Finite Element Analysis of Pressure Vessel and Nozzle …engineering.moonish.biz/...29_FEAofPressureVessel... · Finite Element Analysis of Pressure Vessel and Nozzle Junction Revision:

Finite Element Analysis

of Pressure Vessel and

Nozzle Junction

Revision: 0

Date: 29 March 2013

Author: Dharmit Thakore

2013

MOONISH ENT. PTY. LTD |

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Executive Summary

The main objective of this project was to understand the Finite Element Analysis capability of Open

Source Software Salome for Pre-processing and Post-processing and Code_Aster for analysis of a

Pressure Vessel Nozzle junction. Main goal was to calculate Stresses by hand and compare them

with the Finite Element Analysis results.

Analysis was carried out on a quarter section of a pressure vessel with nozzle in the middle of the

geometry, with sufficient symmetry and other boundary conditions added for stability of the model.

Linear analysis using Tetrahedral elements was carried out for this study.

Salome version 6.3.0 and Aster version 1.10.0 was used for this analysis.

From the study it can be seen that hand calculations closely match the Finite Element Analysis

results. Further studies are required to evaluate stresses and analyse them based on ASME Section

VIII Division 2.

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Table of Contents Executive Summary ................................................................................................................................. 1

Introduction ............................................................................................................................................ 3

Model Geometry ..................................................................................................................................... 4

Loads and Restraints ............................................................................................................................... 5

Mesh ....................................................................................................................................................... 6

Analysis of results ................................................................................................................................... 7

Hoop Stresses ...................................................................................................................................... 7

Longitudinal Stresses .......................................................................................................................... 9

Internal Pressure ............................................................................................................................... 11

Only Force ......................................................................................................................................... 13

Force and Internal Pressure Combined Loading ............................................................................... 15

Conclusions ........................................................................................................................................... 17

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Introduction

The main goal of this study was to validate Finite Element Analysis performed for following cases

1. Internal Pressure with Hoop stress only

2. Internal Pressure with Longitudinal stresses only

3. Internal Pressure with both Hoop and Longitudinal stress

4. Force of 9000N in direction going left to right if facing the nozzle

5. All of the above four cases combined

Based on the results and findings of this study, my higher goal is to learn Pressure Vessel Design

based on ASME Section VIII Division 2 Part 5. A very small part of the Pressure vessel design is

considered in this study, the Junction of Nozzle and Pressure vessel.

In this study Static Linear Finite Element Analysis was used to obtain results. Quadratic mesh was

not considered for this study as the main goal of this study was to investigate whether the real world

experience can be modelled in Finite Element Analysis.

Vonmises stresses were calculated for the 5 load cases above and they were compared with hand

calculations using first principles.

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Model Geometry

The model geometry is a quarter section

of a Pressure Vessel modelled in positive

X-Y-Z zone of the co-ordinate system. This

pressure vessel has a nozzle at the centre

of it pointing in positive X-Y direction.

The geometry modelling is carried out in

Salome Geometry module, meshing was

carried out in Salome Mesh module and

then the mesh was exported in .msh

format. Finite Element Analysis was

carried out in Code_Aster and the result

was exported in another .msh format.

This result mesh was imported in Salome

again and Post Processing was carried out

where Displacements and Vonmises

stresses were evaluated.

Quarter model of the entire pressure

vessel was used in this study as the not-

modelled section of the pressure vessel

was very remote to the Nozzle geometry.

Flange was not modelled on the nozzle end to minimise mesh size and computation time as this is

the standard practice used in commercial software packages.

Solid modelling was carried out in this study. Comparable results can be obtained by using shell

elements, and in future another study may be carried out to understand the difference between the

two modelling approaches.

OD of Pressure Vessel Shell = 3000mm ID of Pressure Vessel Shell = 2980mm

OD of Nozzle = 300mm ID of Nozzle = 280mm

Height of the Pressure Vessel Shell = 3000mm Height of the Nozzle = 200mm

Figure 1: Model Geometry

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Loads and Restraints

Vertical faces are given symmetric boundary

condition. Vertical Face in the XOZ plane

gets boundary condition of DY=0. Vertical

Face in the YOZ plane gets boundary

condition of DX=0. Horizontal bottom face

gets boundary condition of DX=0, DY=0 and

DZ=0

Five Load cases were considered for this

study. To balance the unbalanced pressure

an equivalent force is applied on the front

face of the nozzle.

Loads to be considered for this study are

Internal Pressure = 0.5 MPa

Force = 9000 N

Modulus of Elasticity (E) = 210 GPa

As the nozzle is facing positive XY direction,

force on the nozzle face was reduced in X and

Y direction and then applied to the face. So

the force of 9000N in lateral direction of the nozzle shell junction is reduced to 6363N in +Y direction

and 6363N in –X direction.

DX, DY, DZ = 0

DX=0

DY=0

Figure 2: Restraints

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Mesh

3D tetrahedron mesh was used for this study.

