DESIGN & ANALYSIS OF INDUSTRIAL SPHERICAL PRESSURE …ijirt.org/master/publishedpaper/IJIRT144207_PAPER.pdfClassifications of pressure vessels According to the dimensions 1. Thin shell:

© January 2017 | IJIRT | Volume 3 Issue 8 | ISSN: 2349-6002

IJIRT 144207 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 100

DESIGN & ANALYSIS OF INDUSTRIAL SPHERICAL

PRESSURE VESSEL USING FEA

G.Nagendra1, G Bhemanna2 and Dr P Sampath Rao3 1PG Student,Mechanical Engineering, Vijay Rural Engineering College, Nizamabad, Telangana, India

2Associate Professor, Department of Mechanical Engineering, Vijay Rural Engineering College,

Nizamabad, Telangana, India 3Professor Department of Mechanical Engineering, Vijay Rural Engineering College

Nizamabad, Telangana, India

Abstract—A pressure vessel is a type of container which

is used to store liquids or gases under a pressure different

from the ambient pressure. Different shapes of pressure

vessels exist but most generally cylindrical and spherical

shapes are used. Spherical vessels are theoretically 2

times stronger than cylindrical ones but due to the

manufacturing difficulties, cylindrical ones are generally

preferred in the industry. Mostly the pressure vessels are

thin walled but here we are generating multi layered

wall.

In this project we are designing spherical pressure vessel

by using pro-e and the analysis is done by using ansys.

Here two models are generated one is solid walled which

is regularly used and another one is multi layered

pressure vessel. And the analysis is done on the two

models by changing the actual material with the

composite material. The results are compared actual

solid model with the multi layered pressure vessel and

the comparison further extended to find the better

material for that the actual material results of the model

is compared with the composite material results. By the

comparison we may find better design and the design

proposed to the company.

Index Terms—Friction stir weld, TiAlN Coated tool, Un

– coated welding tool, welding parameters.

I. INTRODUCTION

The main objective of this project is to design a

pressure vessel which is subjected to internal fluid

pressures. This pressure vessel is used to test the

components, which are used in submarine

applications.

The following are determined in design process, The

thickness of the shell wall (t),The diameter of bolt and

number of bolts required for flange and pressure

chamber assembly, The thickness of flange for the

pressure chamber and hemispherical cover plate,

Thicknesses of the end cover plates and The thickness

of the gasket in between the flange and cylindrical

chamber are determined in order to sustain the internal

fluid pressure.

The pressure chambers, when empty are subjected to

atmospheric pressure internally as well as externally.

So the resultant pressure on the walls of chamber is nil.

The component placed in the pressure vessel may fail

in service when subjected to an excessively high

internal fluid pressure.

About pressure vessels

A pressure vessel is a container used to contain things

at more than 15 psi.this means that they can withstand

greater than normal amounts of pressure without

bursting. Pressure vessels are used to contain a

multitude of things, including air, water, chemicals,

nitrogen, and fuel. They are used in paper and pulp,

energy, food and beverage, and chemical industries.

Pressure vessels also frequently control for

temperature as well as for pressure. This is especially

important when they hold more volatile substances.

Gauges on the outside can be read that will show what

the internal pressure and temperature is. If the

substance inside is potentially dangerous, alarms,

pressure releases, and other safety-measures should be

built-in to the pressure vessel.

The fluids being stored may undergo a change of state

inside the pressure vessel as in case of steam boilers or

it may combine with other reagents as in a chemical

plant. The pressure vessels are designed with great

care because rupture of a pressure vessel means an

expression which may cause loss of life and property.



Classifications of pressure vessels

According to the dimensions

1. Thin shell: If the thickness of shell is less

than 1/20th of the diameter of the shell, then the shell

is said to be thin shell.Thin pressure vessels can

withstand only internal fluid pressure, but they cannot

withstand external fluid pressure.

2.Thick shell: If the thickness of the shell is

greater than 1/20th of the diameter the shell, then the

shell is said to be thick shell.

Thick pressure vessels can withstand both internal as

well as external fluid pressure.

According to the internal fluid pressure

1.Thin shell: If the internal fluid pressure (p)

is less than 1/6 of allowable stress (σt), then the shell

is said to be thin shell.

2.Thick shell: If the internal fluid pressure (p)

is greater than 1/6 of the allowable stress (σt), then

the shell is said to be thick shell.

Material selection

The material of pressure vessel may be brittle or

ductile.

1.Brittle material: These materials are weak

in tension, but strong in compression. These materials

fail along a 450 inclined plane.

E.g.: cast iron.

2.Ductile material: These materials are

weak in shear, but strong in tension.

These materials fail by crack formation

along a plane normal to the applied load.

E.g.: Mild steel, copper, brass etc..

a.For boiler tubes, the carbon % used is 0.08

to 0.18.

b.Nickel steel is an alloy of steel, 2% nickel

makes steel more suitable for boilerplates as nickel

increases tensile strength; yield strength, elasticity,

heat resistance and decreases corrosion without

lowering the ultimate strain.

Welded joints

A welded joint is a permanent joint which is obtained

by the fusion of the edges of the two parts to be joined

together, with or without the applications of pressure

and a filler material. The heat required for the fusion

of the material may be obtained by burning of gas (in

case of gas welding) or by an electric arc (in case of

electric arc welding). The latter method is extensively

used because of greater speed of welding.

Welding is extensively used in fabrication as an

alternative method for casting or forging and as a

replacement for bolted and riveted joints.

Welded joint efficiency: Welded joints are not as

strong as the parent plate unless welds are thoroughly

inspected and, if flawed, repaired during manufacture

- all of which is expensive. This strength reduction is

characterized by the weld or joint efficiency, η = joint

strength / parent strength - which varies from 100% for

a perfect weld (i.e. virtually seamless) through 75-85%

for a tolerably good weld. Generally longitudinal or

butt joint is used for getting the required diameter of

pressure vessel.

Longitudinal joint (or) Butt joint

1) Diameter of the rivet: The diameter of rivet

hole is calculated by the empirical relation, d = 6√t.

Where t = thickness of the pressure vessel.

2) Pitch of the rivets: The maximum pitch of

the rivets is given by the empirical relation =

Ct+41.28mm.

Where t = thickness of the shell plate in mm = 8mm.

Assuming two rivets per pitch length,

C = constant=3.06.

