Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation
Assignment name- Simulation of Flow through a pipe in Open Foam (part 2)
Objective-
- To developed a program in MATLAB for file parsing
- Simulation of open pipe (symmetry boundary condition) and obtained the results
- How parameter changes with respect to change in angles.
Analytical solution
Changes between wedge boundary and symmetry boundary condition
- We only change your angle in file parsing i.e. I mentioned theta is variable for file parsing. (Angle 10,25,45)
- Used cosd instead of cos because we need to put angle in degree and d is suggest degree and in MATLAB, we used d while entering the value angle in degree
- We changed only type as symmetry instead of wedge in blockMeshDict file, pressure and velocity file.
MATLAB program
clear all
close all
clc
%%%file preraising for openFoam in matlab
%%simulation of openpipe needed some information
%%flow is laminar
%%input Varibles
%Renoyled number
Re=2100;
%density of water(consider fluid is water)
rho=997;
%Diameter of pipe
D=0.02;
%Radius of pipe
R=D/2;
%entrance length
Le=0.06*Re*D;
%total length
L=Le+0.3;
%dynamic viscosity
dv=0.89e-3;
%kinematic viscosity
kv=dv/rho;
%average velocity
V_avg=(dv*Re)/(rho*D);
%maximum velocity
V_max=2*V_avg;
%wedge angle
theta=25;%(not consider value of theta greater than 5)
%%vertices of open pipe for blockmeshDict
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)];
% please take precaution I am using Captial V for velocity and small v for vertex)
%%calculating shear stress
r=linspace(0,(D/2),500);
for i=1:length(r)
tau(i)=2*dv*V_max*abs(r(i))/R^2;
end
figure(1)
plot(r,tau)
xlabel('Radius of pipe')
ylabel('shear sdtress')
title('shear stress')
legend('shear stress')
%header of script file
h1='/*--------------------------------*- C++ -*----------------------------------*\';
h2= '========= |';
h3= '\\ / F ield | OpenFOAM: The Open Source CFD Toolbox';
h4= '\\ / O peration | Website: https://openfoam.org';
h5= '\\ / A nd | Version: 9';
h6= '\\/ M anipulation |';
h7='\*---------------------------------------------------------------------------*/';
h8='FoamFile';
h9='{';
h10= 'format ascii;';
h11= 'class dictionary;';
h12 = 'object blockMeshDict;';
h13='}';
h14='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
%generated block mesh directory start file prasing
f1=fopen('blockmeshDict.txt','w');
fprintf(f1,'%s\n',h1);
fprintf(f1,'%s\n',h2);
fprintf(f1,'%s\n',h3);
fprintf(f1,'%s\n',h4);
fprintf(f1,'%s\n',h5);
fprintf(f1,'%s\n',h6);
fprintf(f1,'%s\n',h7);
fprintf(f1,'\n');
fprintf(f1,'%s\n',h8);
fprintf(f1,'\n');
fprintf(f1,'%s\n',h9);
fprintf(f1,'%s\n',h10);
fprintf(f1,'%s\n',h11);
fprintf(f1,'%s\n',h12);
fprintf(f1,'%s\n',h13);
fprintf(f1,'%s\n',h14);
fprintf(f1,'\n');
fprintf(f1,'%s\n','convertToMeters 1;');
%vertices
fprintf(f1,'%s\n','vertices');
fprintf(f1,'\n');
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',')');
%%blocks
fprintf(f1,'%s\n','blocks');
fprintf(f1,'\n');
fprintf(f1,'%s\n','(');
fprintf(f1,'\t hex(0 3 4 1 0 3 5 2)(%d %d %d) simpleGrading (1 0.2 1)\n',300,30,1);
fprintf(f1,'%s\n',')');
%edges
fprintf(f1,'%s\n','edges');
fprintf(f1,'\n');
fprintf(f1,'%s\n','(');
fprintf(f1,'\t arc 1 2 (%d %d %d)\n',0,R,0);
fprintf(f1,'\t arc 4 5 (%d %d %d)\n',L,R,0);
fprintf(f1,'%s\n',')');
%%boundary
fprintf(f1,'%s\n','boundary');
fprintf(f1,'\n');
fprintf(f1,'%s\n','(');
%axis
fprintf(f1,'\n');
fprintf(f1,'\t axis\n\t{\n');
fprintf(f1,'\t type empty;\n');
fprintf(f1,'\t faces\n\t (\n');
fprintf(f1,'\t(%d %d %d %d)\n',0,3,3,0);
fprintf(f1,'\t \t);\n\t}\n');
%top wall
fprintf(f1,'\n');
fprintf(f1,'\t wall\n\t{\n');
fprintf(f1,'\t type wall;\n');
fprintf(f1,'\t faces\n\t (\n');
