fea of pressure vessel and nozzle junction -...

FEA of Pressure Vessel

and Nozzle Junction

2013

DHARMIT THAKORE

MOONISH ENTERPRISES PTY LTD |

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. To obtain hexahedral mesh for the Pressure Vessel Half geometry.

To analyse and compare Deflection and Vonmises stresses for three load cases for the geometry,

Internal Pressure only, Force on Nozzle Only and a combination of Internal Pressure and Force on

Nozzle. The main goal was to calculate Stresses by hand and compare them with the Finite Element

Analysis results.

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

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

Linear analysis using hexahedral 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 for the geometry away from the Pressure Vessel and Nozzle junction. An effort has been

made to calculate Membrane and Bending Stresses for comparison only at two Stress Classification

lines at the Nozzle Pressure Vessel Junction. Further studies are required to evaluate stresses and

analyse them based on ASME Section VIII Division 2 Part 5 rules and to obtain Membrane, Bending

and Peak stresses.

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

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

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

Mesh ..................................................................................................................................................... 17

Loads and Restraints ............................................................................................................................. 22

Analysis of results ................................................................................................................................. 26

Internal Pressure only ....................................................................................................................... 26

Force Only ......................................................................................................................................... 29

Pressure and Force applied together ................................................................................................ 32

Conclusions ........................................................................................................................................... 37

Introduction The main goal of this study was

1. To Model Pressure Vessel with Nozzle Geometry (Show step by step method of how is it

done in Salome)

2. Partition it to make it ready for Hexahedral meshing

3. Mesh it with Hexahedral elements

4. Perform Finite Element Analysis with 3 load cases

a. Internal pressure (both Hoop and Longitudinal stresses)

b. Force of 9000N on Nozzle in Lateral direction to vessel geometry

c. Combination of both a and b

5. Study the Stresses developed around the Nozzle Geometry (Discontinuity)

6. Compare the results with Hand Calculations

Salome was used to model the geometry. 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 results were

exported in .msh format. This result mesh was imported in Salome again and Post Processing was

carried out where Displacements and Vonmises stresses were evaluated.

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

used for this study. Quadratic mesh was not considered for this study.

Vonmises stresses were calculated for the 3 load cases above and they were compared with hand

calculations using first principles.

Membrane and Bending stresses were calculated for two Stress Classification Lines (SCL) for all three

load cases and are presented for comparison purposes only.

Model Geometry The model geometry is a half section of a Pressure Vessel modelled in positive X-Z zone of the co-

ordinate system. This pressure vessel has a nozzle at the centre of it pointing in positive X direction.

Half 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 with following parameters.

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

Modelling steps for the entire geometry are described below

Salome -> Geometry Module

New Entity -> Basic -> Point -> First

Argument (Point by 3 Co-ordinates)

Name: Reference1; X: 0; Y: 0; Z: 1500;

Click “Apply and Close”

New Entiry -> Basic -> Vector ->

Second Argument (Vector by 3 Co-

ordinates)

Name: Vx; X: 10; Y: 0; Z: 0; Click

“Apply”

Name: Vy; X: 0; Y: 10; Z: 0; Click

“Apply”

Name: Vz; X: 0; Y: 0; Z: 10; Click

“Apply and Close”

New Entiry -> Primitive ->

Cylinder -> Second Argument

(Cylinder by Radius and Height)

Name: Cylinder_1; Radius:

1500; Height: 3000; Click

“Apply”

Name: Cylinder_2; Radius:

1490; Height: 3000; Click

“Apply”

Still in Cylinder Modelling Select

First Argument (Cylinder by

Base Point, Vector, Radius and

Height)

Name: Cyliner_3; Base Point:

Reference1; Vector: Vx; Radius:

150; Height: 1700; Click “Apply”

Name: Cyliner_4; Base Point:

Reference1; Vector: Vx; Radius:

140; Height: 1700; Click “Apply

and Close”

Operations -> Boolean ->

Fuse -> Default Argument

Name: Fuse_1; Object 1:

Cylinder_1; Object 2:

Cylinder_3; Click “Apply”

Name: Fuse_2; Object 1:

Cylinder_2; Object 2:

Cylinder_4; Click “Apply

and Close”

Operations -> Boolean ->

Cut -> Default Argument

Name: Cut_1; Main

Object: Fuse_1; Tool

Object: Fuse_2; Click


Right Click “Cut_1” in Object Browser and Select “Show Only”

New Entiry -> Primitive -> Box -

> Second Argument Box by

Dimensions at Origin)