3) Distance between rows of rivets:

Assuming riveting to be chain riveting, the distance

between the rows of rivet = 2d

(Where d = diameter of the rivet)

4) Thickness of the butt strap or cover plate

(t1):

t1 = 1.125t (for chain riveting and single

strap butt joint)

Where t = thickness of the shell plate.

5) Margin or marginal pitch (m): Margin or

marginal pitch is the distance between the centers of

the rivet hole to the nearest edge of the plate. Margin

is given by

m = 1.5d

Where d = diameter of the riveted hole.

Rivet materials

Rivets are made of wrought iron or soft steel for most

uses, but where corrosive resistance or light weight is

a requirement, rivets or copper or aluminum alloy are

used. Rivet materials must be strong and highly

ductile, I.S.1960-1962 gives the specifications for

steel rivets and stay bars for boilers. Rivets are used in

such manner that they resist shearing action. However

if the tensile loading is un avoidable the safe tension



value of a rivet may be taken as one half the safe single

shear value.

The materials to be joined and the material used for the

rivet should be carefully considered from the stand

point of electrolytic corrosion in the presence of

moisture. If desired by the purchaser, the rivet shall be

painted with one coat of boiled linseed oil or suitable

preventive material to be agreed mutually between the

supplier and purchaser.

Caulking and Fullering

Joints in pressure vessels like steam boilers, spheres,

air receivers and tanks etc. are made fluid tight by

caulking. A narrow blunt chisel like tool (m) called a

caulking tool, about 5mm. Thick and 38mm in

breadth, the edge ground to an angle of 800. It is

moved after each blow along the edge of the plate,

which is planed to a bevel of 800 to facilitate the

forcing down of edge. It can be noted that the tool

burns down the plate at C forming a metal to metal

joint, care being taken not to damage the plate below

the tool or spring the joint open. Generally both edges

B and C are caulked and the rivet head also as at A.

A more satisfactory way of making the joint staunch

and tight is known as fullering which has largely

superseded caulking. The fullering tool having a

thickness at the end equal to that of the plate, is used

in such a way that the greatest pressure due to the

blows occurs at near the joint giving a clean finish,

with less risk of damaging the plate.

Bolted joints

Initial stresses due to screwing up forces

The following stresses are induced in a bolt, screw or

stud when it is screwed up tightly.

Tensile stress due to stretching of bolt. Since none of

the above mentioned stresses are accurately

determined, therefore bolts are designed on the basis

of direct tensile stress with a large factor of safety in

order to account for the indeterminate stresses. The

initial tension in a bolt, based on experiments, may be

found by the relation

Pi=2840d N

Where,

Pi=initial tension in a bolt, in mm.

d=nominal diameter of bolt, in mm.

The above relation is used for making a joint fluid tight

like steam engine cylinder cover joints etc. when the

joint fluid is not required as tight as fluid tight joint,

then the initial tension in a bolt may be reduced to half

of the above value. In such cases Pi=1420d N.

The small diameter bolts may fail during tightening;

therefore bolts of smaller diameter (less than M16 or

M18) are not permitted in making fluid tight joints.

If the bolt is not initially stressed, then the maximum

safe axial load which may be applied to it, is given by

P= permissible stress*cross sectional area at

bottom of the thread

The stress area may be obtained by stress

area =π/4(dp+dc/2)2

Where,

dp=pitch diameter, and

dc=core or minor diameter.

Stress due to combined forces

The resultant axial load on a bolt depends upon the

following factors

The initial tension due to tightening of the bolt,

The external load, and

The relative elastic yielding (springiness) of the

bolt and the connected members.

When the connected members are very yielding as

compared with the bolt, which is a soft gasket, then the

resultant load on the bolt is approximately equal to the

sum of the initial tension and the external load. On the

other hand, if the bolt is very yielding as compared

with the connected members, then the resultant load

will be either the initial tension or the external load,

whichever load, whichever is greater. The actual

conditions usually lie between the two extremes. In

order to determine the resultant axial load (P) on the

bolt, the following equation may be used

P=P1+(a/1+a)*P2=P1+K.P2

P1=Initial tension due to tightening of

the bolt,

P2=External load on the bolt, and

a=Ratio of elasticity of connected

parts to the elasticity of bolt.

For soft gaskets and large bolts, the value of ‘a’ is high

and the value of a/a+1 is approximately equal to unity,

so that the resultant load is equal to the sum of the

initial tension and the external load.

For hard gaskets or metal to metal contact surfaces and

with small bolts, the value for the resultant load. The

designer thus has control over the influence on the

resultant load on a bolt by proportioning the sizes of



the connected parts and bolts and by specifying initial

tension in the bolt.

The value for soft copper gasket with long through

bolts ranges from 0.50 to 0.75.

Circular flat plates

1. Plates with uniformly distributed load: The

thickness ‘tc’ of the plates of diameter‘d’ supported at

the circumference and subjected to a pressure ‘p’

uniformly distributed over the area is given as :

tc = k1d√(p/ft)

Where ft=allowable design stress

k1 is a coefficient, whose values are

given below. It depends upon the material and method

of holding the edges.

C.I: freely supported, k1=0.54, the maximum stress

occurs at the centre of head.

Fixed k1=0.44, the maximum stress occurs at the edge.

M.S: freely supported, k1=0.42 the maximum stress

occurs at the centre of head.

Fixed k1=0.35 the maximum stress occurs at the edge.

The following equations are used to find the thickness

of the circular plates

tc=√[3F(3+1/m)/8π ft] for plates with edges

freely supported,and tc=√3F/4πft for plates with edges

rigidly fixed,

Where F= total load on the plates=pπr2

1/m =Poisson's ratio.

Hemispherical cover (integral or welded)

tc =p. d/4 ftη.

Flange and bolt (or) stud arrangement

Cover with studs

Thickness of flange, tf = (1.1 to 1.25)*t

= (1.25 to 1.5)*db

The distance, l=t+ db+5

=t+0.5db+5, when nut is spot

faced, so as to keep the arm of the bending moment ‘l’

small.

Design of cylinder covers

The cylinder covers may be secured by means of bolts

or studs, but studs are preferred. The bolts or studs,

cylinders cover plate and cylinder flange may be

designed as discussed below.

In order to find the size and number of bolts or studs,

the following procedure may be adopted.

