Week 12 - Symmetry vs Wedge vs HP equation
Aim:
• To write a MATLAB/Octave code for symmetry boundary conditions of flow through the 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 the same as the one in the wedge boundary condition problem. BlockMesh dict file needs to be updated according to the 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.
a Matlab program that takes an angle as input and generates a blockMesh file for the given angle.
clear all
close all
clc
%input data
D=0.004; %diameter of the pipe
R=D/2 ; %radius of the pipe
Re=2100 ;%reynolds number
Le=0.05*Re*D; %entry length
theta=45; %wedge angle
mu=8.96e-04; %kinematic viscosity of water
rho=997; %density of water
nu=(mu/rho);
L=Le+0.7; %total length of the pipe
%calculating solution according to Hagen poiseuille's 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]; %point o
v1=[0 R*cosd(theta/2) -R*sind(theta/2)];%point 1
v2=[0 R*cosd(theta/2) R*sind(theta/2)];%point 2
v3=[L 0 0];%point 3
v4=[L R*cosd(theta/2) -R*sind(theta/2)];%point4
v5=[L R*cosd(theta/2) R*sind(theta/2)];%point 5
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\n', '// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //');
fprintf(f1, '%s\n\n', 'convertToMeters 1;');
%defining the vertices of the geometry
fprintf(f1, '%s\n', 'vertices');
fprintf(f1, '%s\n\n', '(');
fprintf(f1, '(%d %d %d)\n' ,v0(1),v0(2),v0(3));
fprintf(f1, '(%d %d %d)\n' ,v1(1),v1(2),v1(3));
fprintf(f1, '(%d %d %d)\n' ,v2(1),v2(2),v2(3));
fprintf(f1, '(%d %d %d)\n' ,v3(1),v3(2),v3(3));
fprintf(f1, '(%d %d %d)\n' ,v4(1),v4(2),v4(3));
fprintf(f1, '(%d %d %d)\n\n' ,v5(1),v5(2),v5(3));
fprintf(f1, '%s\n\n',');');
%defining the blocks
fprintf(f1, '%s\n', 'blocks');
fprintf(f1, '%s\n\n', '(');
fprintf(f1, ' hex(0 3 5 2 0 3 4 1) (%d %d %d) simpleGrading(1 1 1)\n\n',250,25,1);
fprintf(f1, '%s\n\n',');');
%defining the edges
fprintf(f1, '%s\n', 'edges');
fprintf(f1, '%s\n\n', '(');
fprintf(f1, '%s\n\n',');');
%defining the boundaries
fprintf(f1, '%s\n','boundary');
fprintf(f1, '%s\n\n','(');
fprintf(f1, '%s\n',' Inlet'); %inlet
fprintf(f1, '%s\n',' {');
fprintf(f1, '%s\n',' type patch;');
fprintf(f1, '%s\n',' faces');
fprintf(f1, '%s\n',' (');
fprintf(f1, '%s\n',' (0 1 2 0)');
fprintf(f1, '%s\n',' );');
fprintf(f1, '%s\n',' }');
fprintf(f1, '%s\n',' outlet'); %outlet
fprintf(f1, '%s\n',' {');
fprintf(f1, '%s\n',' type patch;');
fprintf(f1, '%s\n',' faces');
fprintf(f1, '%s\n',' (');
fprintf(f1, '%s\n',' (3 5 4 3)');
fprintf(f1, '%s\n',' );');
fprintf(f1, '%s\n',' }');
fprintf(f1, '%s\n',' top'); %top
fprintf(f1, '%s\n',' {');
fprintf(f1, '%s\n',' type wedge;');
fprintf(f1, '%s\n',' faces');
fprintf(f1, '%s\n',' (');
fprintf(f1, '%s\n',' (1 4 5 2)');
fprintf(f1, '%s\n',' );');
fprintf(f1, '%s\n',' }');
fprintf(f1, '%s\n',' front'); %front
fprintf(f1, '%s\n',' {');
fprintf(f1, '%s\n',' type wedge;');
fprintf(f1, '%s\n',' faces');
fprintf(f1, '%s\n',' (');
fprintf(f1, '%s\n',' (0 3 4 1)');
fprintf(f1, '%s\n',' );');
fprintf(f1, '%s\n',' }');
fprintf(f1, '%s\n',' back'); %back
fprintf(f1, '%s\n',' {');
fprintf(f1, '%s\n',' type wedge;');
fprintf(f1, '%s\n',' faces');
fprintf(f1, '%s\n',' (');
fprintf(f1, '%s\n',' (0 2 5 3)');
fprintf(f1, '%s\n',' );');
fprintf(f1, '%s\n',' }');
fprintf(f1, '%s\n',' axis'); %axis
fprintf(f1, '%s\n',' {');
fprintf(f1, '%s\n',' type empty;');
fprintf(f1, '%s\n',' faces');
fprintf(f1, '%s\n',' (');
fprintf(f1, '%s\n',' (0 3 3 0)');
fprintf(f1, '%s\n',' );');
fprintf(f1, '%s\n\n',' }');
fprintf(f1, '%s\n\n',');');
fprintf(f1, '%s\n','mergePatchParis');
