Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation
Objective : - To Validate reults of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation.
Angles to test
- 10 deg
- 25 deg
- 45 deg
Solution :
Input parameter :-
Fluid = Water (Incompressible viscous fluid)
density(rho `rho`) = 1000kg/m3
kinematic viscosity(nu `nu`) = 1e-6 m2/sec
dynamic viscosity(mu `mu`) = 1e-3 N-s/m2
Reynold's no. = 2100 (laminar)
Pipe Geometry :-
Length = 2.3m
Diameter = 0.02m ; radius = 0.01m
Analytical calculations :
Hydrodynamic length(Lh) = 0.05 x Reynold's no. x Diameter = 2.1m
Average velocity = (kinematic viscosity x Reynold's no.)/Diameter
`baru =(nu * Re)/D` = `(1e-6*2100)/0.02` = 0.105 m/se`
Max. velocity = 2 x Average velocity = 0.21 m/sec
Umax = `2*baru = 0.21 m/sec`
Pressure drop = 19.32 N/m2
`P2 -P1 = (8*mu*baru*L)/R^2 = (8*1e^-3 * 0.105*2.3)/0.01^2 = 19.32`
Shear stress -
`tau = (delP)/(delx)*r/2`
In hydrodynamically fully developed region, the wall shear stress remains constant.Here Pressure drop & dx(length) are also to be in this region values.
Case 1 : Wedge BC
Matlab code to genrate blockMeshDict file at different wedge angles
clear all
close all
clc
%Inputs of Pipe all are in meters
theta = input('Wedge angle ='); %degress
Dia = 0.02; % Diameter
r =Dia/2; %Radii
L =2.3; %Length
re =2100; %reynold's no.
Lh =0.05*Dia*re; %Hydrodynamic length
kin_viscosity = 1e-6; %Kineamtic viscosity
velocity_avg = (re*kin_viscosity)/Dia; % Average velocity
CFL = (velocity_avg*0.005)/50; %courant no.
%vertices coordinate points
vz=r*sind(theta/2);
vy=r*cosd(theta/2);
%File writing
f2=fopen('blockmesh.txt','w');
fprintf(f2,'%s\n','/*--------------------------------*- C++ -*----------------------------------*\')
fprintf(f2,'%s\n',' ========= |')
fprintf(f2,'%s\n',' \\ / F ield | OpenFOAM: The Open Source CFD Toolbox')
fprintf(f2,'%s\n',' \\ / O peration | Website: https://openfoam.org')
fprintf(f2,'%s\n',' \\ / A nd | Version: 8')
fprintf(f2,'%s\n',' \\/ M anipulation |')
fprintf(f2,'%s\n','\*---------------------------------------------------------------------------*/')
fprintf(f2,'%s\n','FoamFile')
fprintf(f2,'%s\n','{')
fprintf(f2,'%s\n',' version 2.0;')
fprintf(f2,'%s\n',' format ascii;')
fprintf(f2,'%s\n',' class dictionary;')
fprintf(f2,'%s\n',' object blockMeshDict;')
fprintf(f2,'%s\n','}')
fprintf(f2,'%s\n','// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //')
fprintf(f2,'\n')
fprintf(f2,'%s\n','convertToMeters 0.1;')
fprintf(f2,'%s\n','')
fprintf(f2,'%s\n','vertices')
fprintf(f2,'%s\n','(')
fprintf(f2,'%5s%g %g %g)\n','(',0 ,0 ,0)
fprintf(f2,'%5s%g %g %g) \n','(',0 ,vy ,-vz)
fprintf(f2,'%5s%g %g %g) \n','(',0, vy, vz)
fprintf(f2,'%5s%g %g %g) \n','(',L, 0, 0)
fprintf(f2,'%5s%g %g %g) \n','(',L, vy, -vz)
fprintf(f2,'%5s%g %g %g) \n','(',L, vy, vz)
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','blocks')
fprintf(f2,'%s\n','(')
fprintf(f2,'%7s (%g %g %g %g %g %g %g %g) (%g %g %g) %s (%g %g %g)\n','hex', 0, 1, 2, 0, 3, 4, 5, 3, 50, 1, 200, 'simpleGrading', 1, 1, 1)
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','edges')
fprintf(f2,'%s\n','(')
fprintf(f2,'%7s %g %g (%g %g %g)\n','arc', 1, 2, 0, r, 0)
fprintf(f2,'%7s %g %g (%g %g %g)\n','arc', 4, 5, L, r, 0)
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','boundary')
fprintf(f2,'%s\n','(')
fprintf(f2,'%9s \n','Inlet')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type patch;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 0, 1, 2, 0)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%10s\n','Outlet')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type patch;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 3, 5, 4, 3)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%9s\n','front')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type wedge;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 0, 3, 4, 1)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%8s\n','Back')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type wedge;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 0, 2, 5, 3)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%16s\n','Topcurvature')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%18s\n','type wall;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 1, 4, 5, 2)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%12s\n','axisline')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type empty;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 0, 3, 3, 0)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','mergePatchPairs')
