Design of Pressure Vessel by a.B.solanki
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Design of Pressure Vessel
By A.B.Solanki
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INTRODUCTION [1]
Vessels, tanks, and pipelines that carry, store, or receive fluids arecalled pressure vessels.
A pressure vessel is defined as a container with a pressure
differential between inside and outside. The inside pressure is usually higher than the outside, except for
some isolated situations.
Pressure vessels often have a combination of high pressurestogether with high temperatures.
Because of such hazards it is imperative that the design be suchthat no leakage can occur.
Pressure vessels and tanks are, in fact, essential to the chemical,petroleum, petrochemical and nuclear industries. It is in this class ofequipment that the reactions, separations, and storage of rawmaterials occur.
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Pressure vessel
Function
Storage tank
Process vessel
Heat Exchanger
Geometry
Cylindrical
Spherical
Conical
Horizontal/Vertical
Construction
Monowall
Multi Wall
Forged
Service
Cryogenic
Steam
Lethal
Fired/Unfired
CLASSIFICATION OF PRESSURE VESSEL [3]
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COMPONENTS OF PRESSURE VESSELS
The main components of pressure vessel are [4]i. Shell
ii. Heads
iii. Nozzles
iv. Stiffening rings
v. Supports
Photo courtesy: www.theculminates.com
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Shell
The shell is the primary component that contains the
pressure. Pressure vessel shells are welded together to form a
structure that has a common rotational axis.
Most pressure vessel shells are cylindrical, spherical andconical in shape
Head
All pressure vessel shells must be closed at the ends byheads (or another shell section).
Heads are typically curved rather than flat.
Curved configurations are stronger and allow the heads tobe thinner, lighter, and less expensive than flat heads.Heads are usually categorized by their shapes.
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Fig: Different types of heads.(Modified from ASME Boiler and Pressure Vessel Code, ASME, New York.)
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Support
The type of support that is used depends primarily on the size
and orientation of the pressure vessel.
the pressure vessel support must be adequate for the applied
weight, wind, and earthquake loads.
Typical kinds of supports are as follow:
a. Skirt
b. Leg
c. Saddle
d. Lug
Photo courtesy: www.pressurevesslesconsulting.com
Saddle
Leg
Skirt
Lug
Figure showing various
pressure vessel supports.
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Nozzle
A nozzle is a cylindrical component that penetrates the shell or heads of a
pressure vessel.
The nozzle ends are usually flanged to allow for the necessary connections
and to permit easy disassembly for maintenance or access.
Nozzles are used for attaching piping for flow into or out of the vessel and
attach instrument connections, (e.g., level gauges, thermowells, or
pressure gauges).
Stiffener Rings
Rings made of flat bar or plate or structural shapes welded around the
Circumference of the vessel.
These rings are installed on vessels operating under external pressure to
prevent collapse of the vessel.
Photo courtesy: www.pressurevesslesconsulting.com
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Major Failures associated with pressure vessel can usually be classified as 5 types :
1. EXCESSIVE ELASTIC DEFORMATION
It is a type of expansion of vessel till limit of proportionality.
It affects the volume and density of fluid inside the vessel, hence the purpose of
the vessel will fail and effect the process. So excessive elastic deformation is
undesirable.
2. PLASTIC INSTABILITY :
Plastic deformations occur in a pressure vessel if the Internal or external pressure
becomes so high that resultant stresses acting on the pressure vessel exceeds the
yield point.
Elastic instability in vessels is usually associated with the use of thin shells.
Plastic instability
3. BRITTLE RUPTURE :
If the material used for the vessel is brittle than instead of plastic or elastic
deformation, vessel will ruptured instantly after increasing the slight load after yield
point.
Hence for brittle material stresses should be kept low below the yield point.
MAJOR FAILURES ASSOCIATED WITH PRESSURE
VESSELS
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4. CREEP:
Creep is a failure of material due to constant loading and unloading of
material kept at one place for long time.
It arises due to periodic loading and loading. It starts initially from grainboundary where abnormal grains are there.
It increases to cracks in the material after some time and finally material
fails on load much lower than the yield point stress.
