Finite Element Analysis of High Pressure Titanium ...

G. Krishnaveni, J. S. Soni et al. IJECRT- International Journal of Engineering Computational Research and Technology (Volume 4, Issue 1, June 2019)

© 2019 Published by IJECRT 17

International Journal of Engineering Computational Research and Technology

Journal home page: www.ijecrt.org

ISSN (Online): 2456-9852 Volume 4, Issue 1, June 2019

Finite Element Analysis of High Pressure Titanium Spherical Pressure

Vessel

G. Krishnavenia , J. S. Soni

b, * ,C. S. K Prasad Rao

c , D. Krishna Vamshi

d , D. Ajay Kumar

e, L. Lokesh

f

a-f Department of Mechanical Engineering, Bharat Institute of Engineering and Technology, Hyderabad, Telangana-501510, INDIA * Corresponding author:

E-mail address: [email protected] (J. S. Soni).

ABSTRACT

Pressure Vessel is an enclosed container designed to hold or to store compressed air at a pressure substantially

different from the ambient pressure. Different shapes of pressure vessel exist but mostly cylindrical and spherical are

used. Spherical pressure vessels are theoretically two times stronger than cylindrical ones. A spherical thin walled

pressure vessel prepared by Titanium designed using software CREO and then carried out by using ANSYS.

Structural analysis is done for this vessel made of Structural Steel which works at pressure of 100 bar and 440 bar.

The fluid analysis is also done on Spherical Pressure Vessel and Velocity streamline flow.

Keywords: Pressure Vessel

FEA

Ansys

Structural Analysis

1. Introduction

Pressure Vessels have been in wide use for

many years in the chemical, petroleum, industries.

They are subjected to high pressures and

temperatures which may be constant or varying.

Factors such as material, shape, chemical

composition and physical substances used in it, the

atmospheric conditions of Pressure Vessels and etc.

are the factors which can have different effects on

performance of Pressure Vessels. The fluid being

stored may undergo a change of state inside the

Pressure Vessels.

The Pressure Vessels are designed with great

care because rupture of Pressure Vessels causes an

explosion which may cause loss of life and

property. The materials of Pressure Vessels are

brittle like cast iron or ductile such as mild steel.

Cylindrical or spherical Pressure Vessels

The basic requirements for design of Pressure

Vessels are safety, reliability, efficiency and

economy. Two types of analysis are commonly

applied to Pressure Vessels. The most common

method is based on a simple mechanics approach

and is applicable to thin-walled Pressure Vessels by

dentition have a ratio of inner radius “r”, to wall

thickness “t”, of r/t 10. The second method is based

on elasticity solution and is always applicable

regardless of the r/t ratio and can be referred to as

the solution for thick walled Pressure Vessels.

Finite Element Analysis (FEA) is a practical tool in

the study of air bottles, especially in determining

stresses in local areas such as cavities, O-ring



grooves and other areas which are difficult to

analyze manually.

1.2 Applications:

(i) Spherical Pressure Vessels are used in

domestic hot water storage tanks.

(ii) Mining operations- Diving cylinders,

recompression chambers, Distillation

towers, pressure reactors etc.

(iii) Marine applications- used in submarines,

space ship habitats.

(iv) Reservoirs- Pnuematic, hydraulic, rail

vehicle airbrake reservoirs etc.

(v) Liqufied gasses storage like ammonia, LPG.

(vi) Major in Oil refineries, petro chemical

plants, nuclear reactors.

2. Overview

2.1 Spherical Pressure Vessel

Depending on the ASME boiler and pressure

vessel code (BPVC), Code Section VIII, pressure

vessels are containers for containment of pressure,

internal or external. This pressure can be noted from

an external source or by the application of heat from

a source as a result, directly or indirectly from a

process, or any combination.

The ASME code is a construction code for

pressure vessels and includes mandatory

requirements, specific prohibitions and non-

mandatory guidelines for the design of pressure

vessels, manufacture, testing, inspection, testing and

Certification.

2.2 Shape of Pressure Vessel

Pressurized containers can theoretically be

almost all shapes, but spherical section shapes,

cylinders and cones are usually used. A common

configuration is a cylinder having end pieces called

heads. Main forms often either hemispherical or

stamped (torispherical). More complex shapes have

always been much more difficult to analyze for safe

operation and are generally much more difficult to

build.

In theory, a SPHERE is the best form of a

pressure vessel. Unfortunately, a spherical shape is

difficult to produce, therefore, more expensive, so

that most of the pressure vessels are cylindrical with

2:1 of the semi-elliptical heads or end caps at each

end. Less pressure vessels are collected from a pipe

and two lids. One disadvantage of these ships is that

big banks are more expensive.