fprintf(f2,'%s\n','(')
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','// ************************************************************************* //')
fclose(f2);
1) Wedge angle = 25 deg
blockMeshDict file (Output)
/*--------------------------------*- 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)
(0 0.00996195 -0.000871557)
(0 0.00996195 0.000871557)
(2.3 0 0)
(2.3 0.00996195 -0.000871557)
(2.3 0.00996195 0.000871557)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 200) simpleGrading (1 1 1)
);
edges
(
arc 1 2 (0 0.01 0)
arc 4 5 (2.3 0.01 0)
);
boundary
(
Inlet
{
type patch;
faces
(
(0 1 2 0)
);
}
Outlet
{
type patch;
faces
(
(3 5 4 3)
);
}
front
{
type wedge;
faces
(
(0 3 4 1)
);
}
Back
{
type wedge;
faces
(
(0 2 5 3)
);
}
Topcurvature
{
type wall;
faces
(
(1 4 5 2)
);
}
axisline
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
Intial condition (t=0) :
Pressure -
/*--------------------------------*- 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;
}
Topcurvature
{
type zeroGradient;
}
axisline
{
type empty;
}
}
// ************************************************************************* //Velocity -
/*--------------------------------*- 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 (0.105 0 0);
}
Outlet
{
type zeroGradient;
}
front
{
type wedge;
}
Back
{
type wedge;
}
Topcurvature
{
type noSlip;
}
axisline
{
type empty;
}
}
// ************************************************************************* //(controlDict & transportprorperties file are same as reported in part1 of challenge)
Wedge Grid view -
Final Velocity distribution at the Inlet of pipe -
Final Velocity distribution at the Outlet of pipe -
Pressure distribution throughout the pipe -
2) Wedge angle = 25 deg
blockMeshDict file (Output)
/*--------------------------------*- 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)
(0 0.00976296 -0.0021644)
(0 0.00976296 0.0021644)
(2.3 0 0)
(2.3 0.00976296 -0.0021644)
(2.3 0.00976296 0.0021644)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 200) simpleGrading (1 1 1)
);
edges
(
arc 1 2 (0 0.01 0)
arc 4 5 (2.3 0.01 0)
);
boundary
(
Inlet
{
type patch;
faces
(
(0 1 2 0)
);
}
Outlet
{
type patch;
faces
(
(3 5 4 3)
);
}
front
{
type wedge;
faces
(
(0 3 4 1)
);
}
Back
{
type wedge;
faces
(
(0 2 5 3)
);
}
Topcurvature
{
type wall;
faces
(
(1 4 5 2)
);
}
axisline
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //25 deg. Wedge Grid view -
Velocity Distribution -
Pressure distribution -
3) Wedge angle = 45 deg
blockMeshDict file (Output)
/*--------------------------------*- 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)
(0 0.0092388 -0.00382683)
(0 0.0092388 0.00382683)
(2.3 0 0)
(2.3 0.0092388 -0.00382683)
(2.3 0.0092388 0.00382683)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 200) simpleGrading (1 1 1)
);
edges
(
arc 1 2 (0 0.01 0)
arc 4 5 (2.3 0.01 0)
);
boundary
(
Inlet
{
type patch;
faces
(
(0 1 2 0)
);
}
Outlet
{
type patch;
faces
(
(3 5 4 3)
);
}
front
{
type wedge;
faces
(
(0 3 4 1)
);
}
Back
{
type wedge;
faces
(
(0 2 5 3)
);
}
Topcurvature
{
type wall;
faces
(
(1 4 5 2)
);
}
axisline
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //45deg. Wedge Grid view -
Velocity Distribution -
Pressure distribution -
Case 2 : Symmetry BC
Matlab code to genrate blockMeshDict file at different wedge angles
clear all
close all
clc
%Inputs of Pipe all are in meters
theta = input('Wedge angle ='); %degress
Dia = 0.02; % Diameter
r =Dia/2; %Radii
L =2.3; %Length
re =2100; %reynold's no.
