarily a molecular or volume balance. Molar evaluation of combustion Gaseous fuel Molar calculations have a simple and direct appli- cation to gaseous fuels, where the analyses are usu- ally reported on a percent by volume basis. Consider the following fuel analysis: Fuel Gas Analysis, % by Volume CH4 85.3 C2H6 12.6 CO2 0.1 N2 1.7 O2 0.3 Total 100.0 The mole fraction of a component in a mixture is the number of moles of that component divided by the total number of moles of all components in the mix- ture. Because a mole of every ideal gas occupies the same volume, by Avogadro’s Law, the mole fraction of a component in a mixture of ideal gases equals the volume fraction of that component.
- 257. 10-4 Steam 41 / Principles of Combustion The Babcock & Wilcox Company Moles of component Total moles Volume of component Volume of = mixture (2) This is a valuable concept because the volumetric analysis of a gaseous mixture automatically gives the mole fractions of the components. Accordingly, the previous fuel analysis may be ex- pressed as 85.3 moles of CH4 per 100 moles of fuel, 12.6 moles of C2H6 per 100 moles of fuel, etc. The elemental breakdown of each constituent may also be expressed in moles per 100 moles of fuel as follows: C in CH4 = 85.3 × 1 = 85.3 moles C in C2H6 = 12.6 × 2 = 25.2 moles C in CO2 = 0.1 × 1 = 0.1 moles Total C per 100 moles fuel = 110.6 moles H2 in CH4 = 85.3 × 2 = 170.6 moles H2 in C2H6 = 12.6 × 3 = 37.8 moles Total H2 per 100 moles fuel = 208.4 moles O2 in CO2 = 0.1 × 1 = 0.1 moles O2 as O2 = 0.3 × 1 = 0.3 moles Total O2 per 100 moles fuel = 0.4 moles Total N2 per 100 moles fuel = 1.7 moles The oxygen/air requirements and products of com- bustion can now be calculated for each constituent on an elemental basis. These requirements can also be calculated directly using Table 1. Converting the gas- eous constituents to an elemental basis has two ad- vantages. It provides a better understanding of the combustion process and it provides a means for deter- mininganelementalfuelanalysisonamassbasis.This is boiler industry standard practice and is convenient for determining a composite fuel analysis when gas- eous and solid/liquid fuels are fired in combination. Thefollowingtabulationdemonstratestheconversion ofthegaseousfuelconstituentsonamoles/100molesgas basis to a lb/100 lb gas (percent mass) basis. Moles/ Mol Wt lb/ lb/ Consti- 100 lb/ 100 100 tuent Moles Mole Moles lb C 110.6 × 12.011 = 1328.4 /1808.9 × 100 =73.5 H2 208.4 × 2.016 = 420.1 /1808.9 × 100 =23.2 O2 0.4 × 31.999 = 12.8 /1808.9 × 100 = 0.7 N2 1.7 × 28.013 = 47.6 /1808.9 × 100 = 2.6 Total 1808.9 100.0 Solid/liquid fuel The ultimate analysis of solid and liquid fuels is determined on a percent mass basis. The mass analy- sis is converted to a molar basis by dividing the mass fraction of each elemental constituent by its molecu- lar weight. lb Constituent 100 lb Fuel lb Constituent Mole constituent Mo = lle constituent 100 lb Fuel (3) The calculation is illustrated in Table 3. The products of combustion and moles of oxygen required for each combustible constituent are shown. Note that when a fuel contains oxygen, the amount of theoretical O2/air required for combustion is reduced (as designated by the brackets). Composition of air So far, combustion has been considered only as a process involving fuel and oxygen. For normal com- bustion and steam generator applications, the source of oxygen is air. Atmospheric air is composed of oxy- gen, nitrogen and other minor gases. The calculations and derivation of constants which follow in this text are based upon a U.S. standard atmosphere3 composed of 0.20946 O2, 0.78102 N2, 0.00916 argon (Ar) and 0.00033 CO2 moles per mole of dry air, which has an Table 2 Common Chemical Reactions of Combustion Heat of Combustion Combustible Reaction Moles Mass or weight, lb (High) Btu/lb of Fuel Carbon (to CO) 2C + O2 = 2CO 2 + 1 = 2 24 + 32 = 56 3,967 Carbon (to CO2 ) C + O2 = CO2 1 + 1 = 1 12 + 32 = 44 14,093 Carbon monoxide 2CO + O2 = 2CO2 2 + 1 = 2 56 + 32 = 88 4,342 Hydrogen 2H2 + O2 = 2H2O 2 + 1 = 2 4 + 32 = 36 61,029 Sulfur (to SO2 ) S + O2 = SO2 1 + 1 = 1 32 + 32 = 64 3,980 Methane CH4 + 2O2 = CO2 + 2H2O 1 + 2 = 1 + 2 16 + 64 = 80 23,891 Acetylene 2C2H2 + 5O2 = 4CO2 + 2H2O 2 + 5 = 4 + 2 52 + 160 = 212 21,482 Ethylene C2H4 + 3O2 = 2CO2 + 2H2O 1 + 3 = 2 + 2 28 + 96 = 124 21,643 Ethane 2C2H6 + 7O2 = 4CO2 + 6H2O 2 + 7 = 4 + 6 60 + 224 = 284 22,334 Hydrogen sulfide 2H2S + 3O2 = 2SO2 + 2H2O 2 + 3 = 2 + 2 68 + 96 = 164 7,094
- 258. Steam 41 / Principles of Combustion 10-5 The Babcock & Wilcox Company average molecular weight of 28.9625. To simplify the calculations, N2 includes argon and other trace ele- ments; it is referred to as atmospheric nitrogen (N2a) having an equivalent molecular weight of 28.158. (See Table 4.) Air normally contains some moisture. As standard practice, theAmerican Boiler ManufacturersAssocia- tion (ABMA) considers moisture content to be 0.013 lb water/lb dry air, which corresponds to approxi- mately 60% relative humidity at 80F. For combustion calculations on a molar basis, multiply the mass basis moisture by 1.608 (molecular weight of air divided by molecular weight of water). Therefore, 0.013 lb water/ lb dry air becomes 0.0209 moles water/mole dry air. The moisture content in air is normally determined from wet and dry bulb temperatures or from relative humidity using a psychrometric chart, as shown in Fig. 1. Air moisture may also be calculated from: MFWA P P P v b v = × −( ) 0 622. (4) where MFWA = moisture content in air, lb/lb dry air Pb = barometric pressure, psi Pυ = partial pressure of water vapor in air, psi = 0.01 (RH) (Pυ d), psi Pυd = saturation pressure of water vapor at dry bulb temperature, psi RH = relative humidity, % Pυ may also be calculated from Carrier’s equation: P P P P T T T v vw b vw d w w = − −( ) −( ) − ( )2830 1 44. (5) where Td = dry bulb temperature, F Tw = wet bulb temperature, F Pvw = saturation pressure of water vapor at wet bulb temperature, psi The following constants, with values from Table 4, are frequently used in combustion calculations: moles air/mole O2 = 100 20 95. = 4.77 or ft3 air/ft3 O2 moles N2a /mole O2 = 79 05 20 95 . . = 3.77 lb air (dry)/lb O2 = 100 23 14. = 4.32 lb N2a /lb O2 = 76 86 23 14 . . = 3.32 The calculations in Table 2 can be converted to com- bustion with air rather than oxygen by adding 3.77 moles of N2a/mole of O2 to the left and right side of each equation. For example, the combustion of carbon monoxide (CO) in air becomes: 2 CO + O2 + 3.77 N2a = 2CO2 + 3.77 N2a or for methane, CH4: CH4 + 2O2 + 2(3.77) N2a = CO2 + 2H2O + 7.54 N2a Theoretical air requirement Theoretical air is the minimum air required for com- plete combustion of the fuel, i.e., the oxidation of car- Table 3 Calculation of Combustion Products and Theoretical Oxygen Requirements Molar Basis Moles/100 Com- Moles Fuel con- % Molecular lb fuel bustion theoretical stituent by wt weight (2 ÷ 3) product O2 required (1) (2) (3) (4) (5) (6) C 72.0 12.011 = 5.995 CO2 5.995 H2 4.4 2.016 = 2.183 H2O 1.091* S 1.6 32.066 = 0.050 SO2 0.050 O2 3.6 31.999 = 0.113 (0.113) N2 1.4 28.013 = 0.050 N2 0.000 H2O 8.0 18.015 = 0.444 H2O 0.000 Ash 9.0 Total 100.0 8.835 7.023 * Column 6 is based upon moles of oxygen as O2 needed for combustion. Therefore, the moles of H2O need to be divided by 2 to obtain equivalent moles of O2. Table 4 Air Composition Composition of Dry Air % by vol % by wt Oxygen, O2 20.95 23.14 Atmospheric nitrogen, N2a 79.05 76.86 Fig. 1 Psychrometric chart – water content of air for various wet and dry bulb temperatures.
- 259. 10-6 Steam 41 / Principles of Combustion The Babcock & Wilcox Company bon to CO2, hydrogen to water vapor (H2O) and sul- fur to sulfur dioxide (SO2). In the combustion process, small amounts of sulfur trioxide (SO3), nitrogen ox- ides (NOx), unburned hydrocarbons and other minor species may be formed. While these may be of concern aspollutants,theirimpactisnegligiblewithregardtothe quantity of air and combustion products and, therefore, they are not normally considered in these calculations. In practice, it is necessary to use more than the theoretical amount of air to assure complete combus- tion of the fuel. For the example shown in Table 3, consider completing the combustion calculations on a molar basis using 20% excess air. These calculations are summarized in Table 5. Now consider the portion of the combustion prod- ucts attributable to the air. The oxygen in the theo- retical air is already accounted for in the products of combustion: CO2, H2O (from the combustion of hydro- gen) and SO2. That leaves N2a in the theoretical air, N2a in the excess air, O2 in the excess air and H2O in air (as calculated in Table 5) as the products in the combustion gas attributable to the wet combustion air. These constituents are in addition to the combustion products from fuel shown in Table 3. Products of combustion – mass/mass fuel basis Table 6 shows a tabulation of the flue gas products and combustion air on a molar (or volumetric) basis and the conversion to a mass basis (wet and dry). The products of combustion calculated on a molar basis in Tables 3 and 5 are itemized in column A. The mois- ture (H2O) sources are separated from the dry prod- ucts for convenience of calculating the flue gas com- position on a wet and dry basis. The water products shown in columnAare from the combustion of hydrogen in the fuel, from moisture in the fuel and from moisture in the air. The N2a is the sum of nitrogen in the theoretical air plus the nitro- gen in the excess air. The N2a is tabulated separately from the elemental nitrogen in the fuel to differenti- ate the molecular weight of the two. In practice, the nitrogen in the fuel is normally small with respect to the N2a and can be included with the nitrogen in air. For manufactured gases that are formed when com- bustible products oxidize with air (blast furnace gas, for example), the nitrogen in the fuel is predominately atmospheric nitrogen. Flue gas products are normally measured on a volu- metric basis. If the sample includes water products, it is measured on a wet basis, typical of in situ analyz- ers. Conversely, if water products are excluded, mea- surements are done on a dry basis, which is typical of extractive gas sample systems. (See Flue gas analy- sis.) Note that the flue gas products are summed on a dry and wet basis to facilitate calculation of the flue gas constituents on a dry and wet percent by volume basis in columns B and C. The molecular weight of each constituent is given in column D. Finally, the mass of each constituent on a lb/100 lb fuel basis is the prod- uct of the moles/100 lb fuel and the molecular weight. The calculation of the mass of air on a lb/100 lb fuel basis, shown at the bottom of Table 6, follows the same principles as the flue gas calculations. Formostengineeringcalculations,itiscommonU.S. practicetoworkwithairandfluegas(combustionprod- ucts) on a mass basis. It is usually more convenient to calculate these products on a mass basis directly as dis- cussed later. The mole method described above is the fundamental basis for understanding and calculating the chemical reactions. It is also the basis for deriving certain equations that are presented later. For those whopreferusingthemolemethod,Table7presentsthis method in a convenient calculation format. Alternate units – Btu method It is customary within the U.S. boiler industry to use units of mass rather than moles for expressing the quantity of air and flue gas. This is especially true for heat transfer calculations, where the quantity of the working fluid (usually steam or water) is expressed on a mass basis and the enthalpy of the hot and cold fluids is traditionally expressed on a Btu/lb basis. Therefore, if the combustion calculations are per- formed on the mole basis, it is customary to convert the results to lb/100 lb fuel. Table 5 Calculation of Wet Air Requirements for Combustion Molar Basis Line Quantity (mole/ No. Description Source 100 lb fuel) 1 Theoretical From Table 3 7.023 combustion O2 2 Molar fraction O2 Vol fraction O2 in dry air from Table 4 0.2095 3 Theoretical dry Line 1/Line 2 33.523 combustion air 4 Excess air at 20% Line 3 x 0.20 6.705 5 Total dry Line 3 + Line 4 40.228 combustion air 6 Molar fraction * 0.0209 of H2O in dry air 7 H2O in total Line 5 x Line 6 0.841 dry air 8 Molar fraction N2a Vol fraction of N2a in dry air from Table 4 0.7905 9 N2a in theoretical Line 3 x Line 8 26.500 dry air 10 N2a in dry Line 4 x Line 8 5.300 excess air 11 O2 in dry Line 2 x Line 4 1.405 excess air * Standard combustion air: 80F, 60% relative humidity; 0.013 lb H2O/lb dry air; 0.0209 moles H2O/mole dry air.
- 260. Steam 41 / Principles of Combustion 10-7 The Babcock & Wilcox Company Items that are expressed on a unit of fuel basis (mole/100 lb fuel, mass/mass fuel, etc.) can be normal- ized by using an input from fuel basis. For example, knowing that a coal has 10% ash only partly defines the fuel. For a 10,000 Btu/lb fuel, there are 10 lb ash per million Btu input, but for a 5000 Btu/lb fuel there would be 20 lb ash per million Btu input. Consider- ing that fuel input for a given boiler load does not vary significantly with heating value, a boiler firing the lower heating value fuel would encounter approxi- mately twice the amount of ash. The mass per unit input concept is valuable when determining the impact of different fuels on combus- tion calculations. This method is particularly helpful in theoretical air calculations. Referring to Table 8, in the first column, theoretical air has been tabulated for various fuels on a mass per mass of fuel basis. The resulting values have little significance when compar- ing the various fuels. However, when the theoretical air is converted to a mass per unit heat input from fuel basis,thetheoreticalairvarieslittlebetweenfuels.Also refer to the discussion on the Btu Method in the Com- bustion calculations section. The common units are lb/10,000 Btu, abbreviated as lb/10KB. The fuel la- beled MSW/RDF refers to municipal solid waste and refuse derived fuel. Note that the theoretical air is in the same range as that for fossil fuels on a heat input basis. Carbon and hydrogen, the principal combustible fuel elements, are shown for reference. Note that the coals listed in the table are limited to those with a volatile matter (moisture and ash free) greater than 30%. As volatile matter decreases, the carbon content increases and requires more excess air. To check the expected theoretical air for low volatile coals, refer to Fig. 2. The theoretical air of all coals should fall within plus or minus 0.2 lb/10,000 Btu of this curve. Table 9 provides the fuel analysis and theoretical air require- ments for a typical fuel oil and natural gas. Heat of combustion In a boiler furnace (where no mechanical work is done), the heat energy evolved from combining com- bustible elements with oxygen depends on the ulti- mate products of combustion; it does not rely on any intermediate combinations that may occur. For example, one pound of carbon reacts with oxy- gen to produce about 14,093 Btu of heat (refer to Table 2). The reaction may occur in one step to form CO2 or, under certain conditions, it may take two steps. In this process, CO is first formed, producing only 3967 Btu per pound of carbon. In the second step, the CO joins with additional oxygen to form CO2, releasing 10,126 Btu per pound of carbon (4342 Btu per pound of CO). The total heat produced is again 14,093 Btu per pound of carbon. Measurement of heat of combustion In boiler practice, a fuel’s heat of combustion is the amount of energy, expressed in Btu, generated by the complete combustion, or oxidation, of a unit weight of fuel. Calorific value, fuel Btu value and heating value are terms also used. The amount of heat generated by complete combus- tion is a constant for a given combination of combus- tible elements and compounds. It is not affected by the manner in which the combustion takes place, provided it is complete. A fuel’s heat of combustion is usually determined by direct calorimeter measurement of the heat evolved. Combustion products within a calorimeter are cooled to the initial temperature, and the heat absorbed by the cooling medium is measured to determine the higher, or gross, heat of combustion (typically referred to as the higher heating value, or HHV). For all solid and most liquid fuels, the bomb type calorimeter is the industry standard measurement device. In these units, combustible substances are burned in a constant volume of oxygen. When they Table 6 Calculation of Flue Gas and Air Quantities Mass Basis Flue Gas or Combustion Product A (From Tables 3 B C D (From E and 5) (A/A6) (A/A11) Table 1) (A x D) Moles/100 % Vol % Vol Molecular lb/100 Constituent lb Fuel dry wet weight lb Fuel 1 CO2 5.995 15.25 14.02 44.010 263.8 2 SO2 0.050 0.13 0.115 64.065 3.2 3 N2 (fuel) 0.050 0.13 0.115 28.013 1.4 4 N2a (air) 31.800 80.92 74.35 28.158 895.4 (26.500 + 5.300) 5 O2 1.405 3.57 3.29 31.999 45.0 6 Total, dry 39.300 100.00 1208.8 combustion products 7 H2O com- 2.183 bustion 8 H2O fuel +0.444 9 H2O air +0.841 10 Total H2O 3.468 8.11 18.015 62.5 11 Total, wet combustion products 42.768 100.00 1271.3 Air 12 Dry air 40.228 28.963 1165.1 13 H2O 0.841 18.015 15.2 14 Total wet air 1180.3 Fig. 2 Theoretical air in lb/10,000 Btu heating value of coal with a range of volatile matter.