Name: Box_1; Dx: 1500; Dy:

3000; Dz: 3000; Click “Apply

and Close”

Operations ->

Transformations ->

Translation -> First

Argument (By Dx, Dy, Dz)

Objects: Box_1; Dx: -

1500; Dy: -1500; Dz:0;

Uncheck “Create a Copy”;


Operations -> Boolean -> Cut -> Default Argument

Name: Cut_2; Main Object: Cut_1; Tool Object: Box_1; Click “Apply and Close”

Right Click “Cut_2” in Object Browser and Select “Show Only”

New Entiry -> Basic -> Plane ->

First Argument (Plane by Point

and Vector)

Name: Plane_1; Point:

Reference1; Vector: Vy; Size of

Plane: 7000; Click “Apply”

Name: Plane_2; Point:

Reference1; Vector: Vz; Size of

Plane: 7000; Click “Apply and

Close”

Operations -> Partition -> First

Argument (By Objects and Tool

Objects)

Name: Partition_1; Objects:

Cut_2; Tool Objects: Plane_1 &

Plane_2; Click “Apply and

Close”

Right Click “Partition_1” in Object Browser and Select “Show Only”

While Partition_1 is selected in Object Browser

New Entiry -> Group -> Create -> First Argument (Shape Type “Points”)

Group Name: P1; Main Shape: Partition_1; Select Point on the extreme –Y @ Z = 1500 (as

shown in above figure); Click Add; Click “Apply”

Group Name: P2; Main Shape: Partition_1; Select Point on the extreme +Y @ Z = 1500 (as

shown in above figure); Click Add; Click “Apply and Close”

Point

P1

Point

P2

New Entity -> Basic -> Point -> First Argument (Point by 3 Co-ordinates)

Name: P3; X: 1500; Y: 0; Z: 2250; Click “Apply”

Name: P4; X: 1500; Y: 0; Z: 750; Click “Apply and Close”

New Entiry -> Basic -> Plane -> Second Argument (Plane by 3 Points)

Name: Plane_3; Point 1: P1; Point 2: P2; Point 3: P3; Size of Plane: 7000; Click “Apply”

Name: Plane_4; Point 1: P1; Point 2: P2; Point 3: P4; Size of Plane: 7000; Click “Apply and

Close”

Operations -> Partition -> First Argument (By Objects and Tool Objects)

Name: Partition_2; Objects: Partition_1; Tool Objects: Plane_3 & Plane_4; Click “Apply and

Close”


Right Click “Partition_2” -> Transparency: 70%

Right Click “Cylinder_1” in

Object Browser and Select

“Show Only”

New Entiry -> Group -> Create -

> Third Argument (Shape Type

“Faces”)

Group Name: PV_OD; Main

Shape: Cylinder_1; Select

Cylindrical Surface of

Cylinder_1; Click Add; Click


Right Click “Cylinder_3” in

Object Browser and Select

“Show Only”

New Entiry -> Group -> Create -> Third Argument (Shape Type “Faces”)

Group Name: Nozzle_OD; Main Shape: Cylinder_3; Select Cylindrical Surface of Cylinder_3; Click

Add; Click “Apply and Close”


Operations -> Partition -> First Argument (By Objects and Tool Objects)

Name: PV; Objects: Partition_2; Tool Objects: PV_OD & Nozzle_OD; Click “Apply and Close”

Right Click “PV” in Object Browser and Select “Show Only”

New Entiry -> Group -> Create -> Third Argument (Shape Type “Faces”)

Group Name: DxDy; Main Shape: PV; Select Right Vertical Face of the PV Shell if you are

standing at Origin looking at the Nozzle in +X direction; Click Add; Click “Apply”

Group Name: Dx; Main Shape: PV; Select Left Vertical Face of the PV Shell if you are standing

at Origin looking at the Nozzle in +X direction; Click Add; Click “Apply”

Face

“DxDy”

Face

“Dx”

Face

“Dz”

Face

“ForceE”

Face

“PrLong”

Group Name: Dz; Main Shape: PV; Select Bottom Horizontal Face of the PV Shell; Click Add;

Click “Apply”

Group Name: PrLong; Main Shape: PV; Select Top Horizontal Face of the PV; Click Add; Click

“Apply”

Group Name: IntPress; Main Shape: PV; Select All Inside surfaces of the Pressure Vessel Shell

and Nozzle (There should be 20 faces to be selected); Click Add; Click “Apply”

Group Name: ForceE; Main Shape: PV; Select Front face of the Nozzle; Click Add; Click “Apply

and Close”

Following step is only required if you want to have a Sub Mesh in the thickness of the Shell and

Nozzle.