Lh =0.05*Dia*re; %Hydrodynamic length
kin_viscosity = 1e-6; %Kineamtic viscosity
velocity_avg = (re*kin_viscosity)/Dia; % Average velocity
CFL = (velocity_avg*0.005)/50; %courant no.
%vertices coordinate points
vz=r*sind(theta/2);
vy=r*cosd(theta/2);
%File writing
f2=fopen('blockmesh.txt','w');
fprintf(f2,'%s\n','/*--------------------------------*- C++ -*----------------------------------*\')
fprintf(f2,'%s\n',' ========= |')
fprintf(f2,'%s\n',' \\ / F ield | OpenFOAM: The Open Source CFD Toolbox')
fprintf(f2,'%s\n',' \\ / O peration | Website: https://openfoam.org')
fprintf(f2,'%s\n',' \\ / A nd | Version: 8')
fprintf(f2,'%s\n',' \\/ M anipulation |')
fprintf(f2,'%s\n','\*---------------------------------------------------------------------------*/')
fprintf(f2,'%s\n','FoamFile')
fprintf(f2,'%s\n','{')
fprintf(f2,'%s\n',' version 2.0;')
fprintf(f2,'%s\n',' format ascii;')
fprintf(f2,'%s\n',' class dictionary;')
fprintf(f2,'%s\n',' object blockMeshDict;')
fprintf(f2,'%s\n','}')
fprintf(f2,'%s\n','// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //')
fprintf(f2,'\n')
fprintf(f2,'%s\n','convertToMeters 0.1;')
fprintf(f2,'%s\n','')
fprintf(f2,'%s\n','vertices')
fprintf(f2,'%s\n','(')
fprintf(f2,'%5s%g %g %g)\n','(',0 ,0 ,0)
fprintf(f2,'%5s%g %g %g) \n','(',0 ,vy ,-vz)
fprintf(f2,'%5s%g %g %g) \n','(',0, vy, vz)
fprintf(f2,'%5s%g %g %g) \n','(',L, 0, 0)
fprintf(f2,'%5s%g %g %g) \n','(',L, vy, -vz)
fprintf(f2,'%5s%g %g %g) \n','(',L, vy, vz)
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','blocks')
fprintf(f2,'%s\n','(')
fprintf(f2,'%7s (%g %g %g %g %g %g %g %g) (%g %g %g) %s (%g %g %g)\n','hex', 0, 1, 2, 0, 3, 4, 5, 3, 50, 1, 200, 'simpleGrading', 1, 1, 1)
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','edges')
fprintf(f2,'%s\n','(')
fprintf(f2,'%7s %g %g (%g %g %g)\n','arc', 1, 2, 0, r, 0)
fprintf(f2,'%7s %g %g (%g %g %g)\n','arc', 4, 5, L, r, 0)
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','boundary')
fprintf(f2,'%s\n','(')
fprintf(f2,'%9s \n','Inlet')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type patch;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 0, 1, 2, 0)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%10s\n','Outlet')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type patch;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 3, 5, 4, 3)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%9s\n','front')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type symmetry;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 0, 3, 4, 1)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%8s\n','Back')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type symmetry;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 0, 2, 5, 3)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%16s\n','Topcurvature')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%18s\n','type wall;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 1, 4, 5, 2)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%12s\n','axisline')
fprintf(f2,'%5s\n','{')
fprintf(f2,'%19s\n','type empty;')
fprintf(f2,'%13s\n','faces')
fprintf(f2,'%9s\n','(')
fprintf(f2,'%13s%g %g %g %g) \n','(', 0, 3, 3, 0)
fprintf(f2,'%10s\n',');')
fprintf(f2,'%5s\n','}')
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','mergePatchPairs')
fprintf(f2,'%s\n','(')
fprintf(f2,'%s\n',');')
fprintf(f2,'\n')
fprintf(f2,'%s\n','// ************************************************************************* //')
fclose(f2);
1) Wedge angle = 10 deg
blockMeshDict file (Output)
/*--------------------------------*- 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)