- 261. 10-8 Steam 41 / Principles of Combustion The Babcock & Wilcox Company Table 7 Combustion Calculations Molar Basis INPUTS (see also lightly shaded blocks) FUEL − Bituminous coal, Virginia 1 Excess air: at burner/at boiler/econ, % 20/20 4 Fuel input, 1,000,000 Btu/h 330.0 2 Moisture in air, lb/lb dry air 0.013 5 Unburned carbon loss, % efficiency 0.40 3 Fuel heating value, Btu/lb 14,100 6 Unburned carbon (UBC), [5] x [3] / 14,500 0.39 COMBUSTION PRODUCTS CALCULATIONS 7 Ultimate Analysis, % mass 8 Molecular 9 Moles 10 Moles O2 11 Moles Theo. 12 Fuel As- Carbon Weight /100 lb Fuel /Mole Fuel O2/100 lb Fuel Combustion Constituent Fired Burned(CB) lb/mole [7] / [8] Constituent [9] x [10] Product A C 80.31 80.31 B UBC [6] 0.39 C CB [A] − [B] 79.92 12.011 6.654 1.0 6.654 CO2 D S 1.54 32.066 0.048 1.0 0.048 SO2 E H2 4.47 2.016 2.217 0.5 1.109 H2O F H2O 2.90 18.015 0.161 H2O G N2 1.38 28.013 0.049 N2 (fuel) H O2 2.85 31.999 0.089 −1.0 −0.089 I Ash 6.55 K Total 100.00 9.218 7.722 AIR CONSTITUENTS, Moles/100 lb Fuel At Burner At Blr/Econ 13 O2 − excess [11K] x [1] / 100 1.544 1.544 14 O2 − total [13] + [11K] 9.266 9.266 15 N2a − air [14] x 3.77 34.933 34.933 16 Air (dry) [14] + [15] 44.199 44.199 17 H2O − air [16] x [2] x 1.608 0.924 0.924 18 Air (wet) [16] + [17] 45.123 45.123 19 20 Vol % Dry 21 Vol % Wet 22 Molecular 23 Flue Gas Moles 100 x 100 x Weight lb/100 lb Fuel FLUE GAS CONSTITUENTS /100 lb Fuel [19] / [19G] [19] / [19H] lb/mole [19] x [22] A CO2 [9C] 6.654 15.39 14.30 44.010 292.8 B SO2 [9D] 0.048 0.11 0.10 64.065 3.1 C O2 [13] 1.544 3.57 3.32 31.999 49.4 D N2 (fuel) [9G] 0.049 0.11 0.11 28.013 1.4 E N2a (air) [15] 34.933 80.82 75.07 28.158 983.6 F H2O [9E] + [9F] + [17] 3.302 7.10 18.015 59.5 G Total dry Sum [A] through [E] 43.228 100.00 1330.3 H Total wet Sum [A] through [F] 46.530 100.00 1389.8 KEY PERFORMANCE PARAMETERS At Burner At Blr/Econ 24 Molecular weight wet flue gas, lb/mole [23H] / [19H] 29.869 25 H2O in wet gas, % by wt 100 x [23F] / [23H] 4.28 26 Dry gas weight, lb/10,000 Btu 100 x [23G] / [3] 9.435 27 Wet gas weight, lb/10,000 Btu 100 x [23H] / [3] 9.857 28 Wet gas weight, 1000 lb/h [27] x [4] / 10 325.3 29 Air flow (wet), lb/100 lb fuel [16] x 28.966 + [17] x 18.015 1296.9 30 Air flow (wet), lb/10,000 Btu 100 x [29] / [3] 9.198 31 Air flow (wet), 1000 lb/h [30] x [4] / 10 303.5
- 262. Steam 41 / Principles of Combustion 10-9 The Babcock & Wilcox Company are properly operated, combustion is complete and all of the heat generated is absorbed and measured. Heat from external sources can be excluded or proper cor- rections can be applied. For gaseous fuels of 900 to 1200 Btu/ft3 , continu- ous or constant flow type calorimeters are industry standards. The principle of operation is the same as for the bomb calorimeter; however, the heat content is determined at constant pressure rather than at con- stant volume. For most fuels, the difference between the constant pressure and constant volume heating values is small and is usually neglected. However, because fuel is burned under essentially constant pressure condi- tions, the constant pressure heating value is the tech- nically correct value. For solid or liquid fuels, to convert the constant vol- ume higher heating value (HHVCV) measured in the bomb calorimeter to constant pressure (HHVCP), an adjustment for the volume change is required. Dur- ing the constant pressure combustion process: 1. Every mole of carbon combines with one mole of oxygen to form one mole of carbon dioxide. There- fore, there is no volume change. 2. Every mole of sulfur combines with one mole of oxygen to form one mole of sulfur dioxide. There- fore, there is no volume change. 3. Every mole of hydrogen combines with 1/2 mole of oxygen to form one mole of water vapor. Therefore, there is a net increase of 1/2 mole of gas produced. Whenthewatervaporiscondensedtoaliquidinthe bomb calorimeter, there is a net decrease of 1/2 mole of gas for each mole of hydrogen. 4. For every mole of oxygen in the fuel, there is one mole of oxygen gas produced. Therefore, there is a net increase of one mole of gas produced for each mole of oxygen in the fuel. 5. The solid or liquid nitrogen in the fuel is released as a gas. Therefore, there is a net increase of one mole of gas produced for every mole of nitrogen. Using the ideal gas law, the energy change due to the volume change is as follows: ∆HHV N T J k n k = × = ∑1 R , Btu/lb (6) where Nk = number of moles of constituent k R = universal gas constant, 1545 ft-lb/mole-R T = absolute reference temperature for the bomb calorimeter, 537R J = mechanical equivalent of heat, 778.2 ft lbf/ Btu Substituting: ∆HHV T = − + − + × O N H2 2 2 31 9988 28 0134 0 5 2 0159 778 2. . . . . R (7) where O2 = mass fraction of oxygen in fuel N2 = mass fraction of nitrogen in fuel H2 = mass fraction of hydrogen in fuel The corrections for nitrogen and oxygen in typical solid and liquid fuels are small, generally less than 1 and 2 Btu/lbm respectively, and are generally consid- ered negligible. The fuel heating value correction from constant volume to constant pressure then becomes: HHV HHV HCP CV= + 264 4 2. , Btu/lb (8) Gas chromatography is also commonly used to de- termine the composition of gaseous fuels. When the composition of a gas mixture is known, its heat of com- bustion may be determined as follows: Table 8 Theoretical Air Required for Various Fuels Theoretical Theoretical Air Air, lb/lb HHV Typical Range Fuel Fuel Btu/lb lb/104 Btu lb/104 Btu Bituminous coal (VM* >30%) 9.07 12,000 7.56 7.35 to 7.75 Subbituminous coal (VM* >30%) 6.05 8,000 7.56 7.35 to 7.75 Oil 13.69 18,400 7.46 7.35 to 7.55 Natural Gas 15.74 21,800 7.22 7.15 to 7.35 Wood 3.94 5,831 6.75 6.60 to 6.90 MSW* and RDF* 4.13 5,500 7.50 7.20 to 7.80 Carbon 11.51 14,093 8.16 Hydrogen 34.29 61,029 5.62 * VM = volatile matter, moisture and ash free basis MSW = municipal solid waste RDF = refuse-derived fuel Table 9 Fuel Analysis and Theoretical Air for Typical Oil and Gas Fuels Heavy Fuel Oil, Natural Gas, % by wt % by vol S 1.16 CH4 85.3 H2 10.33 C2H6 12.6 C 87.87 CO2 0.1 N2 0.14 N2 1.7 O2 0.50 O2 0.3 Sp Gr 0.626 Btu/ft3 , as-fired 1090 Btu/lb, Btu/lb, as-fired 18,400 as-fired 22,379 Theoretical Air, Fuel and Moisture Theoretical air, 7.437 Theoretical air, 7.206 lb/10,000 Btu lb/10,000 Btu Fuel, lb/ 0.543 Fuel, lb/ 0.440 10,000 Btu 10,000 Btu Moisture, lb/ 0.502 Moisture, lb/ 0.912 10,000 Btu 10,000 Btu
- 263. 10-10 Steam 41 / Principles of Combustion The Babcock & Wilcox Company hc v hc v hc v hca a b b x xmix = + + +… (9) where hcmix = heat of combustion of the mixture vx = volume fraction of each component hcx = heat of combustion of each component For an accurate heating value of solid and liquid fuels, a laboratory heating value analysis is required. Numerous empirical methods have been published for estimating the heating value of coal based on the proximate or ultimate analyses. (See Chapter 9.) One of the most frequently used correlations is Dulong’s formula which gives reasonably accurate results for bituminous coals (within 2 to 3%). It is often used as a routine check of calorimeter-determined values. HHV = + − ( ) + 14 544 62 028 8 4050 2, , /C H O S 2 (10) where HHV = higher heating value, Btu/lb C = mass fraction carbon H2 = mass fraction hydrogen O2 = mass fraction oxygen S = mass fraction sulfur A far superior method for checking whether the heating value is reasonable in relation to the ultimate analysis is to determine the theoretical air on a mass per Btu basis. (See Alternate units – Btu method.) Table 8 indicates the range of theoretical air values. The equation for theoretical air can be rearranged to calculate the higher heating value, HHV, where the median range for theoretical air for the fuel from Table 8, MQTHA, is used: HHV MQTHA = × + + − 100 11 51 34 29 4 31 4 32. . . .C H S O2 2 (11) where HHV = higher heating value, Btu/lb C = mass percent carbon, % H2 = mass percent hydrogen, % S = mass percent sulfur, % O2 = mass percent oxygen, % MQTHA = theoretical air, lb/10,000 Btu Higher and lower heating values Water vapor is a product of combustion for all fuels that contain hydrogen. The heat content of a fuel de- pends on whether this vapor remains in the vapor state or is condensed to liquid. In the bomb calorim- eter, the products of combustion are cooled to the ini- tial temperature and all of the water vapor formed duringcombustioniscondensedtoliquid.Thisgivesthe HHVorgrosscalorificvalue(definedearlier)ofthefuel, and the heat of vaporization of water is included in the reported value. For the lower heating value (LHV) or net calorific value (net heat of combustion at constant pressure), all products of combustion including water are assumed to remain in the gaseous state, and the water heat of vaporization is not available. While the high, or gross, heat of combustion can be accurately determined by established American Soci- ety for Testing and Materials (ASTM) procedures, di- rect determination of the lower heating value is diffi- cult. There is no international standard for calcula- tion of LHV from the measured HHV. The constants used for heats of combustion, and the temperature used to calculate the latent heat of vaporization (HFG), may vary slightly between references. It is important that the temperature used for the calculation of HFG be consistent with the basis for the boiler efficiency calculations, otherwise there can be errors in calcu- lated fuel flow for a given boiler output. ASME Per- formance Test Code PTC 4 specifies a reference tem- perature of 77F (25C). The value given for HFG at 77F in the ASME International Steam Tables for Indus- trial Use, based on IAWPS-IF97 is 1049.7 Btu/lb. Cal- culation of LHV at constant pressure from HHV at con- stant pressure is then as follows: LHV HHV M CP CP= − × +( )1049 7 8 9372. . ,H Btu/lb (12) where H2 = mass fraction of hydrogen in fuel M = mass fraction of water in fuel In some references, the calculation of LHV includes a correction for the difference between constant volume and constant pressure combustion. Combining Equa- tions 8 and 12, the calculation of LHV at constant pressure from HHV at constant volume is as follows: LHV HHV M H CP CV= − × +( ) + 1049 7 8 937 264 4 2 2 . . . , H Btu/lb (13) Ignition temperatures Ignition temperatures of combustible substances vary greatly, as indicated in Table 10. This table lists minimum temperatures and temperature ranges in air for fuels and for the combustible constituents of fuels commonly used in the commercial generation of heat. Many factors influence ignition temperature, so any tabulation can be used only as a guide. Pressure, ve- locity, enclosure configuration, catalytic materials, air/ fuel mixture uniformity and ignition source are ex- amples of the variables. Ignition temperature usually decreases with rising pressure and increases with in- creasing air moisture content. The ignition temperatures of coal gases vary con- siderably and are appreciably higher than those of the fixed carbon in the coal. However, the ignition tem- perature of coal may be considered as the ignition tem- perature of its fixed carbon content, because the gas- eous constituents are usually distilled off, but not ig- nited, before this temperature is attained.
- 264. Steam 41 / Principles of Combustion 10-11 The Babcock & Wilcox Company Adiabatic flame temperature The adiabatic flame temperature is the maximum theoretical temperature that can be reached by the products of combustion of a specific fuel and air (or oxygen) combination, assuming no loss of heat to the surroundings and no dissociation. The fuel’s heat of combustion is the major factor in the flame tempera- ture, but increasing the temperature of the air or the fuel also raises the flame temperature. This adiabatic temperature is a maximum with zero excess air (only enough air chemically required to combine with the fuel). Excess air is not involved in the combustion process; it only acts as a dilutant and reduces the av- erage temperature of the products of combustion. The adiabatic temperature is determined from the adiabatic enthalpy of the flue gas: H HHV g = − +Latent heat H O Sensible heat in air Wet gas weight 2 (14) where Hg = adiabatic enthalpy, Btu/lb Knowing the moisture content and enthalpy of the products of combustion, the theoretical flame or gas temperature can be obtained from Fig. 3 (see pages 12 and 13). Theadiabatictemperatureisafictitiouslyhighvalue that can not exist. Actual flame temperatures are lower for two main reasons: 1. Combustion is not instantaneous. Some heat is lost to the surroundings as combustion takes place. Faster combustion reduces heat loss. However, if combustion is slow enough, the gases may be cooled sufficiently and incomplete combustion may occur, i.e., some of the fuel may remain unburned. 2. At temperatures above 3000F, some of the CO2 and H2O in the flue gases dissociates, absorbing heat in the process. At 3500F, about 10% of the CO2 in a typical flue gas dissociates to CO and O2. Heat absorption occurs at 4342 Btu/lb of CO formed, and about 3% of the H2O dissociates to H2 and O2, with a heat absorption of 61,029 Btu/lb of H2 formed. As the gas cools, the dissociated CO and H2 recombine with the O2 and liberate the heat absorbed in dissociation, so the heat is not lost. However, the overall effect is to lower the maxi- mum actual flame temperature. The term heat available (Btu/h) is used through- out this text to define the heat available to the fur- nace. This term is analogous to the energy term (nu- merator) in the adiabatic sensible heat equation above except that one half of the radiation heat loss and the manufacturer’s margin portion are not considered available to the furnace. Practical combustion application issues In addition to the theoretical combustion evalua- tion methodologies addressed above, several applica- tion issues are very important in accurate combustion calculations of actual applications. These include the impact of the injection of SO2 sorbents and other chemicals into the combustion process, solid ash or residue, unburned carbon and excess air. Sorbents and other chemical additives In some combustion systems, chemical compounds are added to the gas side of the steam generator to reduce emissions. For example, limestone is used uni- versally in fluidized-bed steam generators to reduce SO2 emissions. (See Chapter 17.) Limestone impacts the combustion and efficiency calculations by: 1) altering the mass of flue gas by reducing SO2 and increasing CO2 levels, 2) increas- ing the mass of solid waste material (ash residue), 3) increasing the air required in forming SO3 to produce calcium sulfate, CaSO4, 4) absorbing energy (heat) from the fuel to calcine the calcium and magnesium carbonates, and 5) adding energy to the system in the sulfation reaction (SO2 + ½ O2 + CaO → CaSO4). The impact of sorbent/limestone is shown as a correction to the normal combustion calculations presented later. The limestone constituents that are required in the combustion and efficiency calculations are: Reactive constituents: Calcium carbonate (CaCO3) Magnesium carbonate (MgCO3) Water Inerts Some processes may use sorbents derived from lime- stone. These sorbents contain reactive constituents such as calcium hydroxide [Ca(OH)2] and magnesium hydroxide [Mg(OH)2]. For design purposes, the amount of sorbent is de- termined from the design calcium to sulfur molar ra- tio, MOFCAS. The sorbent to fuel ratio, MFSBF, is a Table 10 Ignition Temperatures of Fuels in Air (Approximate Values or Ranges at Atmospheric Pressure) Combustible Formula Temperature, F Sulfur S 470 Charcoal C 650 Fixed carbon (bituminous coal) C 765 Fixed carbon (semi-anthracite) C 870 Fixed carbon (anthracite) C 840 to 1115 Acetylene C2H2 580 to 825 Ethane C2H6 880 to 1165 Ethylene C2H4 900 to 1020 Hydrogen H2 1065 to 1095 Methane CH4 1170 to 1380 Carbon monoxide CO 1130 to 1215 Kerosene 490 to 560 Gasoline 500 to 800
- 265. 10-12 Steam 41 / Principles of Combustion The Babcock & Wilcox Company Fig. 3 Enthalpy of flue gas above 77F at 30 in. Hg.
