2 ijcmp jan-2018-3-computing fluid dynamics on

International journal of Chemistry, Mathematics and Physics (IJCMP) [Vol-2, Issue-1, Jan-Feb, 2018]
https://dx.doi.org/10.22161/ijcmp.2.1.2 ISSN: 2456-866X
www.aipublications.com/ijcmp Page | 4
Computing fluid dynamics on burner air flow
in natural draft furnaces
Asya Alabdalah, Hassan Al-haj Ibrahim, Ethat Aloosh
Al-Baath University, Homs, Syria
Abstract— The mean key variable to control the burner
performance for safe and efficient operations is the amount
of excess air or oxygen which flow to react with fuel. In
accordance with Typical Draft Profile in a Natural Draft
furnace the numerical results of computing fluid dynamics
model of the air flow from the environment to the burner by
adjusting the area of air box prototype openings will give
the necessary information to adjust the performance of
burner as optimum. The model of air box prototype is useful
tool in applying similarity theory on another burners̕
designs which depends the air box tools to calibrate the
quantity of combustion air flow to the burner.
Keywords— excess air, air box design, computing fluid
dynamics, natural draft furnaces.
I. INTRODUCTION
In many burners of natural furnaces today there are
insufficient means to adjusting the ratio of fuel to air, the
key variable to control the burner performance for safe and
efficient operations is the amount of excess air or oxygen
which flow to react with fuel. While some excess oxygen is
necessary to have safe operation, too much oxygen wastes
fuel, energy, and heat. The Air box is one component of
burner which is used to control the amount of air excess by
modifying its air registers. So the numerical results of
computing fluid dynamics of the air flow from the
environment to the burner by the air box will give the
necessary information to adjust the performance of burner
as optimum.
In result; the process engineer will not depends on the
laboratory analysis about the flue gas data from all sides of
the combustion chamber of furnace at each burner. That is
because the numerical results give a lots of information
about the air flow through the air box to burner and its
quantities from a design point to the operating case as a
result of coupling the average velocity of combustion air
which enter from the gats of air box into burner with the
pressure arise across the burner or the air box.
The pressure arise across combustion equipment like a
burner etc., can be calculated from the following equation
[1]
∆𝑃 = 𝐾
𝜌𝑢2
2
𝑃𝑎
U = velocity of air at burner exit m/s
K is the flow resistance factor where K=1.5 for tangential
burner and K= 3 for swirl burner of gas and heavy oil [1]
But from operation point, the air flow rate in burner can
calculated from [1]
𝑉 𝑎𝑖𝑟 = 𝐵. 𝑉ₒ(𝑛 𝑎𝑖𝑟).
273 + 𝑇𝑎𝑖𝑟
273
𝑉 𝑎𝑖𝑟 The flow of air m3
/s
𝑉ₒ
Theoretical air flow Nm3
/kg
𝐵 Fuel feed rate kg/s
𝑛 𝑎𝑖𝑟 Excess air coefficient at furnace outlet (there is not
leakage into furnace)
𝑇𝑎𝑖𝑟 Air temperature ◦
C
So the numerical results information which are gotten from
the prototype air box can be used to predict the quantity that
may be enter from the doors of the air box by using the
theory of dynamics similarity which related by the
Reynolds number of the air flow into the burner at all times
with its Reynolds number at design case.
From a design point these gates must provide enough air for
fuel’s burning process. The correlative with maximum
amount fuel consumption 𝑩 𝒎𝒂𝒙 and surface area of all gates
𝑭 𝒈 is defined by [2]
𝑭 𝒈(𝒎 𝟐
) =
𝑩 𝒎𝒂𝒙 × 𝒍 𝜶
𝒘 𝒈 × 𝑱 × 𝑲
𝑩 𝒎𝒂𝒙 Maximum amount fuel consumption
𝒍 𝜶 Amount of air providing for burning the fuel
𝒋 Area of activated gate = 1 in this case study
𝒌 Discharge consumption coefficient 0.6-0.75
𝒘 𝒈 Air speed through gate 0.5 m/s
Here the process engineer thinks that in fact the excess air
does not related only by adjusting the air box registers
because it is important to maintain the correct furnace draft.
So too little draft can damage the metal structure and snuff