2.3 Why should we use Spherical Pressure Vessel?

Fig 1. Layout of spherical Pressure Vessel

Consider the stresses on one half of the thin

spherical pressure vessel of inner radius r and wall

thickness t (Fig 2.).

Fig 2. Forces applied in Spherical Pressure vessel



Static equilibrium requires that the load

generated from the tensile stress in the wall be equal

to the load applied by the pressure. Since the vessel

is thin, the load due to the tensile stress in the wall

is 2πrtσ . The load due to the pressure in the vessel

is πr2p . Balancing these gives the expression for

the stress in a spherical vessel as

(1)

Due to symmetry in the spherical pressure

vessel, the stress in all directions tangent to the

surface of the vessel is the same. Depending on

weather one takes a stress element from the inside

or outside surface of the vessel, one will get one of

the two following states of stress (Fig 3.).

Fig 3. Stresses developed inside pressure vessel

Maximum Stress on Outside Surface:

The in and out-of-plane Mohr’s circles for a

stress element taken from the outside surface of the

pressure vessel will look as follows.

Fig 4. Shear stresses on the pressure vessel

As can be seen, the maximum and minimum

normal stresses and maximum shear stress are

(2)

As can also be seen, the maximum shear stress

is on a 45o out-of-plane incline as shown in the

figure 5.

Fig 5. Shear stress on 45o plane

The in and out-of-plane Mohr’s circles for a

stress element taken from the inside surface of the

pressure vessel will look as follows (Fig 6.).



Fig 6. Tension and shear stress in Mohr’s Circle

As can be seen, the maximum and minimum

normal stresses and maximum shear stress are

(3)

2.4 Parts of Spherical Pressure Vessel

A Spherical Pressure Vessel considered in this

work has the following parts:

a) Top Hemisphere

b) Bottom Hemisphere

c) Cap

d) Gasket

e) Bolts and Nuts

2.5 Materials Used For Spherical Pressure Vessel

In general, the materials used for manufacturing

a Pressure Vessel are:

a) Stainless Steel

b) Aluminium

c) Cast Iron

d) Titanium

So in this work, we considered a Spherical

Pressure Vessel made of Titanium (Ti-6Al-4V).

2.6 Design Requirements for Spherical Pressure

Vessel

In this work, the Spherical Pressure Vessel is

designed in the designing software called CREO

3.0. So, the following are design requirements that

are to be considered to fulfil the objectives of this

work.

1) Pressure Vessel:

Internal Diameter: 9.86 meters

Thickness (Diameter): 0.10 meters

Neck Length: 2 meters

Inlet Diameter: 1 meters

Flange Length: 6 meters

2) Cap:

Diameter of hole for Bolt: 1 meters

3) Gasket:

Inner Diameter: 1 meters

Outer Diameter: 2 meters

Thickness: 0.25 meters

4) Bolt and Nuts

Diameter: 0.25 meters

2.7 Properties of Titanium Alloy

The two most useful properties of the metal are

corrosion resistance and strength-to-density ratio,

the highest of any metallic element. In its unalloyed

condition, titanium is as strong as some steels, but

less dense.

The composition of TITANIUM alloy (Ti-6Al-

4V) is:

a) Titanium- 90%

b) Aluminium- 6%

c) Vanadium- 4%

The following (Table 1) are the properties of

Titanium:

Table 1. Properties of Titanium Ti-6Al-4V

Name of Property Metric

Poisson’s Ratio 0.342

Young’s Modulus 113.8 Gpa

Density 4.43 g/cc

Tensile Yield strength 880 Mpa

Compressive Yield Strength 970 Mpa

Tensile ultimate strength 950 Mpa



2.8 Properties of Structural Steel

The percentage of Carbon present in Structural

Steel is 0.3-0.6%.

The properties of Structural Steel is as follows:

Table 2. Properties of Structural Steel



Young’s Modulus 2E+11 Pa

Density 7.85 g/cc




2.9 Analysis Requirements for Spherical Pressure

Vessel

The following are the basic requirements for

undergoing Analysis:

a) Pressure maintained inside Spherical

Pressure Vessel: 400 Bar

b) Nodes taken : Random

c) No of Nodes to be considered: 8

d) Analysis done: Hoop Stress

e) Comparison done between: Titanium and

Structural Steel

3. Methodology

3.1 Problem Description

The work is to analyze spherical pressure vessel

prepared with Titanium and to compare it with

Structural Steel pressure vessel and also to perform

CFD on Spherical Pressure vessel.

Hence, to obtain the above results the

methodology is as follows:

(i) Designing in CREO.