- 266. Steam 41 / Principles of Combustion 10-13 The Babcock & Wilcox Company
- 267. 10-14 Steam 41 / Principles of Combustion The Babcock & Wilcox Company convenient equation that converts sorbent products to a mass of fuel or input from fuel basis. MFSBF MOFCAS MOPCA = × × S 32 066. (15) and MOPCA = + ( ) CaCO Ca OH3 2 100 089 74 096. . (16) where MFSBF = mass ratio of sorbent to fuel, lb/lb MOFCAS = calcium to sulfur molar ratio S = mass percent sulfur in fuel, % MOPCA = calcium in sorbent molar basis, moles/ 100 lb sorbent CaCO3 = mass percent calcium carbonate in sorbent, % Ca(OH)2 = mass percent calcium hydroxide in sorbent, % When calcium carbonate and magnesium carbon- ate are heated, they release CO2, which adds to the flue gas products. This is referred to as calcination. Magnesium carbonate calcines readily; however, at the operating temperatures typical of atmospheric pressure fluidized beds, not all of the calcium carbon- ate is calcined. For design purposes, 90% calcination is appropriate for atmospheric fluidized-bed combus- tion. On an operating unit, the mass fraction of calci- nation can be determined by measuring the CO2 in the ash residue and by assuming it exists as CaCO3. The quantity of CO2 added to the flue gas may be calcu- lated from: MQGSB MOGSB HHV = × ×44 01 100 . (17) and MOGSB MFSBF MFCL = × + CaCO MgCO3 3 100 089 58 320. . (18) where MQGSB = incremental CO2 from sorbent, lb/ 10,000 Btu MOGSB = moles CO2 from sorbent, moles/100 lb sorbent HHV = higher heating value, Btu/lb fuel MFCL = fraction of available CaCO3 calcined,lb/ lb CaCO3 = mass percent calcium carbonate in sor- bent, % MgCO3 = mass percent magnesium carbonate in sorbent, % The water added to the flue gas, MQWSB, includes the free water and water evaporated due to dehydra- tion of calcium and magnesium hydroxide products. MQWSB MOWSB HHV = × ×18 015 100 . (19) and MOWSB = + ( ) + ( ) H O Ca OH Mg OH 84.321 2 2 2 74 096. (20) where MQWSB = water added to flue gas from sorbent, lb/10,000 Btu MOWSB = moles of water from sorbent, moles/100 lb sorbent HHV = higher heating value, Btu/lb fuel H2O = free water from sorbent, moles/100 lb sorbent Ca(OH)2 = mass percent calcium hydroxide in sor- bent, % Mg(OH)2 = mass percent magnesium hydroxide in sorbent, % Spent sorbent refers to the solid products remain- ing due to the use of limestone. Spent sorbent is the sum of the inerts in the limestone, the mass of the re- active constituents after calcination (CaCO3, CaO and MgO), and the SO3 formed in the sulfation reaction. MQSSB MFSSB HHV = × 10 000, (21) and MFSSB MFSBF MOGSB MOWSB MFSC = − ×( ) − ×( ) + × ×( ) 0 4401 0 18015 250 . . S (22) where MQSSB = solids added to flue gas, lb/10,000 Btu MFSSB = solids added to flue gas, lb/lb fuel HHV = higher heating value, Btu/lb fuel MFSBF = mass ratio of sorbent to fuel, lb/lb MOGSB = moles CO2 from sorbent, moles/100 lb sorbent MOWSB = moles H2O from sorbent, moles/100 lb sorbent S = mass percent sulfur in fuel, % MFSC = mass fraction of sulfur in fuel captured, lb/lb The combustion and efficiency values related to lime- stone(sorbent)arecalculatedseparatelyinthistext;they aretreatedasasupplementtothebasiccalculations.(See Combustion and efficiency calculations.) Residue versus refuse The term residue is used within this text to refer to the solid waste products that leave the steam genera- tor envelope. This replaces the term refuse which is now used to refer to municipal solid waste fuels and their derivatives. Unburned carbon Incommercialsolidfuelapplications,itisnotalways practical to completely burn the fuel. Some of the fuel may appear as unburned carbon in the residue or CO in the flue gas, although the hydrogen in the fuel is
- 268. Steam 41 / Principles of Combustion 10-15 The Babcock & Wilcox Company usually completely consumed. The capital and oper- ating (energy) costs incurred to burn this residual fuel are usually far greater than the energy lost. In addi- tion, the evolution of combustion equipment to reduce NOx emissions has resulted in some tradeoffs with increases in unburned carbon and CO. Unburned carbon impacts the combustion calcula- tions and represents an efficiency loss. Therefore, un- burned carbon must be measured when present. The preferred procedure is to determine the quantity of combustible carbon in the boiler flyash and bottom ash in accordance with ASTM D-6316, Determination of Total, Combustible, and Carbonate Carbon in Solid Residues from Coal and Coke. The unburned carbon determined byASTM D-6316 is on the basis of percent carbon in the flyash/bottom ash (lb carbon/100 lb residue). The combustion calcu- lations require unburned carbon on a lb/100 lb fuel basis (percent unburned carbon from fuel) calculated from the following equations: UBC MPCR MFR= × (23) and MFR AF MFSSB MPCR = + ×( ) −( ) 100 100 (24) where UBC = unburned carbon, lb/100 lb fuel MPCR = unburned carbon in residue (measured or reference), mass % MFR = mass fraction residue, fuel basis, lb/lb fuel AF = mass percent ash from fuel, % MFSSB = mass fraction of spent sorbent, lb/lb fuel The quantity of ash in solid fuels is variable, and therefore it is sometimes desirable to correct the mea- sured percent unburned carbon in residue to a refer- ence (or baseline) fuel ash content in order to evalu- ate combustion system performance. For given boiler operating conditions, the heat loss due to unburned carbon (UBCL) is assumed to remain constant for typi- cal variations in fuel ash (and spent sorbent if appli- cable). The unburned carbon as it would appear in a residue produced by the reference fuel (and sorbent flow) may be calculated using the following equation: MPCR AF MFSSB UBCL HHV REF REF REF MEAS REF = × + ×( ) × 100 14 500 100, +1 (25) where MPCRREF = unburned carbon in residue corrected to reference fuel ash (and spent sor- bent), % AFREF = mass percent ash from reference fuel, % MFSSBREF = reference mass fraction of spent sor- bent, lb/lb fuel UBCLMEAS = measured heat loss due to unburned carbon, % HHVREF = higher heating value of reference fuel, Btu/lb Equation 25 assumes that the unburned carbon loss, UBCL, is constant between the test and reference conditions. Excess air For commercial applications, more than theoretical air is needed to assure complete combustion. This ex- cess air is needed because the air and fuel mixing is not perfect. Because the excess air that is not used for combustion leaves the unit at stack temperature, the amount of excess air should be minimized. The energy required to heat this air from ambient to stack tem- perature usually serves no purpose and is lost energy. Typical values of excess air required at the burning equipment are shown in Table 11 for various fuels and methods of firing. When substoichiometric firing is used in the combustion zone, i.e., less than the theo- retical air is used, the values shown would apply to the furnace zone where the final air is admitted to Table 11 Typical Excess Air Requirements at Fuel Burning Equipment Type of Furnace Excess Air Fuel or Burners % by wt Pulverized coal Completely water-cooled 15 to 20 furnace wet or dry ash removal Partially water-cooled 15 to 40 furnace Crushed coal Cyclone furnace 13 to 20 pressure or suction Fluidized-bed combustion 15 to 20 Coal Spreader stoker 25 to 35 Water-cooled vibrating 25 to 35 grate stoker Chain grate and 25 to 35 traveling grate Underfeed stoker 25 to 40 Fuel oil Register type burners 3 to 15 Natural, coke Register type burners 3 to 15 oven and refinery gas Blast furnace Register type burners 15 to 30 gas Wood/bark Traveling grate, water- 20 to 25 cooled vibrating grate Fluidized-bed combustion 5 to 15 Refuse-derived Completely water-cooled 40 to 60 fuels (RDF) furnace traveling grate Municipal solid Water-cooled/refractory 80 to 100 waste (MSW) covered furnace reciprocating grate Rotary kiln 60 to 100 Bagasse All furnaces 25 to 35 Black liquor Recovery furnaces for 15 to 20 Kraft and soda pulping processes
- 269. 10-16 Steam 41 / Principles of Combustion The Babcock & Wilcox Company complete combustion. The amount of excess air at the exit of the pressure parts (where it is usually moni- tored) must be greater than the air required at the burning equipment to account for setting infiltration on balanced draft units (or seal air on pressure-fired units). On modern units with membrane wall con- struction, this is usually only 1 or 2% excess air at full load. On older units, however, setting infiltration can be significant, and operating with low air at the steam generator exit can result in insufficient air at the burn- ers. This can cause poor combustion performance. For units with air heaters, excess air must be mea- sured at the air heater gas inlet to determine efficiency. When equipment such as selective catalytic reduction (SCR) systems or dust collection equipment is located between the exit of the pressure parts and air heater gas inlet, additional air infiltration may occur, includ- ing SCR dilution air for ammonia transport. A typical value for SCR dilution air is 0.8% excess air. Combustion and efficiency calculations The combustion calculations are the starting point for all design and performance calculations for boil- ers and their related component parts. They establish the quantities of the constituents involved in the com- bustion process chemistry (air, flue gas, residue and sorbent), the efficiency of the combustion process and the quantity of heat released.4 The units used for the combustion and efficiency calculations are lb/10,000 Btu. The acronym MQxx also refers here to constituents on a mass per 10,000 Btu basis. For gaseous fuels, the volumetric analysis is converted to an elemental mass basis, as described in Molar evaluation of combustion. Combustion air – theoretical air The combustion air is the total air required for the burning equipment; it is the theoretical air plus the excess air. Theoretical air is the minimum air required for complete conversion of the carbon, hydrogen and sulfur in the fuel to standard products of combustion. For some fuels and/or combustion processes, all of the carbon is not converted. In addition, when limestone or other additives are used, some of the sulfur is not converted to sulfur dioxide. However, additional air is required for the conversion of sulfur dioxide to sul- fur trioxide in the sulfation reaction (CaO + SO2 + 1 /2 O2 → CaSO4). Because the actual air required is the desired calculation result, the theoretical air is cor- rected for unburned carbon and sulfation reactions. MQTHAC THAC HHV = × 100 (26) and THAC CB MFSC = × + × + × × + ×( ) − × 11 51 34 29 4 31 1 0 5 4 32 . . . . . H S O 2 2 (27) where MQTHAC = theoretical air, corrected, lb/10,000 Btu THAC = theoretical air, corrected, lb/100 lb fuel HHV = higher heating value, Btu/lb CB = mass percent carbon burned = percent carbon in fuel − UBC, % H2 = mass percent hydrogen in fuel, % S = mass percent sulfur in fuel, % MFSC = mass fraction sulfur captured by fur- nace sorbent, lb/lb sulfur O2 = mass percent oxygen in fuel, % UBC = unburned carbon percent from fuel, % For test purposes, the unburned carbon is measured. For design calculations, the unburned carbon may be calculated from the estimated unburned carbon loss, UBCL: UBC UBCL HHV = × 14 500, (28) MFSC is the sulfur capture/retention ratio or mass of sulfur captured per mass sulfur available from the fuel. It is zero unless a sorbent, e.g., limestone, is used in the furnace to reduce SO2 emissions. See Flue gas analysis to determine MFSC for test conditions. The mass of dry air, MQDA, water in air, MQWA, and wet air, MQA, are calculated from the following equations: MQDA MQTHAC PXA = × + 1 100 (29) MQWA MA MQDA= × (30) MQA MQDA MQWA MQDA MA = + = × +( )1 (31) where MQDA = mass dry air, lb/10,000 Btu MQTHAC = theoretical air, lb/10,000 Btu PXA = percent excess air, % MQWA = mass of moisture in air, lb/10,000 Btu MA = moisture in air, lb/lb dry air MQA = mass of wet air, lb/10,000 Btu Flue gas The total gaseous products of combustion are re- ferred to as wet flue gas. Solid products or residue are excluded. The wet flue gas flow rate is used for heat transfer calculations and design of auxiliary equip- ment. The total gaseous products excluding moisture are referred to as dry flue gas; this parameter is used in the efficiency calculations and determination of flue gas enthalpy. The wet flue gas is the sum of the wet gas from fuel (fuel less ash, unburned carbon and sulfur captured), combustion air, moisture in the combustion air, addi- tionalmoisturesuchasatomizingsteamand,ifsorbent is used, carbon dioxide and moisture from sorbent. Dry flue gas is determined by subtracting the summation of the moisture terms from the wet flue gas. Wet gas from fuel is the mass of fuel less the ash in the fuel, less the percent unburned carbon and, when
- 270. Steam 41 / Principles of Combustion 10-17 The Babcock & Wilcox Company sorbent is used to reduce SO2 emissions, less the sul- fur captured: MQGF AF UBC MFSC HHV = − − − ×( ) ×100 100 S (32) where MQGF = wet gas from fuel, lb/10,000 Btu AF = mass percent ash in fuel, % UBC = unburned carbon as mass percent in fuel, % MFSC = mass fraction of sulfur captured, lb/lb sulfur S = mass percent sulfur in fuel, % HHV = higher heating value, Btu/lb Water from fuel is the sum of the water in the fuel, H2O and the water produced from the combustion of hydrogen in the fuel, H2: MQWFF HHV = ×( ) + ×8 937 100 2 2. H H O (33) where MQWFF = water from fuel, lb/10,000 Btu H2 = mass percent hydrogen in fuel, % H2O = mass percent moisture in fuel, % Refer to Sorbents and other chemical additives for calculating gas from sorbent (CO2), MQGSB, and water from sorbent, MQWSB. The total wet gas weight, MQG, is then the sum of the dry air, water in air, wet gas from fuel and, when applicable, addi- tional water, gas from sorbent (CO2), and water from sorbent: MQG MQDA MQWA MQGF MQWAD MQGSB MQWSB = + + + + + (34) where MQG = total wet gas weight, lb/10,000 Btu MQDA = mass dry air, lb/10,000 Btu MQWA = mass of moisture in air, lb/10,000 Btu MQGF = wet gas from the fuel, lb/10,000 Btu MQWAD = additional water such as atomizing steam, lb/10,000 Btu MQGSB = gas from the sorbent, lb/10,000 Btu MQWSB = water from the sorbent, lb/10,000 Btu The total moisture in the flue gas, MQWG, is the sum of the water from fuel, water in air and, if appli- cable, additional water and water from sorbent. MQWG MQWFF MQWA MQWAD MQWSB = + + + (35) Dry flue gas, MQDG in lb/10,000 Btu, is the differ- ence between the wet flue gas and moisture in the flue gas: MQDG MQG MQWG= − (36) The percent moisture in flue gas is a parameter re- quired to determine flue gas energy heat content or enthalpy (see Enthalpy of air and gas) and is calcu- lated as follows: MPWG MQWG MQG = ×100 , % (37) For most fuels, the mass of solids, or residue, in the flue gas is insignificant and can be ignored. Even when the quantity is significant, solids do not materi- ally impact the volume flow rate of flue gas. However, solids add to the heat content, or enthalpy, of flue gas and should be accounted for when the ash content of the fuel is greater than 0.15 lb/10,000 Btu or when sorbent is used. The mass of residue from fuel, MQRF in lb/10,000 Btu, is calculated from the following equation: MQRF AF UBC HHV = +( ) × 100 (38) where MQRF = residue from fuel, lb/10,000 Btu AF = mass percent ash in fuel, % UBC = unburnedcarbonasmasspercentinfuel,% The mass percent of solids or residue in the flue gas is then: MPRG MQRF MQSSB MQG = × + 100 (39) where MPRG = mass percent solids or residue in flue gas, % MQSSB = spent sorbent, lb/10,000 Btu MQG = mass of gaseous combustion products excluding solids, lb/10,000 Btu Efficiency Efficiency is the ratio of energy output to energy input and is usually expressed as a percentage. The output term for a steam generator is the energy ab- sorbed by the working fluid that is not recovered within the steam generator envelope. It includes the energy added to the feedwater and desuperheating water to produce saturated/superheated steam, reheat steam, auxiliary steam and blowdown. It does not include the energy supplied to preheat the entering air such as air preheater coil steam supplied by the steam generator. The energy input term is the maxi- mum energy available when the fuel is completely burned, i.e., the mass flow rate of fuel, MRF, multi- plied by the higher heating value of the fuel. This is conventionally expressed as: ηf MRF HHV = × = × × 100 100 Output Input fuel Output %, (40) and is commonly referred to as steam generator fuel efficiency. In the U.S., it is customary to express steam generator efficiency on a higher heating value basis. Steam generator efficiency may also be expressed on