Let D=Diameter of the cylinder,

p=pressure in the cylinder,

dc=Core diameter of the bolts or studs,

n=Number of bolts or studs, and

σtb=Permissible tensile stress for the

bolt or stud material.

We know that upward force acting on the cylinder

cover,

P=π/4(D)2p

This force is resisted by n number of bolts or studs

provided on the cover.

Therefore resisting force offered by n numbers of bolts

or studs,

P=π/4(dc)2σtb*n

From the above equations we have

π/4(D)2p=π/4(dc)2σtb*n

From this equation the number of bolts or studs may

be obtained, if the size of the bolt or stud is known and

vice-versa. Usually the size of the bolt is assumed. If

the value of n as obtained from the above relation is

odd or a fraction, then next higher even number is

adopted.

The bolts or studs are screwed up tightly, along with

metal gasket or asbestos packing, in order to provide a

leak proof joint. We have already discussed that due to

the tightening of bolts, sufficient tensile stress is

produced in the bolts or studs. This may break the bolts

or studs, even before any load due to internal pressure

acts upon them. Therefore a bolt or a stud less than

16mm diameter should never be used.

The tightness of the joint also depends upon the

circumferential pitch of the bolts or studs. The

circumferential pitch should be between 20√d1 and

30√d1, where d1, is the diameter of the hole in mm for

bolt or stud. The pitch circle diameter is usually taken

as D+2t+3d1 and outside diameter of the cover is kept

as.

Do=Dp+3d1=D+2t+6d1

Where t=thickness of the cylinder wall.

Gasket

A gasket is a relatively elastic or plastic device which

is used to create and maintain a barrier against the flow

of fluids across mating surface of a mechanical

assembly, when the surfaces do not have a relative

motion with respect to each other. The common

example of the gasket is the member placed between

the cylinder block of an engine to make the joint tight.

When the gasket is used, the mating surfaces need not

be accurately machined as in the case of metal joint.



A gasket effects a seal by deforming and filling surface

irregularities of the members between which it is

placed and is, therefore, made of relatively soft

material compared to flange mating surfaces.

Although a seal can be obtained without the use of

gasket, it provides the following extra advantages:

It promotes the efficient initial seal.

It prolongs the useful life of an assembly.

It acts as a calking compound in compensating for

errors and irregularities in joined rigid members

of an assembly.

The joint should be designed and constructed to make

the best use of the properties of the gasket. Hence Joint

and gasket design must be considered together. The

forces acting on the gasket are quite complex and

variable. Some of these may be summarized as: bolt

squeeze on gasket, fluid pressure, due to

environmental conditions. Also misalignment, gravity

and thermal movement try to separate faces.

The two basic types of joints are

a) Basic flange joints

b) Metal to metal joints

The flange joint are suitable for all kinds of flat

gaskets. simple flange joint, is suitable for pressures

up to 1.5N/mm2. For higher fluid pressures, the

reduced section joint, and tongue and groove joint, are

preferred.

In reduced section joint, the gasket wall section has

been reduced to give a high gasket stress without

change in bolt stress. The tongue and groove joint is

used for applying extremely high stress to gasket, and

for holding extremely high pressures.

Metal to metal joints are suitable for compressible

material such as cork and rubber. These are useful for

limiting the amount of stress on the gasket and are

particularly good where it is essential to maintain

accurate internal clearances or alignments.

The choice of gasket material for any application

depends upon:

(1) Operating conditions

(2) Mechanical features of the flange

assembly

(3) Gasket characteristics.

The gasket material must meet the following

requirements

(a) Impermeability

(b) Ability to flow into joint imperfections

when compressed

(c) Maintain seal inspite of age, and

variations in temperature and pressure.

(d)Resistance to environmental deterioration.

Depending upon the materials, the gaskets may be

grouped as below

(1) Metallic gaskets.

(2) Non-metallic gaskets.

Non-metallic gaskets are used for low pressures

whereas for high pressures and under severe condition,

metallic or combination gaskets are used. A rough

guide as to whether a metallic or non metallic gasket

should be used for given condition is: If (operating

pressure in N/mm2 *operating temperature in oc is

>900 only metallic gaskets should be used.

Generally, a non-metallic gasket should not be used

for pressures in excess of about 8.7 N/mm2 and

temperatures above 450oc and below -18oc.

The most common composites for non-metallic

gaskets can be written as below

Asbestos products can work efficiently up to a

temperature of about 260oc. these gaskets are tough

and durable and dimensionally stable. These are used

for heavy duty bolted and threaded joints as in water

and steam pipe fitting, manifold connections, etc.

Cork is lightweight, non-capillary, does not deteriorate

with age, practically inert, and has a high coefficient

of friction. It has excellent oil and solvent resistance

but poor resistance to alkalies and corrosive acids.

These gaskets are used for mating rough or irregular

parts, such as glass, light stamping, unfinished casting;

etc. Temperature limit about 70oc Metallic gaskets

may be made of the following metals lead, brasses,

copper, aluminum, soft iron, low carbon steel,

stainless steel, titanium, silver, nickels, Monel and

Inconel.

Metallic gaskets fall into several basic groups:

1. Corrugated or embossed, thin metal.

2. Metal jacketed, soft metal.

3. Spiral wound.

4. Plain or machined flat metal.

5. Round cross section, solid metal.

6. Special, heavy cross-section, solid metal.

7. Pressure actuated, light cross section.

Gasket joints: In bolted assembly of cylinder, cylinder

head and gasket initially the bolt is tightened by a

spanner to induce a preload Pl.. The stiffness or spring

constant k of a machine element is the load required to

produce unit deflection. It is given by the ratio of the



load to the deflection produced by that load. When a

machine member is loaded in tension or compression,

δ=P/k (or)

k=P/ δ= AE/l

The stiffness of the bolt is given by

kb=(πd2/4)E/l

Where

kb= stiffness of the bolt (N/mm)

d=nominal diameter of the bolt (mm)

l=total thickness of the parts held

together by the bolt (mm)

E=modulus of elasticity of bolt

material (N/mm2)

There are three members in the grip of the bolt –

cylinder cover, cylinder flange and gasket. They act as

three compression springs in series. Their combined

stiffness kc is given by

1/kc= 1/k1 +1/k2 + 1/kg

Where k1 and k2 are the stiffness of the cylinder cover

and the cylinder flange respectively and kg is the

stiffness of the gasket. It is difficult to predict the area

of flanges compressed by the bolt. It is assumed that a

hollow circular area of 3d and d as outer and inner

diameters respectively is under the grip of the bolt.