(0 0.00996195 -0.000871557)
(0 0.00996195 0.000871557)
(2.3 0 0)
(2.3 0.00996195 -0.000871557)
(2.3 0.00996195 0.000871557)
);
blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 200) simpleGrading (1 1 1)
);
edges
(
arc 1 2 (0 0.01 0)
arc 4 5 (2.3 0.01 0)
);
boundary
(
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)
);
}
Topcurvature
{
type wall;
faces
(
(1 4 5 2)
);
}
axisline
{
type empty;
faces
(
(0 3 3 0)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //Intial condition (t=0) :
Pressure -
/*--------------------------------*- 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;
}
Topcurvature
{
type zeroGradient;
}
axisline
{
type empty;
}
}
// ************************************************************************* //Velocity -
/*--------------------------------*- 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 (0.105 0 0);
}
Outlet
{
type zeroGradient;
}
front
{
type symmetry;
}
Back
{
type symmetry;
}
Topcurvature
{
type noSlip;
}
axisline
{
type empty;
}
}
// ************************************************************************* //10deg. Wedge Grid view -
Velocity Distribution -
Pressure distribution -
2) Wedge angle = 25 deg
25deg. Wedge Grid view -
Velocity Distribution -
Pressure distribution -
3) Wedge angle = 45 deg
45deg. Wedge Grid view -
Velocity Distribution -
Pressure distribution -
Steady state results for both Symmetry and wedge boundary conditions & analysis of Fully developed flow region with Hagen- Poiseuille's equations :
Using 'Plot over line' feature points data are ploted at Fully developed flow region L=2.2m, below are velocity & shear stress plots along radial & longitudinal direction and pressure drop (length 2.1m to 2.3m) in Hydrodynamically fully developed region.
Velocity distribution for wedge angle =10deg
Pressure distribution for wedge angle =10deg
Shear stress distribution for wedge angle =10deg
Velocity distribution for wedge angle = 25deg
Pressure distribution for wedge angle =25deg
Shear stress distribution for wedge angle =25deg
Velocity distribution for wedge angle =45deg
Pressure distribution for wedge angle =45deg
Shear stress distribution for wedge angle =45deg
Observations :
- Velocity profile curve is more parabolic at 10deg compared to 45 deg Wedge angle, where it is approaching towards linear and Max. velocity is almost remained same.
- Pressure drop gardient in fully developed region for all angle is constant & Diff. value increased with increase in Wedge angle.
- Shear stress plots we can see that near wall it is significantly visible when wedge angle is 10deg. & curve line moves away from wall at 25deg & more in 45deg.
Validation of maximum velocity,Shear stress and pressured drop for fully developed flow
| Numerical | Analytical | ||||||
| Wedge angle | 10 | 25 | 45 | ||||
| Flow variables | Wedge | Symmetry | Wedge | Symmetry | Wedge | Symmetry | |
| Max. velocity(U) m/sec | 0.202 | 0.2 | 0.202 | 0.198 | 0.205 | 0.205 | 0.21 |
|
Pressure drop (Pk) N-m/kg |
0.00175 | 0.00175 | 0.00181 | 0.00181 | 0.00201 | 0.00201 | 0.0017 |
| Shear stress (tou) N/m2 | 0.0425 | 0.0425 | 0.0425 | 0.0425 | 0.045 | 0.045 | 0.438 |
It is clear from the above numerical values that at 10deg. wedge angle values are much closer at exact/analytical solution.
Differences b/w Wedge & Symmetry Boundary conditions :
- Both these basic type BC's will create geometric constraints for axis-symmetry problems, where wedge is considered at front & back and whereas in symmetry as a symmetry planes.
- Simulation time took for symmetry BC was higher than wedge BC.
- Wedge BC calculates in 2D but symmetry in 3D.