Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation
Project
It is continuation of project week11, with different wedge angles and boundary conditions are symmetry instead of wedge.
Flow in a conduit can be either develpoing or fully developed flow. Considering a laminar flow entering the pipe, the velocity profile changes as it moves inside pipe. This region of changing velocity profile is called as developing flow. After the parabolic profile is acheived, the flow profile does not change in streamwise direction and this flow is called as fully developed flow. The distance required for a flow to become developed is called as entrance length and it depends upon shear stresses that act on the wall.
This fully developed flow is termed as Hagen- Poiseuille's flow and forlulae related to this flow are as below,
1) Pressure loss during the fluid flow
where △p is pressure difference
μ is viscosity of fluid
u is average velocity of fluid
L is length of pipe
Le is entrance length of pipe
D is diameter of pipe
2) Reynold's number
For pipe flow applications , it is very important to know whether the flow is laminayr or turbulent. Equations and method that are applied to these flows to analyse the flow are different.
Typical criterion to decide whether pipe flow is laminar or turbulent is value of Reynold's number.
where D is pipe diameter
V is average flow velocity in pipe
ρ is density of flowing fluid
μ is dynamic viscosity of fluid
ν is kinematic viscosity of fluid
Re is dimensionless number
When Re < 2300, it is Laminar flow
Re > 4000, it is Turbulent
Here in this project Re = 2100 as given.
3) Entry length Le = 0.06*Re*D = 0.06* 2100* 0.01 = 1.26m
4) Length of pipe = L = 0.5 + Le = 0.5+1.26 = 1.76 m
5) Average flow velocity = Vavg = Re.μ/(density* D)
6) Shear stress:
BlockMeshDict files for all three angles
1) Angle = 10 degrees
/*--------------------------------*- 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;
/*
wedge angle = 10 degrees
*/
vertices
(
(0 0 0)
(0 0.00498097 -0.0004357) // x dir
(0 0.00498097 0.0004357) // y dir
(1.5 0 0) //z
(1.5 0.00498097 -0.0004357)
(1.5 0.00498097 0.0004357)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (20 1 200) simpleGrading (1 0.2 1)
);
edges
(
/*
arc 1 2 (0 0.01 0)
arc 3 4 (3 0.01 0)
*/
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
noslipwalls
{
type wall;
faces
(
(1 2 5 4)
);
}
front
{
type symmetry;
faces
(
(0 3 5 2)
);
}
back
{
type symmetry;
faces
(
(0 1 4 3 )
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
2) angle = 25
/*--------------------------------*- 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;
/*
wedge angle = 20 degrees
*/
vertices
(
(0 0 0)
(0 0.004881 -0.001082) // x dir
(0 0.004881 0.001082) // y dir
(1.5 0 0) //z
(1.5 0.004881 0.001082)
(1.5 0.004881 -0.001082)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (20 1 200) simpleGrading (1 0.2 1)
);
edges
(
/*
arc 1 2 (0 0.01 0)
arc 3 4 (3 0.01 0)
*/
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
noslipwalls
{
type wall;
faces
(
(1 2 5 4)
);
}
front
{
type symmetry;
faces
(
(0 3 5 2)
);
}
back
{
type symmetry;
faces
(
(0 1 4 3 )
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //3) Angle = 45
/*--------------------------------*- 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;
/*
wedge angle = 45 degrees
*/
vertices
(
(0 0 0)
(0 0.0046194 -0.0019134) // x dir
(0 0.0046194 0.0019134) // y dir
(1.5 0 0) //z
(1.5 0.0046194 -0.0019134)
(1.5 0.0046194 0.0019134)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (20 1 200) simpleGrading (1 0.2 1)
);
edges
(
/*
arc 1 2 (0 0.01 0)
arc 3 4 (3 0.01 0)
*/
);
boundary
(
inlet
{
type patch;
faces
(
(0 2 1 0)
);
}
outlet
{
type patch;
faces
(
(3 4 5 3)
);
}
noslipwalls
{
type wall;
faces
(
(1 2 5 4)
);
}
front
{
type symmetry;
faces
(
(0 3 5 2)
);
}
back
{
type symmetry;
faces
(
(0 1 4 3 )
);
}
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //Pressure setting
We have to change from wedge to symmetry accordingly.
