Chapter 1. dpv a. lal revised

Design of Pressure Vessels
Dr. Achchhe Lal
Department of Mechanical Engineering
SVNIT Surat-395007
Phone: (+91) (261) 2201993, Mobile: 9824442503
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Projectcoordination

Basic References
Theory and Design of Pressure Vessels
John F. Harvey, P.E.
VAN NOSTRAND REINHOLD COMPANY INC., 1985.
Pressure Vessels: Design and Practice
Sobhanath Chattopadyay
CRC Press., 2000.
Pressure Vessels Design Manual
Denis Moss
Gulf Professional Company, 2004.
 Mechanical Design of Heat Exchangers
K.P. Singh & A.L. Soler,, Arcturus Pub. Inc. N.J. 08003, USA.
1984.
Pressure Vessels and Stachs

 Introduction to diverse kinds of Pressure Vessels (PVs)
 Overview of various parts (internal and external) of Pressure vessels and its
functions and applications.
 Various failure modes of PVs, Brief introduction to different pressure vessels
code and importance
 What factors to be considered for the selection of materials and different types of
materials with their characteristic and properties,
 Theory of pressure vessels design on internal pressure basis and external pressure
basis, Autofretage of thick cylinders, Significant of thermal stresses and fatigue
 Design of Shells and Heads for Internal and External Pressure
 Importance and design of different kinds of openings and flanges
 Pressure Vessel design for external loads– Wind/Seismic & Support design
 Evaluation of pressure vessel for different conditions: Hydrotest condition, FEM
analysis,
What will you learn?
“A teacher’s job is to uncover and not cover the syllabus”- Richard M Felder

The following hyperlinks are to file-wise substructure. Content-wise substructure will appear in respective chapters.
1. CHAPTER 1: Introduction
1.1 Introduction to PVs
1.2 Types and Applications of PVs
CHAPTER 2: Factors influencing the design of vessels,
classification of pressure vessels, material selection,
loads & types of failures
3. CHAPTER 3: Stresses in pressure vessels
stresses in circular ring, cylinder & sphere,
membrane stresses in vessels under internal
pressure, thick cylinders, multilayered
cylinders, stress consideration in the selection
of flat plate & conical closures, elliptical,
torispherical,
4. CHAPTER 4: Autofretage of thick cylinders,
thermal stresses & their significance, fatigue of
pressure vessels
.
5. CHAPTER 5: Design of pressure vessels as per ASME & IS codes, externally pressurized
vessels, tall vertical vessels, support for
vertical & horizontal vessels, nozzles & flanges

5
Objectives of Chapter 1
 Introduction of Pressure vessels with applications
in different engineering applications
 Overview of various parts (internal and external)
of Pressure vessels and its functions and
applications.

Pressure vessels –An Introduction
A pressure vessel are a closed container designed to hold gases or
liquids at a pressure (inside the vessels) different from the out side
pressure (known as ambient pressure or Atmospheric pressure).
Pressure vessels are the basic equipment for any fluid processing
system.
The liquid and gaseous chemicals are storage in a pressurized
chambers (pressure vessels) for a chemical reaction.
The inside pressure may be obtained from an external source or by
the application of heat from direct or indirect source, or by other.
PVs are also known as leak proof containers. They may be of any shape and
range from bottles to the sophisticated ones in engineering construction

The pressure vessels is design of great care because of rapture
pressure vessels means an explosion which cause of may cause loss of
life property. The material of pressure vessels may be brittle such that
cast iron or ductile such mild steel.

They are used in
 storage vessels (for liquified gases such as ammonia,
chlorine, propane, butane, house hold gas cylinders, fire
extinguishers, saving cream cans and LPG),
 chemical industries (as distillation tower, domestic hot
water storage tanks).
 medical field (as autoclaves).
 aero space field (as habitat of spaceship).
 nuclear field (as a nuclear vessels).
 pneumatic and hydraulic reservoirs under pressure.
 In Automobiles: rail vehicle airbrake reservoir, road
vehicle airbrake reservoir, power, food and many other
industries.
 In recent years, the use of pressure vessels has become
very expansive due to phenomenal expansion in
fertilizer, petrochemical paint, food, nuclear, drug and
other allied industries.

