Symmetry vs Wedge vs HP equation
All the inputs have been discussed in the exercise of the week - 11.
For 10 degree angle in symmetry boundary condition, all the samples have been given here. For the rest, these will be almost same.
MATLAB Programme to generate block mesh file for 10 degree:
clear all
close all
clc
%% Inputs
L = 1.5;
theta = 10;
r = 0.005;
a = 1;
b = 0.2;
c = 1;
nx = 200;
ny = 20;
nz =1;
%%
line1=\'/*--------------------------------*- C++ -*----------------------------------*\\\';
line2=\' ========= | \';
line3=\' \\\\ / F ield | OpenFOAM: The Open Source CFD Toolbox \';
line4=\' \\\\ / O peration | Version: 4.1 \';
line5=\' \\\\ / A nd | Web: www.OpenFOAM.org \';
line6=\' \\\\/ M anipulation | \';
line7=\'\\*---------------------------------------------------------------------------*/\';
line8=\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *//\';
line9=\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *//\';
bmd = fopen(\'blockMeshDict\',\'wt\')
fprintf(bmd,\'%s\\n\',line1);
fprintf(bmd,\'%s\\n\',line2);
fprintf(bmd,\'%s\\n\',line3);
fprintf(bmd,\'%s\\n\',line4);
fprintf(bmd,\'%s\\n\',line5);
fprintf(bmd,\'%s\\n\',line6);
fprintf(bmd,\'%s\\n\',line7);
fprintf(bmd,\'FoamFile\\n{\\n\');
fprintf(bmd,\'%18s \\t 2.0;\\n\',\'version\');
fprintf(bmd,\'%18s \\t ascii;\\n\',\'format\');
fprintf(bmd,\'%18s \\t dictionary;\\n\',\'class\');
fprintf(bmd,\'%18s \\t blockMeshDict;\\n\',\'object\');
fprintf(bmd,\'}\\n\');
fprintf(bmd, \'%s\\n\\n\',line8);
%% Vertices and blocks
fprintf(bmd, \'convertToMeters 1; \\n\\n\');
fprintf(bmd, \'vertices\\n(\\n\');
fprintf(bmd, \'\\t (%d %d %d)\\n\', 0,0,0);
fprintf(bmd, \'\\t (%d %d %d)\\n\', L,0,0);
fprintf(bmd, \'\\t (%d %d %d)\\n\', L, r*cosd(theta/2), r*sind(theta/2));
fprintf(bmd, \'\\t (%d %d %d)\\n\', 0, r*cosd(theta/2), r*sind(theta/2));
fprintf(bmd, \'\\t (%d %d %d)\\n\', 0, r*cosd(theta/2), -r*sind(theta/2));
fprintf(bmd, \'\\t (%d %d %d)\\n\', L, r*cosd(theta/2), -r*sind(theta/2));
fprintf(bmd, \');\\n\\n\');
fprintf(bmd, \'blocks\\n(\\n\');
fprintf(bmd,\'\\t hex (0 1 5 4 0 1 2 3)(%d %d %d)\', nx,ny,nz);
fprintf(bmd, \'simplegrading (%d %d %d)\\n\',a,b,c);
fprintf(bmd, \');\\n\\n\');
fprintf(bmd, \'edges\\n(\\n\\t arc %d %d (%d %d %d)\\n\',4,3,0,r,0);
fprintf(bmd, \'\\t arc %d %d (%d %d %d)\\n\',5,2,L,r,0);
fprintf(bmd, \');\\n\\n\');
fprintf(bmd, \'boundary\\n(\\n\');
%% Inlet patch
fprintf(bmd, \'\\t inlet\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type patch;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 0,0,3,4);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Outlet : patch
fprintf(bmd, \'\\t outlet\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type patch;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 1,5,2,1);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Front surface: symmetry 1
fprintf(bmd, \'\\t front\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type symmetry;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 0,1,2,3);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Back Surface : symmetry 2
fprintf(bmd, \'\\t back\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type symmetry;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 0,4,5,1);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Axis : empty
fprintf(bmd, \'\\t axis\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type empty;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 0,1,1,0);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
%% Pipe Wall : wall
fprintf(bmd, \'\\t pipewall\\n\');
fprintf(bmd, \'\\t{\\n\');
fprintf(bmd, \'\\t\\t type wall;\\n\');
fprintf(bmd, \'\\t\\t faces\\n\');
