Week 12 - Symmetry vs Wedge vs HP equation
Aim:
• To write a MATLAB/Octave code for symmetry boundary conditions of flow through pipe.
• To obtain results at 10,25 and 45 degree angles of pipe flow
. To compare results of wedge boundary conditions with symmetry boundary conditions.
Theory:
The inputs to the problem are same as the one in wedge boundary condition problem. BlockMesh dict file needs to be updated according to required value of angles ie 10,25 and 45. Wedge type is required to be updated from wedge to symmetry in block Mesh pressure and velocity files.
Pre-Processing Steps:
1. The initial steps for this challenge remains same as wedge challenge.
2. Change the value of theta as per requirement for each case in MATLAB/Octave code and obtain the blockMesh dict file using file parsing technique .
3. Change the wedge type from wdge to symmetry in blockMesh diet file in system folder
4. Similarly make changs in pressure and velocity file in 0 folder and change wedge type
5. Other inputs remain same.
6. Open terminal and navigate to cavity folder in case folder in run folder in OpenFoam.
7. Run blockMesh command after setting of all parameters.
8. Then run icoFoam command as we are using icoFoarn solver.
9. Upon succesfully running of icoFoam command, launch paraview to post process the results by using paraFoam command
Matlab code:
clear all
close all
clc
%input data
D=0.01
R=D/2
Re=2100
Le=0.05*Re*D;
theta=[10];
mu=8.90e-04;
rho=997.130;
nu=(mu/rho);
L=Le+0.45
%calculating solution according to HP equation
V=(Re*mu)/(rho*D); %average velcoity
U_max=2*V; %max velocity
del_Pdel_x=(8*mu*V)/(R^2); % pressure gradient
delta_P=(8*mu*V*L)/(R^2); % pressure drop
Kin_P= delta_P/rho ; % kinematic pressure
%vertices;
v0=[0 0 0]
v1=[0 R*cosd(theta/2) -R*sind(theta/2)]
v2=[0 R*cosd(theta/2) R*sind(theta/2)]
v3=[L 0 0]
v4=[L R*cosd(theta/2) -R*sind(theta/2)]
v5=[L R*cosd(theta/2) R*sind(theta/2)]
f1= fopen('BlockMeshDict.txt','w');
fprintf(f1, '%s\n', '/*--------------------------------*- C++ -*----------------------------------*\');
fprintf(f1, '%s\n', '========= | ');
fprintf(f1, '%s\n', '\\ / F ield | OpenFOAM: The Open Source CFD Toolbox ');
fprintf(f1, '%s\n', ' \\ / O peration | Website: https://openfoam.org ');
fprintf(f1, '%s\n', ' \\ / A nd | Version: 8 ');
fprintf(f1, '%s\n', ' \\/ M anipulation | ');
fprintf(f1, '%s\n', '\*---------------------------------------------------------------------------*/');
fprintf(f1, '%s\n', 'FoamFile');
fprintf(f1, '%s\n', '{');
fprintf(f1, '%s\n', ' version 2.0;');
fprintf(f1, '%s\n', ' format ascii;');
fprintf(f1, '%s\n', ' class dictionary;');
fprintf(f1, '%s\n', ' object blockMeshDict;');
fprintf(f1, '%s\n', '}');
fprintf(f1, '%s\n', '// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //');
fprintf(f1, '%s\n', ' convertToMeters 1;');
%defining the vertices of the geometry
fprintf(f1, '%s\n', 'vertices');
fprintf(f1, '%s\n', '(');
fprintf(f1, '\t(%d %d %d)\n' ,v0(1),v0(2),v0(3));
fprintf(f1, '\t(%d %d %d)\n' ,v1(1),v1(2),v1(3));
fprintf(f1, '\t(%d %d %d)\n' ,v2(1),v2(2),v2(3));
fprintf(f1, '\t(%d %d %d)\n' ,v3(1),v3(2),v3(3));
fprintf(f1, '\t(%d %d %d)\n' ,v4(1),v4(2),v4(3));
fprintf(f1, '\t(%d %d %d)\n' ,v5(1),v5(2),v5(3));
fprintf(f1, '%s\n\n',');');
%defining the blocks
fprintf(f1, '%s\n', 'blocks');
fprintf(f1, '%s\n', '(');
fprintf(f1, '\thex(0 1 2 0 3 4 5 3) (%d %d %d) simpleGrading(1 1 1)\n',300,1,30);
fprintf(f1, '%s\n\n',');');
%defining the edges
fprintf(f1, '%s\n', 'edges');
fprintf(f1, '%s\n', '(');
fprintf(f1, '\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, '%s\n\n',');');
%defining the boundaries
fprintf(f1, '%s\n', 'boundary');
fprintf(f1, '%s\n', '(');
fprintf(f1, '\tinlet\n\t{\n');
fprintf(f1, '\t\ttype patch;\n');
fprintf(f1, '\t\tfaces\n\t\t(\n');
fprintf(f1, '\t\t\t(0 2 1 0)\n');
fprintf(f1, '\t\t);\n\t}\n');
fprintf(f1, '\toutlet\n\t{\n');
fprintf(f1, '\t\ttype patch;\n');
fprintf(f1, '\t\tfaces\n\t\t(\n');
fprintf(f1, '\t\t\t(3 4 5 3)\n');
fprintf(f1, '\t\t);\n\t}\n');
fprintf(f1, '\twedge_front\n\t{\n');
fprintf(f1, '\t\ttype symmetry;\n');