Difference Applications of pressure vessels

Gas Cylinders
•Storage of medical gases.
•Storage of breathing gases in diving cylinder.
•Storage of gaseous fuels for internal combustion
engines,
•heating equipment and cooking such as LP gas,
butane and propane.
•Storage of gases used for oxy-fuel welding and
cutting.
2 and 3 liter diving cylinders.
Some Common Applications of Pressure Vessels

Typical industrial fractional distillation columns
Distillation columns used to
separate various gases in
petroleum refineries,
petrochemical and chemical
plants and natural gas
processing plants.
Chemical engineering
schematic of typical bubble-cap
trays in a distillation tower
Chemical Engineering Fields

An autoclave is a pressurized device
designed to heat aqueous solutions
above their boiling point to achieve
sterilization
Stovetop autoclaves - the
simplest of autoclaves
A modern Front Loading Autoclave
Medical fields

A mine cart toilet used in mining

An oil refinery is an industrial process plant where crude oil is processed
and refined into more useful petroleum products, such as gasoline, diesel
fuel, asphalt base, heating oil, kerosine, and liquefied petroleum gas
Petrochemical fields

Petrochemicals are chemical products made from raw
materials of petroleum (hydrocarbon) origin

A nuclear reactor is a device in which nuclear chain reactions are
initiated, controlled, and sustained at a steady rate, as opposed to a
nuclear bomb, in which the chain reaction occurs in a fraction of a
second and is uncontrolled causing an explosion
In the nuclear fields

The Hubble Space Telescope.
In the aerospace applications

In Automobiles
An air brake is a conveyance braking system applied by
means of compressed air

To Be Continue…
Date: January 27, 2014

Continue...
• In the industrial sector, pressure vessels are designed to
operate safely at a specific pressure and temperature,
technically referred to as the "Design Pressure" and "Design
Temperature".
• Second main important parameter is required thickness.
• A vessel that is inadequately designed to handle a high
pressure constitutes a very significant safety hazard.
• Pressure vessels can theoretically be almost any shape, but
shapes made of sections of spheres, cylinders and conical
types are usually employed. More complicated shapes have
historically been much harder to analyze for safe operation and
are usually far harder to construct.
• Theoretically a sphere would be the optimal shape of a
pressure vessel. Unfortunately the sphere shape is difficult to
manufacture, therefore more expensive, so most of the
pressure vessels are cylindrical shape with 2:1 semi elliptical
heads or end caps on each end.

TYPES OF PRESSURE VESSELS
There are three main types of pressure vessels
in general
• Horizontal Pressure Vessels
• Vertical Pressure Vessels
• Spherical Pressure vessels
However there are some special types of Vessels like
Regeneration Tower, Reactors but these names are given
according to their use only.

VERTICAL PRESSURE VESSEL
• The max. Shell
length to diameter
ratio for a small
vertical drum is
about 5 : 1

TALL VERTICAL TOWER
• Constructed in a wider
range of shell diameter
and height.
• They can be relatively
small in dia. and very
large (e.g. 4 ft dia. And
200 ft tall distillation
column.
• They can be very large in
dia. and moderately tall
(e.g. 3 ft dia. And 150 ft
tall tower).
• Internal trays are
needed for flow
distribution.

VERTICAL REACTOR
• Figure shows a typical
reactor vessel with a
cylindrical shell.
• The process fluid
undergoes a chemical
reaction inside a
reactor.
• This reaction is normally
facilitated by the
presence of a catalyst
which is held in one or
more catalyst beds.

SPHERICAL PRESSURIZED
STORAGE VESSEL

MAIN COMPONENTS OF
PRESSURE VESSEL
Following are the main components of pressure
Vessels in general
• Shell
• Head
• Nozzle
• Support

SHELL
 It is the primary component that contains the
pressure.
 Pressure vessel shells in the form of different
plates are welded together to form a
structure that has a common rotational axis.
 Shells are either cylindrical, spherical or
conical in shape.

SHELL
 Horizontal drums have cylindrical shells and
are constructed in a wide range of diameter
and length.
 The shell sections of a tall tower may be
constructed of different materials, thickness
and diameters due to process and phase
change of process fluid.
 Shell of a spherical pressure vessel is
spherical as well.

HEAD
• All the pressure vessels must be closed at
the ends by heads (or another shell section).
• Heads are typically curved rather than flat.
• The reason is that curved configurations are
stronger and allow the heads to be thinner,
lighter and less expensive than flat heads.
• Heads can also be used inside a vessel and
are known as intermediate heads.
• These intermediate heads are separate
sections of the pressure vessels to permit
different design conditions.