Tetrahedron maximum volume was restricted to

maximum 50 in Salome.

Global geometry was meshed with the above

configuration using automesh. Automatic tetrahedron

Hypothesis was used for global geometry. The edges of

the nozzle (inside and outside) at both ends were given a

Sub-mesh with equi-distance division of 100.

The linear mesh has 88712 tetrahedron elements.

At this stage, linear mesh is used with automatic meshing

for the global mesh with 100 linear elements on the nozzle

edges were modelled as Sub-mesh to make the edges fine

and have more finite elements for better results around

the nozzle shell junction.

Figure 3: Mesh Information

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Analysis of results

Hoop Stresses

For the first load case, stresses were obtained for internal pressure on the shell and nozzle junction

with force modelled on the nozzle face for balancing unbalanced pressure. The displacement and

VonMises plot are shown below in Figures 4 and 5 respectively.

Figure 4: Hoop Stress – Displacement

Change in Diameter for this Pressure Vessel is calculated as follows

Change in Diameter = �∗��

�∗�∗�∗ (2 − ν) =

.�∗� �

�∗� ∗�� ∗ (2 − 0.3) = 0.898mm

FE analysis above in Figure 4 shows displacement in Yellow colour highlight as 0.6mm. One of the

major reason to contribute to the lower displacement compared to manual calculation is that the

boundary conditions are very close to each other and the presence of Nozzle in the centre of the

model.

Hoop stress for this Pressure Vessel is calculated as follows

Hoop Stress = �∗��∗�

= .�∗� �∗�

= 75MPa

As can be seen in Figure 5 below, the VonMises stresses for the majority of the shell away from

boundaries and Nozzle is at an average of 75 MPa

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Figure 5: Hoop Stress – VonMises

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Longitudinal Stresses

For the second load case, stresses were obtained for force acting on the top face of the shell to

simulate Longitudinal Stresses. The displacement and VonMises plot are shown below in Figures 6

and 7 respectively.

Figure 6: Longitudinal Stress - Displacement

Longitudinal stress for this Pressure Vessel is calculated as follows

Longitudinal Stress = �∗��∗�

= .�∗� �∗�

= 37.5MPa

As can be seen in Figure 7 below, the VonMises stresses for the majority of the shell away from

boundaries and Nozzle is at an average of 37 to 40 MPa

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Figure 7: Longitudinal Stress – VonMises

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Internal Pressure

For the third load case, stresses were obtained for both Internal Pressure acting on the internal face

of the Pressure Vessel and Nozzle to simulate Hoop stress and Force acting on the top face of the

shell to simulate Longitudinal Stresses. The displacement and VonMises plot are shown below in

Figures 8 and 9 respectively

Figure 8: Internal Pressure – Displacement

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Figure 9: Internal Pressure - VonMises

Combined stress for this Pressure Vessel is calculated as follows

Combined Stress = �(����������� −�� !"�#$" %&�������) = �(75� − 37.5�) = 64.95MPa

As can be seen in Figure 9 above, the VonMises stresses for the majority of the shell away from

boundaries and Nozzle is at an average of 65 MPa

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Only Force

For the fourth load case, stresses were obtained for Lateral force acting on the nozzle face. The

displacement and VonMises plot are shown below in Figures 10 and 11 respectively

Figure 10: Force Only – Displacement

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Figure 11: Force Only - VonMises

Some close up screen shots of nozzle-shell interface are shown below. First screenshot is for the

VonMises stress on the outside surface of the nozzle shell junction.

Figure 12: ForceOnly Closeup of Outside surface

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Second screenshot below is for the VonMises stress on the Inside surface of the Nozzle shell

junction.

Figure 13: ForceOnly Closeup of Inside surface

Force and Internal Pressure Combined Loading

For the fifth load case, stresses were obtained for Lateral force acting on the nozzle face and Internal

Pressure acting on the inside face of the shell and nozzle. The displacement and VonMises plot are

shown below in Figures 14 and 15 respectively

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Figure 14: Force and Internal Pressure Combined – Displacement

Figure 15: Force and Internal Pressure Combined - VonMises

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Conclusions

From this study it can be concluded that Finite Element analysis results match that of hand

calculations. This study is not exhaustive and was conducted to try doing Finite Element analysis of a

Pressure Vessel Nozzle section using Salome for modelling and post-processing and Code_Aster for

analysis

This study is just a preliminary analysis. For further study following actions are recommended

1. Use of Hexahedral elements

2. Use of 2nd order or Higher order elements

3. Mesh refinement around the nozzle shell junction

4. Have minimum 5 elements in the thickness of the shell and nozzle

5. Evaluate Stresses based on ASME Section VIII Division 2 Part 5 rules.

6. Use larger surface of the shell so that the distance between the nozzle and boundary

conditions is more than what is used in this study.