out the burners or flame and too much draft can pull
excessive amounts of air into the furnace. So the operation
of fired furnaces is complex process and there are different
variables on both the combustion and process sides of the
furnace. In result; there is just enough air to assure complete
combustion. Once, the air registers are adjusted for proper
combustion, the damper should be adjusted for proper draft.
So the engineer can make natural draft Heater adjustment
according to the following flow chart showed in fig (1).
TO benefit from the numerical results information which
are gotten from the prototype air box from a design point,
the process engineer must begin to ultimate the pressure
arise across the burner (draft available at burner level),and
he must follow these general rule which are mentioned for
any duct in furnace not only for burner .
Fig. 1: Natural Draft Heater Adjustment Flow Chart [3]
1- General Rules to ultimate the pressure arise across
any air duct in furnace
By adding the natural draft components of all parts of the
air ducts, the total natural draft ∑ 𝑃𝑛𝑑 is obtained, so the
total pressure drop ∆𝑃𝑎𝑖𝑟 in the air ducts in the furnace can
be obtained by subtraction [1]
∆𝑃𝑎𝑖𝑟 = ∆𝑃𝑟 − ∑ 𝑃𝑛𝑑 Pa
∆𝑃𝑎𝑖𝑟 Is the total pressure drop in the air ducts in the
furnace, Fig.(2) Shows typical draft Profile in a natural draft
furnace
∆𝑃𝑟 Is the total pressure drop after correction of elevation.
∆𝑃𝑟 = ∑ ∆𝑃
101325
𝑃𝑎𝑣
The sum of resistance of all parts of the air duct gives the
total resistance of the air duct∑ ∆𝑃.
Fig.2: Typical Draft Profile in a Natural Draft furnace [3]
∑ 𝑃𝑛𝑑 Is the total natural draft of all parts of the air duct
- Natural draft in air ducts in furnace can be calculated from
𝑃𝑛𝑑 = 𝐻. 𝑔 . (𝜌 𝑎
´´
− 𝜌 𝑎
´
) 𝑃𝑎
𝑃𝑛𝑑 Is the natural draft in air duct.
𝐻 Is the height between the start and end sections of the
duct m
𝑔 Is the Gravitational constant 9.8kg/s2
𝜌 𝑎
´´
Is the density of air at the lowest point of duct kg/m3
𝜌 𝑎
´
Is the density of air at the highest point of duct kg/m3
2- Mathematical model on air flow into swirl burner as
case study
The burner used in this study consists of two concentric
tube with a tangential and radial swirler placed in annular
arrangement. Fig. (4) and (5, B) illustrates the important
aerodynamics feature of the vertical low NOX swirl burner.
The combustion air is introduced through two concentric
annular nozzles of which the positions of the primary,
secondary air, and fuel tube are adjusted to produce the

desired internally staged flame, the burner utilizes swirl
induces centrifugal body forces to dampen turbulent
exchange between the fuel and air stream allowing an
extended residence for fuel conversion chemistry in locally
fuel –rich environment prior to burn out [4].The NOx
emission is at its peak at stoichiometric conditions when
other pollutants, like CO and VOC, is at its minimum (see
Fig.(3)).This is mainly because of the strong relation
between temperature and thermal NOx production [5]
Fig.3: NOx formation rate driven by temperature at equivalence ratio 𝜆 and Schematic drawing of (a) air staging, and (b) fuel
staging [5]
NOx reduction needs to apply correct operating parameters
and used as a design basis, so in accordance with NOx
reduction work, it is essential that excess air levels be
reduced to close to 2–4% O2 as all
NOx emissions are corrected to3% O2 (see fig. (4))[3]. The
most significant useful phenomenon of the swirling flows is
the existence of internal recirculation zone IRZ which aids
in flame stabilization by providing a storage of hot flow flue
gas, so its flow field is thank for its effect in internal flue
gas recirculated to the combustion zone to reduce the NOX
emissions, by reducing the oxygen concentration as well as
lowering the flame temperature. In internal FGR, the fuel
gas is recycled into the flame zone due to burner
aerodynamics [5]
Fig.4: Excess Air vs. Oxygen Content in Flue Gas (A) [3] and typical low NOX swirl burners̕ flow field with internal staging
schematic (B) [4]