NOZZLE
• A nozzle is a cylindrical component that
penetrates into the shell or head of pressure
vessel.
• They are used for the following applications.
• Attach piping for flow into or out of the vessel.
• Attach instrument connection (level gauges,
Thermowells, pressure gauges).
• Provide access to the vessel interior at
MANWAY.
• Provide for direct attachment of other equipment
items (e.g. heat exchangers).

SUPPORT
• Support is used to bear all the load of
pressure vessel, earthquake and wind loads.
• There are different types of supports which
are used depending upon the size and
orientation of the pressure vessel.
• It is considered to be the non-pressurized part
of the vessel.

TYPES OF SUPPORTS
SADDLE SUPPORT:
 Horizontal drums are typically supported at two
locations by saddle support.
 It spreads over a large area of the shell to prevent an
excessive local stress in the shell at support point.
 One saddle support is anchored whereas the other is
free to permit unstrained longitudinal thermal
expansion of the drum.

TYPES OF SUPPORTS
LEG SUPPORT:
 Small vertical drums are typically supported on legs
that are welded to the lower portion of the shell.
 The max. ratio of support leg length to drum diameter
is typically 2 : 1
 Reinforcing pads are welded to the shell first to
provide additional local reinforcement and load
distribution.
 The number of legs depends on the drum size and
loads to be carried.
 Support legs are also used for Spherical pressurized
storage vessels.
 Cross bracing between the legs is used to absorb wind
or earth quake loads.

TYPES OF SUPPORTS
LUG SUPPORT:
 Vertical pressure vessels may
also be supported by lugs.
 The use of lugs is typically
limited to pressure vessels of
small and medium diameter (1
to 10 ft)
 Also moderate height to
diameter ratios in the range of
2:1 to 5:1
 The lugs are typically bolted to
horizontal structural members
in order to provide stability
against overturning loads.

TYPES OF SUPPORTS
SKIRT SUPPORT:
 Tall vertical cylindrical pressure vessels are typically
supported by skirts.
 A support skirt is a cylindrical shell section that is
welded either to the lower portion of the vessel shell
or to the bottom head (for cylindrical vessels).
 The skirt is normally long enough to provide enough
flexibility so that radial thermal expansion of the shell
does not cause high thermal stresses at its junction
with the skirt.

THIN WALLED PRESSURE
VESSELS
• Thin wall refers to a vessel having an inner-radius-to-wall-
thickness ratio of “10” or more (r / t ≥ 10).
• When the vessel wall is thin, the stress distribution
throughout its thickness will not vary significantly, and so
we will assume that it is uniform or constant.
• Following this assumption, the analysis of thin walled
cylindrical and spherical pressure vessel will be carried out.
• In both cases, the pressure in the vessel will be considered
to be the gauge pressure, since it measure the pressure
above atmospheric pressure existing at inside and outside
the vessel’s walls.

VESSELS
• The above analysis indicates that an element of material
taken from either cylindrical or spherical pressure vessel is
subjected to biaxial stress, i.e. normal stress existing in only
two directions.
• Actually material of the vessel is also subjected to a radial
stress, σ3, which acts along a radial line. This stress has a
max. value equal to the pressure p at the interior wall and
decreases through the wall to zero at the exterior surface of
the vessel, since the gauge pressure there is zero.
• For thin walled vessels, however, the redial stress
components are ignored because r / t = 10 results in σ1 & σ2
being, respectively, 5 & 10 times higher than the max. radial
stress, (σ3)max = p

VESSELS
• It must be emphasized that the formula derived for thin
walled pressure vessels should be used only for cases
of internal pressure.
• If a vessel is to be designed for external pressure as in
the case of vacuum tank, or submarine, instability
(buckling) of the wall may occur & stress calculations
based on the formulae derived can be meaningless.

Types of pressure vessels
Storage Tank to Heat Exchanger
Pressure Vessels & Reactors
storage tanks from carbon steel,
stainless steel and nickel alloy vessels

Single Pass & Multiple Pass Heat Exchangers used in the chemical process industry.