fprintf(f1, '%s\n','(');
fprintf(f1, '%s\n\n',');');
fprintf(f1, '%s\n\n','// ************************************************************************* //');
For wedge
1. 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)//point 0
(0 1.9923e-3 1.743e-4)//point 1
(0 1.9923e-3 -1.743e-4)//point 2
(1.12 0 0)//point 3
(1.12 1.9923e-3 1.743e-4)//point 4
(1.12 1.9923e-3 -1.743e-4)//point 5
);
blocks
(
hex (0 3 5 2 0 3 4 1) (100 10 1) simpleGrading (1 0.2 1)
);
edges
(
);
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)
);
}
front
{
type wedge;
faces
(
(0 3 4 1)
);
}
back
{
type wedge;
faces
(
(0 2 5 3)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //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;
}
front
{
type wedge;
}
back
{
type wedge;
}
axis
{
type empty;
}
}
// ************************************************************************* //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 (0.4718 0 0);
boundaryField
{
Inlet
{
type fixedValue;
value uniform (0.4718 0 0);
}
outlet
{
type zeroGradient;
}
top
{
type noSlip;
value uniform 0;
}
front
{
type wedge;
}
back
{
type wedge;
}
axis
{
type empty;
}
}
// ************************************************************************* //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 5;
deltaT 0.0007;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Geometry:
Velocity profile:
at 0.1
velocity profile at 0.56
2. angle 25
only the vertices parameters are changed
Geometry
Wedge angle 45:
For symmetry boundary condition
1. for angle 10
blockMesh
/*--------------------------------*- 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)//point 0
(0 1.9923e-3 1.743e-4)//point 1
(0 1.9923e-3 -1.743e-4)//point 2
(1.12 0 0)//point 3
(1.12 1.9923e-3 1.743e-4)//point 4
(1.12 1.9923e-3 -1.743e-4)//point 5
);
blocks
(
hex (0 3 5 2 0 3 4 1) (100 10 1) simpleGrading (1 0.2 1)
);
edges
(
);
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)
);
}
front
{
type symmetry;
faces
(
(0 3 4 1)
);
}
back
{
type symmetry;
faces
(
(0 2 5 3)
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //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;
}
front
{
type symmetry;
}
back
{
type symmetry;
}
axis
{
type empty;
}
}
// ************************************************************************* //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 (0.4718 0 0);
boundaryField
{
Inlet
{
type fixedValue;
value uniform (0.4718 0 0);
}
outlet
{
type zeroGradient;
}
top
{
type noSlip;
value uniform 0;
}
front
{
type symmetry;
}
back
{
type symmetry;
}
axis
{
type empty;
}
}
// ************************************************************************* //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 5;
deltaT 0.0007;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Geometry:
2.angle 25
geometry:
3.angle 45
| angle | analytical velocity | numerical velocity | error | execution time | courant number |
| 10 | 0.914 | 0.9436 | 3.23 | 39 | 0.0604 |
| 25 | 0.915 | 0.9436 | 3.12 | 40 | 0.0609 |
| 45 | 0.9155 | 0.9436 | 3.06 | 42 | 0.0618 |
Conclusion:
By comparing the different cases for symmetry boundary condition
There is not much difference in analytical velocity for different angles but there is a slight difference when we compared with the analytical and numerical values.
As the angle increases the execution time also increases
And with the increase in the angle, there will be a slight increase in the courant number
And lastly, the symmetry boundary condition is more accurate when we compared with wedge boundary condition and it also takes less execution time.