STRUCTURAL AND STATISTICAL ANALYSIS OF HORIZONTAL SPHERICAL END PRESSURE … · 2018-05-06 · system and also an agitator system. High Pressure vessels are used for a pressure range

STRUCTURAL AND STATISTICAL ANALYSIS OF

HORIZONTAL SPHERICAL END PRESSURE VESSEL

Dr.T.Mothilal1, A.K.Manikandan

2, B.Aravind

3, J.Jayakumar

4, S.Arokyaraj

5S.Kaliappan

6M.D.Rajkamal

7

1 Professor, Velammal Institute of Technology, Chennai, India, [email protected]

2345 UG Students,Department of Mechanical Engineering, Velammal Institute of Technology, Chennai, India,

6Associate Professor, Department of Mechanical Engineering, Velammal Institute of Technology , Chennai-601204, India. 7Assistant Professor, Department of Mechanical Engineering, Velammal Institute of Technology, Chennai-601204, India.

Abstract— Pressure vessels are closed containers used

for handling and storing the fluids, chemicals and

gaseous things at high pressure are used in fertilizer

industries, petroleum and petro-chemical industries for

performing various operations. To improve the

withstanding capacity of the pressure vessels, in this

paper the material of the pressure vessel is changed to

Duplex2205 stainless steel. It will reduce the weight of

the pressure vessel and increase the withstanding

capacity of the pressure vessels. The significance of the

project comes to front with designing structure of the

pressure vessel for static loading and its assessment by

ANSYS. The increment in the thickness beyond a

certain value not only possesses fabrication difficulties

but also demands stronger material for the vessel

construction. To find the effect of residual stress and its

bursting pressure. The material selection was based on

the American Society of Mechanical Engineering

(ASME) codes. The theoretical result and simulation

result are compared.

Keywords—ASME codes, ANSYS, Bursting pressure.

I. INTRODUCTION

The term pressure vessel referred to those reservoirs

or containers, which are subjected to internal or

external pressures. The pressure vessels are used to

store fluids under pressure. The fluid being stored may

undergo a change of state inside the pressure vessels

as in case of steam boilers or it may combine with

other reagents as in chemical plants. Pressure vessels

find wide applications in thermal nuclear power

plants, chemical industries [1]. The inside pressure is

usually higher than the outside pressure, except for

some isolated situations. The fluid inside the vessel

may undergo a change in state as in the case of steam

boilers, or may combine with other reagents as in the

case of a chemical reactor. Pressure vessels often have

a combination of high pressures together with high

temperatures, in some cases flammable fluids or

highly radioactive materials, because of such hazards

it is imperative that the design be such that no leakage

can occur. In addition these vessels have to be

designed carefully to cope with the operating

temperature and pressure. It should be borne in mind

that the rupture of a pressure vessel has a potential to

cause extensive physical injury and property damage.

Plant safety and integrity are of fundamental concern

in pressure vessel design and these of course depend

on the adequacy of design codes. When discussing

pressure vessels we must also consider tanks. Pressure

vessels and tanks are significantly different in both

design and construction: tanks, unlike pressure

vessels, are limited to atmospheric pressure. The use

of a bi-material cylindrical body of large dimensions

ending by two half-spheres as nuclear reactor pressure

vessel (NRPV) is very common. The two structural

materials forming the NRPV wall are: (i) stainless

steel, for the inner layer of the wall acting as cladding

or reinforcement material, and (ii) low carbon steel,

for the outer layer of the wall acting as base material

[7]. Cylindrical pressure vessels are used in various

fields such as chemical and nuclear industries, rocket

motor case manufacturing and production of many

weapon systems. Evaluation of failure pressure that a

cylindrical pressure vessel can withstand is an

important consideration in the design of pressure

vessels. While prediction of failure pressure of

pressure vessels, it is also necessary to consider the

residual stresses already present in the pressure vessels

[2]. It is important, but difficult to validate the

theoretical stress formulations for complex structures,

and only few works have been reported for FGM

(Functionally graded materials) structures in open

literatures. Various efforts would have done to find the

theoretical solutions for FGM structures using FE

theory [3]. Manufacturing of High Strength Low

Alloy Steel is Capable for manufacturing pressure

vessel because of its ease of fabrication and welding

and also the properties of the materials [4, 5]. Storage

cylinders for compressed natural gas (CNG) used in

vehicles are pressure vessels that have been

traditionally produced using isotropic materials, such

as steel and Aluminium. Nevertheless, polymer

composites have recently been introduced for that

purpose [7], usually relying on the composite

manufacturing technique of filament winding (FW)

[6]. The size and geometric form of pressure vessels

vary greatly from the large cylindrical vessels used for

high-pressure gas storage to the small size used as

hydraulic units for aircraft.

