Week 12 - Symmetry vs Wedge vs HP equation
Symmetry vs Wedge Boundary Condition vs HP equation.
We have results of simulation from previous challenge for Hagen Poiseuille's equation from Analytical solution and Wedge boundary condition for 2,3and 4 degree wedge angles.
Here we will compare results for wedge angle of 10,25 and 45 degrees with Symmetry boundary condition.
First we will create Matlab code that can generate computational Mesh for any wedge angle same as in previous challenge.That code will be a blockMeshDict file which will be used in OpenFoam for creating Mesh.
Wedge boundary condition need to be replaced with symmetry boundary condition in blockMeshDict file,and in Pressure and velocity boundary file.
Matlab Code file:
clear all;
close all;
clc
D=0.02%Diameter of pipe in m
R=D/2 %Radius of pipe
theta=input('Enter the value of theta in degrees---'); %%wedge angle in degrees
L=3; %%Length of pipe in m
%Wedge dimension at 4 degrees
Point1=D/2*cosd(theta/2);
Point2=D/2*sind(theta/2);
%%File for writing blockMesh code
f2=fopen('blockMeshDict.txt','w')
%%Vertex and other parameters defined
Vertex_0=[0 0 0];
Vertex_1=[0 0 L];
Vertex_2=[Point1 -Point2 0];
Vertex_3=[Point1 Point2 0];
Vertex_4=[Point1 -Point2 L];
Vertex_5=[Point1 Point2 L];
Block=[0 2 3 0 1 4 5 1]
Cells=[50 1 300]
Grading=[0.1 1 1];
Inlet_face=[0 2 3 0];
Outlet_face=[1 4 5 1];
wall=[2 3 5 4];
wedge1=[0 1 4 2];
wedge2=[0 1 5 3];
axis=[0 1 1 0];
fprintf(f2,['/*------------------------------*- C++ -*----------------------------------',...
'*\\',...
'\n| ========= | |',...
'\n| \\\\ / F ield | OpenFOAM: TheOpen Source CFD Toolbox |',...
'\n| \\\\ / O peration | Version: plus |',...
'\n| \\\\ / A nd | Web: www.OpenFOAM.com |'...
'\n| \\\\ / M anipulation | |',...
'\n\\*-------------------------------------------------------------------------*/',...
'\nFoamFile',...
'\n{',...
'\n version 2.0;',...
'\n format ascii;',...
'\n class dictionary;',...
'\n object blockMeshDict;',...
'\n}',...
'\n// ******************************************************************* //'])
fprintf(f2,'\n%s %.3f','convertToMeters', 1,';');
fprintf(f2,'\n')
fprintf(f2,'\nvertices');
fprintf(f2,'\n(');
fprintf(f2,'\n(');
fprintf(f2,'%12.6f',Vertex_0);
fprintf(f2,')');
fprintf(f2,'\n(');
fprintf(f2,'%12.6f',Vertex_1);
fprintf(f2,')');
fprintf(f2,'\n(');
fprintf(f2,'%12.6f',Vertex_2);
fprintf(f2,')');
fprintf(f2,'\n(');
fprintf(f2,'%12.6f',Vertex_3);
fprintf(f2,')');
fprintf(f2,'\n(');
fprintf(f2,'%12.6f',Vertex_4);
fprintf(f2,')');
fprintf(f2,'\n(');
fprintf(f2,'%12.6f',Vertex_5);
fprintf(f2,')');
fprintf(f2,'\n);');
fprintf(f2,'\n');
fprintf(f2,'\nblocks');
fprintf(f2,'\n(');
fprintf(f2,'\n');
fprintf(f2,' hex (');
fprintf(f2,'%2.0f',Block);
fprintf(f2,') ');
fprintf(f2,'(');
fprintf(f2,'%4.0f',Cells);
fprintf(f2,') ');
fprintf(f2,'simpleGrading')
fprintf(f2,' (');
fprintf(f2,'%5.1f',Grading);
fprintf(f2,')');
fprintf(f2,'\n);');
fprintf(f2,'\n');
fprintf(f2,'\nedge')
fprintf(f2,'\n(')
fprintf(f2,'\n);')
fprintf(f2,'\n')
fprintf(f2,'\nboundary')
fprintf(f2,['\n(',...
'\ninlet',...
'\n{',...
'\n type patch;',...
'\n faces',...
'\n(',...
'\n('])
fprintf(f2,'%2.0f',Inlet_face)
fprintf(f2,[')',...
'\n);',...
'\n}',])
fprintf(f2,['\noutlet',...
'\n{',...
'\n type patch;',...
'\n faces',...
'\n(',...
'\n('])
fprintf(f2,'%2.0f',Outlet_face)
fprintf(f2,[')',...
'\n);',...
'\n}',])
fprintf(f2,['\nwall',...
'\n{',...
'\n type wall;',...
'\n faces',...
'\n(',...