(ii) Structural analysis of Titanium Spherical

Pressure vessel and Structural Steel in

ANSYS.

(iii) Compare the results of both Titanium and

Structural Steel.

(iv) CFD of Spherical Pressure Vessel in

ANSYS.

3.2 Solution Methodology

Designing

The designing is as follows:

A. Top Part: Open CREO→select new→select name→select top

plane→click sketch

Select→circle→click on origin→give radius as 9.86→draw

another circle→give radius as 9.96

select→line→draw line from outer circle parallel to vertical

axis→give length as 2→draw line parallel to horizontal axis

away from vertical axis→give length as 3→draw line parallel

to vertical axis away from horizontal axix→give length as

0.5→draw line parallel to horizontal axis towards vertical

axix→ give length as 4→draw line joining inner circle→esc.

Select→trim→remove unnecessary arcs→click ok.

Select→revolve→select 360 degrees→click ok.

select→top plane→click sketch→draw circle of diameter

3→click ok.

Select→centre lines→draw 2 centrelines at 45 degrees.

select→8 circles→give diameter 0.25→click ok.

select→extrude→select through the body→click ok.

B. Bottom Part Open CREO→select new→select name→select top


Select→circle→click on origin→give radius as 9.86→draw

another circle→give radius as 9.96

Select→trim→remove unnecessary arcs

select→line→draw line joining two circles→click ok.

select→ revolve→select 360 degrees→click ok.

C. Gasket: Open CREO→select new→select name→select top


Select→circle→click on origin→give radius as →draw

another circle→give radius as

2→click ok

Select extrude→give distane as 0.25→click ok



D. Cap: Select→line→draw line of 1.5 on horizontal axis from

origin→draw line of 6 parallel to vertical axis→draw line

parallel to vertical axis of 0.5 length→draw line parallel to

vertical axis of 8→draw line of 1.5 parallel to horizontal

axis→draw line joining other one→click ok.

Select→centre lines→draw horizontal and vertical centre

lines→esc.

Select→revolve→select 360 degrees→click ok.

Select→top plane→click sketch→draw circle of diameter

3→click ok.

Select→centre lines→draw 2 centrelines at 45 degrees.

Select→8 circles→give diameter 0.25→click ok.

Select→extrude→select through the body→click ok.

E. Bolt:

Draw a bolt of diameter 0.25 according to the

formulas and calculations.

F. NUT:

Draw a nut of diameter 0.25 according to the

formulas and calculations.

G. ASSEMBLY:

Fig 7 shows assembly

Fig 7. Assembly

3.3 Structural Analysis

Step 1: Static Structural

Engineering data= Titanium Alloy

Step 2: Geometry

Insert =import part

Step 3: Mesh

Generate mesh

Step 4: Static Structural

a) Selected inlet nozzle as Fixed Support

b) Selected remaining body as pressure applied

c) Pressure Applied = 100 bar, 440 bar, 1000

bar

Step 5: Solution

a) Total deformation

b) Von mises Stress

c) Von mises Strain

3.4 Analysis Procedure for Titanium Spherical

Pressure Vessel

Selection of analysis type, element type,

defining material properties, defining geometric

properties (real constants) are common steps for all

blade geometries.

1) Selection of Analysis Type:

The analysis type used for straight wind turbine

blade model is static structural steady state analysis.

By using following GUI path, the analysis type is

selected as shown below:

GUI Path: Main menu> tool box >structural

2) Defining Material Properties:

The material properties of materials are

specified as below table 3. Double click Geometry

and enter the properties of Titanium.

Table 3. The material properties of materials



Young’s Modulus 113.8 Gpa

Density 4.43 g/cc




3) Importing the File:

The blade models created in CATIA V5

SOFTWARE can be imported for the analysis in the

ANSYS WORKBENCH. The blade importing



procedure is given in the following GUI path .The

imported is shown below:

GUI Path: geometry>right click> Import > I.G.E.S >

Ok > Browse the file > Open > Ok>model>right

click>edit.

4) Meshing:

For meshing (Fig 8.) straight wind turbine blade

models (Table 4.), the following GUI Path is used

as shown below:

GUI Path: Main menu>

toolbox>structural>geometry>aqua>meshing>generate

meshing>ok.

Fig 8. Meshing

Table 4. Elements and Nodes

Blade

model Elements Nodes

Solid 3349 1497

5) Solution:

Case 1: The nozzle part is given fixed support (Fig

9.). Select all the three faces of the nozzle.

GUI Path: Main Menu >AQAV >static structural >fixed

support>Apply

Fig 9. Fixed Support

Remaining body is given pressure at different

pressures (Fig 10.).