A. HIGH PRESSURE VESSELS:

High Pressure vessels are used as reactors,

separators and heat exchangers. They are vessel with

an integral bottom and a removable top head, they are

generally provided with an inlet, heating and cooling

International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 13493-13501ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

13493

system and also an agitator system. High Pressure

vessels are used for a pressure range of 15 N/mm2 to a

maximum of 300 N/mm2. These pressure ranges are

essentially thick walled cylindrical vessels, ranging in

size from small tubes to several meters diameter.

B. CONSTRUCTION OF HIGH-PRESSURE

VESSELS:

1. A solid wall vessel is produced by forging,

boring a solid rod of metal.

2. A cylinder vessel is formed by bending a

sheet of metal and welded in the

longitudinal edges of the sheet metal.

3. Shrink fit construction in which, the vessel

is built up of two or more concentric

shells, each shell progressively shrunk

from the inside wall to outward. From

economic and fabrication considerations,

the number of shells should be limited to

two.

4. A vessel built up by wire winding around a

central cylinder. The wire is wound under

tension around a cylinder of about 6 to 10

mm thick.

5. A vessel built up by wrapping a series of

sheets of relatively thin metal tightly round

one another over a core tube, and holding

each sheet with a longitudinal weld. Rings

are inserted in the ends to hold the inner

shell round while subsequent layers are

added. The liner cylinder generally up to12

mm thick, while the subsequent layers are

up to 6 mm thick.

6. Making proper insulations on inner wall of

pressured vessel.

Fig.1 High pressure vessel

C. DESIGN OBJECTIVES:

1. Multilayer pressure vessels are suitable for

high operating pressures than solid wall

pressure vessels.

2. Significant saving in weight of material may

be made by use of a multilayer vessel in place

of a solid wall vessel.

3. Suitability of using different materials for

Liner shell and remaining layers for reducing

the cost of the construction of the vessel.

4. Theoretical stress distribution caused by

internal pressure at outside surface of the shell

and to ascertain that the stresses do not reach

yield point value during testing.

II. PROBLEM IDENTIFICATION

Normally pressure vessel faces different problems.

Some of them are noticed below: Cracking due to an

external load,this occurs as a result of abnormally high

nozzle loads that exceeded the designed nozzle load.

The root cause for the high external load is poor

design or poor functioning support system, this occurs

when the load transferred from the support system to

the nozzle. Cracking due to lack of penetration is the

lack of adequate weld filler metal deposit at the root of

the joint. The root of the nozzle joint is interface

between the nozzle wall and head of the pressure

vessel. Cracking due to chemical attacks occurs in the

inner wall of pressure vessel, due to the lack of

insulating material deposited on the inner walls of the

cylinder.

Some of the principle causes for the failure of

pressure vessel are:

Poor design

Poor maintenance of equipment

An unsafe system of work

Operator errors (improper training or

supervisions)

Poor installations

Inadequate repairs or modifications

III. DESIGN PAREMETERS

The design of solid pressure vessel includes

1. Vessel thickness

2. Hydrostatic Test Pressure

3. Bursting Pressure

A. MATERIAL

The material chosen for manufacturing the pressure

vessel is Duplex 2205 Stainless Steel. The main

reason for choosing this materialisbased on the

following properties:

High strength and toughness

Good corrosion resistance and weldability

Light weightand High magnetic strength

International Journal of Pure and Applied Mathematics Special Issue

13494

Table No 1: Chemical Composition:

Table No 2: Physical properties:

Table No 3: Mechanical Properties:

IV. THEORITICAL ANALYSIS

The design of solid pressure vessel includes,

(a) Design of Vessel thickness

(b) To find Thin or Thick cylinder

(c) Calculation of Radial and Tangential stress

(d) Calculation of shear stress

(e) Calculating bursting pressure

Input Data:

Inner Diameter Di = 381mm,

Inner Radius Ri= 190.5mm

Internal Pressure P = 300N/mm2

Design of Vessel thickness:

Thickness = PDi

2SE−0.2P

= 300x381

2x1303−0.2x300

= 56.45 mm

To find Thin (or) Thick cylinder: di

t =

381

56.45 = 6.749 < 20

Therefore, it is Thick cylinder.