/*--------------------------------*- 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;
}
front
{
type wedge;
}
back
{
type wedge;
}
axis
{
type empty;
}
noslipwalls
{
type zeroGradient;
}
}
// ************************************************************************* //Velocity setting
/*--------------------------------*- 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 (0.1869 0 0);
}
outlet
{
type zeroGradient;
}
noslipwalls
{
type noSlip;
}
axis
{
type empty;
}
front
{
type wedge;
}
back
{
type wedge;
}
}
// ************************************************************************* //Matlab codes to automate blockMeshDict file:
1) theta = 10
clear all
close all
clc
% File parsing
% inputs
Re = 2100;
rho = 1000;
mu = 8.9e-7;
v = 0.1869 % m/s
prompt = 'What is pipe diameter' ;
D = input(prompt);
% Total pipe length
L = 1.5; %m
% Le = 0.06*Re*D ;
% L = Le + 0.5;
% angle of wedge
theta = 10;
a = (D/2)*cosd(theta/2);
b = (D/2)*sind(theta/2);
v0 = [0 ,0 ,0];
v1= [0 ,a, -b];
v2= [0, a, b];
v3= [L, 0, 0];
v4= [L, a, -b];
v5= [L, a, b];
f1 = fopen('blockmeshdict10.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', '// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //');
% For a space for one line
fprintf(f1, '\n');
fprintf(f1, '%s \n','convertToMeters 1;')
% For a space for one line
fprintf(f1, '\n');
fprintf(f1, '%s \n','vertices');
fprintf(f1, '%s \n','(');
fprintf(f1, '(%f %f %f)\n',v0(1), v0(2),v0(3));
fprintf(f1, '(%f %f %f)\n',v1(1), v1(2),v1(3));
fprintf(f1, '(%f %f %f)\n',v2(1), v2(2),v2(3));
fprintf(f1, '(%f %f %f)\n',v3(1), v3(2),v3(3));
fprintf(f1, '(%f %f %f)\n',v4(1), v4(2),v4(3));
fprintf(f1, '(%f %f %f)\n',v5(1), v5(2),v5(3));
fprintf(f1, '%s \n',');');
fprintf(f1, '\n');
fprintf(f1, '%s \n','blocks');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',' hex (0 1 2 0 3 4 5 3) (20 1 200) simpleGrading (1 0.2 1)');
fprintf(f1, '\n');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','edges');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','boundary');
fprintf(f1, '%s \n','(');
fprintf(f1, '\n');
fprintf(f1, '%s \n',' 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 2 1 0)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' 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 4 5 3)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' noslipwalls');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type wall;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (1 2 5 4)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' front');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type symmetry;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (0 3 5 2)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' back');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type symmetry;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (0 1 4 3)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' 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','}');
fprintf(f1, '\n');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','mergePatchPairs');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',');');
fprintf(f1, '\n');
fprintf(f1, '%s \n','// ************************************************************************* //');
2) theta = 20 degrees
clear all
close all
clc
% File parsing
% inputs
Re = 2100;
rho = 1000;
mu = 8.9e-7;
v = 0.1869 % m/s
prompt = 'What is pipe diameter' ;
D = input(prompt);
% Total pipe length
L = 1.5; %m
% Le = 0.06*Re*D ;
% L = Le + 0.5;
% angle of wedge
theta = 20;
a = (D/2)*cosd(theta/2);
b = (D/2)*sind(theta/2);
v0 = [0 ,0 ,0];
v1= [0 ,a, -b];
v2= [0, a, b];
v3= [L, 0, 0];
v4= [L, a, -b];
v5= [L, a, b];
f1 = fopen('blockmeshdict25.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', '// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //');
% For a space for one line
fprintf(f1, '\n');
fprintf(f1, '%s \n','convertToMeters 1;');
% For a space for one line
fprintf(f1, '\n');
fprintf(f1, '%s \n','vertices');
fprintf(f1, '%s \n','(');
fprintf(f1, '(%f %f %f)\n',v0(1), v0(2),v0(3));
fprintf(f1, '(%f %f %f)\n',v1(1), v1(2),v1(3));
fprintf(f1, '(%f %f %f)\n',v2(1), v2(2),v2(3));
fprintf(f1, '(%f %f %f)\n',v3(1), v3(2),v3(3));
fprintf(f1, '(%f %f %f)\n',v4(1), v4(2),v4(3));
fprintf(f1, '(%f %f %f)\n',v5(1), v5(2),v5(3));
fprintf(f1, '%s \n',');');
fprintf(f1, '\n');
fprintf(f1, '%s \n','blocks');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',' hex (0 1 2 0 3 4 5 3) (20 1 200) simpleGrading (1 0.2 1)');