- 271. 10-18 Steam 41 / Principles of Combustion The Babcock & Wilcox Company a lower heating value basis (common in Europe). For the same mass flow rate of fuel, the LHV efficiency may be 3 to 10 percentage points higher than the HHV efficiency, depending upon the amount of H2 and H2O in the fuel. When comparing steam generator effi- ciency and/or plant heat rate, they must be on the same basis, i.e., HHV or LHV. Efficiency may be determined by measuring the mass flow rate of fuel and steam generator output, which is referred to as the input-output method, or by the energy balance method. The energy balance method is generally the preferred method. It is usu- ally more accurate than the input-output method and is discussed below. According to the law of conservation of energy, for steady-state conditions, the energy balance on the steam generator envelope can be expressed as:5 QRF QRO QHB= + , Btu/h (41) where QRF is the input from fuel, Btu/h, QRO is the steam generator output, Btu/h, and QHB is the en- ergy required by heat balance for closure, Btu/h. The heat balance energy associated with the streams en- tering the steam generator envelope and the energy added from auxiliary equipment power are commonly referred to as heat credits, QRB (Btu/h). The heat bal- ance energy associated with streams leaving the steam generator and the heat lost to the environment are commonly referred to as heat losses, QRL (Btu/h). This steam generator energy balance may be written as: QRF QRO QHB QRO QRL QRB = + = + − , Btu/h (42) and the efficiency may be expressed as: ηf QRO QRO QRL QRB = × + − 100 , % (43) When losses and credits are expressed as a func- tion of percent input from fuel, QPL and QPB, the efficiency may be calculated from: ηf QPL QPB= − +100 , % (44) Most losses and credits are conveniently calculated onapercentinputfromfuelbasis.However,somelosses are more conveniently calculated on a Btu/h basis. The following expression for efficiency allows the use of mixed units; some of the losses/credits are calculated on a percent basis and some on a Btu/h basis. ηf QPL QPB QRO QRO QRL QRB = − +( ) × + − 100 , % (45) For a more detailed understanding of losses and credits, refer to the American Society of Mechanical Engineers (ASME) Performance Test Code, PTC 4, for steam generators. The general form for calculating losses (QPLk) us- ing the mass per unit of heat input basis to express the percent heat loss for individual constituents is: QPL MQ MCP TO TR MQ HO HR k k k k k k k = × × −( ) = × −( ) 100 100 , % (46) where MQk = mass of constituent k, lb/10,000 Btu MCPk = mean specific heat between TOk and TR, Btu/lb F TOk = outlet temperature, F TR = reference temperature, F HOk = outlet enthalpy, Btu/lb HRk = reference enthalpy, Btu/lb For units with gas to air heat exchangers, there is usually some air leakage from the air inlet to the gas outlet. This leakage lowers the gas temperature leav- ing the air heater (measured gas temperature) with- out performing any useful work. It is recommended that the calculated gas temperature leaving the air heater without leakage be used for TOk above, in ac- cordance with PTC 4 (see Chapter 20 for calculation). For this case, the dry gas weight is based on the ex- cess air entering the air heater. Other codes, includ- ing the older PTC 4.1, may use the measured gas tem- perature leaving the air heater, in which case, the dry gas weight must be based on the excess air leaving the air heater. The reference temperature for PTC 4 is 77F (25C) and the calculation of both losses and credits are re- quired to determine efficiency. The energy credit will be negative for any stream entering the steam gen- erator envelope at a temperature lower than the ref- erence temperature. The most significant credit is generally the energy in the entering air. The enter- ing air temperature (air temperature entering the boundary) is the air temperature leaving the forced draft fans or leaving the air pre-heater coils (enter- ing an air to gas heat exchanger) if the source of en- ergy (steam) is external to the steam generator. When air pre-heater coils are used and the energy is sup- plied by steam from the steam generator, the enter- ing air temperature is the air temperature entering the pre-heater coils. The air temperature entering the fan(s) is usually taken as the design ambient condi- tion, but may be some other specified condition such as when the fan inlets are supplied by air from within the building. The fan compression energy (typically 1/2 degree F per 1 in. wg fan pressure rise) may be considered to establish the fan discharge temperature. Some test codes, including the older PTC 4.1, may use some other arbitrary reference temperature or the entering air temperature as the reference tempera- ture.An advantage of using the entering air tempera- ture as the reference temperature is that it eliminates the need to calculate credits for entering air and mois- ture in air. The general form for calculating credits (QPBk) us-
- 272. Steam 41 / Principles of Combustion 10-19 The Babcock & Wilcox Company ing the mass per unit of input basis to express the quantity of individual constituents is: QPB MQ MCP TI TR MQ HI HR k k k k k k k = × × −( ) = × −( ) 100 100 , % (47) where TIk = inlet temperature, F HIk = inlet enthalpy, Btu/lb and other terms were defined in Equation 46. The terms used to calculate losses and credits that are a function of fuel input have been discussed previ- ously. The other losses and credits are described below. Surface radiation and convection loss This is the heat lost to the atmosphere from the boiler envelope between the first and the last heat trap (commonly between the steam generator air inlet and the boiler exit or air heater exit). Surfaces include the boiler casing, flues and ducts, piping and other sur- faces above ambient temperature as a result of the energy entering the unit. It is a function of the aver- age velocity and the difference between the average surface temperature and average ambient tempera- ture. The U.S. industry and PTC 4 standard for cal- culating this heat loss use a temperature differential of 50F (for insulated surfaces) and a surface velocity of 100 ft/min. For PTC 4, the heat loss is based on the actual flat projected area of the unit and standard ASME Performance Test Code heat transfer coeffi- cients. For convenience, the American Boiler Manu- facturersAssociation (ABMA) standard radiation loss chart, shown in Chapter 23, may be used for an ap- proximation. TheABMAcurve expresses the radiation loss on a percent of gross heat input basis as a func- tion of steam generator output (percent gross heat input may be interpreted as heat input from fuel for most applications). This curve is the basis for the sur- face radiation and convection loss prior to the release of PTC 4 and is approximately the same as PTC 4 for oil- and gas-fired units. For coal-fired units, due to the requirement for a larger furnace and convection sur- face area due to the requirement for lower gas veloci- ties, the PTC 4 radiation loss is typically on the order of 2 to 2.5 times greater than the ABMA curve. Unburned carbon loss Fordesignofaunit,thisisnormallyestimatedbased on historical data and/or combustion models. For an ef- ficiency test, this item is calculated from measured un- burned carbon in the residue. (See Unburned carbon.) Other losses and manufacturers’ margins When testing a unit, it is usually only economically practical to measure the major losses and credits. The other minor losses (and credits) are estimated or based on historical data.Accordingly, when designing a unit, the individual losses and credits to be tested are item- ized separately and the estimated losses (and credits) are grouped together and referred to as Other losses and credits (also referred to as Unaccounted for or Unmeasured losses). The most typical Other losses are CO (0.05% loss for 145 ppm or 0.12 lb/106 Btu), NOx (0.01% for 50 ppm or 0.07 lb/106 Btu), radiation to the furnace ash pit (0.03% loss for a typical radiation rate of 10,000 Btu/ft2 h), pulverizer rejects (0.02% loss for a reject rate of 0.25% of fuel flow at a higher heating value of 1000 Btu/lb and 170F/77C mill outlet tem- perature), and unburned hydrocarbons/VOCs (nor- mally negligible and assumed to be zero). In addition, the manufacturer normally adds a margin, or safety factor, to the losses to account for unexpected perfor- mance deviations and test measurement uncertainty. Typical design values for these margins are 0 to 0.5% of heat input for gas, oil and coals with good combus- tion characteristics and slagging/fouling properties to 0 to 1.5% of heat input or higher for fuels with poor combustion characteristics and poor slagging/fouling characteristics. In the evaluation of actual unit effi- ciency, the minor or Other losses that are not measured should be estimated and agreed to. Enthalpy Enthalpy of air and gas Enthalpy, H, in Btu/lb is an indication of the rela- tive energy level of a material at a specific tempera- ture and pressure. It is used in thermal efficiency, heat loss, heat balance and heat transfer calculations (see Chapter 2). Extensive tabulated and graphical data are available such as the ASME Steam Tables sum- marized in Chapter 2. Except for steam and water at high pressure, the pressure effect on enthalpy is neg- ligible for engineering purposes. Enthalpies of most gases used in combustion cal- culations can be curve-fitted by the simple second or- der equation: H aT bT c= + +2 (48) where H = enthalpy in Btu/lb T = temperature in degrees, F To determine the enthalpy of most gases used in combustion calculations at a temperature, T, Equation 48 can be used with the coefficients summarized in Table 12. Reference 6 is the source for the properties and the curve fits are in accordance with Reference 7. The curve fits are within plus or minus 0.2 Btu/lb for enthalpies less than 40 Btu/lb and within plus or minus 0.5% for larger values. If the enthalpy of a fluid is known, the temperature in degrees F can be evalu- ated from the quadratic equation: T b b a c H a = − + − −( )2 4 2 (49) For mixtures of gases, such as dry air and water vapor or flue gas and water vapor, Equation 48 coef- ficient, a, b and c can be determined by a simple mass
- 273. 10-20 Steam 41 / Principles of Combustion The Babcock & Wilcox Company average: n x ni imix = ∑ (50) where nmix = equivalent coefficient a, b or c of the mixture xi = mass fraction of constituent i ni = coefficient a, b or c for constituent i For convenience, Table 12 lists coefficients for a number of gas mixtures including standard wet air with 0.013 lb H2O per lb dry air. In addition, Figs. 3 and 4 provide graphical representations of flue gas and standard air enthalpy. Another method of evaluating the change in specific enthalpy of a substance between conditions 1 and 2 is toconsiderthespecificheatandtemperaturedifference: H H c T Tp2 1 2 1− = −( ) (51) where H = enthalpy, Btu/lb cp = specific heat at constant pressure, Btu/lb F T = temperature, F Enthalpy of solids and fuels Enthalpy of coal, limestone and oil can be evalu- ated from the following relationships: Coal:8 H W VM W TF F= −( ) +( )+ −( )1 0 217 0 00248 77. . (52) Limestone: H W H W TF LS F= −( ) + −( )1 77 (53) and H T TLS = ( ) + ×( ) −− 0 179 0 1128 10 14 453 2 . . . (54) Oil:9 H C C API C T C API T C C API T = + ( ) + + ( ) + + ( ) 1 2 3 4 5 6 2 (55) and API SPGR SPGR= −( )141 5 131 5. . / (56) Fig. 4 Enthalpy of air assuming 0.987 mass fraction dry air plus 0.013 mass fraction of water vapor. Table 12 Enthalpy Coefficients for Equation 48 Coefficient a b c Dry air (a) 0 to 500 8.299003E-06 0.2383802 −18.43552 500 to 1500 1.474577E-05 0.2332470 −17.48061 1500 to 2500 8.137865E-06 0.2526050 −31.64983 2500 to 4000 4.164187E-06 0.2726073 −56.82009 Wet air (b) 0 to 500 8.577272E-06 0.2409682 −18.63678 500 to 1500 1.514376E-05 0.2357032 −17.64590 1500 to 2500 8.539973E-06 0.2551066 −31.89248 2500 to 4000 4.420080E-06 0.2758523 −58.00740 Water vapor 0 to 500 2.998261E-05 0.4400434 −34.11883 500 to 1500 4.575975E-05 0.4246434 −30.36311 1500 to 2500 3.947132E-05 0.4475365 −50.55380 2500 to 4000 2.413208E-05 0.5252888 −149.06430 Dry flue gas (c) 0 to 500 1.682949E-05 0.2327271 −18.03014 500 to 1500 1.725460E-05 0.2336275 −18.58662 1500 to 2500 8.957486E-06 0.2578250 −36.21436 2500 to 4000 4.123110E-06 0.2821454 −66.80051 Dry turbine exhaust gas (d) 0 to 500 1.157682E-05 0.2369243 −18.35542 500 to 1500 1.553788E-05 0.2343280 −18.04780 1500 to 2500 8.510000E-06 0.2550950 −33.38583 2500 to 4000 4.168439E-06 0.2768102 −60.53935 Ash/SiO2 0 to 500 7.735829E-05 0.1702036 −13.36106 500 to 1500 2.408712E-05 0.2358873 −32.88512 1500 to 2500 1.394202E-05 0.2324186 −4.85559 2500 to 4000 1.084199E-05 0.2460190 −19.48141 N2a − Atmospheric nitrogen (e) 0 to 500 5.484935E-06 0.2450592 −18.93320 500 to 1500 1.496168E-05 0.2362762 −16.91089 1500 to 2500 8.654128E-06 0.2552508 −31.18079 2500 to 4000 3.953408E-06 0.2789019 −60.92904 O2 − Oxygen 0 to 500 1.764672E-05 0.2162331 −16.78533 500 to 1500 1.403084E-05 0.2232213 −19.37546 1500 to 2500 6.424422E-06 0.2438557 −33.21262 2500 to 4000 4.864890E-06 0.2517422 −43.18179 CO2 − Carbon dioxide 0 to 500 5.544506E-05 0.1943114 −15.23170 500 to 1500 2.560224E-05 0.2270060 −24.11829 1500 to 2500 1.045045E-05 0.2695022 −53.77107 2500 to 4000 4.595554E-06 0.2989397 −90.77172 SO2 − Sulfur dioxide 0 to 500 3.420275E-05 0.1439724 −11.25959 500 to 1500 1.366242E-05 0.1672132 −17.74491 1500 to 2500 4.470094E-06 0.1923931 −34.83202 2500 to 4000 2.012353E-06 0.2047152 −50.27639 CO − Carbon monoxide 0 to 500 5.544506E-05 0.1943114 −15.23170 500 to 1500 2.559673E-05 0.2269866 −24.10722 1500 to 2500 1.044809E-05 0.2695040 −53.79888 2500 to 4000 4.630355E-06 0.2987122 −90.45853 Notes: (a) Dry air composed of 20.946% O2, 78.105% N2, 0.916% Ar and 0.033% CO2 by volume. (b) Wet air contains 0.013 lb H2O/lb dry air. (c) Dry gas composed of 3.5% O2, 15.3% CO2, 0.1% SO2 and 81.1% N2a by volume. (d) Dry turbine exhaust gas (TEG) composed of 11.48% O2, 5.27% CO2 and 83.25% N2a by volume (natural gas with 110% excess air). See PTC 4.4 for a rigorous determination of TEG enthalpy. (e) N2a composed of the atomic nitrogen, Ar and CO2 in standard air. Source: JANAF Thermochemical Tables, 2nd Ed., NSRDS-NBS 37, 1971. Curve fits developed from NASA SP-273, 1971 correlations.
- 274. Steam 41 / Principles of Combustion 10-21 The Babcock & Wilcox Company where H = enthalpy of coal, limestone or oil at T, Btu/lb WF = massfractionfreemoistureincoalorlime- stone, lb/lb VM = volatile matter on a moisture and ash free basis, % T = temperature, F HLS = enthalpy of dry limestone, Btu/lb API = degrees API SPGR = specific gravity, dimensionless = density in lb/ft3 divided by 62.4 at 60F C1 = −30.016 C2 = −0.11426 C3 = 0.373 C4 = 0.143 × 10-2 C5 = 0.2184 × 10-3 C6 = 7.0 × 10-7 Measurement of excess air One of the most critical operating parameters for attaining good combustion is excess air. Too little air can be a source of excessive unburned combustibles and can be a safety hazard. Too much excess air in- creases stack gas losses. Flue gas analysis The major constituents in flue gas are CO2, O2, N2 and H2O. Excess air is determined by measuring the O2 and CO2 contents of the flue gas. Before proceed- ing with measuring techniques, consider the form of the sample. A flue gas sample may be obtained on a wet or dry basis. When a sample is extracted from the gas stream, the water vapor normally condenses and the sample is considered to be on a dry basis. The sample is usually drawn through water near ambi- ent temperature to ensure that it is dry. The major con- stituents of a dry sample do not include the water vapor in the flue gas. When the gas is measured with an in situ analyzer or when precautions are taken to keep the moisture in the sample from condensing, the sample is on a wet basis. The amount of O2 in the flue gas is significant in defining the status of the combustion process. Its pres- ence always means that more oxygen (excess air) is being introduced than is being used. Assuming com- plete combustion, low values of O2 reflect moderate excess air and normal heat losses to the stack, while highervaluesofO2 meanneedlesslyhigherstacklosses. The quantity of excess O2 is very significant since it is a nearly exact indication of excess air. Fig. 5 is a dry flue gas volumetric combustion chart that is uni- versally used in field testing; it relates O2, CO2 and N2a (by difference). For complete uniform combustion of a specific fuel, all points should lie along a straight line drawn through the pivot point. This line is referred to as the combustion line. The combustion line should be determined by calculating the CO2 content at zero O2 for the test fuel (see Table 15). Lines indicating con- stant excess air have been superimposed on the volu- metric combustion chart. Note that excess air is essen- tially constant for a given O2 level over a wide range of fuels. The O2 is an equally constant indication of excess air when the gas is sampled on a wet or in situ basis because the calculated excess air result is insen- sitive to variations in moisture for specific types/ sources of fuel. The current industry standard for boiler operation is continuous monitoring of O2 in the flue gas with in situ analyzers that measure oxygen on a wet basis. Fortesting,thepreferredinstrumentisanelectronic oxygen analyzer. The Orsat unit, which measures (CO2 + SO2) and O2 on a dry volumetric basis, remains a trusted standard for verifying the performance of electronic equipment. The Orsat uses chemicals to absorb the (CO2 + SO2) and O2, and the amount of each is determined by the reduction in volume from the original flue gas sample. When an Orsat is used, the dry flue gas volumetric combustion chart should be used to plot the results. Valid results for any test with a consistent fuel should fall on a single combustion line (plus or minus 0.2 points of O2 /CO2 is a reason- able tolerance). The Orsat has several disadvantages. It lacks the accuracy of more refined devices, an ex- perienced operator is required, there are a limited number of readings available in a test, and the results do not lend themselves to electronic recording. Elec- tronic CO2 analyzers may be used in addition to oxy- gen analyzers to relate the O2 /CO2 results to the fuel line on the volumetric combustion chart. When CO2 is measured, by Orsat or a separate electronic ana- lyzer, it is best to calculate excess air based on the O2 result due to the insensitivity of excess air versus O2 results in the fuel analysis. Depending upon whether O2 is measured or excess air known, the corresponding excess air, O2, CO2 and SO2 can be calculated using procedures provided in ASME Performance Test Code 4, Steam Generators.5 The calculations are summarized in Table 15 at the end of this chapter in the Combustion calculations – examples section. Flue gas sampling To ensure a representative average gas sample, samples from a number of equal area points should be taken. Reference the U.S. Environmental Protec- tion Agency (EPA) Method 1 standards and ASME Performance Test Code PTC 19.10. For normal per- formance testing, equal areas of approximately 9 ft2 (0.8 m2 ) up to 24 points per flue are adequate. For continuous monitoring, the number of sampling points is an economic consideration. Strategies for lo- cating permanent monitoring probes should include point by point testing with different burner combina- tions. As a guideline, four probes per flue located at quarter points have been used successfully on large pulverized coal-fired installations. Testing heterogeneous fuels When evaluating the performance of a steam gen- erator firing a heterogeneous fuel such as municipal solid waste (MSW) (see Chapter 29), it is generally not possible to obtain a representative fuel sample. Waste fuel composition may vary widely between samples and is usually not repeatable.
- 275. 10-22 Steam 41 / Principles of Combustion The Babcock & Wilcox Company Fig. 5 Dry flue gas volumetric combustion chart.