A= π/4[(3d)2-d2]=2πd2 and

k=AE/l= 2πd2E/t

k= 2πd2E/t

Where t is thickness of the member under

compression.

When the gasket is very soft relative to the flanges, it

is the gasket which is compressed during the

tightening of bolt. In such cases, the flanges are

neglected and the stiffness of the gasket is considered

to be kc.

Danger of pressure vessels

Because they are containing substances at greater than

normal pressures, upkeep and maintenance of the

vessels is very important. If they were to rupture, not

only would the vessel be damaged (and would

probably be unsalvageable) but injury could result due

to shrapnel and dangerous chemicals. It is important to

buy pressure vessels that have been approved by the

ASME as safe. These have been inspected and

conform to industry-wide standards of strength.

Corrosion

In design, corrosion which occurs over the life of a

vessel is catered for by a corrosion allowance, whose

design value depends upon the vessel duty and

contents' corrosiveness - for example 1 mm is typical

for air receivers in which condensation of air moisture

is normally inevitable. It is important to realize that

when dimensions in any formula refer to a corrodible

surface, then the dimensions inserted into the formula

are those at the end of the vessel's life, when all the

corrosion allowance has been eaten away. So, if a plate

is of nominal thickness T now, and is subject to

corrosion on one side, then (T - c ) must be substituted

whenever nominal thickness appears in an equation.

Similarly a tube of current bore Di which corrodes will

have a bore of (Di + 2c) at the end of its life.

Failures of pressure vessel

Fig.1.1 Failure of a cylindrical shell along the

longitudinal section

The above figure 1.1 shows the failure along the

longitudinally section(i.e. circumferentially) splitting

the cylinder into two troughs i.e. it might fail by

bursting along a path following the circumference of

the cylinder, under normal circumstance it fails by

bursting along a path parallel to the axis. This indicates

that hoop stress is significantly higher than axial stress

Fig.1.2 Failure of cylindrical shell along the transverse

section

The failure across the transverse section (i.e.

longitudinally) splitting the cylinder into two

cylindrical shells as shown in fig 1.2.



Literature review

The main theme of the presented work is to design a

pressure vessel which is subjected to internal fluid

pressure .This pressure vessel is used to test the

components, which are used in submarine

applications. The some of the researches are worked

on the pressure vessels and related areas and few them

discussed below.

II. BRIEF OVERVIEW OF RELATED

RESEARCH

David Heckman1 et.al (1998) Finite element analysis

is an extremely powerful tool for pressure vessel

analysis when used correctly. Tested models were run

with errors ranging from seven to nearly zero percent

error and could be run in a relatively short time.

However, even with such results the operator still is

required to be knowledgeable of not just how to run

the finite element analysis, but also how to read the

results. Data must be verified with hand calculations

to confirm that solutions are relatively accurate.

Where results are questionable, such as in the final

contact element model, one must understand just what

the finite element model is modeling and how well this

approximates the actual subject. For this pressure

vessel, the model had a sharp corner, where in the

actual pressure vessel there is a small radius which

reduces the stress. For pressure vessels finite element

analysis provides an additional tool for use in analysis.

However, it must be compared to other available data,

not taken as being correct just because it looks right.

Used with this understanding, finite element analysis

offers great insight into the complex interactions found

in pressure vessel design

Farhad Nabhani2 et.al Three main factors are seen to

contribute extensively to the development of stresses

in pressure vessels. These are thickness, nozzle

positions and the joints of the enclosure heads. From

the model design cases used in this research, it could

be seen that as the thickness of pressure vessel

increases, the stresses decreases, however this is not a

viable solution due to cost. Nozzles though are safety

relief devices and important component of pressure

vessels comes with its own disadvantages of

increasing weak areas and stress concentration.

However, this was mitigated by use of high alloy

reinforcement pads as applied in the design case two

and three of this work. The high strength

reinforcement pad used has a chemical composition of

titanium 0.4 to 1.20%; hollow disc shaped with

rectangular section can also reduce the stresses

concentration around the nozzle. Finally, the joints of

enclosure heads either welded or bolted were

identified as areas with the highest concentration of

stresses i.e. with peak stress. Addition of 254 mm skirt

length at the end of enclosure heads provide more

room for the stresses to develop slowly in the wall of

the head regions, thus making the pressure vessels

more resistant to the loadings.

Siva Krishna Raparla13 et.al The theoretical values

and ANSYS values are compared for both solid wall

and multilayer pressure vessels. There is a percentage

saving in material of 26.02% by using multilayered

vessels in the place of solid walled vessel. This

decreases not only the overall weight of the

component but also the cost of the material required to

manufacture the pressure vessel. This is one of the

main aspects of designer to keep the weight and cost

as low as possible. The Stress variation from inner side

to outer side of the multilayered pressure vessel is

around 12.5%, where as to that of solid wall vessel is

17.35%. This means that the stress distribution is

uniform when compared to that of solid wall vessel.

Minimization of stress concentration is another most

important aspect of the designer. It also shows that the

material is utilized most effectively in the fabrication

of shell. Theoretical calculated values by using

different formulas are very close to that of the values

obtained from ANSYS analysis. This indicates that

ANSYS analysis is suitable for multilayer pressure

vessels.Owing to the advantages of the multi layered

pressure vessels over the conventional mono block

pressure vessels, it is concluded that multi layered

pressure vessels are superior for high pressures and

high temperature operating conditions.

Shaik Abdul Lathuef4 et.al In the past several years

there have been significant changes to the American

Society of Mechanical Engineers (ASME)Boiler and

Pressure Vessel (B&PV) Code and the use of

international pressure vessel codes such as EN13445.

This paper discusses some of the potential unintended

consequences related to Governing Thickness of shell

as per ASME. Here have a scope to change the code

values by take the minimum governing thickness of



pressure vessel shell to the desired requirements and

also relocate of nozzle location to minimize the

stresses in the shell. A low value of the factor of safety

results in economy of material this will lead to thinner

and more flexible and economical vessels. Here we

evaluated the stress in the vessel by Zick analysis

approach.A numerical design study was performed to

examination structural failure of pressure vessels

exposed to internal pressure by varying the shell

thickness and nozzle location. By inspecting these

plots it apparent that the minimum thickness 8mm will

taken safe for design conditions.