Fig.5: Shows a schematic diagram of the air and fuel flow velocities of a swirled jet burner (a) [6] and burner geometry (b).
In result, combustion product are recirculated and by this
phenomena reduced velocity region is created, the boundary
of the recirculation eddy is determined by the radial points
at which the forward mass flow equals the reverse mass
flow at the axial station so the region which is enclosed
where the axial velocity reaches zero magnitude in each
axial plane [6].
3- Computing fluid dynamics for the air box of burner:
-air box geometry:
Air box Consists of Two cylinders, the internal one is fixed
with thickness 2 mm and dimensions 8041
×370 mm and
diameter 258-0.5
mm, and the outside is movable one with
thickness 2 mm, dimensions 823+2
×268 mm and diameter
264+1
mm. These two cylinders have the same gates and by
moving the outer cylinder against the fixed cylinder,
changes the air flow area. See (fig. (6) Air box fluid
domain)
Fig.6: Air box fluid domain (full opining)
Ambient air temperature, pressure and humidity affect the
air flow rate if the air temperature increases the air flow rate
decreases. As definite temperature, pressure and humidity
of air increase, water vapor in ambient air is decreased and
leads to decrease of the percentage of O2. So the air flow
rate through the air box at definite pressure drop by using
corresponding – state is defined by [7]
𝑚 𝑎𝑖𝑟 = √
2𝑔𝜌 𝑎𝑖𝑟 𝐴 𝑏∆𝑝 𝑏
𝑘 𝑝