- 276. Steam 41 / Principles of Combustion 10-23 The Babcock & Wilcox Company For boiler design, an ultimate analysis for an aver- age fuel and a range of the most significant compo- nents, such as moisture and ash, are used. Therefore, the design calculations are the same as those for ho- mogeneous fuels. When firing a heterogeneous fuel, the current in- dustry practice used to evaluate average fuel proper- ties and determine boiler efficiency is to test using the boiler as a calorimeter (BAC). The BAC method fea- tures the same principles for determining efficiency as those used when the fuel analysis is known. The significant difference is that the mass/volume flow rate of flue gas and moisture in the flue gas are measured directly rather than being calculated based upon the measured fuel analysis and O2 in the flue gas. The additional measurements that are required for the BAC test method versus conventional test meth- ods are flue gas flow, moisture in flue gas, O2 and CO2 in the flue gas, and residue mass flow rates from the major extraction points. BAC calculation method This section describes how to calculate excess air, dry gas weight and water from fuel (water evapo- rated). The results are on a mass per unit of time ba- sis and losses and credits, therefore, are calculated as Btu/h. Refer to the basic efficiency equations for ap- plication. (See Equations 42 and 43.) The wet gas weight and water in the wet gas are measured. The dry gas weight is then calculated as the difference of the two. The composition of flue gas is determined by mea- suringO2 andCO2.N2a isdeterminedbydifferencefrom 100%. The nitrogen in flue gas is considered to be atmospheric with a molecular weight of 28.158 lb/mole. Because waste fuel combustors operate at high levels of excess air and the nitrogen in the fuel is small, this nitrogen can be ignored. The moisture in the flue gas may be from vapor or liquid sources. Vapor sources include moisture in the air and atomizing steam. Water sources are moisture in the fuel, moisture formed by combustion of H2, water from ash quenching systems, and fuel pit wa- ter spray. The moisture in air and that from other vaporous sources must be measured, so the sensible heat efficiency loss may be differentiated from the water evaporated loss. The water evaporated is the total moisture in the flue gas less the vaporous sources. The water evaporation loss is calculated in the same manner as the water from fuel loss and is analogous to the total water from fuel loss if miscellaneous wa- ter sources are accounted for. The total dry air flow at the point of flue gas mea- surement is calculated from the nitrogen in the flue gas. Excess air is determined from the measured O2 and theoretical air is calculated by difference from the total air flow. The percent excess air is calculated from the excess air and theoretical air weight flow rates. Combustion calculations – examples The detailed steps in the solution of combustion problems are best illustrated by examples. The ex- amples in this section are presented through calcula- tion forms which are a convenient method for orga- nizing the calculations in a logical sequence. The in- put required to complete the forms is located at the top of the form.An elemental fuel analysis on a mass basis is used for all of the examples. For gaseous fuels, the analysis on a volume basis must be converted to an elemental mass basis as described in Molar evaluation of combustion. The calculations required are shown as a combination of item numbers (enclosed in brack- ets) and constants. Mole method The mole method is the fundamental basis for all combustion calculations. It is the source for the con- stants used in other more simplified methods. The only constants the user needs are the molecular weights of the fuel and air constituents. The reader should understand the mole method before proceeding with the Btu method. Table 7 is an example of the combustion calculations for a bituminous coal on a molar basis. Items 1 through 6 are the required input. If the unburned carbon is known (Item 6), the unburned carbon loss (Item 5) is calculated. Provision is made for entering the excess air to the burners and excess air leaving the boiler if the user desires to account for setting infil- tration (Item 1). For this example, the excess air to the burners is assumed to be the same as that leaving the boiler. An intermediate step in the calculations on a molar basis is the volumetric flue gas analysis (Items 20 and 21). Air and gas mass flow rates are shown on a lb/10,000 Btu basis as well as a 1000 lb/h basis. Btu method Once the reader understands the principles of the combustion calculations on a mole basis, the Btu method is the preferred method for general combus- tion calculations. The calculations provided in Table 13A are more comprehensive than the simple calcu- lation of air and gas weights shown in Table 7. Provi- sion is made for handling the impact of sorbent on the combustion calculations, the calculation of efficiency and finally heat available to the furnace. The inputs to Table 13A are similar to those used in Table 7. The same fuel analysis and excess air are used and the calculated input from fuel is very nearly the same. These inputs are also the same as those used in the example performance problem in Chapter 22. Items 1 through 19 are the inputs and initial calcula- tions required for the combustion calculations. For the efficiency calculations, Items 44 through 46 must be provided. If sorbent is used, Table 14, Combustion Calculations – Sorbent, must be completed first. (See Items 11 through 14 and 46). Because the entering air temperature and fuel temperature are the same as the reference temperature selected (80F), the effi- ciency credits are zero. The total fuel heat is calculated from the efficiency, Item 53, and steam generator output, Item 10. Flue gas and air flow rates are cal- culated from the fuel input and the results of the com- bustion gas calculations. Table 13A shows the calculation results for a typi-
- 277. 10-24 Steam 41 / Principles of Combustion The Babcock & Wilcox Company cal eastern U.S. coal. A similar set of calculations can be made for a typical western subbituminous coal which has an increased moisture content (30% by weight) and reduced LHV (8360 Btu/lb). For the same boiler rating and other boundary con- ditions, the results can be compared on a lb per 10,000 Btu basis: Eastern Western No. 6 Natural Bit. Subbit. Oil Gas Theoretical air 7.572 7.542 7.437 7.220 Dry air 9.086 9.050 8.924 8.664 Dry gas weight 9.442 9.463 8.965 8.194 Wet gas weight 9.864 10.303 9.583 9.236 H2O in gas 0.422 0.840 0.618 1.042 Efficiency, % 86.91 82.10 85.30 80.79 The theoretical air, dry air and resulting dry gas weight are approximately the same for each coal. The wet gas weight and H2O in gas are higher for the sub- bituminous coal due to the higher moisture content. Referring to the efficiency calculations and losses, the efficiency is lower for the subbituminous coal essen- tially due to the higher moisture content, not the lower heating value. However, if the actual mass flow rates for subbituminous coal versus an eastern bituminous coal are compared, it will be found that a higher air weight is required primarily due to the lower efficiency, while a higher gas weight is required due to the higher moisture in the fuel and the lower efficiency. Table 13B is the same example as shown in Table 13A except that it is assumed that a limestone sorbent is used in a fluidized bed at a calcium to sulfur molar ratio of 2.5. A sulfur capture of 90% is expected. A higher unburned carbon loss is used, typical of this combustion process. It is necessary to complete the calculations shown in Table 14 to develop input for this Table. The net losses due to sorbent, Item 46 in Table 13B, are not overly significant. Therefore, the differ- ence in efficiency from the example in Table 13A is primarily due to the difference in the assumed un- burned carbon loss. When testing a boiler, the excess air required for the combustion calculations is determined from mea- sured O2 in the flue gas. Table 15A, Excess Air Calcu- lations from Measured O2, demonstrates the calcula- tion of excess air from O2 on a wet basis. The fuel analy- sis and unburned carbon are the same as in Tables 7 and 13A. These tables can also be used to determine the volumetric composition of wet or dry flue gas when excess air is known (Items 25 through 32). These val- ues can be compared to the flue gas composition cal- culated on a molar basis, Table 7. Table 15B is an example of calculating excess air from O2 when a sorbent is used. All of the sulfur in the fuel will not be converted to sulfur dioxide. There- fore, the sulfur capture must first be determined from Table 16, Sulfur Capture Based on Gas Analysis. The example presented in Tables 13B and 14 is used as the basis for this example. The flue gas composition in Tables 13A and 13B can be compared to assess the impact of adding the sorbent. When units firing municipal solid waste or refuse- derived fuels are tested, it is not practical to determine the ultimate analysis of the fuel. Table 17, Combus- tion Calculations – Measured Gas Weight, shows the combustion calculations for determining dry gas weight, water evaporated and excess air using mea- sured gas weight. 1. American Gas Association, Segeler, C.G., Ed., Gas En- gineers Handbook, Industrial Press, Inc., New York, New York, 1965. 2. “Standard Practice for Calculating Heat Value, Com- pressibility Factor, and Relative Density of Gaseous Fuel,” ASTM 3588-98, Annual Book of ASTM Standards, Vol. 05.06, September, 2003. 3. Jones, F.E., “The Air Density Equation and the Trans- fer of Mass Unit,” Journal of Research of the National Bureau of Standards, Vol. 83, No. 5, September-October, 1978. 4. Gerhart, P.M., Heil, T.C., and Phillips, J.T., “Steam Generator Performance Calculation Strategies for ASME PTC 4,” Technical Paper 91-JPGC-PTC-1, American So- ciety of Mechanical Engineers, New York, New York, Oc- tober, 1991. References 5. Entwistle, J., Heil, T.C., and Hoffman, G.E., “Steam Generation Efficiency Revisited,” Technical Paper 88- JPGCLPTC-3, American Society of Mechanical Engineers, New York, New York, September, 1988. 6. JANAF Thermochemical Tables, Second Ed., Publica- tion NSRDS-NBS 37, United States National Bureau of Standards (now National Institute of Standards and Tech- nology), Washington, D.C., 1971. 7. Taken from NASA Publication SP-273, Chemical Equi- librium Code, 1971. 8. Elliot, M.A., Ed., Chemistry of Coal Utilization, Sec- ond Supplemental Volume, Wiley, New York, New York, 1981. 9. Dunstan, A.E., The Science of Petroleum, Oxford Uni- versity Press, Oxford, United Kingdom, 1938.
- 278. Steam 41 / Principles of Combustion 10-25 The Babcock & Wilcox Company See the following pages for Tables 13 through 17. Bibliography ASME Steam Properties for Industrial Use, Based on IAPWS-IF97, Professional Version 1.1, The American Society of Mechanical Engineers, New York, New York, 2003. International Boiler & Pressure Vessel Code, “ASME Performance Test Code PTC4,” The American Society of Mechanical Engineers, New York, New York, 2004. Parry, W.T., et al., ASME International Steam Tables for Industrial Use, Based on IAPWS-IF97, The American Society of Mechanical Engineers, New York, New York, January, 2000.
- 279. 10-26 Steam 41 / Principles of Combustion The Babcock & Wilcox Company Table 13A Combustion Calculations (Efficiency per PTC 4.1) Btu Method INPUT CONDITIONS − BY TEST OR SPECIFICATION FUEL − Bituminous coal, Virginia: no sorbent 1 Excess air: at burners; leaving boiler/econ/entering AH, % by wt. 20/20 15 Ultimate Analysis 16 Theo Air, lb/100 lb fuel 17 H2O, lb/100 lb fuel 2 Entering air temperature, F 80 Constituent % by weight K1 [15] x K1 K2 [15] x K2 3 Reference temperature, F (tRA = 77 for PTC 4) 80 A C 80.31 11.51 924.4 4 Fuel temperature, F 80 B S 1.54 4.31 6.6 5 Air temperature leaving air heater, F 350 C H2 4.47 34.29 153.3 8.94 39.96 6 Flue gas temperature leaving (excluding leakage), F 390 D H2O 2.90 1.00 2.90 7 Moisture in air, lb/lb dry air 0.013 E N2 1.38 8 Additional moisture, lb/100 lb fuel 0 F O2 2.85 −4.32 −12.3 9 Residue leaving boiler/econ/entering AH, % Total 85 G Ash 6.55 10 Output, 1,000,000 Btu/h 285.5 H Total 100.00 Air 1072.0 H2O 42.86 Corrections for sorbent (if used) 11 Sulfur capture, lbm/lbm sulfur Table 16, Item [24] 0 18 Higher heating value (HHV), Btu/lb 14,100 12 CO2 from sorbent, lb/10,000 Btu Table 14, Item [19] 0 19 Unburned carbon loss, % fuel input 0.40 13 H2O from sorbent, lb/10,000 Btu Table 14, Item [20] 0 20 Theoretical air, lb/10,000 Btu [16H] x 100 / [18] 7.603 14 Spent sorbent, lb/10,000 Btu Table 14, Item [24] 0 21 Unburned carbon, % of fuel [19] x [18] / 14,500 0.39 COMBUSTION GAS CALCULATIONS, Quantity per 10,000 Btu Fuel Input 22 Theoretical air (corrected), lb/10,000 Btu [20] − [21] x 1151 / [18] + [11] x [15B] x 216 / [18] 7.571 23 Residue from fuel, lb/10,000 Btu ([15G] + [21]) x 100 / [18] 0.049 24 Total residue, lb/10,000 Btu [23] + [14] 0.049 A At Burners B Infiltration C Leaving Furnace D Leaving Blr/Econ/Entering AH 25 Excess air, % weight 20.0 0.0 20.0 20.0 26 Dry air, lb/10,000 Btu (1 + [25] / 100) x [22] 9.085 9.085 27 H2O from air, lb/10,000 Btu [26] x [7] 0.118 0.118 0.118 0.118 28 Additional moisture, lb/10,000 Btu [8] x 100 / [18] 0.000 0.000 0.000 0.000 29 H2O from fuel, lb/10,000 Btu [17H] x 100 / [18] 0.304 0.304 30 Wet gas from fuel, lb/10,000 Btu (100 − [15G] − [21] − [11] x [15B]) x 100 / [18] 0.660 0.660 31 CO2 from sorbent, lb/10,000 Btu [12] 0.000 0.000 32 H2O from sorbent, lb/10,000 Btu [13] 0.000 0.000 0.000 0.000 33 Total wet gas, lb/10,000 Btu Summation [26] through [32] 9.863 9.863 34 Water in wet gas, lb/10,000 Btu Summation [27] + [28] + [29] + [32] 0.422 0.422 0.422 0.422 35 Dry gas, lb/10,000 Btu [33] − [34] 9.441 9.441 36 H2O in gas, % by weight 100 x [34] / [33] 4.28 4.28 37 Residue, % by weight (zero if < 0.15 lbm/10KB) [9] x [24] / [33] 0.00 0.00 EFFICIENCY CALCULATIONS, % Input from Fuel Losses 38 Dry gas, % [35D] x (HFg[6] − HFg[3]) / 100 9.441 x (75.3 − 0.7) / 100 7.04 39 Water from Enthalpy of steam at 1 psia, T = [6] H1 = (3.958E − 5 x T + 0.4329) x T + 1062.2 1237.1 40 fuel, as fired Enthalpy of water at T = [3] H2 = [3] − 32 48.0 41 % [29] x ([39] − [40]) / 100 0.304 x 1189.1 / 100 3.61 42 Moisture in air, % [27D] x (HWv[6] − HWv[3]) / 100 0.118 x (142.0 − 1.3) / 100 0.17 43 Unburned carbon, % [19] or [21] x 14,500 / [18] 0.39 x 14,500 / 14,100 0.40 44 Surface radiation and convection See surface radiation and convection loss 0.40 45 Other, % (include manufacturers margin if applicable) 1.50 46 Sensible heat of residue, % (PTC 4) [24] x (100 − [9]) x 516 + [9] x HRs[6] / 10,000 HRs[6] = 0 (or Table 14, Item [40]) 0.00 47 Sorbent net losses, % if sorbent used From Table 14, Items ([30] − [31] + [37]) 0.00 48 Summation of losses, % Summation [38] through [46] 13.12 Credits 49 Entering dry air, % [26D] x (HDA[2] − HDA[3]) / 100 9.085 x (0.7 − 0.7) / 100 0.00 50 Moisture in entering air, % [27D] x (HWv[2] − HWv[3]) / 100 0.118 x (1.3 − 1.3) / 100 0.00 51 Sensible heat in fuel, % 100 x (HF[4] − HF[3]) / [18] 100 x (1.0 − 1.0) / 14,100 0.00 52 Other, % 0.00 53 Summation of credits, % Summation [48] through [51] 0.00 54 Efficiency, % 100 − [48] + [53] 86.88 KEY PERFORMANCE PARAMETERS Leaving Furnace Leaving Blr/Econ/Entering AH 55 Input from fuel, 1,000,000 Btu/h 100 x [10] / [54] 328.6 56 Fuel rate, 1000 lb/h 1000 x [55] / [18] 23.3 57 Wet gas weight, 1000 lb/h [55] x [33] / 10 324.1 324.1 58 Air to burners (wet), lb/10,000 Btu (1 + [7]) x (1 + [25A] / 100) x [22] 9.203 59 Air to burners (wet), 1000 lb/h [55] x [58] / 10 302.4 60 Heat available, 1,000,000 Btu/h [55] x {([18] − 10.30 x [17H]) / [18] − 0.005 Ha = 66.0 Btu/lb x ([44] + [45]) + Ha[5] x [58] / 10,000} 335.2 61 Heat available/lb wet gas, Btu/lb 1000 x [60] / [57] 1034.2 62 Adiabatic flame temperature, F From Fig. 3 at H = [61], % H2O = [36C] 3560
