Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation
Objective -
Perform simulation for the below mentioned angles using both symmetry and wedge boundary conditions and validate them with HP equations like you did in week 11 challenge.
Angles to test:
- `10^o`
- `25^o`
- `45^o`
Expected Results
- Validate Hydro-dynamic length with the numerical result
- Validate the fully developed flow velocity profile with its analytical profile
- Validate maximum velocity and pressured drop for fully developed flow
- Post-process Shear stress and validate wall shear stress for fully developed flow
- Highligh the differences in both boundary conditions in terms of their usage and aplication
Calculation of endTime -
This an important parameter to follow in the simulation process. So that, Fluid flow compeletes through entire section of the pipe length.
We know that,
Time = Distance/Velocity
L - length of pipe from inlet to outlet=2.6 m
v_avg- Velocity=0.0937 m/s
Time=27.748 sec
Total time required = 55.496 sec ~56 sec
Code -
MatLab Wedge Condition -
clear all
close all
clc
%Given Data for Analysis
Re=2100; %Reynolds Number
mu=input("Enter Dynamic Viscosity of watern")
rho=input("Enter Density of watern")
d=input("Enter Diameter of pipen")
theta=input("Enter Wedge Angle for pipen") %Wgde Andle should be <5 Degrees
%Entry Lenght of pipe
Le=d*(0.05*Re)
%Actual lenght of pipe
L=0.5+Le
R=d/2 %Radius of pipe
v_avg=(Re*mu)/(rho*d) %average velocity
v_max=2*v_avg % maximium velocity
T_wall=4*((mu*v_avg)/R)
dp=(32*mu*v_avg)/((d)^2)
nu=mu/rho %Nuseltte Number
r=linspace(0,R,300);
v=v_max*(1-(r.^2./R^2));
plot(r,v,'linewidth',2)
xlabel('radius')
ylabel('velocity')
title('velocity profile at fully developed region')
%-------------------------------------------------------------------------------------------------------------------------------
%%writting the header part for BlockMeshDict File in Matlab
h1='/*--------------------------------*- C++ -*----------------------------------*';
h2=' ========= |';
h3=' / F ield | OpenFOAM: The Open Source CFD Toolbox';
h4=' / O peration | Website: https://openfoam.org';
h5=' / A nd | Version: 8';
h6=' / M anipulation |';
h7='*---------------------------------------------------------------------------*/';
h8='FoamFile';
h9='{';
h10=' version 2.0;';
h11=' format ascii;';
h12=' class dictionary;';
h13=' object blockMeshDict;';
h14='}';
h15='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
h16='// ************************************************************************* //';
conv='convertToMeters 1;';
v0=[0 0 0];
v1=[L 0 0];
v2=[L R*cosd(theta/2) R*sind(theta/2)];
v3=[0 R*cosd(theta/2) R*sind(theta/2)];
v4=[0 R*cosd(theta/2) -R*sind(theta/2)];
v5=[L R*cosd(theta/2) -R*sind(theta/2)];
block='hex (0 1 5 4 0 1 2 3) (500 20 1) simpleGrading (1 0.01 1)';
inlet='(0 1 2 0)';
outlet='(1 5 2 1)';
top='3 2 5 4';
front='0 1 2 3';
back='0 4 5 1';
axis='0 1 1 0';
s1=blanks(4);
s2=blanks(7);
s3=blanks(11);
s4=blanks(3);
%Generating blockMeshDict File
f1=fopen('blockMeshDict.txt','w');
fprintf(f1,'%sn',h1);
fprintf(f1,'%sn',h2);
fprintf(f1,'%sn',h3);
fprintf(f1,'%sn',h4);
fprintf(f1,'%sn',h5);
fprintf(f1,'%sn',h6);
fprintf(f1,'%sn',h7);
fprintf(f1,'%sn',h8);
fprintf(f1,'%sn',h9);
fprintf(f1,'%sn',h10);
fprintf(f1,'%sn',h11);
fprintf(f1,'%sn',h12);
fprintf(f1,'%sn',h13);
fprintf(f1,'%sn',h14);
fprintf(f1,'%sn',h15);
fprintf(f1,'n');
fprintf(f1,'%sn',conv);
fprintf(f1,'n');
fprintf(f1,'%sn','vertices');
fprintf(f1,'%sn','(');
fprintf(f1,'%s(%d %d %d)n',s1,v0(1),v0(2),v0(3));
fprintf(f1,'%s(%d %d %d)n',s1,v1(1),v1(2),v1(3));
fprintf(f1,'%s(%d %d %d)n',s1,v2(1),v2(2),v2(3));
fprintf(f1,'%s(%d %d %d)n',s1,v3(1),v3(2),v3(3));
fprintf(f1,'%s(%d %d %d)n',s1,v4(1),v4(2),v4(3));
fprintf(f1,'%s(%d %d %d)n',s1,v5(1),v5(2),v5(3));