Still in Group Create -> Select Second Argument (Shape Type “Wire”)

Group Name: Sub5; Main Shape: PV; Select all Edges in the Shell Thickness at the Vertical

and Horizontal Faces of the Shell, Select all Edges in the Nozzle Thickness (hdf file for

this study is available for download); Click Add; Click “Apply”

Right Click “PV” in Object Browser and Select “Show Only”

This concludes Modelling exercise for the Pressure Vessel.

Mesh Entire geometry is meshed with 3D Linear Hexahedral elements.

Global geometry was meshed with 3D Algorithm of Hexahedron (I,j,k), 2D Algorithm of Quadrangle

(Mapping) and 1D Algorithm of Wire Discretisation with Hypothesis of Nb Segments of 50

Equidistant distribution.

Following steps assumes that you are in Mesh module of Salome

Mesh -> Create Mesh

Name: PV; Geometry: PV (Select PV geometry from Geometry Module); 3D Tab: Algorithm:

Hexahedron (i,j,k); 2D Tab: Algorithm: Quadrangle (Mapping); 1D Tab: Algorithm: Wire

discretisation: Hypothesis: (Click Add Hypothesis Button and select) Nb_Segment; In Hypothesis

Construction: Name: (Default) Nb. Segments_1; Number of Segments: 40; Type of distribution:

Equidistant distribution; Click Ok; Click “Apply and Close”

Shell thickness was given a Sub

Mesh with 1D Algorithm of Wire

discretisation, with Hypothesis of

Nb Segments of 5 Equidistant

distribution and Additional

Hypothesis of Propogation of 1D

Hypothesis on opposite edge.

Right Click “PV” in Mesh Module in

Object Browser and Select “Create

Sub-mesh”

Name: (Default)

SubMesh_1; Mesh: PV; Geometry:

(Select) Sub5 (from Geometry Module); 1D Tab: Algorithm: Wire discretisation: Hypothesis: (Click

Add Hypothesis Button and select) Nb_Segment; In Hypothesis Construction: Name: (Default) Nb.

Segments_2; Number of Segments: 5; Type of distribution: Equidistant distribution; Click Ok; Add.

Hypothesis: (Click Add Hypothesis Button and select) Propagation of 1D Hyp. On opposite edges;


Right Click “PV” in Object Browser and Select “Compute”

Close-up of the Nozzle Mesh.

This mesh is suitable for Studying

stresses generated in Pressure

Vessel Shell. It is good for evaluating

Bending, Peak and Membrane

stresses in and around the Shell

Nozzle junction. Better Stress

distribution can be obtained by

using Quadratic meshing which will

be done in future studies.

Right Click “PV” in Object Browser

and Select “Create Groups from

Geometry”

Mesh:PV; Geometry: (Select DxDy

from Geometry Module) DxDy; Click

“Apply”

Mesh:PV; Geometry: (Select Dx from

Geometry Module) Dx; Click “Apply”

Mesh:PV; Geometry: (Select Dz from Geometry Module) Dz; Click “Apply”

Mesh:PV; Geometry: (Select PrLong from Geometry Module) PrLong; Click “Apply”

Mesh:PV; Geometry: (Select IntPress from Geometry Module) IntPress; Click “Apply”

Mesh:PV; Geometry: (Select ForceE from Geometry Module) ForceE; Click “Apply and Close”

Right Click “PV” in Object Browser and Select “Export to MED file”

Select a location for the med file and save it.

Loads and Restraints To provide Symmetric Boundary Condition to the Pressure Vessel following Boundary Conditions

were used.

1. Face “DxDy” was given Boundary condition of DX = 0.0 and DY = 0.0

2. Face “Dx” was given Boundary condition of DX = 0.0

3. Face “Dz” was given Boundary condition of DZ = 0.0

Three load cases were considered in this analysis

1. Internal Pressure of 0.5MPa applied on the Internal Face of the pressure vessel

2. Force of Fy = 9000N applied on the face of the flange

3. Combined Internal Pressure and Force

To account for the discontinuity in the Pressure Vessel shell, force equivalent to the Pressure acting

on the inside of the Nozzle was applied in Fx direction on face “ForceE”. If this balancing force was

not applied, Pressure Vessel Ovalization occurred due to un-balanced distribution of the Pressure on

internal face.