fprintf(bmd, \'\\t\\t ( \\n\');
fprintf(bmd, \'\\t\\t\\t (%d %d %d %d)\\n\', 3,2,5,4);
fprintf(bmd, \'\\t\\t ); \\n\');
fprintf(bmd, \'\\t } \\n\');
fprintf(bmd, \');\\n\');
%%
fprintf(bmd, \'mergePatchPairs\\n(\\n\');
fprintf(bmd, \');\\n\');
fprintf(bmd, \'%s \\n\', line9);
fclose (bmd)Generated BlockmeshDict file for 10 degree symmetry angle:
/*--------------------------------*- C++ -*----------------------------------*\\
========= |
\\\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\\\ / O peration | Version: 4.1
\\\\ / A nd | Web: www.OpenFOAM.org
\\\\/ M anipulation |
\\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *//
convertToMeters 1;
vertices
(
(0 0 0)
(1.500000e+00 0 0)
(1.500000e+00 4.980973e-03 4.357787e-04)
(0 4.980973e-03 4.357787e-04)
(0 4.980973e-03 -4.357787e-04)
(1.500000e+00 4.980973e-03 -4.357787e-04)
);
blocks
(
hex (0 1 5 4 0 1 2 3)(200 20 1)simplegrading (1 2.000000e-01 1)
);
edges
(
arc 4 3 (0 5.000000e-03 0)
arc 5 2 (1.500000e+00 5.000000e-03 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 0 3 4)
);
}
outlet
{
type patch;
faces
(
(1 5 2 1)
);
}
front
{
type symmetry;
faces
(
(0 1 2 3)
);
}
back
{
type symmetry;
faces
(
(0 4 5 1)
);
}
axis
{
type empty;
faces
(
(0 1 1 0)
);
}
pipewall
{
type wall;
faces
(
(3 2 5 4)
);
}
);
mergePatchPairs
(
);
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *// Pressure Boundary Condition:
/*--------------------------------*- 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 0.0802;
}
axis
{
type empty;
}
front
{
type symmetry;
}
back
{
type symmetry;
}
pipewall
{
type zeroGradient;
}
}
// ************************************************************************* //Velocity Boundary Condition:
/*--------------------------------*- 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 (0.1874 0 0);
}
outlet
{
type zeroGradient;
}
axis
{
type empty;
}
front
{
type symmetry;
}
back
{
type symmetry;
}
pipewall
{
type fixedValue;
value uniform (0 0 0);
}
}
// ************************************************************************* //Control Dict 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 5;
deltaT 0.00005;
writeControl timeStep;
writeInterval 1000;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Transport Property 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] 8.90e-07;
// ************************************************************************* //Meshing File (For 10 degree):
Velocity Visualization from inlet (at the left):
Pressure Visualization (Left is inlet):
Velocity Magnitude (At x= 0.02 m):
Velocity Magnitude (At x= 1 m):
Pressure Magnitude (x axis: Inlet to outlet; Y-axis: Pressure):
To compare between wedge and symmetry boundary condition the case for 3 degree with wedge boundary condition has been simulated with symmetry condition. A result from the same has been compared at x=1 which shows no difference in velocity magnitude. But the time taken is different. For the wedge b.c., time taken is lesser than the symmetry b.c. But the calculated courant no turns out to be more than symmetry condition.
For the comparison of the different wedge angle in symmetry condition, the velocity profiles have been plotted at x= 0.02m and x=1 m. In both the cases, profiles have been plotted for 10, 25 and 45 degree of included angle between the symmetry faces.
From the result it has been found that near the wall viscosity is effecting more for lower angles and that\'s why for a longer transverse length near-wall the velocity is almost zero. Near the free stream i.e. near the axis, velocity is almost same for every angles.
Another conclusion is the time. The simulation time for larger angles are more than smaller angles.