fprintf(f1,'%sn',');');
fprintf(f1,'n');
fprintf(f1,'%sn','blocks');
fprintf(f1,'%sn','(');
fprintf(f1,'%s%sn',s4,block);
fprintf(f1,'n');
fprintf(f1,'%sn',');');
fprintf(f1,'n');
fprintf(f1,'%sn','edges');
fprintf(f1,'%sn','(');
fprintf(f1,'%s %s %d %d(%d %d %d)n',s4,'arc',3,4,0,R,0);
fprintf(f1,'%s %s %d %d(%d %d %d)n',s4,'arc',2,5,L,R,0);
fprintf(f1,'%sn',');');
fprintf(f1,'n');
fprintf(f1,'%sn','boundary');
fprintf(f1,'%sn','(');
fprintf(f1,'%s %sn',s4,'inlet');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type patch;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,0,3,4,0);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'outlet');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type patch;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,1,5,2,1);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'top');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type wall;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,3,2,5,4);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'front');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type wedge;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,0,1,2,3);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'back');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type wedge;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,0,4,5,1);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'axis');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type empty;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,0,1,1,0);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%sn',s2,');');
fprintf(f1,'n');
fprintf(f1,'%sn','mergePatchPairs');
fprintf(f1,'%sn','(');
fprintf(f1,'%sn',');');
fprintf(f1,'%sn',h16);
fclose(f1);
%---------------------------------------------------------------------------------------------------------------------------
BlockMeshDict file -
/*--------------------------------*- 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)
(2.600000e+00 0 0)
(2.600000e+00 9.762960e-03 2.164396e-03)
(0 9.762960e-03 2.164396e-03)
(0 9.762960e-03 -2.164396e-03)
(2.600000e+00 9.762960e-03 -2.164396e-03)
);
blocks
(
hex (0 1 5 4 0 1 2 3) (500 20 1) simpleGrading (1 0.01 1)
);
edges
(
arc 3 4(0 1.000000e-02 0)
arc 2 5(2.600000e+00 1.000000e-02 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 3 4 0)
);
}
outlet
{
type patch;
faces
(
(1 5 2 1)
);
}
top
{
type wall;
faces
(
(3 2 5 4)
);
}
front
{
type wedge;
faces
(
(0 1 2 3)
);
}
back
{
type wedge;
faces
(
(0 4 5 1)
);
}
axis
{
type empty;
faces
(
(0 1 1 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
ControlDict file -
/*--------------------------------*- 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 56;
deltaT 0.005;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //
U-
/*--------------------------------*- 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 (0.11 0 0);
boundaryField
{
inlet
{
type fixedValue;
value uniform (0.11 0 0);
}
outlet
{
type zeroGradient;
}
front
{
type wedge;
}
back
{
type wedge;
}
top
{
type noSlip;
}
axis
{
type empty;
}
}
// ************************************************************************* //
p-
/*--------------------------------*- 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;
}
top
{
type zeroGradient;
}
axis
{
type empty;
}
}
// ************************************************************************* //
transportProperties -
/*--------------------------------*- 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 "constant";
object transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
nu [0 2 -1 0 0 0 0] 8.97e-7;
// ************************************************************************* //
Geometry Generated -
Analytical Velocity Profile -
Simulation Results for wedge boundary condition -
At `theta=10^o`