.comm file used for analysis with Code_Aster is shown here for easy reference. This file is

commented sufficiently to give information on what is going on.

DEBUT();

#Define Material Steel

Steel=DEFI_MATERIAU(ELAS=_F(E=210000.0,

NU=0.3,),);

#Read the mesh in 'MED' format

MAIL=LIRE_MAILLAGE(FORMAT='MED',);

#Assign the model Mechanical and in 3D

MODE=AFFE_MODELE(MAILLAGE=MAIL,

AFFE=_F(TOUT='OUI',

PHENOMENE='MECANIQUE',

MODELISATION='3D',),);

#Assign the material Steel previously defined

MATE=AFFE_MATERIAU(MAILLAGE=MAIL,

AFFE=_F(TOUT='OUI',

MATER=Steel,),);

#Boundary Condition 'Base' is Fixed in all directions

BCs=AFFE_CHAR_MECA(MODELE=MODE,

FACE_IMPO=(_F(GROUP_MA='Dx',

DX=0.0,),

_F(GROUP_MA='DxDy',

DX=0.0,

DY=0.0,),

_F(GROUP_MA='Dz',

DZ=0.0,),),);

#To Balance Internal Pressure at Nozzle Junction

Press1 = 0.5;

NozOR = 150.0;

NozIR = 140.0;

NozArIR = 3.14 * NozIR * NozIR;

ForceBal = NozArIR * Press1;

ForceBal = ForceBal / (3.14 * (NozOR * NozOR - NozIR * NozIR));

#To apply Longitudinal Stress

PVOR = 1500.0;

PVIR = 1490.0;

PVArIR = 3.14 * PVIR * PVIR;

LongStr = PVArIR * Press1;

#Pressure is applied on 1/2 Area for Hoop and is resisted by 1/2 Area so 1/2 cancels out

LongStr = LongStr / (3.14 * (PVOR * PVOR - PVIR * PVIR));

#Force of 9000N is distributed over the Area of Nozzle Tip

ForceY = 9000. / (3.14 * (NozOR * NozOR - NozIR * NozIR));

Loads=AFFE_CHAR_MECA(MODELE=MODE,

PRES_REP=_F(GROUP_MA=('IntPress'),

PRES=Press1,),

FORCE_FACE=(_F(GROUP_MA='PrLong',

FZ=LongStr,),

_F(GROUP_MA='ForceE',

FY=ForceY,),

_F(GROUP_MA='ForceE',

FX=ForceBal,),),);

RESU=MECA_STATIQUE(MODELE=MODE,

CHAM_MATER=MATE,

EXCIT=(_F(CHARGE=BCs,),

_F(CHARGE=Loads,),),);

#Calculate fields on Elements

RESU=CALC_ELEM(reuse =RESU,

RESULTAT=RESU,

OPTION=('SIEF_ELNO','SIEQ_ELNO','SIGM_ELNO'),);

#Calculate fields on Nodes

RESU=CALC_NO(reuse =RESU,

RESULTAT=RESU,

OPTION=('SIGM_NOEU','SIEQ_NOEU','REAC_NODA',),);

#Dump the entire result in a text file

IMPR_RESU(FORMAT='RESULTAT',

RESU=_F(MAILLAGE=MAIL,

RESULTAT=RESU,

NOM_CHAM=('SIEQ_ELNO','SIEQ_NOEU','DEPL','REAC_NODA','SIGM_NOEU'),),);

#Dump the result in .med file that can be read by Salome

IMPR_RESU(FORMAT='MED',

UNITE=80,

RESU=_F(MAILLAGE=MAIL,

RESULTAT=RESU,

NOM_CHAM=('SIEQ_ELNO','SIEQ_NOEU','DEPL','REAC_NODA','SIGM_NOEU'),),);

FIN();

The output from the analysis is saved as a .med file that can be read by Salome and used for Post

processing.

Analysis of results - Present the displacement and Stress results (Including plots and animation)

Internal Pressure only

The first of the three cases analysed was Internal Pressure only

Internal Pressure of 0.5MPa is applied to the inside of the Pressure Vessel and Nozzle. The

displacement and VonMises stresses are shown below

Below is the snapshot of displacement with scale factor of 100. Maximum displacement is 1.2mm.

This is inline with the growth of diameter of the vessel as calculated manually.

Below is the displacement upclose near the nozzle.