GUI Path: Main Menu >AQAV >static

structural>pressure >Apply > Structuralarea>ok

Fig 10. Pressure Applied

Solution: Form the above given boundary

conditions the problem can be solved.

Main Menu > Solution (A6) > Solve > Ok.

Case 2: The same method is applied for Pressure

vessel made of Structural Steel. The properties are

shown in table 5.

Table 5. The properties for Pressure vessel made of Structural Steel



Young’s Modulus 2E+11 Pa

Density 7.85 g/cc






6) Deformations Obtained:

Von mises Stress (Fig 11.):

Fig 11. Stresses on Pressure Vessel

Von mises Strain (Fig 121.):

Fig 12. Strains induced in Spherical Pressure Vessel

3.5 Fluid Analysis

Start ANSYS Workbench by choosing the Start

menu, then select the Workbench option in the

ANSYS program group.

Start → All Programs → ANSYS 17.2 →Workbench.

This display the Save As dialog, where you can

browse to a specific folder and enter a specific

name for the ANSYS Workbench project.

Step 1: Click on Geometry → Import geometry→

browse the file→ prompted to select the desired system

of length units to work → select Meter → Ok.

If it is not prompted then click → units →meters.

Click on generate and the object is imported.

Step 2: Click on mesh → generate mesh → object has

been meshed (Fig 13.).

Fig 13: Meshing

Then click on mesh right click and chose edit option

and create Inlet, walls and Outlet through name and

selection option (Fig 14, Fig 15, Fig 16).

Fig 14: Fixed support

Fig 15. Walls



Fig 16. Outlet

Step 3: Click on Setup→ Edit→ Double precision→

Serial→ok.

General→ check → Report quality → Aspect

Ratio → 2.82360e+01→materials →air→

create/edit→ ρ=1.225→ν=1.7894e-0.5→

change/create→ close

Set some general settings for the CFD analysis.

Select General in the navigation plane to

perform the mesh-related activities and to

choose a solver.

Set up your models for the CFD simulation.

Models → Energy → Edit.

Select viscous and select turbulent flow.

Set up the boundary conditions for the CFD

analysis

Boundary Conditions → velocity-inlet-large →

Edit.

Select Components from the Velocity

Specification Method drop-down list.

Step 4: Calculate a solution. Start the calculation by

requesting 500 iterations.

(i) Enter 500 for Number of Iterations.

(ii) Click Calculate.

As the calculation progresses, the residuals will be

plotted in the graphics window and a popup appears on

the screen as calculations done and the solution gets

converged.

Step 5: Displaying Results in ANSYS FLUENT and

ANSYS CFD-Post

Display results in ANSYS FLUENT. With

ANSYS FLUENT still running, we can perform

a simple evaluation of the velocity and

temperature contours on the symmetry plane.

Later, we will use ANSYS CFD-Post (from

within ANSYS Workbench) to perform the same

evaluation (Fig 17, Fig 18, Fig 19, Fig 20, Fig

21).

Fig 17. Residuals for the Converged Solution

Fig 18. Velocity Streamline Flow

Fig 19. Velocity with volume rendering



Fig 20. Pressure with Volume rendering

Fig 21. Inner wall temperature

4. Results

4.1 Comparison between Titanium Spherical

Pressure Vessel made and Steel:

1) At Pressure 100 Bar:

Table 6. Comparison between Spherical Pressure Vessel made of

Titanium and Structural Steel at 100 bar

Titanium Structural Steel Max Min Max Min

Stress 5.3839e8 92000 5.3928e8 1.1026e5

Strain 0.005037 2.221e-6 0.002931 1.110e-6

2) At pressure 440 Bar

Table 6. Comparison between Spherical Pressure Vessel made of

Titanium and Structural Steel at 440 bar

Titanium Structural Steel Max Min Max Min

Stress 2.3689e9 4.480e5 2.2738e9 4.4555e5

Strain 0.022165 9.537e-6 0.012896 4.885e-6

4.2 Comparison using Graphs

1) Stresses developed

Fig 22. Stresses produced

2) Strains induced:

Fig 23. Strains induced

4.3 Flow Analysis Results

Fig 24. Residuals for the Converged Solution



Fig 25. Velocity Streamline Flow

Fig 26. Velocity with volume rendering

Fig 27. Pressure with Volume rendering

Fig 28. Inner wall temperature

5. Conclusion

A spherical thin walled pressure vessel prepared

by Titanium designed using software CREO and

then carried out by using ANSYS. Structural

analysis is done for this vessel made of Structural

Steel which works at pressure of 100 bar and 440

bar. The fluid analysis is also done on Spherical

Pressure Vessel and Velocity streamline flow.

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