- 280. Steam 41 / Principles of Combustion 10-27 The Babcock & Wilcox Company Table 13B Combustion Calculations (Efficiency per PTC 4) Btu Method (with Sorbent) INPUT CONDITIONS − BY TEST OR SPECIFICATION FUEL − Bituminous coal, Virginia: with sorbent 1 Excess air: at burners; leaving boiler/econ/entering AH, % by wt. 18/20 15 Ultimate Analysis 16 Theo Air, lb/100 lb fuel 17 H2O, lb/100 lb fuel 2 Entering air temperature, F 80 Constituent % by weight K1 [15] x K1 K2 [15] x K2 3 Reference temperature, F (tRA = 77 for PTC 4) 77 A C 80.31 11.51 924.4 4 Fuel temperature, F 80 B S 1.54 4.31 6.6 5 Air temperature leaving air heater, F 350 C H2 4.47 34.29 153.3 8.94 39.96 6 Flue gas temperature leaving (excluding leakage), F 390 D H2O 2.90 1.00 2.90 7 Moisture in air, lb/lb dry air 0.013 E N2 1.38 8 Additional moisture, lb/100 lb fuel 0 F O2 2.85 −4.32 −12.3 9 Residue leaving boiler/econ/entering AH, % Total 90 G Ash 6.55 10 Output, 1,000,000 Btu/h 285.5 H Total 100.00 Air 1072.0 H2O 42.86 Corrections for sorbent (if used) 11 Sulfur capture, lbm/lbm sulfur Table 16, Item [24] 0.9000 18 Higher heating value (HHV), Btu/lb 14,100 12 CO2 from sorbent, lb/10,000 Btu Table 14, Item [19] 0.0362 19 Unburned carbon loss, % fuel input 2.50 13 H2O from sorbent, lb/10,000 Btu Table 14, Item [20] 0.0015 20 Theoretical air, lb/10,000 Btu [16H] x 100 / [18] 7.603 14 Spent sorbent, lb/10,000 Btu Table 14, Item [24] 0.0819 21 Unburned carbon, % of fuel [19] x [18] / 14,500 2.43 COMBUSTION GAS CALCULATIONS, Quantity per 10,000 Btu Fuel Input 22 Theoretical air (corrected), lb/10,000 Btu [20] − [21] x 1151 / [18] + [11] x [15B] x 216 / [18] 7.426 23 Residue from fuel, lb/10,000 Btu ([15G] + [21]) x 100 / [18] 0.064 24 Total residue, lb/10,000 Btu [23] + [14] 0.146 A At Burners B Infiltration C Leaving Furnace D Leaving Blr/Econ/Entering AH 25 Excess air, % weight 18.0 1.0 19.0 20.0 26 Dry air, lb/10,000 Btu (1 + [25] / 100) x [22] 8.837 8.911 27 H2O from air, lb/10,000 Btu [26] x [7] 0.115 0.115 0.116 0.116 28 Additional moisture, lb/10,000 Btu [8] x 100 / [18] 0.000 0.000 0.000 0.000 29 H2O from fuel, lb/10,000 Btu [17H] x 100 / [18] 0.304 0.304 30 Wet gas from fuel, lb/10,000 Btu (100 − [15G] − [21] − [11] x [15B]) x 100 / [18] 0.636 0.636 31 CO2 from sorbent, lb/10,000 Btu [12] 0.036 0.036 32 H2O from sorbent, lb/10,000 Btu [13] 0.002 0.002 0.002 0.002 33 Total wet gas, lb/10,000 Btu Summation [26] through [32] 9.626 9.701 34 Water in wet gas, lb/10,000 Btu Summation [27] + [28] + [29] + [32] 0.421 0.421 0.422 0.422 35 Dry gas, lb/10,000 Btu [33] − [34] 9.205 9.279 36 H2O in gas, % by weight 100 x [34] / [33] 4.37 4.35 37 Residue, % by weight (zero if < 0.15 lbm/10KB) [9] x [24] / [33] 1.37 1.35 EFFICIENCY CALCULATIONS, % Input from Fuel Losses 38 Dry gas, % [35D] x (HFg[6] − HFg[3]) / 100 9.279 x (75.3 − 0.0) / 100 6.99 39 Water from Enthalpy of steam at psia, T = [6] H1 = (3.958E − 5 x T + 0.4329) x T + 1062.2 1237.1 40 fuel, as fired Enthalpy of water at T = [3] H2 = [3] − 32 45.0 41 % [29] x ([39] − [40]) / 100 0.304 x 1192.1 / 100 3.62 42 Moisture in air, % [27D] x (HWv[6] − HWv[3]) / 100 0.116 x (142.0 − 0.0) / 100 0.16 43 Unburned carbon, % [19] or [21] x 14,500 / [18] 2.43 x 14,500 / 14,100 2.50 44 Surface radiation and convection See surface radiation and convection loss 0.40 45 Other, % (include manufacturers margin if applicable) 1.50 46 Sensible heat of residue, % (PTC 4) [24] x (100 − [9]) x 516 + [9] x HRs[6] / 10,000 HRs[6] = 65.1 (or Table 14, Item [40]) 0.15 47 Sorbent net losses, % if sorbent used From Table 14, Items ([30] − [31] + [37]) −0.03 48 Summation of losses, % Summation [38] through [46] 15.45 Credits 49 Entering dry air, % [26D] x (HDA[2] − HDA[3]) / 100 8.911 x (0.7 − 0.0) / 100 0.06 50 Moisture in entering air, % [27D] x (HWv[2] − HWv[3]) / 100 0.116 x (1.3 − 0.0) / 100 0.00 51 Sensible heat in fuel, % 100 x (HF[4] − HF[3]) / [18] 100 x (1.0 − 0.0) / 14,100 0.01 52 Other, % 0.00 53 Summation of credits, % Summation [49] through [51] 0.07 54 Efficiency, % 100 − [48] + [53] 84.78 KEY PERFORMANCE PARAMETERS Leaving Furnace Leaving Blr/Econ/Entering AH 55 Input from fuel, 1,000,000 Btu/h 100 x [10] / [54] 336.8 56 Fuel rate, 1000 lb/h 1000 x [55] / [18] 23.9 57 Wet gas weight, 1000 lb/h [55] x [33] / 10 324.2 326.7 58 Air to burners (wet), lb/10,000 Btu (1 + [7]) x (1 + [25A] / 100) x [22] 8.877 59 Air to burners (wet), 1000 lb/h [55] x [58] / 10 299.0 60 Heat available, 1,000,000 Btu/h [55] x {([18] − 10.30 x [17H]) / [18] − 0.005 Ha = 66.0 Btu/lb x ([44] + [45]) + Ha[5] x [58] / 10,000} 342.8 61 Heat available/lb wet gas, Btu/lb 1000 x [60] / [57] 1057.4 62 Adiabatic flame temperature, F From Fig. 3 at H = [61], % H2O = [36C] 3627
- 281. 10-28 Steam 41 / Principles of Combustion The Babcock & Wilcox Company H2O from sorbent, % INPUTS (see also lightly shaded blocks) FUEL − Bituminous coal, Virginia 1 Sulfur in fuel, % by weight 1.54 6 Sulfur capture, lb/lb sulfur 0.90 2 Ash in fuel, % by weight 6.55 7 Reference temperature, F 80.0 3 HHV of fuel, Btu/lb 14,100 8 Exit gas temperature (excluding leakage), F 390.0 4 Unburned carbon loss, % fuel input 2.5 9 Sorbent temperature, F 80.0 5 Calcium to sulfur molar ratio 2.5 SORBENT PRODUCTS 10 Chemical 11 Molecular 12 Ca 13 14 Molecular 15 CO2 16 H2O Analysis Weight mole/100 lb sorb Calcination Weight lb/100 lb sorb lb/100 lb sorb % Mass lb/mole [10] / [11] Fraction lb/mole [10]x[13]x[14]/[11] [10]x[13]x[14]/[11] A CaCO3 89.80 100.089 0.897 0.90 44.010 35.529 B MgCO3 5.00 84.321 1.00 44.010 2.610 C Ca(OH)2 0.00 74.096 0.000 1.00 18.015 0.000 D Mg(OH)2 0.00 58.328 1.00 18.015 0.000 E H2O 1.60 18.015 1.00 18.015 1.600 F Inert 3.60 G Total Ca, mole/100 lb sorbent 0.897 Total 38.139 1.600 SORBENT/GAS CALCULATIONS, lb/10,000 Btu Except as Noted 17 Sorbent, lb/lb fuel [1] x [5] / [12G] / 32.066 0.1339 18 Sorbent, lb/10,000 Btu 10,000 x [17] / [3] 0.0950 19 CO2 from sorbent, lb/10,000 Btu [15G] x [18] / 100 0.0362 20 H2O from sorbent, lb/10,000 Btu [16G] x [18] / 100 0.0015 21 Additional theoretical air, lb/10,000 Btu 216 x [1] x [6] / [3] 0.0212 22 SO2 reduction, lb/10,000 Btu 200 x [1] x [6] / [3] 0.0197 23 SO3 formed, lb/10,000 Btu 0.2314 x [21] + [22] 0.0246 24 Spent sorbent, lb/10,000 Btu [18] − [19] − [20] + [23] 0.0819 25 Unburned carbon, lb/10,000 Btu [4] x 100 / 14,500 0.0172 26 Residue from fuel, lb/10,000 Btu [2] x 100 / [3] + [25] 0.0637 27 Total residue, lb/10,000 Btu [24] + [26] 0.1456 LOSSES DUE TO SORBENT, % Input from Fuel 28 H of steam at 1 psi, T = [8] H1 = (3.958E − 5 x [8] + 0.4329) x [8] + 1062.2 1237.1 29 H of water H2 = [9] − 32 48.0 30 0.01 x [20] x ([28] − [29]) 0.018 31 Sensible heat sorbent (dry), % [18] x (1.0 − [10E] / 100) x (H at T = [9] − H at T = [7]) / 100 H of limestone (dry) = (0.1128E − 3 x T + 0.179) x T − 14.45 0.000 Calcination/Dehydration, % 32 CaCO3, % [10A] x [13A] x [18] x 766 / 10,000 0.588 33 MgCO3, % [10B] x 1.0 x [18] x 652 / 10,000 0.031 34 Ca(OH)2, % [10C] x 1.0 x [18] x 636 / 10,000 0.000 35 Mg(OH)2, % [10D] x 1.0 x [18] x 625 / 10,000 0.000 36 Heat gain due to sulfation, % [6] x [1] x 6733 / [3] 0.662 37 Total of losses due to chemical reactions, % [32] + [33] + [34] + [35] − [36] −0.043 Sensible Heat of Residue Loss, % 38 Temp 39 Loss Location Residue, F % A Bed drain 1500 0.055 B Economizer 600 0.017 C Flyash 390 0.074 H Residue = (( −2.843E − 8 x T + 1.09E − 4) x T + 0.16) x T − 12.95 40 Total 0.146 41 Summation losses due to sorbent, % [30] − [31] + [37] + [40] 0.121 Table 14 Combustion Calculations Sorbent Mass Flow x [27] x ( H at T = [38] − H at T = [7] ) / 10,000 = Rate, % Total x lb/10,000 Btu x ( Btu/lb − Btu/lb ) / 10,000 = 10 x 0.1456 x ( 376.3 − 0.5 ) / 10,000 = 10 x 0.1456 x ( 116.2 − 0.5 ) / 10,000 = 80 x 0.1456 x ( 64.3 − 0.5 ) / 10,000 =
- 282. Steam 41 / Principles of Combustion 10-29 The Babcock & Wilcox Company Table 15A Excess Air Calculations from Measured O2 Bituminous coal, Virginia − O2 on wet basis INPUTS (see also lightly shaded blocks) SORBENT DATA (if applicable) 1 Moisture in air, lb/lb dry air 0.013 6 CO2 from sorbent, moles/100 lb fuel, Table 16 [17] 0 2 Additional moisture, lb/100 lb fuel 0.00 7 H2O from sorbent, moles/100 lb fuel, Table 16 [16] 0 3 HHV fuel, Btu/lb 14,100 8 Sulfur capture, lb/lb sulfur fuel, Table 16 [24] 0 4 Unburned carbon loss, % fuel input 0.40 5 Unburned carbon (UBC), [3] x [4] / 14,500 0.39 COMBUSTION PRODUCTS 9 Ultimate Analysis, % Mass 10 Theoretical Air 11 Dry Products from Fuel 12 Wet Products from Fuel Fuel As- Carbon lb/100 lb Fuel mole/100lb Fuel mole/100 lb Fuel Constituent Fired Burned (CB) K1 [9] x K1 K2 [9] / K2 K3 [9] / K3 A C 80.31 80.31 B UBC [5] 0.39 C CB [A] − [B] 79.92 11.51 919.9 12.011 6.654 D S 1.54 4.31 6.6 32.066 0.048 E H2 4.47 34.29 153.3 2.016 2.217 F H2O 2.90 18.015 0.161 G N2 1.38 28.013 0.049 H O2 2.85 −4.32 −12.3 I Ash 6.55 K Total 100.00 1067.5 6.751 2.378 13 Dry products of combustion, mole/100 lb fuel [11K] − [11D] x [8] + [6] 6.751 14 Wet products of combustion, mole/100 lb fuel [12K] + [13] + [7] 9.129 15 Theoretical air (corrected), mole/100 lb fuel ([10K] + [8] x [9D] x 2.16) / 28.963 36.857 EXCESS AIR WHEN O2 KNOWN 16 O2, % volume (input) 3.315 17 O2 measurement basis 0 = Dry 1 = Wet 1 Dry Wet 18 Moisture in air, mole/mole dry air 0.0 [1] x 1.608 0.021 19 Dry/wet products of combustion, mole/100 lb fuel [13] [14] 9.129 20 Additional moisture, mole/100 lb fuel 0.0 [2] / 18.016 0.000 21 Intermediate calculation, step 1 [15] x (0.7905 + [18]) 29.909 22 Intermediate calculation, step 2 [19] + [20] + [21] 39.038 23 Intermediate calculation, step 3 20.95 − [16] x (1 + [18]) 17.565 24 Excess air, % by weight 100 x [16] x [22] / [15] / [23] 20.0 O2, CO2, SO2 WHEN EXCESS AIR KNOWN 25 Excess air, % by weight 20.0 26 Dry gas, mole/100 lb fuel [13] + [15] x (0.7905 + [25] / 100) 43.258 27 Wet gas, mole/100 lb fuel [14] + [15] x (0.7905 + [18] + (1 + [18]) x [25] / 100) + [20] 46.565 Dry Wet 28 O2, % by volume [25] x [15] x 0.2095 / ([26] or [27]) [26] [27] 3.32 29 CO2, % by volume 100 x ([11C] + [6]) / ([26] or [27]) [26] [27] 14.29 30 SO2, % by volume 100 x (1 − [8]) x [11D] / ([26] or [27]) [26] [27] 0.1031 31 H2O, % by volume H2O = 0.0 if dry or 100 x ([27] − [26]) / [27] NA [27] 7.10 32 N2 (fuel), % by volume 100 x [11G] / ([26] or [27]) [26] [27] 0.11 33 N2a (air), % by volume 100 − [28] − [29] − [30] − [31] − [32] 75.08 34 MW wet flue gas, lbm/mole 0.32 x [28] + 0.4401 x [29] + 0.64064 x [30] + 0.18015 x [31] + 0.28013 x [32] + 0.28158 x [55] 29.868 35 Density flue gas, lbm/ft3 at 60F and 29.92 in. Hg 0.0026356 x [34] Wet basis 0.07872
- 283. 10-30 Steam 41 / Principles of Combustion The Babcock & Wilcox Company Table 15B Excess Air Calculations from Measured O2 Bituminous coal, Virginia: with sorbent − O2 on wet basis INPUTS (see also lightly shaded blocks) SORBENT DATA (if applicable) 1 Moisture in air, lb/lb dry air 0.013 6 CO2 from sorbent, moles/100 lb fuel, Table 16 [17] 0.116 2 Additional moisture, lb/100 lb fuel 0.00 7 H2O from sorbent, moles/100 lb fuel, Table 16 [16] 0.012 3 HHV fuel, Btu/lb 14,100 8 Sulfur capture, lb/lb sulfur fuel, Table 16 [24] 0.90 4 Unburned carbon loss, % fuel input 2.50 5 Unburned carbon (UBC), [3] x [4] / 14,500 2.43 COMBUSTION PRODUCTS 9 Ultimate Analysis, % Mass 10 Theoretical Air 11 Dry Products from Fuel 12 Wet Products from Fuel Fuel As- Carbon lb/100 lb Fuel mole/100lb Fuel mole/100 lb Fuel Constituent Fired Burned (CB) K1 [9] x K1 K2 [9] / K2 K3 [9] / K3 A C 80.31 80.31 B UBC [5] 2.43 C CB [A] − [B] 77.88 11.51 896.4 12.011 6.484 D S 1.54 4.31 6.6 32.066 0.048 E H2 4.47 34.29 153.3 2.016 2.217 F H2O 2.90 18.015 0.161 G N2 1.38 28.013 0.049 H O2 2.85 −4.32 −12.3 I Ash 6.55 K Total 100.00 1044.0 6.581 2.378 13 Dry products of combustion, mole/100 lb fuel [11K] − [11D] x [8] + [6] 6.654 14 Wet products of combustion, mole/100 lb fuel [12K] + [13] + [7] 9.044 15 Theoretical air (corrected), mole/100 lb fuel ([10K] + [8] x [9D] x 2.16) / 28.963 36.149 EXCESS AIR WHEN O2 KNOWN 16 O2, % volume (input) 3.315 17 O2 measurement basis 0 = Dry 1 = Wet 1 Dry Wet 18 Moisture in air, mole/mole dry air 0.0 [1] x 1.608 0.021 19 Dry/wet products of combustion, mole/100 lb fuel [13] [14] 9.044 20 Additional moisture, mole/100 lb fuel 0.0 [2] / 18.016 0.000 21 Intermediate calculation, step 1 [15] x (0.7905 + [18]) 29.335 22 Intermediate calculation, step 2 [19] + [20] + [21] 38.379 23 Intermediate calculation, step 3 20.95 − [16] x (1 + [18]) 17.565 24 Excess air, % by weight 100 x [16] x [22] / [15] / [23] 20.0 O2, CO2, SO2 WHEN EXCESS AIR KNOWN 25 Excess air, % by weight 20.0 26 Dry gas, mole/100 lb fuel [13] + [15] x (0.7905 + [25] / 100) 42.460 27 Wet gas, mole/100 lb fuel [14] + [15] x (0.7905 + [18] + (1 + [18]) x [25] / 100) + [20] 45.761 Dry Wet 28 O2, % by volume [25] x [15] x 0.2095 / ([26] or [27]) [26] [27] 3.31 29 CO2, % by volume 100 x ([11C] + [6]) / ([26] or [27]) [26] [27] 14.42 30 SO2, % by volume 100 x (1 − [8]) x [11D] / ([26] or [27]) [26] [27] 0.0105 31 H2O, % by volume H2O = 0.0 if dry or 100 x ([27] − [26]) / [27] NA [27] 7.21 32 N2 (fuel), % by volume 100 x [11G] / ([26] or [27]) [26] [27] 0.11 33 N2a (air), % by volume 100 − [28] − [29] − [30] − [31] − [32] 74.94 34 MW wet flue gas, lbm/mole 0.32 x [28] + 0.4401 x [29] + 0.64064 x [30] + 0.18015 x [31] + 0.28013 x [32] + 0.28158 x [55] 29.843 35 Density flue gas, lbm/ft3 at 60F and 29.92 in. Hg 0.0026356 x [34] Wet basis 0.07866
- 284. Steam 41 / Principles of Combustion 10-31 The Babcock & Wilcox Company INPUTS 1 SO2, ppm 105 / 10,000 = % 0.0105 2 O2 Flue gas at location SO2 measured, % 3.31 Data from Table 15, Excess Air Calculations from Measured O2 3 Moisture in air, lb/lb dry air [1] 0.013 7 Theoretical air, lb/100 lb fuel [10K] 1044.0 4 Additional moisture, lb/100 lb fuel [2] 0 8 Dry products of fuel, mole/100 lb fuel [11K] 6.581 5 Sulfur in fuel, % by weight [9D] 1.54 9 Wet products of fuel, mole/100 lb fuel [12K] 2.378 6 HHV fuel, Btu/lb fuel [3] 14,100 Data from Table 14, Combustion Calculations - Sorbent 10 CO2 from sorbent, lb/100 lb sorbent [15G] 38.139 12 Sorbent, lb sorbent/lb fuel [17] 0.134 11 H2O from sorbent, lb/100 lb sorbent [16G] 1.600 CALCULATIONS, Moles/100 lb Fuel Except As Noted SO2 / O2 Measurement basis 0 = Dry 1 = Wet 1 Dry Wet 13 Moisture in air, mole/mole dry air 0.0 [3] x 1.608 0.0209 14 Additional moisture 0.0 [4] / 18.015 0.000 15 Products of combustion from fuel [8] [8] + [9] 8.959 16 H2O from sorbent [11] x [12] / 18.015 0.0 Calculate 0.012 17 CO2 from sorbent [10] x [12] / 44.01 0.116 18 Intermediate calculation, step 1 (0.7905 + [13]) x [7] / 28.963 29.245 19 Intermediate calculation, step 2 Summation [14] through [18] 38.332 20 Intermediate calculation, step 3 1.0 − (1.0 + [13]) x [2] / 20.95 0.8387 21 Intermediate calculation, step 4 (0.7905 + [13]) x 2.387 − 1.0 0.9368 22 Intermediate calculation, step 5 [1] x [19] x 32.066 / [5] / [20] 9.992 23 Intermediate calculation, step 6 [21] x [1] / [20] 0.0117 24 Sulfur capture, lb/lb sulfur (100 − [22]) / (100 + [23]) 0.90 25 SO2 released, lb/1,000,000 Btu 20,000 x (1.0 − [24]) x [5] / [6] 0.22 Table 16 Sulfur Capture Based on Gas Analysis Bituminous coal, Virginia INPUTS A Wet Analysis B Dry (not required) Analysis 1 O2, % volume 9.28 Measured dry or 100 / (100 − [3A]) x [1A] 10.55 2 CO2, % volume 8.56 Measured dry or 100 / (100 − [3A]) x [2A] 9.73 3 H2O, % volume 12.00 4 Mass flow wet gas, 1000 lb/h 539.2 5 Moisture in wet gas, lb/lb wet gas 0.0754 6 Moisture in air, lb/lb dry air 0.0130 7 Additional moisture (sources other than fuel and air), 1000 lb/h 0 CALCULATIONS 8 Water in wet gas, 1000 lb/h [4] x [5] 40.7 9 Dry gas weight, 1000 lb/h [4] − [8] 498.5 10 N2a in dry gas, % dry volume 100 − [1B] − [2B] 79.72 11 Molecular weight of dry gas, lb/mole 0.32 x [1B] + 0.4401 x [2B] + 0.28158 x [10] 30.11 12 Dry gas, 1000 moles/h [9] / [11] 16.56 13 Dry air weight, 1000 lb/h 0.28161 x [10] x [12] / 0.7685 483.8 14 Water in dry air, 1000 lb/h [13] x [6] 6.3 15 Water evaporated, 1000 lb/h [8] − [7] − [14] 34.4 16 Excess air, 1000 lb/h [1B] x [9] x 0.32 / 0.2314 / [11] 241.5 17 Theoretical air, 1000 lb/h [13] − [16] 242.3 18 Excess air, % by weight 100 x [16] / [17] 99.7 Table 17 Combustion Calculations Measured Gas Weight
- 285. 10-32 Steam 41 / Principles of Combustion The Babcock & Wilcox Company 450 MW midwest power station firing pulverized subbituminous coal.