The Vonmises stress snapshot is shown below

Below is the Vonmises stresses upclose

Vonmises stresses on the inside of the Pressure Vessel

Vonmises stresses on the inside upclose

Vonmises stresses remote to the nozzle is 65MPa which is inline with the hand calculation.

Force Only

Force of 9000N is applied on the face of the Nozzle in Fy direction.

The displacement and Vonmises stresses for Force Only case is shown below.

Displacement upclose

Vonmises stresses for the Force only is shown below

Vonmises stresses upclose

Vonmises on the inside of the Pressure Vessel

Vonmises on the inside upclose

Pressure and Force applied together

The combination of Pressure and Force will see some stresses around the nozzle increase but the

overall stresses in the pressure vessel remote to the nozzle should remain unchanged and that is

what is seen in the analysis.

Displacement for Pressure and Force.

Displacement upclose

Vonmises stresses

Vonmises upclose

Vonmises on the inside of the pressure vessel

Vonmises stresses on the inside of the pressure vessel upclose

As can be seen above in the Vonmises stresses on the inside of the Pressure Vessel, the equivalent

stresses have fallen from 231 MPa in Pressure Only case to 198 MPa in Pressure and Force case.

For evaluation and comparison purposes, Bottom Negative Y Quarter section of the nozzle is shown

with VonMises Stresses for all three load cases. First Column is for Pressure Only Load case, Second

Column is for Force Only Load Case and Third Column is for combined case. First Row is showing

complete Clipped Model, Second Row is showing SCL2 and Third row is showing SCL1.

Pressure Only Force Only Pressure and Force

Two stress Classification Lines were taken for this study and the tabulated SIXX, SIYY, SIZZ, SIXY, SIYZ,

SIZX, Vonmises total along with Membrane and Bending stresses are presented here

Pressure Only Force Only Pressure and Force Only

SCL1 SCL1 SCL1

Membrane

Stress (MPa)

Bending

Stress (MPa)

Membrane

Stress (MPa)

Bending

Stress (MPa)

Membrane

Stress (MPa)

Bending

Stress (MPa)

SIXX 1.788 23.151 0.785 9.095 -0.477 38.419

SIYY 144.799 25.550 -0.978 13.669 8.365 60.677

SIZZ 15.043 32.353 -0.927 11.156 32.305 44.083

SIXY -0.749 8.916 -3.143 4.090 -11.720 17.051

SIYZ 0.820 4.348 -0.010 -0.003 -0.022 -0.007

SIZX -0.027 -0.012 -0.041 0.001 -0.093 0.004

Total 136.878 19.068 5.715 8.119 35.708 35.689

SCL2 SCL2 SCL2

Membrane

Stress (MPa)

Bending

Stress (MPa)

Membrane

Stress (MPa)

Bending

Stress (MPa)

Membrane

Stress (MPa)

Bending

Stress (MPa)

SIXX -0.5452 20.4399 -0.192 -0.816 3.052 23.185

SIYY 40.758 16.022 0.225 -1.435 161.190 8.121

SIZZ -27.977 36.552 0.026 -1.651 26.079 41.271

SIXY -7.528 1.658 -0.771 0.016 -0.773 0.011

SIYZ 0.676 9.302 0.087 -0.407 1.197 14.879

SIZX -0.075 -0.018 -2.992 4.272 -3.014 4.256

Total 61.342 24.862 5.365 7.470 148.087 39.305

Evaluation of the stresses is left to the reader.

Future aspirations from this analysis are to perform FEA based on ASME Section VIII Division 2 Part 5

rules. Use Stress Classification line to find out Membrane, Bending and Peak stresses which shall be

carried out in future analysis and documented in a report.

Vonmises stresses were used as a criteria to determine equivalent stress for comparison.

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

calculations at location remote to the Nozzle Pressure Vessel junction. This study is not exhaustive

and was conducted to try modelling Pressure Vessel geometry and partition it to make it ready for

meshing, To mesh the Pressure Vessel geometry with Hexahedral mesh, To carry out Finite Element

analysis of a Pressure Vessel Nozzle section using Code_Aster for analysis, And to perform Post

Processing using Salome.

Outcome of the analysis can be summarised as

1. Salome can be used as a competent software to model the geometry, Mesh it and perform

Post Processing on the results

2. Code_Aster is a powerful software but due to it being in Non-english format is a restriction.

3. Open Source softwares can be used for performing FEA based on ASME Section VIII Division

2 Part 5.

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

1. Use of 2nd order or Higher order elements

2. Mesh refinement around the nozzle shell junction

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

fea of pressure vessel and nozzle junction -...

Documents