5. CORROSION: If excessive corrosion occurs than material thickness will decrease
constantly and after a certain limit the material will fail
Due to this the vessels are provided with corrosion allowance thickness.
Generally taken 3mm at inside boundary layer.
At outside some corrosion resistant material are used to prevent the
rusting.
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SHELL UNDER INTERNAL
PRESSURE
Calculate internaldesign pressure
P = Pi+ Pliquid level
HOOP STRESS
Classical Equation
ASME CODE EQUATION
LONGITUDINAL STRESS
Classical Equation
ASME CODE EQUATION
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Design of Thin Cylinders
In the design of thin cylinders the following assumptions are
made.
1.The curvature of cylinder wall ignored.
2.The tensile stresses induced at the cross section of the wall aredistributed uniformly.
3.Restraning effect of cylinder head is ignored.
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Stresses in Pressurized CylindersCylindrical pressure vessels, hydraulic cylinders, shafts with components mounted
on (gears, pulleys, and bearings), gun barrels, pipes carrying fluids at high
pressure,.. develop tangential, longitudinal, and radial stresses.
Wall
thickness
t
A pressurized cylinder is considered a thin-walled vessel if the wall
thickness is less than one-twentieth of the radius.
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Stresses in Thin-walled Pressure Vessels (I)
)y2()y2(1 drdt p
t
pr1 (Hoop Stress)
)r()rt2( 2
2 p
t
pr
2
2 (Longitudinal Stress)
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Design of thick wall Cylinder
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Thick wallrefers to a vessel having an inner-radius-to-wall-thickness ratio less than
10.Thick wall: 10
t
ri
Example of thick walled applications:
Gun barrel
Very high pressure hydraulic cylinder
For thick wall cylinder, R(radial stress) no longer be neglected.
Introduction
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Thick Cylinder wall subject to InternalPressure
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Consider a thick walled cylinder with internal
pressure Piand external pressure Po. Thecylinder has inner radius riand outer radius ro.
The stress analysis in thick cylinder can beobtained using Lames Equation.
2
2
r
BA
and
r
BA
H
R
(1)
(2)
where A and B are constant which may
be found using the boundary conditions.
Thick cylinder
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Boundary conditions
1. Internal and external pressure
at r = ri, R = -pi(pressure being negative sign)and r = ro, R = -po
subtituting these values to equation (1) and (2), we get:
22222
22
22
222
22
22
22
22
22
22
22
)(
)(
)(
io
oioi
io
ooiiH
io
oioi
io
ooiiR
io
ooii
io
oioi
rrr
rrpp
rr
rprp
rrr
rrpp
rr
rprp
sorr
rprpAand
rr
rrppB
2
2
2
2
2
2
2
2
2
2
2
2
111
1
111
1
r
rkp
r
rp
k
r
rkp
r
rp
k
io
oiH
io
oiR
Let the radius ratio ro/ri=k
then
Thick cylinder
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2. Internal pressure only
If the external pressure is atmospheric only,po= 0
2
2
22
2
22
2
2
2
22
2
22
2
1
1
1
11
1
r
r
k
p
r
r
rr
rp
r
r
k
p
r
r
rr
rp
oio
io
iiH
oio
io
iiR
At the inner surface (where r=ri),
Rand Heach have their maximum magnitude.
R=-pi(radial compressive stress)
At the outer surface(where r=ro)
1
20
2 k
pand iHR
i
io
i
io
ioH
prr
k
prr
rr
22
2
22
22
1
Thick cylinder
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Stress distribution for and R
internalpressure=pi
1 2 3
-pi
-1.5pi
-pi
-1.5pi
R
Stress
Thick cylinder
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Maximum shear stress in the cylinder
Maximum shear stress in the plane of the cross section isgiven by,
2
2
max
1
2
r
r
k
p oi
RH
Thick cylinder
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Example:
Given that:
Pi= 20 MPaPo= 10 MPaRi = 100 mm
Ro= 200 mm
Determine the hoop and radial stress atradius 150 mm.