Stainless Steel Pressure Vessel (painted)
Stainless Steel Pressure Vessels and
Heat Exchangers

Components of Pressure Vessels

Vessels with hemispherical head

Classification of pressure Vessels
Based on Construction:
• Mono wall: Depending on the specific
conditions, either monowall or multilayer construction
can be used, with finished high-pressure vessels
having unit weights of up to and in excess of 300t.
• Multi Wall: Various layered construction, used for all
types of PVs, large diameters, length, and wall thickness.
• Thermal conduction is lowers and easily made by reinforced
by shrinkage of one seamlessly forged cylinders on to the
core of shell
• The use of a multiwall pressure vessel is often necessary in
carrying out a reaction process under high pressure, and
when the reaction substances are corrosive, a multi-walled
pressure vessel provided with a special lining is often
utilized.
•

Analysis of PV based on internal pressure
Two types of analysis are commonly applied to pressure vessels.
1. Analysis based on a simple mechanics approach
2. Analysis based on based on elasticity solution
The most common method is based on a simple mechanics
approach and is applicable to “thin wall” pressure vessels which
by definition have a ratio of inner radius, r, to wall thickness, t, of
r/t≥10.
The second method is based on elasticity solution and is always
applicable regardless of the r/t ratio and can be referred to as the
solution for “thick wall” pressure vessels.
Both types of analysis are discussed here, although for most
engineering applications, the thin wall pressure vessel can be used.

Cylindrical or spherical pressure vessels (e.g.,
hydraulic cylinders, gun barrels, pipes, boilers and
tanks) are commonly used in industry to carry both
liquids and gases under pressure.
When the pressure vessel is exposed to this
pressure, the material comprising the vessel is
subjected to pressure loading, and hence stresses,
from all directions.
The normal stresses resulting from this pressure are
functions of the radius/diameter of the element
under consideration, the shape of the pressure vessel
(i.e., open ended cylinder, closed end cylinder, or
sphere) as well as the applied pressure.
Pressure Vessels: Combined Stresses

Thin-Walled Pressure Vessels
under internal pressure
1) Plane sections remain plane
2) r/t ≥ 10 with t being uniform and constant
3) The applied pressure, p, is the gage pressure (note that
p is the difference between the absolute pressure and
the atmospheric pressure)
4) Material is linear-elastic, isotropic and homogeneous.
5) Stress distributions throughout the wall thickness will not
vary, however, stress distribution varies parabolic nature
for thick walled pressure vessels.
6) Working fluid has negligible weight.

1.1. Stresses in Cylinders and Spheres

Longitudinal Stress in Spherical Pressure Vessel
Thin Wall type
Thin-walled pressure vessels are one of the most typical
applications of plane stress.
Consider a spherical pressure vessel with radius r and wall
thickness t subjected to an internal gage pressure p.
The normal stresses σ can be related to the pressure p by
inspecting a free body diagram of the pressure vessel. To
simplify the analysis, we cut the vessel in half as illustrated.
Since the vessel is under static equilibrium, it must satisfy
Newton's first law of motion. In other words, the stress around
the wall must have a net resultant forces acting in the pressure
vessel to balance the internal pressure across the cross-section.

Hoop Stress Cylindrical Pressure
Vessel
To determine the hoop stress σh, we
make a cut along the longitudinal axis
and construct a small slice as
illustrated on the right.
The free body is in static equilibrium.
According to Newton's first law of
motion, the hoop stress yields,
Hoop and longitudinal stress in a thin sphere
subjected to internal pressure may be found to be
equal to and same as longitudinal stress in a Cylinder

The above formulas are good for thin-walled pressure
vessels. Generally, a pressure vessel is considered to be
"thin-walled" if its radius r is larger than 5 times its wall
thickness t (r > 5 · t).
 When a pressure vessel is subjected to external
pressure, the above formulas are still valid. However, the
stresses are now negative since the wall is now in
compression instead of tension.
 The hoop stress is twice as much as the longitudinal
stress for the cylindrical pressure vessel. This is why an
overcooked hotdog usually cracks along the longitudinal
direction first (i.e. its skin fails from hoop stress, generated
by internal steam pressure).
Important Remarks

For example, the ASME Boiler and Pressure Vessel
Code (BPVC) (UG-27) formulas are:
Spherical shells:
Cylindrical shells:
where E is the joint efficient, and all others variables
as stated above.
The Factor of safety is often included in these
formulas as well, in the case of the ASME BPVC this
term is included in the material stress value when
solving for Pressure or Thickness.

Dilation or radial growth of pressure vessels

Axi-symmetric Pressure Vessels
• provides the derivation of the
governing equations for membrane
stress in pressure vessels having
circular crosssection, which includes
cylinders and any other shape
having a revolved axis of symmetry
• Consider an element of size ds1 by
ds2 by thickness t, extracted from
the internally pressurized thin-
shelled enclosure shown in Figure
2.1.1
• Note that for computational
simplicity, the chosen element is
oriented along the principal
(longitudinal and circumferential)
directions of the part, so that only
normal forces act on its sectioned
faces.