𝑚 𝑎𝑖𝑟 Air mass flow rate kg/s, g Gravitational constant
9.8kg/s2
,𝐴 𝑏 Cross section area in internal cylinder m2
, ∆𝑝 𝑏
Air side pressure drop across air box in pascal (natural draft
is available at air box level),𝑘 𝑝Pressure loss coefficient
through air box and can be estimated as equal to 0.6-0.75
- Cold mathematical model flow of vertical air box:
As in the case of any problem in flow filed this particular
type of flow described by the mathematical expressions of
continuity and momentum in Cartesian coordinates:
Continuity equations:
∂u̅
∂x
+
𝜕𝑣̅
𝜕𝑦
+
𝜕𝑤̅
𝜕𝑧
= 0
Momentum Equations:
In this situation the body force with constant density equals
to the balance between the driving force of buoyancy and
the initial hydrostatic pressure, so at any point in the fluid
domain the equation of motion is:
ρ [
𝜕𝑢̅ 𝑖
𝜕𝜏
+
𝜕(𝑢𝑗 𝑢𝑖̅̅̅̅̅)
𝜕𝑥𝑗
] = −
𝜕𝑝
𝜕𝑥𝑖
+
∂T𝑖𝑗
∂x𝑗
+ 𝐵 𝑇. 𝑔. (𝑇 − 𝑇∞)
Where: 𝑇 is the actual temperature applicable locally. 𝑇∞ :
is the undisturbed constant temperature. 𝐵 𝑇: is the
coefficient of the thermal expansion of air and by using the
equation of stat for the perfect gas
𝜌 =
𝑝
𝑅𝑇
Where 𝑅 is universal gas constant, 𝑝 is the local static
pressure, and 𝜌 is the local density so ( 𝐵 𝑇 = 1/𝑇), T𝑖𝑗 is
the Reynolds stress tensor divided by the density and it is
computed by using the Boussinesq model equation
T𝑖𝑗 = −𝑢𝑖
´
𝑢𝑗
´
= 𝜈Τ (
𝜕𝑢̅ 𝑖
𝜕𝑥𝑗
+
𝜕𝑢̅𝑗
𝜕𝑥𝑖
−
2
3
𝜕𝑢̅ 𝑘
𝜕𝑥 𝑘
𝛿𝑖𝑗) −
2
3
Κ𝛿𝑖𝑗
Where is the turbulent kinetic energy, 𝛿𝑖𝑗 is Kronecker
Delta Function, Then the letters i, j, k ...can be used as
variables, running from 1 to 3 so Instead of using x, y, and z
to label the components of a vector, we use 1, 2, 3 and 𝜈Τ is
the turbulent eddy viscosity can be calculated by K-Epsilon
model so
𝜈Τ = 𝐶𝜇
Κ
2
ε
Where 𝐶𝜇 is constant equals to 0.09
These models are not valid near wall to model wall effect so
wall function have to be employed.
- Wall y+ Strategy for Dealing with Wall-bounded
Turbulent Flows for air box geometry:
A wall y+ in the range of 30 to 60 is determined to be
sufficiently accurate. Where the log-law region is resolved.
It is also advisable to avoid having the wall-adjacent mesh
in the buffer region since neither wall functions nor near
wall modelling approach accounts for it accurately, so for
the existence of deferent boundary layers in air box
geometry enhanced wall function is used
- Boundary condition:
Here the air box was opened to the environment from
surrounding sides of the gates at the maximum fuel gas
consumption which it was 𝐵 𝑚𝑎𝑥 = 0.02𝑁𝑚3
/𝑠 and
( 𝒍 𝜶 = (
12𝑁𝑚 𝑎𝑖𝑟
3
1𝑁𝑚 𝑓𝑢𝑙,𝜆=1
3 ) ) . In result from design point, air mass
flow will be equal to (𝜌 𝑎𝑖𝑟. 𝐵 𝑚𝑎𝑥. 𝒍 𝜶) at 𝜆 = 1.15
So calculating the air mass flow yields
(𝒍 𝜶 = (
14𝑁𝑚 𝑎𝑖𝑟
3
1𝑁𝑚 𝑓𝑢𝑙,𝜆=1.15
3 ) ), and the following are the technical
data of burner:
- Burner axis: vertical
- Regulating range of capacity of burner 20%-60%
- Excess of air nair 𝜆 =1.15
- Required type of the burner: gas type with natural draft of
air fitted with a gas injector stabilization torch; Hydrogen
content in the heating gas must not exceed 60% volume,
and the fuel doesn’t contain any nitrogen compounds
- Chemical composition %-vol for gaseous fuel:
H2-28, C1- 34, C2-17, C3-17, C4-3, C5- 1, H2O-1.5, H2S-
max.5mg/Nm3
* Net calorific value: 11000kcal/kg
* Density kg/Nm3
0.924
* Flammability limits% 3.4-16.5
- Temperature in the spot of the burner inlet 30◦
C
- Heating gas consumption of I burner Nm3
/h;
For min. output 23.2, for nominal output 58.0 and for max.
Output 69.6
II. RESULTS AND CONCLUSIONS
The wall y+ is a non-dimensional number similar to local
Reynolds number, determining whether the influences in
the wall-adjacent cells are laminar or turbulent, hence
indicating the part of the turbulent boundary layer that they
resolve [8], and it can be seen below as well as Velocity
vector plots, can be seen below in the photos of Fig. (a), (b)
and (c). These plots give a lot of information about the ﬂow
field of the air box of the burner. The recirculation at the
corners of air gates and air flow by the area of gates is also
obvious from these figures. The air combustion tends to
move into the air box by natural draft of the furnace at its
level.