Outer diameter do = di + 2t

= 381+2x56.45

= 493.9 mm

Usually the internal high pressure fluid develops two

kinds of stresses namely,

Tangential stress

Radial stress.

1. Longitudinal stress calculation

ro= od

2 =

493.9

2 =246.95

r1 = 190.5

σl = -PoClo, = ro

r1 =

246.95

190.5 = 1.296

Where,

Clo= (2+1)/(

2-1)

Clo=(1.2962+1)/(1.296

2-1)= 3.942 mm

2

σl = PoCl

= 29x3.942

= 114.318 N/mm2 (compressive)

2. Radial and Tangential stress:

Inner radius (r = ri)

Clo = 1/(2-1)

= 1/(1.2962-1)

= 1.4714 mm2

σt= -PoClo

= -300x1.4714

σt = -441.42 N/mm2 (compressive)

σr (r = ri) = 0 Natural Boundary condition for

Pi= o

Outer radius (r = ro)

Ct = (2+1)/(

2-1)

= (1.2962+1)/(1.296

2-1)

= 3.9429 mm2

σt (r = ro) = -PoCti= -300x3.9429

= -1182.87 N/mm2 (compressive)

σrr = ri) = -Po (Natural Boundary condition)

= -300 N/mm2

3. Define Principal stress:

Inner Radius

σ1= σr= 0

σ2=σl=-1182.85N/mm2

σ3=σt=-441.42 N/mm2

Material Limit C Mn Si P S Cr Mo Ni N

Duplex 2205 Min - - - - - 21.0 2.5 4.5 0.08

Max 0.030 2.00 1.00 0.030 0.020 23.0 3.5 6.5 0.20

Material Density Elastic

modulus

Mean Coefficient of Thermal Expansion Thermal Conductivity Specific Heat Electrical

Resistivity 0-100°c 0-315°c 0-538°c at 100°c at 500°c

Unit Kg/m³ GPa µm/m/°c µm/m/°c µm/m/°c W/m.K W/m.K J/Kg.K nΩ.m

Duplex

2205

7800 200 13.7 14.7 - 19.0 - 450 850

Material

Tensile Strength

Yield Strength

Elongation

Hardness

Rockwell C Brinell

Unit MPa MPa % in 50 mm HR C HB

Duplex 2205 620 450 25 31 293


13495

Outer Radius

σ1 = σr = -300N/mm2

σ2=σl=-1182.85 N/mm2

σ3=σt=-1182.87 N/mm2

4. Maximum shear stress:

Inner Radius = σ1−σ3

2

= 0+441.42

2

= 220.7 N/mm2

Outer Radius=σ1−σ3

2

=−300+1182 .87

2

=441.435 N/mm2

5. Bursting pressure:

Pb= UTS * (K2-1/K

2+1)

= 620* (1.2962-1/1.296

2+1)

=157.32 N/mm2

Table No 4: Theoretical result

SL.N

O.

PARAMET

ER

DESCRIPTI

ON

INFEREN

CE

1. Material DUPLEX

2205

STAINLES

S STEEL

2. Vessel

Thickness

56.45 mm Fabrication

is difficult.

Cost is very

high.

3. Maximum

Tangential

stress(N/mm2

)

-441.42

N/mm2

(compressive)

At the inner

radius of

vessel

4. Minimum

Tangential

stress(N/mm2

)

-1182.87

N/mm2

(compressive)

At the outer

radius of

vessel

5. Bursting

Pressure

157.32 N/mm2

Develops a

stress of

inside vessel

V. SOFTWARE ANALYSIS

INTRODUCTION TO CREO PARAMETRIC 3.0:

PTC Creo Parametric offers powerful, reliable, yet easy-

to use modelling tools that accelerate the design process.