Bandarupalli Praneeth5 et.al The main objective of this

paper is finite element analysis of pressure vessel and

piping design. Features of multilayered high pressure

vessels, their advantages over mono block vessel are

discussed. Various parameters of Solid Pressure

Vessel are designed and checked according to the

principles specified in American Society of

Mechanical Engineers (A.S.M.E)Sec VIII Division 1.

Various parameters of Multilayer Pressure vessels are

designed and checked according to the principles

specified in American Society of Mechanical

Engineers (A.S.M.E)Sec VIII Division 1.The stresses

developed in Solid wall pressure vessel and Multilayer

pressure vessel is analyzed by using ANSYS, a

versatile Finite Element Package. The theoretical

values and ANSYS values are compared for both solid

wall and multilayer pressure vessels

III. OBJECTIVE OF THE WORK

The main objective of this project is to design a

pressure vessel using Ansys. This pressure vessel has

to withstand an internal fluid pressure of 75 bar.

Design the thickness of plate material and also

thickness of the hemispherical cover plate.

Finally the Von-Mises stresses are found in the

pressure vessel. The design should be safe for the

applied load.

IV. METHODOLOGY

To achieve the above objective the following

methodology has been adopted in the present work.

A pressure vessel which will withstand a pressure

of 75bar has been theoretically designed.

Modeling of the pressure vessel is done using pro-

E

The model is imported to Ansys and analysis is

preformed as follows.

Shell element is chosen & a real constant of 3mm

is added which is the thickness of the shell.

Material properties are added.

Meshing is done, finally the boundary conditions

are applied & it is solved.

After solution the results are viewed in general

postprocessor.

Then the results from the analytical method & the

Ansys are compared.

The shear stress induced in the plate is less than

allowable stress in the plate material. Hence the

design is safe.

V. DESIGN OF PRESSURE VESSEL

Thin cylindrical pressure vessel

The analysis of stresses in the thin cylindrical shell is

made on the following assumptions.

1. The normal stress (tensile or compressive) is

uniformly distributed over the thickness of wall.

2. The stress along the radial direction will be small

and negligible.

3. Thickness is small compared to radius.

4. There are no discontinuities in curves.

5. Bending of the wall of the shell is neglected.

6. Shear stress across a cross section is negligible.

Stresses

1. Hoop stress or circumferential stress (σh).

2. Longitudinal stress (σl).

3. Radial stress is zero.

Strains

1. Hoop Strain (Єh).

2. Longitudinal Strain (Єl).

Hoop strain (єh): Єh= (σh/E)-(σl/mE)

Therefore Єh= (pd/2tE) (1-1/2m)

Longitudinal strain (єl): Єl=(σl/E)-(σh/mE)

Therefore Єl=pd/2tE {(1/2)-(1/m)}

Volumetricstrain(єv):δv/v=Єv=(δl/l)+2(δd/d)orЄv=Є+2

Єh

Єv=pd/2tE{(5/2-2/m)}.

Thick cylindrical pressure vessel

The analysis is made on the following Lame’s

assumptions:

1. The material is homogeneous and isotropic.



2. Plane sections of the cylinder perpendicular to the

longitudinal axis remain plane under the pressure i.e..,

longitudinal strain independent of radius.

3. Longitudinal stress is assumed to be zero.

Stresses in Thick vessels:

1. Hoop/tangential stress (σh).

2. Radial stress (σr).

Design equations for thick vessels:

Lame’s equation:

Hoop stress, σh =a+b/x2

Radial stress,σr = a-b/x2

For internal fluid pressure, σh is tensile and σr is

compressive.

Special cases:

Internal pressure =p; external pressure =0

Hoop stress σh= p (ri)2/(ro)2-(ri)2[1+ (ro)2/x2]

Radial stress σr=p (ri)2/(ro)2-(ri)2[1+ (ro)2/x2]

Birnie’s equation:

According to maximum strain theory, the failure

occurs when the strain reaches a limiting value.

Birnie’s equation for the wall thick of the cylinder is

t=ri [√ (σt+ (1-μ)p)/ (σt - (1+μ) p)-1]

The above equation is applicable to open ended

cylinders (such as gun barrels, rams, pump cylinders)

Clavarino’s equations:

This equation is also based on the maximum strain

theory of failure. According to this equation the

thickness of a cylinder is

t=ri [√(σt+(1-2μ)p)/ (σt -(1+μ)p)-1]

Barlow’s equations:

This equation is generally used for high pressure oil

and gas pipes. According to this equation the thickness

of a cylinder is

t=pro/σt

According to maximum shear stress theory:

τmax = [σt(max) - σt(min) ]/2 from which the thickness

of the cylinder is

t=ri[√ (ז/ז-p)-1]

Where τ = σt/2

t=ri [√(σt/σt-2p)-1]

Longitudinal strain:

єl = (σi –νσh-νσr)= constant

Where ν = Poisson’s ratio.

Hoop strain: It is used to determine the change in the

diameter of the pressurevessel which is subjected to

internal pressure.From the above strains we calculate

the volumetric change in the pressure vessel єv =

2(δd/d)+ δl/l.

Problem Description:

Material = mild steel

Height of the cylinder = 400 mm

Young’s modulus (Ε) = 207Gpa =207000N/mm2

Poisson’s ratio (μ) = 0.3 ;Yield strength (σy) =400Mpa

Hemispherical Cover Plate

Flange

Fig.Thickness of hemispherical cover plate

The above figure 3.3 shows the Hemispherical cover

plate, the thickness of the cover plate obtained by

analytical calculation is 3.75mm. But, it is

approximated to 4mm, as this is the standard thickness

available.

Longitudinal joint or Butt joint

Longitudinal joint or butt joint is used to get the

required diameter of the pressure vessel. For this

purpose riveted joints are used along with caulking

and fullering in order to make the joints leak proof.

1) Diameter of the rivet:

The diameter of rivet hole is calculated by the

empirical relation, d = 6√t.

Where t = thickness of the pressure vessel =

8mm

Therefore, d = 6√8 = 17mm.

But the next available diameter of the rivet, d = 18mm

The corresponding diameter of the rivet hole = 19mm

2) Pitch of the rivets:

The maximum pitch of the rivets is given by the

empirical relation,



P = Ct+41.28mm

Where t = thickness of the shell plate in

mm = 8mm.