- 286. The Babcock & Wilcox Company Steam 41 / Oil and Gas Utilization 11-1 Chapter 11 Oil and Gas Utilization Before the industrial revolution, distilled petroleum products were used primarily as a source of illumina- tion. Today, petroleum finds its primary importance as an energy source and greatly influences the world’s economy. The following discusses the use of petroleum products and natural gas as energy sources for steam generation. Fuel oil Preparation Petroleum or crude oil is the source of various fuel oils used for steam generation (Fig. 1, facing page). Most petroleum is refined to some extent before use although small amounts are burned without process- ing. Originally, refining petroleum was simply the process of separating the lighter compounds, higher in hydrogen, from the heavier compounds by frac- tional distillation. This yielded impure forms of kero- sene, gasoline, lubricating oils and fuel oils. Through the development of refining techniques, such as ther- mal cracking and reforming, catalytic reforming, po- lymerization, isomerization and hydrogenation, petro- leum is now regarded as a raw material source of hydrogen and carbon elements that can be combined as required to meet a variety of needs. In addition to hydrocarbons, crude oil contains com- pounds of sulfur, oxygen and nitrogen and traces of vanadium, nickel, arsenic and chlorine. Processes are used during petroleum refinement to remove impuri- ties, particularly compoundsofsulfur.Purificationpro- cessesforpetroleumproductsincludesulfuricacidtreat- ment,sweetening,mercaptanextraction,claytreatment, hydrogen treatment and the use of molecular sieves. The refining of crude oil yields a number of prod- ucts having many different applications. Those used as fuel include gasoline, distillate fuel, residual fuel oil, jet fuels, still gas, liquefied gases, kerosene and petroleumcoke.Productsforotherapplicationsinclude lubricants and waxes, asphalt, road oil, and petro- chemical feedstock. Fuel oils for steam generation consist primarily of residues from the distillation of crude oil. As refinery methods improve, the quality of residual oil available for utility and industrial steam generation is deterio- rating. High sulfur fuels containing heavy compo- nents create challenges during combustion that range from high particulate and sulfur oxide emissions to higher maintenance costs due to the corrosive constitu- ents in the flue gas. Transportation, storage and handling The high heating value per unit of volume of oil, its varied applications, and its liquid form have fos- tered a worldwide system of distribution. The use of supertankers for the transportation of crude oil has significantly reduced transportation costs and has allowed refineries to be located near centers of con- sumption rather than adjacent to the oil fields. Large supertankers, up to 250,000 t (227,000 tm), are capable of transporting nearly 2,000,000 bbl (318,000 m3 ) of crude oil at a time to deepwater ports. Tanker and barge shipments on coastal and inland waterways are by far the cheapest method of trans- porting the various grades of oil. With the depletion of oil fields in the eastern United States (U.S.), crude oil trunk lines were developed in the early 1900s to transport oil from points west of the Mississippi River to the east coast refineries. Today, more than 170,000 mi(274,000km)ofpipeline,includingsmallfeederlines, are used for the transportation of oil within the U.S. Much smaller quantities of oil are shipped overland by rail and truck because of the higher cost of haulage. Fuel oil systems require either underground or sur- face storage tanks. Oil is usually stored in cylindrical shaped steel tanks to eliminate evaporation loss. Loss in storage of the relatively nonvolatile heavy fuel oils is negligible. Lighter products, such as gasoline, may volatilize sufficiently in warm weather to cause ap- preciable loss. In this instance, storage tanks with floating roofs are used to eliminate the air space above the fuel where vapors can accumulate. The National Fire Protection Association (NFPA) has prepared a standard set of codes for the storage and handling of oils (NFPA 30 and 31). These codes serve as the basis for many local ordinances and are required for the safe transportation and handling of fuel products. Extensive piping and valving and suitable pump- ing and heating equipment are necessary for the
- 287. The Babcock & Wilcox Company 11-2 Steam 41 / Oil and Gas Utilization transportation and handling of fuel oil. Storage tanks, piping and heaters for heavy oils must be cleaned pe- riodically because of fouling or sludge accumulation. Fuel properties Safe and efficient transportation, handling and com- bustion of fuel oil requires a knowledge of fuel charac- teristics.Principalphysicalpropertiesoffueloils,impor- tant to boiler applications, are summarized below (see Chapter 9 for typical fuel oil physical property values): Viscosity The viscosity of an oil is the measure of its resistance to internal movement, or flow. Viscosity is important because of its effect on the rate at which oil flows through pipelines and on the degree of at- omization obtained by oil firing equipment. Ultimate analysis An ultimate analysis is used to determine theoretical air requirements for combustion of the fuel and also to identify potential environmen- tal emission characteristics. Heating value The heating value of a liquid fuel is the energy produced by the complete combustion of one unit of fuel [Btu/lb (J/kg)]. Heating value can be reported either as the gross or higher heating value (HHV) or the net or lower heating value (LHV). To determine HHV, it is assumed that any water vapor formed during combustion is condensed and cooled to the initial temperature (i.e., all of the chemical energy is available). The heat of vaporization of the water formed is included in the HHV. For LHV, it is assumed that the water vapor does not condense and is not available. The heating value determines the quantity of fuel necessary to achieve a specified heat input. Specific gravity Specific gravity (sp gr) is the ratio of the density of oil to the density of water. It is im- portant because fuel is purchased by volume, in gal- lons (l) or barrels (m3 ). The most widely used fuel oil gravity scale is degree API devised by the American Petroleum Institute; its use is recommended by the U.S. Bureau of Standards and the U.S. Bureau of Mines. The scale is based on the following formula: degreesAPI = 141 5. sp gr at 60/60F (16/16C) – 131.5 [sp gr at 60/60F (16/16C) means when both oil and water are at 60F (16C)] Flash and fire point Flash point is the lowest tem- perature at which a volatile oil will give off explosive or ignitable vapors. It is important in determining oil handling and storage requirements. The fire point is the temperature to which a liquid must be heated to produce vapors sufficient for continuous burning when ignited by an external flame. Pourpoint Thepourpointisthetemperatureatwhich aliquidfuelwillfirstflowunderstandardizedconditions. Distillation Distillation determines the quantity and number of fractions which make up the liquid fuel. Water and sediment Water and sediment are a mea- sure of the contaminates in a liquid fuel. The sediment normally consists of calcium, sodium, magnesium, and iron compounds. Impurities in the fuel provide an indication of the potential for plugging of fuel han- dling and combustion equipment. Carbon residue Residue that remains after a liquid fuel is heated in the absence of air is termed carbon resi- due. The tests commonly used to determine carbon resi- duearetheConradsonCarbonTestandtheRamsbottom Carbon Test. Carbon residue gives an indication of the coking tendency of a particular fuel (i.e. the tendency of oil, when heated, to form solid compounds). Asphaltene content Asphaltenes are long chain, high molecular weight hydrocarbon compounds. The asphaltene content of a petroleum product is the per- centage by weight of wax free material insoluble in n-heptane but soluble in hot benzene. Their structure requires high temperatures and high atomization energy for the fuel to burn completely. Higher asphaltene content indicates a higher potential to produce particulate emissions. Burning profile Burning profile is a plot of the rate at which a sample of fuel burns under standard con- ditions as temperature is increased at a fixed rate. The burning profile is a characteristic fingerprint of the fuel oxidized under standard conditions and is not in- tended to provide absolute kinetic and thermodynamic data. It helps evaluate combustion characteristics of various fuels on a relative basis to determine excess air and residence time necessary for complete combustion. Natural gas Preparation Natural gas, found in crude oil reservoirs, either dis- solved in the oil or as a gas cap above the oil, is called associated gas. Natural gas is also found in reservoirs that contain no oil and is termed non-associated gas. Natural gas, directly from the well, must be treated to produce commercially marketable fuels. Initially, natural gas undergoes a process to remove conden- sate which is distilled to produce butane, propane and stabilized gasoline. Propane and butane are widely used as bottle gas. They are distributed and stored liquefied under pressure. When the pressure is re- leased, the liquid boils, producing a gaseous fuel. Natural gas may contain enough sand or gaseous sulfur compounds to be troublesome. The sand is usu- ally removed at the source. Natural gas containing excessive amounts of hydrogen sulfide, commonly known as sour gas, can be treated by a process known as sweetening. Sweetening removes hydrogen sulfide as well as carbon dioxide. Additional treatments in- clude the removal of mercaptan by soda fixation and the extraction of long chain hydrocarbons. Where natural gas is used to replace or supplement manufactured gas, it is sometimes reformed to bring its heating value in line with the manufactured gas. Natu- ral gas may also be mixed directly with manufactured gas to increase the heating value of the final product. Transportation, storage and handling Pipelines are an economical means of transporting natural gas in its gaseous form. The rapid increase in consumption of natural gas in areas far from the source has resulted in an extensive system of long distance pipelines. Natural gas can also be transported
- 288. The Babcock & Wilcox Company Steam 41 / Oil and Gas Utilization 11-3 by tanker when liquefied under pressure producing liquefied natural gas (LNG). The distribution of natural gas is subject to some practical limitations because of the energy required for transportation. High pressures, in the order of 1000 psig (6895 kPa), are necessary for economic pipeline transportation over long distances. Compression sta- tions are needed at specified intervals to boost the pressure due to losses in the line. In general, it is not practical to vary the supply of natural gas to accommodate the hourly or daily fluc- tuations in consumer demand. For economic reasons, long distance pipelines operate with a high load fac- tor. The rate of withdrawal from the wells may often be limited for conservation reasons, and the cost of the pipeline to provide the peak rate would be prohibitive. Therefore, to meet fluctuations in demand, it is usu- ally necessary to provide localstorageortosupplement the supply with manufactured gas for brief periods. Above ground methods of storage include: 1) large water seal tanks, 2) in-pipe holders laid parallel to commercial gas lines, and 3) using the trunk trans- mission line as a reservoir by building up the line pressure. In consumer areas where depleted or par- tially depleted gas and oil wells are available, under- ground storage of gas pumped back into these wells provides, at minimum cost, the large storage volume required to meet seasonal variations in demand. In liquid form, natural gas can be stored in insulated steel tanks or absorbed in a granular substance, released by passing warm gas over the grains. Fuel properties Natural gas is comprised primarily of methane and ethane. Physical properties of practical importance to boiler applications include constituents by volume percent, heating value, specific gravity, sulfur content and flammability (see Chapter 9 for typical natural gas physical property values). Other liquid and gaseous fuels Numerous combustion system applications utilize liquid or gaseous fuels other than conventional fuel oils or natural gas. These fuels include Orimulsion® , blast furnace gas, coke oven gas, refinery gas, regen- erator offgas, landfill gas, and other byproduct gases. The large heavy hydrocarbon and bitumen reserves available in Venezuela have led to a bitumen oil emul- sion fuel that has gained acceptability. Orimulsion is the trade name for a commercially established fossil fuel oil emulsion. It consists of natural bitumen dis- persed in water, in approximately a 70/30 proportion split. The resulting emulsion is stabilized by a surfac- tant package. Orimulsion can be transported over land or water and stored for extended periods while main- taining a consistent quality. Although it can be handled using most of the equipment and systems originally designed for heavy fuel oil, Orimulsion re- quires some special handling and combustion consid- erations because of its emulsified state. In addition, although the fuel exhibits very good combustion char- acteristics, it contains relatively high levels of sulfur, nitrogen, ash, asphaltenes, vanadium and other met- als. Thus, careful design and cleanup considerations are important when firing a fuel with high levels of these constituents. Steel mill blast furnaces generate a byproduct gas containing about 25% carbon monoxide by volume. This fuel can be burned to produce steam for mill heat- ing and power applications. Many mills also have their own coke producing plant, another source of byproduct fuel. Coke oven gas is an excellent fuel that burns readily because of its high free hydrogen content. With these gases, available supply pressures and the volumetric heating value of fuel may be different from that of natural gas. Therefore, gas components must be designed to accommodate the particular character- istics of the gas to be burned. In the petroleum industry, refinery gas and regen- erator offgas are frequently used as energy sources for boilers. Refinery gas is a mixture of gaseous hy- drocarbon streams from various refinery processes. Depending on economic and technical considerations within the refinery, the compositions of these indi- vidual streams vary with process modifications and thus, the resultant refinery gas can change over time. Combustion equipment and controls for refinery gas must be suitably designed for this variability. Regen- erator offgas, or CO (carbon monoxide) gas, is a high- temperature gas produced in catalytic cracking units. CO boilers have been developed to reclaim the ther- mal energy present in this gas (see Chapter 27). Landfill gas is a combustible gas recovered by a gas collection system at a landfill. Its primary constituents are methane and carbon dioxide. Landfill gas process- ing systems filter suspended particulates and conden- sate from the gas stream. Additional processing may be done to further purify the gas, but trace contami- nants that typically remain in the gas require special attention when designing fuel handling systems to minimize corrosion concerns. Oil and gas combustion – system design The burner is the principal equipment component for the combustion of oil and natural gas (Fig. 2). In utility and industrial steam generating units (both wall and corner-fired designs), the burner admits fuel and air to the furnace in a manner that ensures safe and efficient combustion while realizing the full capa- bility of the boiler. Burner design determines mixing characteristics of the fuel and air, fuel particle size and distribution, and size and shape of the flame envelope. The means of transporting, measuring and regu- lating fuel and air to the furnace, together with the burners, igniters and flame safety equipment, com- prises the overall combustion system. The following factors must be considered when designing the com- bustion system and when establishing overall perfor- mance requirements: 1. the rate of feed of the fuel and air to comply with load demand on the boiler over a predetermined operating range, 2. the types of fuel to be fired including elemental con- stituents and characteristic properties of each fuel,
- 289. The Babcock & Wilcox Company 11-4 Steam 41 / Oil and Gas Utilization 3. the efficiency of the combustion process to mini- mize unburned combustibles and excess air re- quirements, 4. imposed limitations on emissions, 5. physical size and complexity of the furnace and burners to establish the most efficient and eco- nomic design, 6. hardware design and material properties of the combustion equipment to ensure reliable uninter- rupted service for long firing periods, and 7. safety standards and procedures for control of the burners and boiler, including starting, stopping, load changes and variations in fuel. The combustion system must be designed for opti- mum flexibility of operation, including the potential for variations in fuel type, fuel firing rate and combi- nations of burners in and out of service. Control must be simple and direct to ensure rapid response to vary- ing load demands. Combustion air is typically conveyed to the burn- ers by forced draft fans. To improve both thermal and combustion efficiency and further ensure burner sta- bility, combustion air is normally preheated to a tem- perature of 400 to 600F (204 to 316C) by air preheaters located downstream of the fans. The fans must be capable of delivering adequate quantities of air for complete combustion at a pressure sufficient to over- come losses across the air preheaters, burners, control dampers, and intervening duct work. The total com- bustion air is that required to theoretically burn all the fuel plus excess air necessary for complete com- bustion. (See Chapter 10.) The fuel delivery system must be able to regulate fuel pressure and flow to the burners and must be safeguarded in accordance with applicable fire protec- tion codes. Proper distribution of fuel to the burners, in multiple burner applications, is critical to safe and efficient operation of the combustion system. Piping and valves must be designed for allowable velocity lim- its,absolutepressurerequirements,andpressurelosses. Performance requirements Excess air Excess air is the air supplied for combustion and cooling of idle burners in excess of that theoretically required for complete oxidation of the fuel. Excess air is generally required to compensate for imperfections in the air delivery system that results in maldistribu- tion of combustion air to the burners. Excess air also helps compensate for imperfect mixing of the air and fuel in the furnace. At full load, with all burners in service, excess air required for gas and oil firing, ex- pressed as a percent of theoretical air, is typically in the range of 5 to 10%, depending upon fuel type and the requirements of the combustion system. Operation at excess air levels below these values is possible if combustion efficiency does not deteriorate. Combus- tion efficiency is measured in terms of carbon monox- ide, unburned combustibles in the ash, soot, particu- late matter and stack opacity. Through careful design of the burners and the air delivery system, excess air can be held to a minimum, thereby minimizing sen- sible heat loss to the stack. Operation at partial load requires additional excess air. When operating with all burners in service at re- duced load, lower air velocity at the burners results in reduced mixing efficiency of the fuel and air. In- creasing the excess air improves combustion turbu- lence and maintains overall combustion efficiency. Additional excess air and improved burner mixing also compensate for lower furnace temperature during partial load operation. In some instances, boiler per- formance dictates the use of higher than normal ex- cess air at reduced loads to maintain steam tempera- ture or to minimize cold end corrosion. Additional excess air is also necessary when oper- ating with burners out of service. Sufficient cooling air must be provided to idle burners to prevent over- heat damage. Permanent thermocouples installed on selected burners measure metal temperatures and establish the minimum excess air necessary to main- tain burner temperatures below the maximum use limits of the steel. Excess air for burner cooling varies with the percentage of burners out of service. Stability and turndown Proper burner and combustion system design will permit stable operation of the burners over a wide operating range. A stable burner, best determined through visual observation, is one where the flame front remains relatively stationary and the root of the flame is securely anchored near the burner fuel ele- ment. To ensure stable combustion, the burner must be designed to prevent blowoff or flashback of the flame for varying rates of fuel and air flow. It is often desirable to operate over a wide boiler load range without taking burners out of service. This reduces partial load excess air requirements to cool idle burners. The burners must therefore be capable of operating in a turned down condition. Burner turn- down is defined as the ratio of full load fuel input to partial load input while still maintaining stable com- bustion. Limitations in burner turndown are gener- Fig. 2 Typical oil and gas utility boiler burner front.