'\n('])
fprintf(f2,'%2.0f',wall)
fprintf(f2,[')',...
'\n);',...
'\n}',])
fprintf(f2,['\nfront',...
'\n{',...
'\n type symmetry;',...
'\n faces',...
'\n(',...
'\n('])
fprintf(f2,'%2.0f',wedge1)
fprintf(f2,[')',...
'\n);',...
'\n}',])
fprintf(f2,['\nback',...
'\n{',...
'\n type symmetry;',...
'\n faces',...
'\n(',...
'\n('])
fprintf(f2,'%2.0f',wedge2)
fprintf(f2,[')',...
'\n);',...
'\n}',])
fprintf(f2,['\naxis',...
'\n{',...
'\n type empty;',...
'\n faces',...
'\n(',...
'\n('])
fprintf(f2,'%2.0f',axis)
fprintf(f2,[')',...
'\n);',...
'\n}',])
fprintf(f2,'\n);')
fprintf(f2,'\nmergePatchPairs')
fprintf(f2,'\n(')
fprintf(f2,'\n);')
fprintf(f2,'\n// ********************************************************* //')
fclose(f2); %%File close after writing
OpenFoam Case setup files:
BlockMeshDict:
/*------------------------------*- C++ -*----------------------------------*\
| ========= | |
| \\ / F ield | OpenFOAM: TheOpen Source CFD Toolbox |
| \\ / O peration | Version: plus |
| \\ / A nd | Web: www.OpenFOAM.com |
| \\ / M anipulation | |
\*-------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
object blockMeshDict;
}
// ******************************************************************* //
convertToMeters 1.000
;
vertices
(
( 0.000000 0.000000 0.000000)
( 0.000000 0.000000 3.000000)
( 0.009763 -0.002164 0.000000)
( 0.009763 0.002164 0.000000)
( 0.009763 -0.002164 3.000000)
( 0.009763 0.002164 3.000000)
);
blocks
(
hex ( 0 2 3 0 1 4 5 1) ( 50 1 300) simpleGrading ( 0.1 1.0 1.0)
);
edge
(
);
boundary
(
inlet
{
type patch;
faces
(
( 0 2 3 0)
);
}
outlet
{
type patch;
faces
(
( 1 4 5 1)
);
}
wall
{
type wall;
faces
(
( 2 3 5 4)
);
}
front
{
type symmetry;
faces
(
( 0 1 4 2)
);
}
back
{
type symmetry;
faces
(
( 0 1 5 3)
);
}
axis
{
type empty;
faces
(
( 0 1 1 0)
);
}
);
mergePatchPairs
(
);
// ********************************************************* //ControlDict file:
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application icoFoam;
startFrom latestTime;
startTime 0;
stopAt endTime;
endTime 30;
deltaT 5e-3;
writeControl timeStep;
writeInterval 40;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Pressure boundary condition file:
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class volScalarField;
object p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 2 -2 0 0 0 0];
internalField uniform 0;
boundaryField
{
inlet
{
type zeroGradient;
}
outlet
{
type fixedValue;
value uniform 0.0167;
}
wall
{
type zeroGradient;
}
front
{
type symmetry;
}
back
{
type symmetry;
}
axis
{
type empty;
}
}
// ************************************************************************* //Velocity Boundary condition file:
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class volVectorField;
object U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 1 -1 0 0 0 0];
internalField uniform (0 0 0);
boundaryField
{
inlet
{
type fixedValue;
value uniform (0 0 0.093);
}
outlet
{
type zeroGradient;
}
wall
{
type noSlip;
}
front
{
type symmetry;
}
back
{
type symmetry;
}
axis
{
type empty;
}
}
// ************************************************************************* //Transport Properties file:
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
location "constant";
object transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
nu [0 2 -1 0 0 0 0] 9e-07;
// ************************************************************************* //For `25^o` degree wedge angle:
At Hydrodynamic Entrance Length:
Simulation result for Velocity at Inlet
Simulation result for Velocity at Outlet:
For wedge angle `10^o`
For wedge angle `45^o`:
Outcomes:
1. A wedge boundary condition is used for axial and spherical symmetry ,but the symmetry boundary condition defines a mirror face/surface. It should only be used if the physical object or geometry and the expected flow field pattern of the developed solution are mirrored along that surface.
2.Though simulation using symmetry boundary condition take more time for execution than wedge boundary,but it gives less error and accurate results close to Analytical solution.
| Wedge Angle | Execution Time | Max. Velocity obtained by simulation | Max. Velocity (by Hagen Poiseuille equation) |
Error (in %) |
| 10 | 5592 | 0.18455 | 0.186 | 0.78 |
| 25 | 5585 | 0.18472 | 0.186 | 0.69 |
| 45 | 5490 | 0.18509 | 0.186 | 0.49 |
3.From results above it can be figured out that with increase in wedge angle ,execution time decreases as well as results obtained are more accurate,less error.