Assuming two rivets per pitch length, C =

constant=3.06

Therefore pitch, P = 3.06*8+41.28 = 65.76mm

= 66mm (approx).

3) Distance between rows of rivets:

Assuming riveting to be chain riveting, the distance

between the rows of rive = 2d

(Where d = diameter of the rivet)

= 2*18= 36mm

4) Thickness of the butt strap or cover plate (t1):

t1 = 1.125t (for chain riveting and single strap butt

joint) Where t = thickness of the shell plate.

t1 = 1.125*8 = 9mm.

5) Margin or marginal pitch (m):

Margin or marginal pitch is the distance between the

centers of the rivet hole to the nearest edge of the plate.

Margin is given by

m = 1.5d

Where d = diameter of the riveted hole = 18mm

m = 1.5*18 = 27mm.

Design of gasket

Assuming ‘Silicone’ as a gasket material because it

has high performance against high temperature and

low temperature applications.

There are three members in the grip of the bolt. They

are cylinder cover, cylinder flange and gasket. They

act as three compression springs in series. Their

combined stiffness ‘kc’ is given by

1/kc = 1/k1+1/k2+1/kg

Where ‘k1’ and ‘k2’ are the stiffness of the cylinder

cover and the cylinder flange respectively and kg is the

stiffness of the gasket.

k1 = k2 = 2πd2Ef/tf

kg = 2πd2Eg/tg

Where ‘tf’ and ‘tg’ are the thicknesses of cylinder

flange and gasket respectively and d is the diameter of

the bolt.

tf = 10mm

d = 18mm.

tg is to be calculated.

Young’s modulus of

1) Bolt Eb = 207GPa = 207000MPa

2) Gasket Eg = 1200*103 lb/in2

=1200*6.8947Mpa(1000lb/in2=6.8947MPa)

= 8273.64MPa

Stiffness of the bolt, kb = (π/4)d2*Eb/l

Where Eb = Young’s modulus of bolt material

= 207000MPa

L = combined thickness of the three members in series

= 10+tg+10 = 20+tg

Therefore kb = (π/4)*182 *207000/(20+tg)

= 52675084.02/(20+tg)

kg=2πd2Eg/tg=2π*182*8273.64/tg=16843079.

5/tgN/mm

k1 = k2 = 2πd2Ef/tf = 2π*182*207000/10

= 42140067202N/mm

but K = 0.75 = kc/(kc+kb)

Therefore kc/kb = 3

Kc = 3kb = 3*52675084.02/(20+tg)

= (158.025*106)/(20+tg)

Therefore, 1/kc = 1/k1+1/k2+1/kg

(20+tg)/(158.025*106) = {(1/421.4)+(tg/16.843)}/(106)

20+tg = 0.75+9.3822tg

19.25 = 8.3822tg

tg = 2.29mm

= 3mm (approx)

Therefore the thickness of the gasket is found to be tg

= 3mm

VI. MODELLING AND ANALYSYS OF

PRESSURE VESSEL

Modelling software

There are different software’s available for modelling.

Some of them are

Solid works

1. Pro-E

2. Ideas

3. Inventor

4. Mechanical Desktop

5. Unigraphics

6. Catia

Pro-E is used as the modelling tool in this project

which is discussed as follows.

Introduction of PRO-E

The Pro-E provides the power of parametric design.

With parametrics, we define the model according to

the size, shape and positional relationship of its parts.

Part modeling

Many mechanical designs consist of complex

assemblies made from angular shaped parts. This type

of design work can be made easier by part and

assembly modeling capabilities that are well

integrated. The Pro-E is a 3D parametric solid modeler



with both part and assembly modeling abilities. You

can use the Pro-E to model piece parts and then

combine them into more complex assemblies.

With Pro-E, you design a part by sketching its

component shapes and defining their size, shape, and

inter-relationships. By successively creating these

shapes, called features, you construct the part in a

building block fashion.

Because the Pro-E has parametric features, you can

change one feature and all related features are

automatically updated to reflect the change and its

effects throughout the part.

The Pro-E can be used to create angular shaped parts,

to which you can apply 3D surfaces to create hybrid

parts consisting of a mixture of angular and curved

shapes. The Pro-E provides the ability to create mode

designs with shapes of varying types.

You can apply surfaces to Pro-E parts and use them to

cut material from a solid to create the hybrid shapes

that your design requires.

Follow the same general modeling process for each

Part :

Plan the part

Create the base feature

Create the remaining features

Analyze the part

Modify the features as necessary

Assembly Modeling

You create assemblies from parts, either combined

individually or grouped in subassemblies. The Pro-E

builds these individual parts and subassemblies into an

assembly in a hierarchical manner according to

relationships defined by constrains.

As in part modeling, the parametric relationship

allows you to quickly update an entire assembly based

on a change in one of its parts.

We can also use the Pro-E to create subassembly and

assembly models from previously made parts. You can

build 3D solid assembly models from two or more

parts or subassemblies. Like part features, parts and

subassemblies act as building blocks.

The general process used to build assemblies and

subassemblies is similar to that for building parts :

Lay out the assembly

Create the base part

Create and attach the remaining parts

Analyze the assembly

Modify the assembly as necessary.

Fundamental

Pro-E employs two operating modes for part

modeling, Model mode for modeling 3D parametric

parts and Drawing mode for creating 2D drawings of

them. These modes operate independently but share

the same design data. You can switch back and forth

between modes at any time. Part modeling requires

you to begin your design work in Model mode where

you immediately build a model of the part. You then

use Drawing mode at any point to document the

design.

In traditional computer-aided design, you began by

creating a 2D drawing and then building a 3D model

to analyze, verify and refine the initial concept. With

Pro-E, you are not limited to using 2D drawings to

stimulate thinking about 3D design concepts. Pro-E

recognizes and supports the creation of models and

drawings in their natural order.

Design process

The process to build a Pro-E part is same for all as

described below.

Layout the part

Creating the base feature

Creating the remaining part features

Modify the features as necessary

Half of the sketch of the model is generated and it is

revolved to get the solid model. It is converted into a

iges file and is imported into Ansys.

The drawing views are to be identified and the Pro-E

software automatically removes the hidden lines and

also places the dimensions on the drawing. Changes

made to the part update the drawing also.