fprintf(f1, '\n');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','edges');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','boundary');
fprintf(f1, '%s \n','(');
fprintf(f1, '\n');
fprintf(f1, '%s \n',' 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 2 1 0)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' 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 4 5 3)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' noslipwalls');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type wall;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (1 2 5 4)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' front');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type symmetry;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (0 3 5 2)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' back');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type symmetry;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (0 1 4 3)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' 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','}');
fprintf(f1, '\n');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','mergePatchPairs');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',');');
fprintf(f1, '\n');
fprintf(f1, '%s \n','// ************************************************************************* //');
3) theta = 45 degrees
clear all
close all
clc
% File parsing
% inputs
Re = 2100;
rho = 1000;
mu = 8.9e-7;
v = 0.1869 % m/s
prompt = 'What is pipe diameter' ;
D = input(prompt);
% Total pipe length
L = 1.5; %m
% Le = 0.06*Re*D ;
% L = Le + 0.5;
% angle of wedge
theta = 45;
a = (D/2)*cosd(theta/2);
b = (D/2)*sind(theta/2);
v0 = [0 ,0 ,0];
v1= [0 ,a, -b];
v2= [0, a, b];
v3= [L, 0, 0];
v4= [L, a, -b];
v5= [L, a, b];
f1 = fopen('blockmeshdict45.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', '// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //');
% For a space for one line
fprintf(f1, '\n');
fprintf(f1, '%s \n','convertToMeters 1;');
% For a space for one line
fprintf(f1, '\n');
fprintf(f1, '%s \n','vertices');
fprintf(f1, '%s \n','(');
fprintf(f1, '(%f %f %f)\n',v0(1), v0(2),v0(3));
fprintf(f1, '(%f %f %f)\n',v1(1), v1(2),v1(3));
fprintf(f1, '(%f %f %f)\n',v2(1), v2(2),v2(3));
fprintf(f1, '(%f %f %f)\n',v3(1), v3(2),v3(3));
fprintf(f1, '(%f %f %f)\n',v4(1), v4(2),v4(3));
fprintf(f1, '(%f %f %f)\n',v5(1), v5(2),v5(3));
fprintf(f1, '%s \n',');');
fprintf(f1, '\n');
fprintf(f1, '%s \n','blocks');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',' hex (0 1 2 0 3 4 5 3) (20 1 200) simpleGrading (1 0.2 1)');
fprintf(f1, '\n');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','edges');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','boundary');
fprintf(f1, '%s \n','(');
fprintf(f1, '\n');
fprintf(f1, '%s \n',' 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 2 1 0)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' 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 4 5 3)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' noslipwalls');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type wall;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (1 2 5 4)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' front');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type symmetry;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (0 3 5 2)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' back');
fprintf(f1, '%s \n',' {');
fprintf(f1, '%s \n',' type symmetry;');
fprintf(f1, '%s \n',' faces');
fprintf(f1, '%s \n',' (');
fprintf(f1, '%s \n',' (0 1 4 3)');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','}');
fprintf(f1, '%s \n',' 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','}');
fprintf(f1, '\n');
fprintf(f1, '%s \n',');');
fprintf(f1, '%s \n','mergePatchPairs');
fprintf(f1, '%s \n','(');
fprintf(f1, '%s \n',');');
fprintf(f1, '\n');
fprintf(f1, '%s \n','// ************************************************************************* //');
Results :
SYMMETRY front and back
1) For theta = 10
a) Velocity graph
b) Pressure graph
c) Shear stress graph
2) theta = 20 degrees
a) Velocity graph
b) Pressure graph
c) Shear stress graph
3) theta = 45 degrees
a) Velocity graph
b) Pressure graph
c) Shear stress graph
WEDGE front and back
1) theta = 10degrees
a) Velocity profile
b) Pressure profile
c) Shear stress profile
2) theta = 20 degrees
a) Velocity graph
b) Pressure graph
c) Shear stress graph
3) theta = 45 degrees
a) Velocity graph
b) Pressure graph
c) Shear stress graph
Results :