At `theta=25^o`
At `theta=45^o`
MatLab code for Symmetry Condition -
clear all
close all
clc
%Given Data for Analysis
Re=2100; %Reynolds Number
mu=input("Enter Dynamic Viscosity of watern")
rho=input("Enter Density of watern")
d=input("Enter Diameter of pipen")
theta=input("Enter Wedge Angle for pipen") %Wgde Andle should be <5 Degrees
%Entry Lenght of pipe
Le=d*(0.05*Re)
%Actual lenght of pipe
L=0.5+Le
R=d/2 %Radius of pipe
v_avg=(Re*mu)/(rho*d) %average velocity
v_max=2*v_avg % maximium velocity
T_wall=4*((mu*v_avg)/R)
dp=(32*mu*v_avg)/((d)^2)
nu=mu/rho %Nuseltte Number
r=linspace(0,R,300);
v=v_max*(1-(r.^2./R^2));
%-------------------------------------------------------------------------------------------------------------------------------
%%writting the header part for BlockMeshDict File in Matlab
h1='/*--------------------------------*- C++ -*----------------------------------*';
h2=' ========= |';
h3=' / F ield | OpenFOAM: The Open Source CFD Toolbox';
h4=' / O peration | Website: https://openfoam.org';
h5=' / A nd | Version: 8';
h6=' / M anipulation |';
h7='*---------------------------------------------------------------------------*/';
h8='FoamFile';
h9='{';
h10=' version 2.0;';
h11=' format ascii;';
h12=' class dictionary;';
h13=' object blockMeshDict;';
h14='}';
h15='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
h16='// ************************************************************************* //';
conv='convertToMeters 1;';
v0=[0 0 0];
v1=[L 0 0];
v2=[L R*cosd(theta/2) R*sind(theta/2)];
v3=[0 R*cosd(theta/2) R*sind(theta/2)];
v4=[0 R*cosd(theta/2) -R*sind(theta/2)];
v5=[L R*cosd(theta/2) -R*sind(theta/2)];
block='hex (0 1 5 4 0 1 2 3) (500 30 1) simpleGrading (1 0.01 1)';
inlet='(0 1 2 0)';
outlet='(1 5 2 1)';
top='3 2 5 4';
front='0 1 2 3';
back='0 4 5 1';
axis='0 1 1 0';
s1=blanks(4);
s2=blanks(7);
s3=blanks(11);
s4=blanks(3);
%Generating blockMeshDict File
f1=fopen('blockMeshDict.txt','w');
fprintf(f1,'%sn',h1);
fprintf(f1,'%sn',h2);
fprintf(f1,'%sn',h3);
fprintf(f1,'%sn',h4);
fprintf(f1,'%sn',h5);
fprintf(f1,'%sn',h6);
fprintf(f1,'%sn',h7);
fprintf(f1,'%sn',h8);
fprintf(f1,'%sn',h9);
fprintf(f1,'%sn',h10);
fprintf(f1,'%sn',h11);
fprintf(f1,'%sn',h12);
fprintf(f1,'%sn',h13);
fprintf(f1,'%sn',h14);
fprintf(f1,'%sn',h15);
fprintf(f1,'n');
fprintf(f1,'%sn',conv);
fprintf(f1,'n');
fprintf(f1,'%sn','vertices');
fprintf(f1,'%sn','(');
fprintf(f1,'%s(%d %d %d)n',s1,v0(1),v0(2),v0(3));
fprintf(f1,'%s(%d %d %d)n',s1,v1(1),v1(2),v1(3));
fprintf(f1,'%s(%d %d %d)n',s1,v2(1),v2(2),v2(3));
fprintf(f1,'%s(%d %d %d)n',s1,v3(1),v3(2),v3(3));
fprintf(f1,'%s(%d %d %d)n',s1,v4(1),v4(2),v4(3));
fprintf(f1,'%s(%d %d %d)n',s1,v5(1),v5(2),v5(3));
fprintf(f1,'%sn',');');
fprintf(f1,'n');
fprintf(f1,'%sn','blocks');
fprintf(f1,'%sn','(');
fprintf(f1,'%s%sn',s4,block);
fprintf(f1,'n');
fprintf(f1,'%sn',');');
fprintf(f1,'n');
fprintf(f1,'%sn','edges');
fprintf(f1,'%sn','(');
fprintf(f1,'%s %s %d %d(%d %d %d)n',s4,'arc',3,4,0,R,0);
fprintf(f1,'%s %s %d %d(%d %d %d)n',s4,'arc',2,5,L,R,0);
fprintf(f1,'%sn',');');
fprintf(f1,'n');
fprintf(f1,'%sn','boundary');
fprintf(f1,'%sn','(');
fprintf(f1,'%s %sn',s4,'inlet');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type patch;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,0,3,4,0);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'outlet');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type patch;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,1,5,2,1);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'top');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type wall;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,3,2,5,4);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'front');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type symmetry;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,0,1,2,3);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'back');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type symmetry;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,0,4,5,1);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%s %sn',s4,'axis');