This software helps to design parts, assemblies, create

manufacturing drawings, pre-form analysis, create

renderings and animations and optimize the productivity

across a full range of other mechanical design tasks. PTC

Creo Parametric will help to design with higher quality-

products in a faster manner and communicate more

efficiently with the manufacturing industry and your

suppliers.

FEATURES:

Creating the 3D models of any parts or

assembly in a short period of time.

Design aesthetics are improved with

comprehensive surface capabilities.

Large number of tools are present in Creo

parametric 3.0 for making the part or assemblies

in an easier manner.

Solid models which are created through other

than Creo parametric 3.0 is easy to import.

INTRODUCTION TO ANSYS WORKBENCH 15.0:

ANSYS Workbench environment is a finite element

analysis tool that is used in conjunction with CAD

systems and/or Design Modeller. ANSYS Workbench is

a software environment for performing structural,

thermal, and electromagnetic analyses. The class focuses

on geometry creation and optimization, attaching

existing geometry, setting up the finite element model,

solving, and reviewing results. The class will describe

how to use the code as well as basic finite element

simulation concepts and results interpretation.

MODEL OF PRESSURE VESSEL:

Fig.2 Isometric view of Pressure Vessel


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Fig.3 Finite Mesh of Pressure Vessel

ANALYSIS RESULTS:

For Duplex 2205 Stainless steel:

The result of total deformation, shear stress and strain

for the applied load (50 MPa) is obtained through Ansys

15.0

Fig.4 Total Deformation under Load

Fig.5 Equivalent Stress under load

Fig.6 Equivalent Strain under load

For Carbon Steel:

The result of total deformation, shear stress and strain for

the applied load (50 MPa) is obtained through Ansys

15.0


13497

Fig.7 Total Deformation under Load

Fig.8 Equivalent Stress under load

Fig.9 Equivalent Strain under load

Table No 5. Analysis Result:

Graph No 1: Stress-Strain Curve

The above graph represents the stress- strain

relationship of pressure vessel for the given load of 50

MPa. The above graph increase linearly. It shows that

there is no breaking point occurs on the pressure vessel.

So the design of the pressure vessel is safe for the given

load.

0.00E+00

5.00E+07

1.00E+08

1.50E+08

2.00E+08

2.50E+08

0.00E+00 5.00E-04 1.00E-03 1.50E-03

Stre

ss (

Pa)

Strain

Result Total Deformation Shear Stress Shear Strain

Unit M Pa m/m

Material Min Max Min Max Min Max

Duplex 2205 0.0001017 0.00022423 1.2728e5 2.354e8 6.414e-7 0.0011774

Carbon Steel 0.00010894 0.00023392 1.2787e5 2.354e8 6.6971e-7 0.0012197


13498

VI. CONCLUSIONS

This paper reports about the evaluation of certain

horizontal spherical end pressure vessel. It is observed

that all the pressure vessel components are selected on

basis of available ASME standards. The manufactures

also follow the ASME standards while manufacturing

the components. Based on ASME standards the pressure

vessel dimensions are chosen and the designed with the

help of PTC Creo Parametric 3.0. With the help of the

dimensional values theoretical calculations were made

and then the bursting pressure of the pressure vessel is

calculated. The designed pressure vessel is analyzed

through ANSYS 15.0, and the analysis results are taken

to verify the safeness of the pressure vessel. The material

here we are chosen is compared with the existing

pressure vessel material carbon steel. The values

obtained for duplex 2205 from ansys is less than the

values obtained for carbon steel. Stress-strain curve is

drawn through the analyzed data’s. Here the curve

increases linearly, because for the given load there is no

breakage for the pressure vessel. So the curve shows that

the pressure vessel design is safe for the given load. The

bursting pressure of the pressure vessel is less than the

maximum shear stress noted from the analysis result. It is

clear that our pressure vessel design is safe forthe given

load.

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STRUCTURAL AND STATISTICAL ANALYSIS OF HORIZONTAL SPHERICAL END PRESSURE … · 2018-05-06 · system and also an agitator system. High Pressure vessels are used for a pressure range