Design of Pressure Vessel by a.B.solanki

8/11/2019 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



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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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Design of Pressure Vessel by a.B.solanki

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