fprintf(f1,'%s %sn',s4,'{');
fprintf(f1,'%s %sn',s2,'type empty;');
fprintf(f1,'%s %sn',s2,'faces');
fprintf(f1,'%s %sn',s2,'(');
fprintf(f1,'%s (%d %d %d %d)n',s3,0,1,1,0);
fprintf(f1,'%s %sn',s2,');');
fprintf(f1,'%s %sn',s4,'}');
fprintf(f1,'%sn',s2,');');
fprintf(f1,'n');
fprintf(f1,'%sn','mergePatchPairs');
fprintf(f1,'%sn','(');
fprintf(f1,'%sn',');');
fprintf(f1,'%sn',h16);
fclose(f1);
%---------------------------------------------------------------------------------------------------------------------------
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 56;
deltaT 0.005;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;BlockMeshDict File -
/*--------------------------------*- 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)
(2.600000e+00 0 0)
(2.600000e+00 9.238795e-03 3.826834e-03)
(0 9.238795e-03 3.826834e-03)
(0 9.238795e-03 -3.826834e-03)
(2.600000e+00 9.238795e-03 -3.826834e-03)
);
blocks
(
hex (0 1 5 4 0 1 2 3) (500 30 1) simpleGrading (1 0.01 1)
);
edges
(
arc 3 4(0 1.000000e-02 0)
arc 2 5(2.600000e+00 1.000000e-02 0)
);
boundary
(
inlet
{
type patch;
faces
(
(0 3 4 0)
);
}
outlet
{
type patch;
faces
(
(1 5 2 1)
);
}
top
{
type wall;
faces
(
(3 2 5 4)
);
}
front
{
type symmetry;
faces
(
(0 1 2 3)
);
}
back
{
type symmetry;
faces
(
(0 4 5 1)
);
}
axis
{
type empty;
faces
(
(0 1 1 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
U-
/*--------------------------------*- 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 (0.0937 0 0);
boundaryField
{
inlet
{
type fixedValue;
value uniform (0.0937 0 0);
}
outlet
{
type zeroGradient;
}
front
{
type symmetry;
}
back
{
type symmetry;
}
top
{
type noSlip;
}
axis
{
type empty;
}
}
// ************************************************************************* //
p-
/*--------------------------------*- 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 symmetry;
}
back
{
type symmetry;
}
top
{
type zeroGradient;
}
axis
{
type empty;
}
}
// ************************************************************************* //
TransportProperties -
/*--------------------------------*- 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 "constant";
object transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
nu [0 2 -1 0 0 0 0] 8.97e-7;
// ************************************************************************* //
Analytical Velocity Profile for Fully Developed region of pipe -
Simulation Results obtained for symmetry boundary condition -
At `theta=10^o`
At `theta=25^o`
At `theta=45^o`
Validation -
Wedge Condition
| Parameters | Analytical Solution | Numerical Solution |
| V_max | 0.1875 | 0.2021 |
| Velocity Profile | Parabolic | Parabolic |
| Le | 2.1m | 2.5 |
| T_Wall @ `theta=10^o` | 0.0334 | 0.0416 |
| @ `theta=25^o` | 0.04217 | |
| @ `theta=45^o` | 0.04322 |
Symmetry Condition
| Parameters | Analytical Solution | Numerical Solution |
| V_max @ `theta=10^o` | 0.1875 | 0.1765 |
| @ `theta=25^o` | 0.1732 | |
| @ `theta=45^o` | 0.1797 | |
| Velocity Profile | Parabolic | Parabolic |
| Le | 2.1m | 2.5 |
| T_Wall @ `theta=10^o` | 0.0334 | 0.03466 |
| @ `theta=25^o` | 0.03533 | |
| @ `theta=45^o` | 0.03708 |
Conclusion -
- Wedge boundary condition works really fine with theta of small angles, ideally with angles while simulating in OpenFoam `theta<5^o`.
- Whereas incase of symmetry condition the results tends to be better when increase in theta.
- Both the condition are different in nature, its just that the user needs to know how to use them accordingly.