fprintf(f1,'\t(%d %d %d %d)\n',1,4,5,2);
fprintf(f1,'\t \t);\n\t}\n');
%inlet
fprintf(f1,'\n');
fprintf(f1,'\t inlet\n\t{\n');
fprintf(f1,'\t type patch;\n');
fprintf(f1,'\t faces\n\t (\n');
fprintf(f1,'\t(%d %d %d %d)\n',0,1,2,0);
fprintf(f1,'\t\t);\n\t}\n');
%outlet
fprintf(f1,'\n');
fprintf(f1,'\t outlet\n\t{\n');
fprintf(f1,'\t type patch;\n');
fprintf(f1,'\t faces\n\t (\n');
fprintf(f1,'\t(%d %d %d %d)\n',3,5,4,3);
fprintf(f1,'\t\t);\n\t}\n');
%frontAndback
fprintf(f1,'\n');
fprintf(f1,'\t front\n \t{\n');
fprintf(f1,'\t type wedge;\n');
fprintf(f1,'\t faces \n\t (\n');
fprintf(f1,'\t(%d %d %d %d)\n',0,3,4,1);
fprintf(f1,'\t\t);\n\t}\n');
fprintf(f1,'\n');
fprintf(f1,'\t back\n\t{\n');
fprintf(f1,'\t type wedge;\n');
fprintf(f1,'\t faces \n\t (\n');
fprintf(f1,'\t(%d %d %d %d)\n',0,2,5,3);
fprintf(f1,'\t\t);\n\t}\n');
% all boundary condition is given
fprintf(f1,'\n');
fprintf(f1,'%s\n','meargePatchPair;');
fprintf(f1,'\t(\n\t\t);\n');
fprintf(f1,'// ************************************************************************* //');
fclose(f1);
Theta=25 degree
Pressure directory
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class volScalarField;
object p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 2 -2 0 0 0 0];
internalField uniform 0;
boundaryField
{
axis
{
type empty;
}
inlet
{
type zeroGradient;
}
outlet
{
type fixedValue;
value uniform 0.018;
}
wall
{
type zeroGradient;
}
front
{
type symmetry;
}
back
{
type symmetry;
}
}
// ************************************************************************* //
Velocity directory
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class volVectorField;
object U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 1 -1 0 0 0 0];
internalField uniform (0.0937 0 0);
boundaryField
{
axis
{
type empty;
}
inlet
{
type fixedValue;
value uniform (0.0937 0 0);
}
outlet
{
type zeroGradient;
}
wall
{
type fixedValue;
value uniform (0 0 0);
}
front
{
type symmetry;
}
back
{
type symmetry;
}
}
// ************************************************************************* //
Block mesh directory
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0 0 0)
(0 9.9762960e-03 -2.164396e-03)
(0 9.9762960e-03 2.164396e-03)
(2.820000e+00 0 0)
(2.820000e+00 9.9762960e-03 -2.164396e-03)
(2.820000e+00 9.9762960e-03 2.164396e-03)
);
blocks
(
hex (0 3 4 1 0 3 5 2) (300 30 1) simpleGrading (1 0.1 1)
);
edges
(
arc 1 2 (0 1.000000e-02 0)
arc 4 5 (2.820000e+00 1.000000e-02 0)
);
boundary
(
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
wall
{
type wall;
faces
(
(1 4 5 2)
);
}
inlet
{
type patch;
faces
(
(0 1 2 0)
);
}
outlet
{
type patch;
faces
(
(3 5 4 3)
);
}
front
{
type symmetry;
faces
(
(0 3 4 1)
);
}
back
{
type symmetry;
faces
(
(0 2 5 3)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
Control directory
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application icoFoam;
startFrom startTime;
startTime 0;
stopAt endTime;
endTime 10;
deltaT 0.01;
writeControl timeStep;
writeInterval 10;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //
Transport directory
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
location "constant";
object transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
nu [0 2 -1 0 0 0 0] 8.917e-7;
// ************************************************************************* //
Velocity profile at 25 degree
Post processing result screenshot (angle 25degree)
Comparison chart
Conclusions
- Above chart give you detailed explanation and comparisons between analytical solution and wedge BC and Symmetry BC
- With increasing the value of wedge angle courant number is increases
- From above table we can say that symmetric BC plays important role in accuracy in the solution