Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation
The octave code to make blockmesh files for wedge and symmetry boundary conditions at 10,25 and 45 degree is as follows
clear all
close all
clc
%input
Re=2100; %ReynoldsNumber
d=0.01; %diameter of the pipe
r=d/2; %radius
le=0.05*Re*d; %entry length for laminar flow
l=le+0.3;
myu=1.002e-3;%absolute viscosity of water at 20 degree celsius
rho=997; %density
nu=1.004e-6; %kinematic viscosity of water at 20 degree C
grade_x=0.1;%grading along x
grade_y=1;%grading along y
grade_z=1;%grading along zzz
type={"wedge" "symmetry"}
for i=1:length(type)
for theta=[10 25 45]
%vertices
p0=[0 0 0];
p1=[0 r*cosd(theta/2) -r*sind(theta/2)];
p2=[0 r*cosd(theta/2) r*sind(theta/2)];
p3=[l 0 0];
p4=[l r*cosd(theta/2) -r*sind(theta/2)];
p5=[l r*cosd(theta/2) r*sind(theta/2)];
name=sprintf("blockMeshDict_%s_%d",type{i},theta);
f1=fopen(name,"w");
fprintf(f1,'/*--------------------------------*- C++ -*----------------------------------*\\\n');
fprintf(f1,' ========= |\n');
fprintf(f1,' \\ / F ield | OpenFOAM: The Open Source CFD Toolbox\n');
fprintf(f1,' \\ / O peration | Website: https://openfoam.org\n');
fprintf(f1,' \\ / A nd | Version: 8\n');
fprintf(f1,' \\/ M anipulation |\n');
fprintf(f1,'\\*---------------------------------------------------------------------------*/\n');
fprintf(f1,'FoamFile\n');
fprintf(f1,'{\n');
fprintf(f1,' version 2.0;\n');
fprintf(f1,' format ascii;\n');
fprintf(f1,' class dictionary;\n');
fprintf(f1,' object blockMeshDict;\n');
fprintf(f1,'}\n');
fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\n\n');
fprintf(f1,'convertToMeters 1;\n\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,' (%d %d %d)//0\n',p0(1),p0(2),p0(3));
fprintf(f1,' (%d %d %d)//1\n',p1(1),p1(2),p1(3));
fprintf(f1,' (%d %d %d)//2\n',p2(1),p2(2),p2(3));
fprintf(f1,' (%d %d %d)//3\n',p3(1),p3(2),p3(3));
fprintf(f1,' (%d %d %d)//4\n',p4(1),p4(2),p4(3));
fprintf(f1,' (%d %d %d)//5\n',p5(1),p5(2),p5(3));
fprintf(f1,');\n\n');
fprintf(f1,'blocks\n(\n');
fprintf(f1,' hex (0 1 2 0 3 4 5 3) (50 1 100) simpleGrading (%d %d %d)\n',grade_x,grade_y,grade_z);
fprintf(f1,');\n\n');
fprintf(f1,'edges\n(\n');
fprintf(f1,' arc 1 2 (%d %d %d)\n',0,r,0);
fprintf(f1,' arc 4 5 (%d %d %d)\n',l,r,0);
fprintf(f1,');\n\n');
fprintf(f1,'boundary\n(\n');
fprintf(f1,' inlet\n');
fprintf(f1,' {\n');
fprintf(f1,' type patch;\n');
fprintf(f1,' faces\n');
fprintf(f1,' (\n');
fprintf(f1,' (0 2 1 0)\n');
fprintf(f1,' );\n');
fprintf(f1,' }\n');
fprintf(f1,' outlet\n');
fprintf(f1,' {\n');
fprintf(f1,' type patch;\n');
fprintf(f1,' faces\n');
fprintf(f1,' (\n');
fprintf(f1,' (3 4 5 3)\n');
fprintf(f1,' );\n');
fprintf(f1,' }\n');
fprintf(f1,' left\n');
fprintf(f1,' {\n');
fprintf(f1,' type %s;\n',type{i});
fprintf(f1,' faces\n');
fprintf(f1,' (\n');
fprintf(f1,' (0 3 5 2)\n');
fprintf(f1,' );\n');
fprintf(f1,' }\n');
fprintf(f1,' right\n');
fprintf(f1,' {\n');
fprintf(f1,' type %s;\n',type{i});
fprintf(f1,' faces\n');
fprintf(f1,' (\n');
fprintf(f1,' (0 1 4 3)\n');
fprintf(f1,' );\n');
fprintf(f1,' }\n');
fprintf(f1,' wall\n');
fprintf(f1,' {\n');
fprintf(f1,' type wall;\n');
fprintf(f1,' faces\n');
fprintf(f1,' (\n');
fprintf(f1,' (1 2 5 4)\n');
fprintf(f1,' );\n');
fprintf(f1,' }\n');
fprintf(f1,' axis\n');
fprintf(f1,' {\n');
fprintf(f1,' type empty;\n');
fprintf(f1,' faces\n');
fprintf(f1,' (\n');
fprintf(f1,' (0 3 3 0)\n');
fprintf(f1,' );\n');
fprintf(f1,' }\n');
fprintf(f1,');\n\n');
fprintf(f1,'mergePatchPairs\n(\n);\n\n');
fprintf(f1,'// ************************************************************************* //\n');
fclose(f1);
end
endThe velocity and pressure conditions are 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 volVectorField;
object U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 1 -1 0 0 0 0];
internalField uniform (0 0 0);
boundaryField
{
inlet
{
type fixedValue;
value uniform (0.211053 0 0);
}
outlet
{
type zeroGradient;
}
left
{
type symmetry;
}
right
{
type symmetry;
}
wall
{
type fixedValue;
value uniform (0 0 0);
}
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 volScalarField;
object p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 2 -2 0 0 0 0];
internalField uniform 0;
boundaryField
{
inlet
{
type zeroGradient;
}
outlet
{
type fixedValue;
value uniform 0.09162;
}
left
{
type symmetry;
}
right
{
type symmetry;
}
wall
{
type zeroGradient;
}
axis
{
type empty;
}
}
// ************************************************************************* //The pressure and velocity plots are attached below
The `DeltaP` from simulation is 0.22721.
FRom calculations
Vmax=`delta`P*R^2/4*μ*L=0.4153
We know,
`u(r)=v_max*(1-r^2/R^2)`
from this we velocity plot will be a downward parabola.
`DeltaP=(V_(avg)*mu*L)/D^2`
which is 0.201243
There is an error of 12.9%.
This is due to the fact as the wedge angle increase the size of the cell increases and acccuracy decreases. This can solved by reducing the element size but this greatly increases the computation time.
It can be observed that as the angle increases keeping the sizing same the results deviate from that of calculated.