A sketch plane is a planar surface or workplace on the

active part, in a 3D space. New features are sketched

on this plane. All the profiles must lie on the active

sketch plane.



The solid modelling of pressure vessel, which is done

pro_e modeling software as shown in fig4.1.

Finite element method

The finite element is a mathematical method for

solving ordinary and partial differentials equations.

Because it is a numerical method, it has the ability to

solve complex problems that can be represented in

differential equation form. As these types of equations

occur naturally in virtually all fields of the physical

sciences, the applications of the finite element method

are limitless as regards the solution of practical design

problems.

Due to high cost of computing power of years gone by,

FEA has history of being used to solve complex and

cost critical problems. Classical methods alone usually

cannot provide adequate information to determine the

safe working limits of a major civil engineering

construction or an automobile or an aircraft. If a tall

building, a large suspension bridge or an automobile

or a nuclear reactor failed catastrophically, the

economic and social cost would be unacceptably high.

In recent years, FEA has been used almost universally

to solve structural engineering problems. One

discipline that has relied heavily on this technology is

the automotive and aerospace industry. Due to the

need to meet the extreme demands for faster, stronger,

efficient and light weight automobiles and aircrafts,

manufacturers have to rely on the technique to stay

competitive. But more importantly, due to safety, high

manufacturing costs of components and the high

media coverage that the industry is exposed to,

automotive and aircraft companies need to ensure that

none of their components fail, that is to cease

providing the services that the design intended.

FEA has been used routinely in high volume

production and manufacturing industries for many

years, as to get a product design wrong would be

detrimental. For example, if a large manufacturer had

to recall one model alone due to a piston design fault,

they would end up having to replace up to 10 million

pistons. Similarly, if an oil platform had to shut down

due to one of the major components failing (platform

frames, turrets, etc), the cost of lost revenue is far

greater than the cost of fixing or replacing the

components, not to mention the huge environmental

and safety costs that such an incident could incur.

The finite element is a very important tool for those

involved in engineering design; it is now used

routinely to solve problems in the following areas:

Structural strength design

Structural interaction with fluids flows

Analysis of shock (underwater and in materials)

Acoustics

Thermal analysis

Vibrations

Crash simulations

Fluid flows

Electrical analysis

Mass diffusion

Buckling problems

Dynamic analysis

Electromagnetic evaluations

Metal forming

Coupled analysis

Nowadays, even the most simple of products rely on

the finite element for design evaluation. This is

because contemporary design problems usually cannot

be solved as accurately and cheaply using any other

method that is currently available. Physical testing was

the norm in years gone by, but now it is simply too

expensive and time consuming.

More about FEA

Finite element analysis was first developed for use in

the aerospace and nuclear industries where the safety

of structures is critical. Today, the growth in usage of

the method is directly attributable to the rapid

advances in Computer technology in recent years. As

a result, commercial finite element packages exist that

are capable of solving the most sophisticated

problems, not just in structural analysis, but for a wide

range of phenomena such as steady state and dynamic

temperature distributions, fluid flow and

manufacturing process such as Injection moulding and

metal forming.

FEA consists of a computer model of a material or

design that is loaded and analyzed for specific results.

It is used in used in new product design, and existing

product refinement. A Design Engineer shall be able

to verify a proposed design, which is intended to meet

the customer specifications prior to manufacturing or

Construction.

Things such as, modifying the design of an existing

product or structure in order to qualify the product or



structure for a new service condition. Can also be

accomplished in case of structural failure. FEA may be

used to help determine the design modifications to

meet the new condition.

The basic steps involved in ‘FEA’

Mathematically, the structure to be analyzed is

subdivided into a mesh of finite sized elements of

simple shape. Within each element, the variation of

displacement is assumed to be determined by simple

polynomial shape functions and nodal displacements.

Equations for the strains and stresses are developed in

terms of the unknown nodal displacements. From this,

the equations of equilibrium are assembled in a matrix

from which can be easily be programmed and solved

on a computer. After applying the appropriate

boundary conditions, the nodal displacements are

found by solving the matrix stiffness equation. Once

the nodal displacements are known, element stresses

and strains can be calculated.

Within each of these modeling schemes, the Engineer

can insert numerous algorithms (functions) which may

make the system behave linearly or non linearly.

Linear systems are far less complex and generally

ignore many subtleties of model loading and behavior.

Non linear systems can account for more realistic

behavior such as plastic deformation, changing loads

etc. and is capable of testing a component all the way

to failure.

The following are the five basic steps involved in an

FEA analysis:

1. Discretization of the domain

2. Applications of field/boundary conditions

3. Assembling the system equations

4. Solution for the system equations

5. Review of results

Let us understand the above five steps one by one

sequentially and see what it really means to an

Engineer.

Discretization of the domain

Here the task would be to divide the continuum under

study into a number of subdivisions called elements.

Based upon the geometry, the continuum or the system

under study can be divided into a numbers of elements

.FEA permits us to do so!

• If the continuum is a single point it can discretized

using point elements.

• If the continuum is 1D it can be discretized using line

elements.

• If the continuum is 2D it can be discretized using

area elements.

• If the continuum is 3D it can be discretized using

volume elements.

Once the discretization is done, we shall include

the known field/boundary conditions which shall

serve as references and help us in solving for the

unknowns.

Once the reference or known conditions are

imposed, we shall define sets of equations which

are suitable to define the behavior of system. This

involves formulation of respective characteristic

(stiffness in case of structural ) equation matrices.

Once the equations are set up we shall solve the

same to know the unknowns and get insight into

system behavior. That is basically the system of

matrices which are nothing but a set of

simultaneous equations are solved.

Upon the completion of solution, we shall review

the results.

When we use CAE software either developed in house

of commercially available, the first three steps are

called as pre- processing phase, the fourth phase is

called solution phase and the fifth phase is called post-

processing phase. Since FEA involves matrix

operations, it was referred to as Matrix methods for

structural analysis, in the initial days where it was used

only for structural behavior simulations.

Despite the proliferation and power of commercial

software packages available, it is essential to have an

understanding of the technique and physical processes

involved in the analysis. Only then can an appropriate

and accurate analysis model be selected, correctly

defined and subsequently interpreted.

Before proceeding further to learn more, we shall

familiarize our selves with the following:

What is an element?