Thick cylinder
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Solution:
2
2
r
BA
and
r
BA
H
R
2
)1.0(
20 B
A
Boundary condition:
At r = 0.1, R= -20 MPa
At r = 0.2, R= -10 MPa
Therefore,
2)2.0(10
BA
(1)
(2)
Solve the equation (1) and (2) simultaneously, we get: :
A = - 6.7
B = 0.133
Thick cylinder
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Substitute all the value A, B and r into the equation, then:
2rBAR
2r
BAH
2)15.0(
133.07.6
2)15.0(
133.07.6
= -12.6 MPa
= -0.79 MPa
Thick cylinder
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Design of thick wall Cylinder
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Thick Cylinder Subject to External
Pressure
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Design of thick cylinder
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d li d
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Compound cylindermade from two
cylinders of different size and could be also
from different materials.
They are used to increased the pressure
that can be obtained in cylinders.
Method of fabrication:
Shrinkage
Force fit
Compound Cylinder
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Compound Cylinder
Compound Cylinder
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The assembly (shrink fit)
Compound Cylinder
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In a compound cylindrical shell, as shown in Fig. the outer
cylinder (having inside diameter smaller than the outsidediameter of the inner cylinder) is shrunk fit over the inner cylinder
by heating and cooling. On cooling, the contact pressure is
developed at the junction of the two cylinders, which induces
compressive tangential stress in the material of the inner cylinder
and tensile tangential stress in the material of the outer cylinder.
When the cylinder is loaded, the compressive stresses are first
relieved and then tensile stresses are induced. Thus, a compound
cylinder is effective in resisting higher internal pressure than a
single cylinder with the same overall dimensions. The principle ofcompound cylinder is used in the design of gun tubes.
Compound Cylinder
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Compound Cylinder
Compound Cylinder
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The method of solution for compound cylinder constructed form similar
material is break the problem down into three separate effects:
(a) shrinkage pressure only on the outside cylinder
(b) shrinkage pressure only on the inside cylinder
(c) internal pressure only on the complete cylinder
Lames equation can be for both inner and outer cylinder.
For each of resulting load, there are two value knows of the radial stress.
Stress Calculation
BC1: shrinkage internal cylinder
At r = ri, R= 0
At r = rc, R= -pc
Compound Cylinder
C d C li d
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BC2: shrinkage external cylinder
At r = rc R= -pcAt r = ro, R= 0
BC3: internal pressure complete cylinder
At r = ri R= -piAt r = ro, R= 0
For each condition, the hoop and radial stress at any radius can be
evaluated.
The various stresses are the combined algebraicallyto produce the stress in
compound cylinder subjected to both shrinkage and internal pressure.
Compound Cylinder
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PRESTRESSTING OF THICK CYLINDER
PRESTRESSTING OF THICK CYLINDER
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PRESTRESSTING OF THICK CYLINDER
Method of Increasing Pressure
Capacity
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COMPOUND CYLINDER
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Autofrettage
In order to use the material effectively and achieve theuniform stress distribution across the cylinder wallthickness, the pre stressing is done to the cylinder
In pre stressing residual compressive stresses are
induced at the inner surface and tensile stresses atouter surface.
When the cylinder is loaded in service the residualcompressive stresses at the inner surface begin to
decrease, become zero and finally become tensile asthe pressure is further increased.
Increase the pressure capacity.
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Autofrettage
Overloading Portion of cylinder near the inner
diameter is subjected to stresses in plastic
range while outer portion still in elastic range.
When the pressure is released the outerportion contracts exerting pressure on the
inner portion which has undergone
permanent deformation. This induces theresidua compressive stresses at the inner
surface and tensile stresses at outer surface.
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COMPOUND CYLINDER
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In a compound cylindrical shell, as shown in Fig. the outer
cylinder (having inside diameter smaller than the outsidediameter of the inner cylinder) is shrunk fit over the inner
cylinder by heating and cooling. On cooling, the contact
pressure is developed at the junction of the two cylinders,
which induces compressive tangential stress in the material of
the inner cylinder and tensile tangential stress in the material of
the outer cylinder. When the cylinder is loaded, the compressive
stresses are first relieved and then tensile stresses are induced.
Thus, a compound cylinder is effective in resisting higher
internal pressure than a single cylinder with the same overalldimensions. The principle of compound cylinder is used in the
design of gun tubes.
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