fprintf(f1, '\t\tfaces\n\t\t(\n');
fprintf(f1, '\t\t\t(0 3 5 2)\n');
fprintf(f1, '\t\t);\n\t}\n');
fprintf(f1, '\twedge_back\n\t{\n');
fprintf(f1, '\t\ttype symmetry;\n');
fprintf(f1, '\t\tfaces\n\t\t(\n');
fprintf(f1, '\t\t\t(0 1 4 3)\n');
fprintf(f1, '\t\t);\n\t}\n');
fprintf(f1, '\ttop\n\t{\n');
fprintf(f1, '\t\ttype wall;\n');
fprintf(f1, '\t\tfaces\n\t\t(\n');
fprintf(f1, '\t\t\t(1 2 5 4)\n');
fprintf(f1, '\t\t);\n\t}\n');
fprintf(f1, '\taxis\n\t{\n');
fprintf(f1, '\t\ttype empty;\n');
fprintf(f1, '\t\tfaces\n\t\t(\n');
fprintf(f1, '\t\t\t(0 3 3 0)\n');
fprintf(f1, '\t\t);\n\t}\n');
fprintf(f1, ');\n\n');
fprintf(f1, 'mergePatchPairs\n(\n);\n\n');
fprintf(f1, '// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //');
fclose(f1)
WEDGE BOUNDARY CONDITION:
Angle 10:
BlockMeshDict:
/*--------------------------------*- 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 4.9809735e-03 -4.357787e-04)
(0 4.9809735e-03 4.357787e-04)
(1.5 0 0)
(1.5 4.9809735e-03 -4.357787e-04)
(1.5 4.9809735e-03 4.357787e-04)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (30 1 100) simpleGrading (0.2 1 1)
);
edges
(
arc 1 2 (0 5.000000e-03 0)
arc 4 5 (1.5 5.000000e-03 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
top
{
type wall;
faces
(
(2 5 4 1)
);
}
wedge_back
{
type wedge;
faces
(
(0 1 4 3)
);
}
wedge_front
{
type wedge;
faces
(
(0 3 5 2)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //ControlDict:
/*--------------------------------*- 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;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application icoFoam;
startFrom startTime;
startTime 0;
stopAt endTime;
endTime 10;
deltaT 1e-2;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Velocity:
/*--------------------------------*- 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 (0.187462 0 0);
boundaryField
{
inlet
{
type fixedValue;
value uniform (0.187462 0 0);
}
outlet
{
type zeroGradient;
}
top
{
type noSlip;
value uniform 0;
}
wedge_back
{
type wedge;
}
wedge_front
{
type wedge;
}
axis
{
type empty;
}
}
// ************************************************************************* //Pressure:
/*--------------------------------*- 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;
}
top
{
type zeroGradient;
}
wedge_back
{
type wedge;
}
wedge_front
{
type wedge;
}
axis
{
type empty;
}
}
// ************************************************************************* //Results:
Angle 25:
BlockMeshDict:
/*--------------------------------*- 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 4.88148e-03 -1.0821981e-03)
(0 4.88148e-03 1.0821981e-03)
(1.5 0 0)
(1.5 4.88148e-03 -1.0821981e-03)
(1.5 4.88148e-03 1.0821981e-03)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (30 1 100) simpleGrading (0.2 1 1)
);
edges
(
arc 1 2 (0 5.000000e-03 0)
arc 4 5 (1.5 5.000000e-03 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
top
{
type wall;
faces
(
(2 5 4 1)
);
}
wedge_back
{
type wedge;
faces
(
(0 1 4 3)
);
}
wedge_front
{
type wedge;
faces
(
(0 3 5 2)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //Results:
Angle 45:
BlockMeshDict:
/*--------------------------------*- 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 4.6193977e-03 -1.9134172e-03)
(0 4.6193977e-03 1.9134172e-03)
(1.5 0 0)
(1.5 4.6193977e-03 -1.9134172e-03)
(1.5 4.6193977e-03 1.9134172e-03)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (30 1 100) simpleGrading (0.2 1 1)
);
edges
(
arc 1 2 (0 4.600000e-03 0)
arc 4 5 (1.5 4.600000e-03 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
top
{
type wall;
faces
(
(2 5 4 1)
);
}
wedge_back
{
type wedge;
faces
(
(0 1 4 3)
);
}
wedge_front
{
type wedge;
faces
(
(0 3 5 2)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //Results:
SYMMETRY BOUNDARY CONDITION:
Angle 10:
BlockMeshDict:
/*--------------------------------*- 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 4.9809735e-03 -4.357787e-04)
(0 4.9809735e-03 4.357787e-04)
(1.5 0 0)
(1.5 4.9809735e-03 -4.357787e-04)
(1.5 4.9809735e-03 4.357787e-04)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (30 1 100) simpleGrading (0.2 1 1)