- 290. The Babcock & Wilcox Company Steam 41 / Oil and Gas Utilization 11-5 ally dictated by fuel characteristics, fuel and air ve- locity, full load to partial load fuel pressures, and ad- equacy of the flame safety system. Automated and reliable flame safety supervision, with proper safe- guards, must be available to achieve high burner turndown ratios. With gas firing, a turndown ratio of 10:1 is not un- common. Natural gas is easily burned and relatively easy to control. Residual oil, on the other hand, is more difficulttoburn.Combustioncharacteristicsarehighly sensitive to particle size distribution, excess air and burner turbulence. A typical turndown ratio for oil is in the order of 6:1, depending upon fuel characteris- tics, flexibility of the delivery system and atomization technique. Burner pulsation Burner pulsation is a phenomenon frequently as- sociated with natural gas firing and, to a lesser de- gree, with oil firing. Pulsation is thought to occur when fuel rich pockets of gas suddenly and repeat- edly ignite within the flame envelope. The resultant pulsating burner flame is often accompanied by a noise referred to as combustion rumble. Combustion rumble may transmit frequencies that coincide with the natu- ral frequency of the furnace enclosure resulting in ap- parent boiler vibration. In some instances, these vi- brations may become alarmingly violent. Boiler vibration on large furnaces can sometimes be attributed to a single burner. Minor air flow adjust- ment to a given burner, or removing select burners from service, may suddenly start or stop pulsations. Pulsation problems can be corrected through changes to burner hardware that affect mixing patterns of the fuel and air. Changes to the burner throat profile to correct anomalies in burner aerodynamics or changes to the fuel element discharge ports have successfully eliminated pulsation. Historical operating data has enabled the develop- ment of empirical curves that are useful in designing burners to avoid pulsation. These curves relate the potential for burner pulsation to the ratio of burner fuel to air velocity. Together with careful consideration of furnace geometry, burner firing patterns and burner aerodynamics, problems with burner pulsation are becoming less common. Combustion efficiency Many factors influence combustion efficiency in- cluding excess air, burner mixing, fuel properties, furnace thermal environment, residence time, and particle size and distribution. Complete combustion occurs when all combustible elements and compounds of the fuel are entirely oxidized. In utility and indus- trial boilers, the goal is to achieve the highest degree of combustion efficiency with the lowest possible ex- cess air. Thermal efficiency decreases with increasing quantities of excess air. Combustion performance is then measured in terms of the boiler efficiency loss due to incomplete combustion together with the efficiency loss due to sensible heat in the stack gases. From the standpoint of optimum combustion effi- ciency, the following factors are critical to proper design: 1. careful distribution and control of fuel and air to the burners, 2. burner and fuel element design that provides thor- ough mixing of fuel and air and promotes rapid, turbulent combustion, and 3. proper burner arrangement and furnace geometry to provide sufficient residence time to complete chemical reactions in a thermal environment con- ducive to stable and self-sustained combustion. In most cases, boiler efficiency loss due to unburned carbon loss (UCL) when firing oil and natural gas is virtually negligible. However, depending on fuel oil properties and the condition of the combustion system, the percent UCL can be in the order of 0.10% while firing oil. Combustion efficiency with these fuels is usually measured in terms of carbon monoxide (CO) emissions, particulate emissions and stack opacity. Generally, CO levels less than 200 ppm (corrected to 3% O2) are considered satisfactory. Emission control techniques Ever increasing concern over atmospheric pollut- ants is changing the focus of wall and corner-fired boiler and combustion system designs. The combus- tion of fossil fuels produces emissions that have been attributed to the formation of acid rain, smog, changes to the ozone layer, and the so-called greenhouse effect. To mitigate these problems, federal and local regula- tions are currently in place that limit oxides of nitro- gen, oxides of sulfur, particulate matter and stack opacity. While emission limits vary depending upon state and local regulations, the trend is toward more stringent control. (See also Chapter 32.) Many combustion control techniques have emerged to reduce fossil fuel emissions. These techniques gen- erally focus on the reduction of nitrogen oxides (NOx), as changes to the combustion process can greatly in- fluence NOx formation and destruction. Oxides of nitrogen Nitrogen oxides in the form of NO and NO2 are formed during combustion by two primary mecha- nisms: thermal NOx and fuel NOx.Asecondary mecha- nism called prompt NOx can also contribute to overall NOx formation. Thermal NOx results from the dissociation and oxi- dation of nitrogen in the combustion air. The rate and degree of thermal NOx formation is dependent upon oxygen availability during the combustion process and is exponentially dependent upon combustion tempera- ture. Thermal NOx reactions occur rapidly at combus- tion temperatures in excess of 2800F (1538C). Ther- mal NOx is the primary source of NOx formation from natural gas and distillate oils because these fuels are generally low in or devoid of fuel-bound nitrogen. Fuel NOx, on the other hand, results from oxidation of nitrogen organically bound in the fuel and is the primary source of NOx formation from heavy fuel oil. Fuel bound nitrogen in the form of volatile compounds is intimately tied to the fuel hydrocarbon chains. For this reason, the formation of fuel NOx is linked to both
- 291. The Babcock & Wilcox Company 11-6 Steam 41 / Oil and Gas Utilization fuel nitrogen content and fuel volatility. Inhibiting oxygen availability during the early stages of combus- tion, where the fuel devolatilizes, is the most effective means of controlling fuel NOx formation. Prompt NOx is formed during the early, low tem- perature stages of combustion. Hydrocarbon frag- ments may react with atmospheric nitrogen under fuel-rich conditions to yield fixed nitrogen species. These, in turn, can be oxidized to NO in the lean zone of the flame. In most flames, especially those from ni- trogen-containing fuels, the prompt mechanism is re- sponsible for only a small fraction of the total NOx. Numerous combustion process NOx control tech- niques are commonly used. These vary in effective- ness and cost. In all cases, control methods are mainly aimed at reducing either thermal NOx, fuel NOx, or a combination of both.Arange of typical anticipated NOx emission levels relative to various NOx control mecha- nisms is shown in Fig. 3. Low excess air Low excess air (LEA) effectively re- duces NOx emissions with little, if any, capital expen- diture. LEA is a desirable method of increasing ther- mal efficiency and has the added benefit of inhibit- ing thermal NOx. If burner stability and combustion efficiency are maintained at acceptable levels, lower- ing the excess air may reduce NOx by as much as 5 to 15% from an uncontrolled baseline. The success of this method depends largely upon fuel properties and the ability to carefully control fuel and air distribution to the burners. Operation may require more sophisti- cated methods of measuring and regulating fuel and air flow to the burners and modifications to the air delivery system to ensure equal distribution of com- bustion air to all burners. Burners out of service Essentially a simple form of two-stage combustion, burners out of service (BOOS) is a simple and direct method of reducing NOx emis- sions. When removing burners from service in mul- tiple burner applications, active burner inputs are typically increased to maintain load. Without chang- ing total air flow, increased fuel input to the active burners results in a fuel rich mixture, effectively lim- iting oxygen availability and thereby limiting both fuel and thermal NOx formation. Air control registers on the out of service burners remain open, essentially serving as staging ports. While a fairly significant NOx reduction is possible with this method, lower NOx is frequently accompa- nied by higher levels of CO in the flue gas and boiler back-end oxygen (O2) imbalances. With oil firing, an increase in particulate emissions and increased stack opacity are likely. Through trial and error, some pat- terns of burners out of service may prove more suc- cessful than others. A limiting factor is the ability of existingburnerstohandletheincreasedinputnecessary to maintain full load operation. Short of derating the unit, changes to fuel element sizes may be required. Two-stage combustion Two-stage combustion is a relatively long standing and accepted method of achieving significant NOx reduction. Combustion air is directed to the burner zone in quantities less than that required to theoretically burn the fuel, with the remainder of the air introduced through overfire air ports. By diverting combustion air away from the burners, oxygen concentration in the lower furnace is reduced, thereby limiting the oxidation of chemi- cally bound nitrogen in the fuel. By introducing the total combustion air over a larger portion of the fur- nace, peak flame temperatures are also lowered. Appropriate design of a two-stage combustion sys- tem can reduce NOx emissions by as much as 50% and simultaneously maintain acceptable combustion per- formance. The following factors must be considered in the overall design of the system. 1. Burner zone stoichiometry The fraction of theo- retical air directed to the burners is predetermined to allow proper sizing of the burners and overfire air ports. Normally a burner zone stoichiometry in the range of 0.85 to 0.90 will result in desired levels of NOx reduction without notable adverse effects on combustion stability and turndown. 2. Overfire air port design Overfire air ports must be designed for thorough mixing of air and com- bustion gases in the second stage of combustion. Ports must have the flexibility to regulate flow and air penetration to promote mixing both near the furnace walls and toward the center of the furnace. Mixing efficiency must be maintained over the an- ticipated boiler load range and the range in burner zone stoichiometries. 3. Burner design Burners must be able to operate at lower air flow rates and velocities without det- riment to combustion stability. In a two-stage combustion system, burner zone stoichiometry is typically increased with decreasing load to ensure thatburnerairvelocitiesaremaintainedabovemini- mum limits. This further ensures positive windbox- to-furnace differential pressures at reduced loads. 4. Overfire air port location Sufficient residence time from the burner zone to the overfire air ports and from the ports to the furnace exit is critical to proper system design. Overfire air ports must be located to optimize NOx reduction and combustion efficiency andtolimitchangetofurnaceexitgastemperatures. 5. Furnace geometry Furnace geometry influences burner arrangement and flame patterns, residence time and thermal environment during the first and second stages of combustion. Liberal furnace siz- ing is generally favorable for lower NOx as com- bustion temperatures are lower and residence times are increased. 100 80 60 40 20 0 Gas Firing Oil Firing Uncontrolled LEA BOOS TSC FGR + TSC RelativeNOEmissions,% Fig. 3 Approximate NOx emission reductions for oil and gas burners using various control techniques. (LEA = low excess air; BOOS = burner out of service; TSC = two-stage combustion; FGR = flue gas recirculation.)
- 292. The Babcock & Wilcox Company Steam 41 / Oil and Gas Utilization 11-7 6. Air flow control Ideally, overfire air ports are housed in a dedicated windbox compartment. In this manner, air to the NOx ports can be metered and controlled separately from air to the burners. This permits operation at desired stoichiometric levels in the lower furnace and allows for compen- sation to the flow split as a result of air flow ad- justments to individual burners or NOx ports. Additional flexibility in controlling burner fuel and air flow characteristics is required to optimize combus- tion under a two-stage system. Improved burner de- signs have addressed these needs. In the reducing gas of the lower furnace, sulfur in the fuel forms hydrogen sulfide (H2S) rather than sulfur dioxide (SO2) and sulfur trioxide (SO3). The corrosiveness of reducing gas and the potential for increased corrosion of lower furnace wall tubes is highly dependent upon H2S concentration. Two-stage combustion is therefore not normally recommended when firing high sulfur residual fuel oils except when extra furnace wall protection measures are included. Flue gas recirculation Flue gas recirculation (FGR) to the burners is instrumental in reducing NOx emis- sions when the contribution of fuel nitrogen to total NOx formation is small. For this reason, the use of gas recirculation is generally limited to the combustion of natural gas and fuel oils. By introducing flue gas from the economizer outlet into the combustion air stream, burner peak flame temperatures are lowered and NOx emissions are significantly reduced. (See Fig. 4.) Air foils are commonly used to mix recirculated flue gas with the combustion air. Flue gas is introduced in the sides of the secondary air measuring foils and exits through slots downstream of the air measurement taps. This method ensures thorough mixing of flue gas andcombustionairbeforereachingtheburnersanddoes not affect the air flow metering capability of the foils. In general, increasing the rate of flue gas recircu- lation to the burners results in an increasingly signifi- cant NOx reduction. Target NOx emission levels and limitations on equipment size and boiler components dictate the practical limit of recirculated flue gas for NOx control. Other limiting factors include burner sta- bility and oxygen concentration of the combustion air. Typically, oxygen content must be maintained at or above 17% on a dry basis for safe and reliable opera- tion of the combustion equipment. The expense of a flue gas recirculation system can be significant. Gas recirculation (GR) fans may be required for the desired flow quantities at static pres- sures capable of overcoming losses through the flues, ducts, mixing devices and the burners themselves. Additionalcontrolsandinstrumentsarealsonecessary to regulate GR flow to the windbox at desired levels over the load range. In retrofit applications, signifi- cant cost is associated with routing of flues and ducts to permit mixing of the flue gas with combustion air. Also, the accompanying increase in furnace gas weight at full load operation may require modifications to convection pass surfaces or dictate changes to stan- dard operating procedures. From an operational standpoint, the introduction of flue gas recirculation as a retrofit NOx control tech- nique must, in virtually all cases, be accompanied by the installation of overfire air ports. Oil and gas burn- ers, initially designed without future consideration to FGR, are not properly sized to accommodate the in- crease in burner mass flow as a result of recirculated flue gas. The quantity of flue gas necessary to signifi- cantly reduce NOx emissions will, in all likelihood, re- sult in burner throat velocities that exceed standard design practices. This, in turn, may cause burner in- stability, prohibitive burner differentials and in the case of gas firing, undesirable pulsation. Therefore, the installation of overfire air ports in conjunction with FGR serves two useful purposes, 1) lower NOx emis- sions through two-stage combustion, and 2) a decrease in mass flow of air to the burners to accommodate the increased burden of recirculated flue gas. When employing flue gas recirculation in combina- tion with overfire air, it is desirable to house the overfire air ports in a dedicated windbox compartment separate from the burners. In this manner, it is pos- sible to introduce recirculated flue gas to the burners only. This permits more efficient use of the GR fans and overall system design as only that portion of flue gas introduced through the burners is considered ef- fective in controlling NOx emissions. An inexpensive means of recirculating lesser amounts of flue gas is induced FGR, or IFGR. Here, flue gas is introduced through the forced draft fan(s) and is restricted by the fans’ capacity for flue gas. The effectiveness of IFGR is, as a result, limited. Reburning Reburning is an in-furnace NOx control technique that divides the furnace into three distinct zones (main, reburn, and burnout). By effectively stag- ing both fuel and combustion air, NOx emission reduc- tions of 50 to 75% from baseline levels can be achieved. Heatinputisspreadoveralargerportionofthefurnace, with combustion air carefully regulated to the various zones to achieve optimum NOx reduction (Fig. 5). In reburning, the lower furnace or main burner zone provides the major portion of the total heat in- Fig. 4 Flue gas recirculation low NOx system for oil and gas firing.
- 293. The Babcock & Wilcox Company 11-8 Steam 41 / Oil and Gas Utilization put to the furnace. Depending on the percent NOx reduction and the specific combustion system require- ments, the main zone burners can be designed to op- erate at less than theoretical air to normal excess air levels. Combustion gases from the main burner zone then pass through a second combustion zone termed the reburning zone. Here, burners provide the remain- ing heat input to the furnace to achieve full load op- eration but at a significantly lower stoichiometry. By injecting reburn fuel above the main burner zone, a NOx reducing region is produced in the furnace where hydrocarbon radicals from the partially oxidized reburn fuel strip oxygen from the NO molecules, form- ing nitrogen compounds and eventually molecular nitrogen (N2). Overfire air ports are installed above the reburningzonewheretheremainderofairisintroduced to complete combustion in an environment both chemi- cally and thermally non-conducive to NOx formation. Application of this technology must consider a num- ber of variables. System parameters requiring defini- tion include: fuel split between the main combustion zone and the reburn zone, stoichiometry to the main and reburn burners, overall stoichiometry in the reburn and burnout zones of the furnace, residence time in the reburn zone, and residence time required above the overfire air ports to complete combustion. An optimum range of values has been defined for each of these parameters through laboratory tests and field application and is largely dependent upon the type of fuel being fired. For example, fuels with high sulfur contents (Orimulsion or some heavy fuel oils) are not as suitable in applications where operating the main combustion zone under low sub-stoichiometric condi- tions is required to reduce NOx levels due to corrosion concerns. For these fuels, reburning technology can be effectively used by operating the main zone at higher stoichiometries, thus minimizing corrosion con- cerns while still achieving good NOx reduction results. Although implementation of the reburning technol- ogy adds complexity to operation and maintenance of the overall combustion system, it also provides consid- erable emission performance optimization flexibility. In addition, higher initial costs for a reburn system as compared to other combustion techniques need to be factored into the evaluation process. From an eco- nomic standpoint, the potential benefits and techni- cal merit of the reburning process must be commen- surate with long term goals for NOx abatement. Oxides of sulfur The sulfur content of fuel oils can range anywhere from a fraction of a percent for lighter oils to 3.5% for some residual oils. During the combustion process, sulfur contained in the fuel is converted to either sul- fur dioxide, SO2, or sulfur trioxide, SO3 (SOx emis- sions). The control of SOx emissions is a key environ- mental concern and sulfur compounds in the flue gas can also cause corrosion problems in the boiler and downstream equipment. SO3 will form sulfuric acid when cooled in the pres- ence of water vapor. In addition to corrosion problems, it can produce emissions of acid smut and visible plumeopacityfromthestack.EmissionsofSO3 arebest controlled during combustion through low excess air operation and can also be reduced by use of magne- sium based fuel additives. Techniques to control sulfur oxides during the com- bustion process have been investigated in laboratory and pilot scale tests with varying degrees of success.At present, however, the most effective and commercially accepted method, short of firing low sulfur fuels, is to install flue gas cleanup equipment. (See Chapter 35.) Particulate matter Particulate matter in the form of soot or coke is a byproduct of the combustion process resulting from carryover of inert mineral matt