Fig.a: y+ and velocity vector plots in the field of air box for solution 1.
Solution 1 by iteration method at a steady state-physical relaxation step equals to 0.05 sec, the convergence criteria of RMS
residuals is 0.0002, first order is used for advection scheme, distorted fluid elements are 6927elements , and the following table 1
ultimate the data of this solution
Table.1: Ultimates the data of solution1
Computing costy+ information on adiabatic facesNumber of
element
Computing Reynold
number
52min 24sec+
ave. ymax y+min y+38108495
1.8×10
5.721
3.28×101-
1.59×10
Fig.b: y+
and velocity vector plots in the field of air box for solution 2.

residuals is 0.0002, first order is used for advection scheme, distorted fluid elements are 22432 elements , and the following table
2 ultimate the data of this solution
element
Computing Reynold
number
12min 20secave. y+
max y+min y+12366191.8×105
6.264.08×101
3.70×10-1
Fig.c: y+ and velocity vector plots in the field of air box for solution 3.
residuals is 0.0002, first order is used for advection scheme, distorted fluid elements are 331 elements , and the following table 3
ultimate the data of this solution
element
Computing Reynold
number
23min59sec+
ave. ymax y+min y+19225145
1.8×10
5..441
3.24×101-
2.78×10
The comparison between these three solutions emphasis that solution 2 is preferred. That is because it gives the necessary
information by the best computing cost as it is clear from fig. (c) Which shows the same velocity profiles for the three solutions
at the same path.

Fig.d: Shows the same velocity profiles for the three solutions at the same path.
Fig.e: Which shows low NOx burner with two air boxes
In fact, by industry these kinds of air boxes are used as tools
to adjust the fuel /air ratio in many burners’ designs which
work on natural draft as it can be seen from fig. (e) Which
shows low NOx burner with physical separate between two
stages (two air stages and two fuel stages). Here burner
depends on two air boxes for natural draft of the
combustion air. So in result this model for air box in the
low NOx swirl burner which is studied is too useful to get
the important information and calibrate another burners
performances by using the similarity theory as dynamics
and geometry parameters, or to build different air boxes
models by the same methodology to get the best from the
system as large efficiency and less pollution especially for
adjusting NOX emissions.
REFERENCES
[1] Sasu, P. Kefa, C. Jestin, L. Boilers and Burners Design
and Theory .Springer ISBN0-387-98703-7
[2] Hay, N.Researching On Burner, Construction
Equation Of Air Flow Velocity And Defining
Appropriate Drayer Wall for Tobacco Dryer In
Vietnam. Nong Lam University
[3] Electronically reproduced by special permission from
HYDROCARBON PROCESSING (June 1997).
Optimized Fired Heater Operation Saves Money.
Copyright © 1997, Gulf Publishing, Texas
[4] Shihadeh,A.L. Toqan, M.A. Beér, J.M. Lewis P.F,
Teare, J.D. Jiménez, J.L. and Barta, L. 1994. LOW
NOx EMISSION FROM AERODYNAMICALLY

STAGED OIL-AIR TURBULENT DIFFUSION
FLAMES. ASME FACT-18, Combustion Modeling,
Scaling and Air Toxins
[5] Fiskum,A. 2008. Calculation of NOx Formation in a
Swirl Burner. Department of Energy and Process
Engineering, Norwegian University of Science and
Technology.
[6] Ashworth,D.A.2017.An Analytical Model to Predict
the Length of Oxygen-Assisted, Swirled, Coal and
Biomass Flames. Department of Mechanical
Engineering Brigham Young University
[7] Masoumi,M.E.Izakmehri,z. 2011.Improving Of
Refinery Furnaces Efficiency Using Mathematical
Modeling. International Journal of modeling and
optimization .volume1:pages74-79
[8] Salim, M.Cheah, S.C.2009. Wall y+ Strategy for
Dealing with Wall-bounded Turbulent Flows.
Proceedings of the International MultiConference of
Engineers and Computer Scientists, Vol II IMECS
2009, March 18 - 20, Hong Kong

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