);
edges
(
arc 1 2 (0 5.000000e-03 0)
arc 4 5 (1.5 5.000000e-03 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
top
{
type wall;
faces
(
(2 5 4 1)
);
}
wedge_back
{
type symmetry;
faces
(
(0 1 4 3)
);
}
wedge_front
{
type symmetry;
faces
(
(0 3 5 2)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //ControlDict:
/*--------------------------------*- 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;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application icoFoam;
startFrom startTime;
startTime 0;
stopAt endTime;
endTime 10;
deltaT 1e-2;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Velocity:
/*--------------------------------*- 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 (0.187462 0 0);
boundaryField
{
inlet
{
type fixedValue;
value uniform (0.187462 0 0);
}
outlet
{
type zeroGradient;
}
top
{
type noSlip;
value uniform 0;
}
wedge_back
{
type symmetry;
}
wedge_front
{
type symmetry;
}
axis
{
type empty;
}
}
// ************************************************************************* //Pressure:
/*--------------------------------*- 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;
}
top
{
type zeroGradient;
}
wedge_back
{
type symmetry;
}
wedge_front
{
type symmetry;
}
axis
{
type empty;
}
}
// ************************************************************************* //Results:
Angle 25:
BlockMeshDict:
/*--------------------------------*- 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 4.88148e-03 -1.0821981e-03)
(0 4.88148e-03 1.0821981e-03)
(1.5 0 0)
(1.5 4.88148e-03 -1.0821981e-03)
(1.5 4.88148e-03 1.0821981e-03)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (30 1 100) simpleGrading (0.2 1 1)
);
edges
(
arc 1 2 (0 5.000000e-03 0)
arc 4 5 (1.5 5.000000e-03 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
top
{
type wall;
faces
(
(2 5 4 1)
);
}
wedge_back
{
type symmetry;
faces
(
(0 1 4 3)
);
}
wedge_front
{
type symmetry;
faces
(
(0 3 5 2)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //Results:
Angle 45:
BlockMeshDict:
/*--------------------------------*- 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 4.6193977e-03 -1.9134172e-03)
(0 4.6193977e-03 1.9134172e-03)
(1.5 0 0)
(1.5 4.6193977e-03 -1.9134172e-03)
(1.5 4.6193977e-03 1.9134172e-03)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (30 1 100) simpleGrading (0.2 1 1)
);
edges
(
arc 1 2 (0 4.600000e-03 0)
arc 4 5 (1.5 4.600000e-03 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
top
{
type wall;
faces
(
(2 5 4 1)
);
}
wedge_back
{
type symmetry;
faces
(
(0 1 4 3)
);
}
wedge_front
{
type symmetry;
faces
(
(0 3 5 2)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //Results:
Comparison:
Here by comparing there is no much change in the max.velocities. The only difference observed is execution time little high than type-wedge.
Wedge angle Max velocity Max velocity Error clock Max courant
(Analytical) (Numerical) (%) Time(sec) number
10 0.374924 0.37900 1.08% 49s 0.124629
25 0.374924 0.37770 0.74% 38s 0.493524
45 0.374924 0.37750 0.71% 39s 0.504651
While the angle increases the error in the maximum velocity is decreased. Though there is not much difference between analytical and numerical results and also with increasing the angle of the wedge, The Courant number is slightly increasing.
From the above results, we can surely say that symmetricplane BC plays an important role in terms of accuracy in the result. Take a look at the value of the maximum velocity at the center of pipe in case of wedge BC value of maximum velocity varies with an increase in the angle of the wedge or we can say that if we prefer lesser wedge angle percentage error also reduces due to size of mesh element.
In the case of symmetry Plane BC, it mirrors all the value which reduces computational efforts, hence computation needs not to do on sub-domain of the complete setup
As this symmetryPlane BC mirrors faces/surfaces which enable us to go for a higher wedge angle, unlike wedge BC which is constrained to <5 degrees because it is axis symmetric boundary condition.