Element is an entity, into which a system under study

can be divided into. Nodes can specify an element

definition. The shape (area, length and volume)

element depends upon the nodes with which it is made

up of.

What are nodes?

Nodes are the corner point of an element. Nodes are

independent entities in space. These are similar to

points in geometry. By moving a node in space an

element shape can be changed.

Procedure for finite element analysis



ANSYS is a general purpose finite element modeling

package for numerically solving a wide variety of

mechanical problems. These problems include:

static/dynamic structural analysis(both linear and non-

linear), heat transfer and fluid problems, as well as

acoustic and electro-magnetic problems. Basically

there are four stages which are to be executed while

solving any simulation problem by using ANSYS.

They are as follows

Preferences:

In this stage, the option structural is selected out of

structural, thermal, Ansys fluid because the problem to

be solved belongs to structural category.

Preprocessor:

In this stage, the following steps are executed.

1) Initially, geometry of required size and shape is

build or imported from other CAD files.

2) Depending upon the geometry, element shape is

selected i.e.., for the current problem ‘SHELL-93’

is selected.

3) Inputting the real constants such as thickness of

the shell (t=8mm), thickness of the circular flat

plate (=34mm), thickness of the flange (=10mm),

thickness of the hemispherical cover plate

(=4mm).

4) Defining the element material and its properties.

E.g. Either isotropic or composite material, etc.

For the present problem Isotropic material (Mild steel)

is selected whose material properties are Poisson’s

ratio (μ=0.3), Young’s modulus (E=207GPa).

5) Finite Element Modeling.

Solution:

In this stage the type of analysis is selected. Again in

which either ‘STATIC’ or ‘DYNAMIC’ option is

selected.

For E.g. Structural, Thermal, etc.

For the current problem the option structural along

with static is selected because the pressure vessel is

designed for static pressure load.

A pressure of 7.5bar is applied on the inner walls of

the pressure vessel and degrees of freedom are arrested

wherever required. Finally the option ‘solve current

LS’ is executed.

General postprocessor:

In this stage, results are viewed and plotted.

Time history postprocessor:

By executing this option, graphs are plotted.

For e.g. Displacement vs time, etc are plotted.

2.1 Structural Analysis of spherical pressure vessel

with hydrostatic pressure.

Fig 1.Vector sum displacement Fig 2. Von-misses

stresses

Structural Analysis of spherical pressure vessel with

burst pressure


stresses

Structural Analysis of dished end of the multi layer

pressure vessel with hydrostatic pressure 27.3 N/mm2


stresses


pressure vessel with burst pressure 64.52 N/mm2



Fig 7.Vector sum displacement Fig 8.Von-misses


pressure vessel with hydrostatic pressure 27.3 N/mm2

Fig. 9.Vector sum displacement Fig10.Von-

misses stresses


pressure vessel with burst pressure 64.52 N/mm2

Fig 11.Von-misses stresses

.

VII. CONCLUSION

The following conclusions have been drawn from the

present work.

1. At present multilayered vessels are being used

extensively in many industries when compare to

solid wall pressure vessels. Because, there is a

huge difference in weight of the vessel and

uniform stress distribution among the vessel wall

thickness.

2. There is a percentage saving in material of

28.48% by using multilayered vessels in the

place of solid walled vessel when both the

vessels are manufactured with same material i.e.

SA515 Grade 70 steel .

3. There is a percentage saving in material of

91.62% by using multilayered CFRP material

vessels when compared to multilayered SA515

Grade 70 steel material vessels.

4. This decreases not only the overall weight of the

component but also the cost of the material

required to manufacture the pressure vessel. This

is one of the main aspects of designer to keep the

weight and cost as low as possible.

5. The Stress variation from inner side to outer side

of the multilayered pressure vessel is around

11.76%, where as to that of solid wall vessel is

17.32%. This means that the stress distribution is

uniform when compared to that of solid wall

vessel.

6. Minimization of stress concentration is another

most important aspect of the designer. It also

shows that the material is utilized most

effectively in the fabrication of shell.

7. Owing to the advantages of the multi layered

pressure vessels over the conventional single

walls pressure vessels, it is concluded that multi

layered pressure vessels are superior for high

pressures and high temperature operating

conditions.

8. The burst pressures for various fiber orientations

are predicted using the Tsai-Wu failure criteria.

The ± 25° fiber orientation angle is obtained as

the optimum fiber orientation angle for the

composite pressure vessel subjected to high

internal pressure loading.

FUTURESCOPE

1. Analysis on different layer materials to reduce

cost of production

2. Optimization of shell thickness for the given

conditions

REFERENCES

[1] “Finite Element Analysis of Pressure Vessels”

David Heckman, University of California,



Davis Mentor: Gene Massion, Mark Greise

Summer 1998

[2] “Reduction of Stresses in Cylindrical Pressure

Vessels Using Finite Element Analysis” Farhad

Nabhani, Temilade Ladokun and Vahid Askari

Teesside University, School of Science and

Engineering, Middlesbrough, TS1 3BA, UK.

[3] “Design and analysis of multilayer high

pressure vessels” department of mechanical

engineering qis college of engineering

&technology ongole, andhra Pradesh.

[4] “Design and structural analysis of pressure

vessel due to change of nozzle location and

shell thickness” shaik abdul lathuef department

of mechanical engineering, qis college of

engineering and technology, ongole, andhra

pradesh.

[5] “Finite Element Analysis of Pressure Vessel

and Piping Design”Bandarupalli Praneeth,

Dept. of M.E, Nimra Institute of Science &

Technology, Vijayawada, A.P., India

[6] Mechanics of solids by ROGER .T. FENNER.

[7] Machine Design by SHIGLEY.

[8] Mechanics of solids by EGOR. POPOV

[9] Machine Design by Dr.P.C.SHARMA &

Dr.D.K.AGGARWAL.

[10] Machine Design by V.BHANDARI.

[11] Strength of materials by B.C.PUNMIA.Design

Data book by P.S.G.

[12] Mechanics of solids by SADHU SINGH

[13] www.pressurevessels.com

[14] www.thick pressurevessels.com

Documents

DESIGN & ANALYSIS OF INDUSTRIAL SPHERICAL PRESSURE …ijirt.org/master/publishedpaper/IJIRT144207_PAPER.pdfClassifications of pressure vessels According to the dimensions 1. Thin shell: