Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation
objective-
1. To simulate the same problem as in previous challenge but by applying Symmetry Boundary Condition. for thrta 10 25 nad 45.
and here is matlab code for theta 10 to genrate the blockMeshDict file
L=1
theta=10
D=0.006
r=D/2
line1='/* --------------------------------------------------------------- C++ ---------------------------------------------*\';
line2='|= = = = = = = = = | |'
line3='| \\ / | F ield openFoam :The open SourceCFD Toolbox'
line4='| \\ / | O peration Version; 4.1'
line5='| \\ / | A nd Web: www.openFoam.org'
line6='| \\ / | M anipulation'
line7='\-----------------------------------------------------------------------------------------------------------------------\'
f1=fopen('blockMeshDict' , 'w')
fprintf(f1,'%s\n', line1)
fprintf(f1,'%s\n', line2)
fprintf(f1,'%s\n', line3)
fprintf(f1,'%s\n', line4)
fprintf(f1,'%s\n', line5)
fprintf(f1,'%s\n', line6)
fprintf(f1,'%s\n', line7)
fprintf(f1 ,'FoamFile\n{\n')
fprintf(f1, '%12s \t 2.0; \n' ,'version')
fprintf(f1, '%12s \t ascii; \n' ,'format')
fprintf(f1, '%12s \t dictionary; \n' ,'class')
fprintf(f1, '%12s \t blockMeshDict; \n' ,'object')
fprintf(f1, '}\n')
header8 ='// * * * * * * ****//'
fprintf(f1,'%s\n\n',header8)
fprintf(f1, 'convertToMeters 1 ;\n\n')
fprintf(f1 , 'vertices\n')
fprintf(f1,'(\n')
fprintf(f1, '\t (%d %d %d)\n', 0 ,0,0)
fprintf(f1, '\t (%d %d %d)\n', 0 ,r*cosd(theta/2),sind(theta/2))
fprintf(f1, '\t (%d %d %d)\n', 0 ,r*cosd(theta/2),-sind(theta/2))
fprintf(f1, '\t (%d %d %d)\n', L,0,0)
fprintf(f1, '\t (%d %d %d)\n', L ,r*cosd(theta/2),sind(theta/2))
fprintf(f1, '/t (%d %d %d)\n', L ,r*cosd(theta/2),-sind(theta/2))
fprintf(f1, '); \n\n')
fprintf(f1,' blocks\n')
fprintf(f1,'(\n')
fprintf(f1, '\t hex (0 3 5 2 0 3 4 1) (%d %d %d)',300,30,1)
fprintf(f1,' SimpleGrading (1 0.1 1)\n\n')
fprintf(f1,');\n')
fprintf(f1, 'edges\n(\n\tarc %d %d (%d %d %d)\n',1,2,0 ,r,0)
fprintf(f1, '\tarc %d %d (%d %d %d)\n',4,5,L ,r,0)
fprintf(f1, ');\n\n')
fprintf(f1, 'boundary\n')
fprintf(f1,'(\n')
fprintf(f1, '\t inlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type patch ;\n')
fprintf(f1, '\t \t faces\n')
fprintf(f1,'\t\t (\n')
fprintf(f1, ' \t \t \t (0 1 2 0)\n')
fprintf(f1,'\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t outlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type patch ;\n')
fprintf(f1, '\t \t faces\n')
fprintf(f1,'\t\t (\n')
fprintf(f1, ' \t \t \t (3 5 4 3)\n')
fprintf(f1,'\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t top \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wall ;\n')
fprintf(f1, '\t \t faces\n')
fprintf(f1,'\t\t (\n')
fprintf(f1, ' \t \t \t (1 4 5 2)\n')
fprintf(f1,'\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t back \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type symmetry ;\n')
fprintf(f1, '\t \t faces\n')
fprintf(f1,'\t\t (\n')
fprintf(f1, ' \t \t \t (0 2 5 3)\n')
fprintf(f1,'\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t front \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type symmetry ;\n')
fprintf(f1, '\t \t faces\n')
fprintf(f1,'\t\t (\n')
fprintf(f1, ' \t \t \t (0 3 4 1)\n')
fprintf(f1,'\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '\t axis \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type empty ;\n')
fprintf(f1, '\t \t faces\n')
fprintf(f1,'\t\t (\n')
fprintf(f1, ' \t \t \t (0 3 3 0)\n')
fprintf(f1,'\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1,');\n')
fprintf(f1,'mergePatchPairs\n(\n')
fprintf(f1, ');\n')
fprintf(f1, '%s\n',header8)
fclose(f1)and generated blockMeshDict file is as follows
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 8
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0 0 0)
(0 2.988584e-03 8.715574e-02)
(0 2.988584e-03 -8.715574e-02)
(1 0 0)
(1 2.988584e-03 8.715574e-02)
(1 2.988584e-03 -8.715574e-02)
);
blocks
(
hex (0 3 5 2 0 3 4 1) (300 30 1) SimpleGrading (1 0.1 1)
);
edges
(
arc 1 2 (0 3.000000e-03 0)
arc 4 5 (1 3.000000e-03 0)
);
boundary
(
inlet
{
type patch ;
faces
(
(0 1 2 0)
);
}
outlet
{
type patch ;
faces
(
(3 5 4 3)
);
}
top
{
type wall ;
faces
(
(1 4 5 2)
);
}
back
{
type symmetry ;
faces
(
(0 2 5 3)
);
}
front
{
type symmetry ;
faces
(
(0 3 4 1)
);
}
axis
{
type empty ;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// * * * * * * ****//
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 8
\\/ 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 0.1552516;
}
top
{
type zeroGradient;
}
back
{
type symmetry;
}
front
{
type symmetry;
}
axis
{
type empty;
}
}
// ************************************************************************* //
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 8
\\/ 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 (0.3115 0 0);
}
outlet
{
type zeroGradient;
}
top
{
type noSlip;
}
back
{
type symmetry;
}
front
{
type symmetry;
}
axis
{
type empty;
}
}
// ************************************************************************* //
for 25
for 45
the velocity for fully developed for theta 45 at distance of 0.75m
comparsion of analytical and simulation
| wedge angle | cournant number | simulation_time | velocity analytical | simulation velocity | error |
| 10 | 0.341082 | 504.7 | 0.623 | 0.62269 | 0.00031 |
| 25 | 0.343641 | 498.49 | 0.623 | 0.6285 | 0.00015 |
| 45 | 0.350561 | 507.43 | 0.623 | 0.62 | 0.003 |
| wedge angle(theta) | courant number | simulation time(sec) | analytical maximum velocity(m/sec) |
simulation velocity |
| 3 | ||||
| 10 | 0.341082 | 504.7 | ||
| 25 | 0.343641 | 498.49 | ||
| 45 | 0.350561 | 507.43 |