Ellipsoidal vessels under internal pressure

Thick Walled Cylindrical Vessels
When the thickness of the cylindrical vessel is relatively
large, as in the case of gun barrel, high pressure hydraulic
ram cylinders etc., the variation in the stress from the inner
surface to outer surface becomes appreciable and the
ordinary membrane or average stress formula are not
satisfactory indication of significant stress.

Deformation (Radial) of thick cylinder

Thermal Stresses and their significance
Uniaxial Thermal
Strain=
Thermal Stress=

Assigments-1
Solve the unsolved numerical problem of Hohn F Harvey
Problems 1 to 16 Page no. 97 to 100
17. Explain the Shink-fit stresses in built-up cylinders.
18. Explain the autofrettage phenomenon in thick cylinders.
19. Explain the importance of brusting strength in Pressure
vessels.
20.Expalin the effect of thermal stresses and significant in
cylindrical vessels.

Shrink-fit stresses in builtup cylinders

Autofrettage of thick cylinders

• Autofrettage is a metal fabrication technique in which a pressure vessel is
subjected to enormous pressure, causing internal portions of the part to
yield and resulting in internal compressive residual stresses.
• The goal of autofrettage is to increase the durability of the final product.
• Inducing residual compressive stresses into materials can also increase
their resistance to stress corrosion cracking; that is, non-mechanically-
assisted cracking that occurs when a material is placed in a suitable
environment in the presence of residual tensile stress.
• The technique is commonly used in manufacturing high-pressure pump
cylinders, warship and tank gun barrels, and fuel injection systems for
diesel engines. While some work hardening will occur, that is not the
primary mechanism of strengthening.
The tube (a) is subjected to internal pressure past its elastic limit (b), leaving an inner
layer of stressed metal (c).

• The start point is a single steel tube of internal diameter slightly
less than the desired calibre. The tube is subjected to internal
pressure of sufficient magnitude to enlarge the bore and in the
process the inner layers of the metal are stretched beyond their
elastic limit.
• This means that the inner layers have been stretched to a point
where the steel is no longer able to return to its original shape
once the internal pressure in the bore has been removed.
Although the outer layers of the tube are also stretched the
degree of internal pressure applied during the process is such
that they are not stretched beyond their elastic limit.
• The reason why this is possible is that the stress distribution through
the walls of the tube is non-uniform. Its maximum value occurs in the
metal adjacent to the source of pressure, decreasing markedly
towards the outer layers of the tube.
• The strain is proportional to the stress applied within elastic limit;
therefore the expansion at the outer layers is less than at the bore.
Because the outer layers remain elastic they attempt to return to their
original shape; however, they are prevented from doing so
completely by the now permanently stretched inner layers.
• The effect is that the inner layers of the metal are put under
compression by the outer layers in much the same way as though an
outer layer of metal had been shrunk on as with a built-up gun.

• The next step is to subject the strained inner layers to low
temperature heat treatment which results in the elastic limit
being raised to at least the autofrettage pressure employed in
the first stage of the process.
• Finally the elasticity of the barrel can be tested by applying
internal pressure once more, but this time care is taken to
ensure that the inner layers are not stretched beyond their new
elastic limit.[1]
• When autofrettage is used for strengthening gun barrels, the
barrel is bored to a slightly undersized inside diameter, and
then a slightly oversized die is pushed through the barrel. The
amount of initial underbore and size of the die are calculated to
strain the material past its elastic limit into plastic deformation,
sufficiently far that the final strained diameter is the final desired
bore.
• The technique has been applied to the expansion of tubular
components down hole in oil and gas wells. The method has
been patented by the Norwegian oil service company, Meta,
which uses it to connect concentric tubular components with
sealing and strength properties outlined above.

Factors to be Considered for Selection of Material
The art of material selection lies in designing an economic system with maximum
reliability in operation.
Factors to be Considered for Selection of Material
• Mechanical strength at design conditions
– UTS
– Yield
– Impact
– Creep Rupture
– Fatigue
• Operating conditions and environment
– Corrosive/Non corrosive
– Cryogenic/Low Temp./Moderate Temp/High Temp.
– Steady load/Cyclic or fluctuating load
• Fabricability
• Cost
• Availability in market

Theory of pressure vessels design

Lecture 4
Design of Shell and Head for Internal Pressure

Chapter 1. dpv a. lal revised

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