Challenge

Week 12 - Symmetry vs Wedge vs HP equation

MMohammed Mansoor Ali Khan16 Oct 2020

Objective: In this we simulate the sector of pipe for different wedge angle thetha=10,25,45 in accordance to hagen poisuelles flow conditions with symmetry boundary condition and compare with the results obtained by different wedge angles.

Hagen poiseuilles's flow equations:

Hagen poiseuille's flow is a physical law that gives the pressure drop in an incompressible and newtonian fluid. And the velocity profile for the flow through a pipe in this case. Assumptions are made in deriving the hagen poiseuilies equation regarding the dimension that the length of the pipe is much larger than its diameter (L>>D). An average velocity is calculated across the flow which is used to calculate the maximum velocity.

we derive the flow of viscous fluid through a circular pipe to find

velocity distribution across the section
maximum velocity
average velocity
ratio of maximum velocity to average velocity
pressure drop in the pipe `Deltap=(32muoverlineuL)/(D^2)`
the shear stress distruibution

consider a pipe of length L =3 metres and diameter D=0.02metres .Dynamic viscosity of water `mu`=0.00091Ns/m^2 . The reynolds number is taken as 2100. Instead of taking the whole pipe we take a small sector of pipe this is due to the fact that a huge computational load is to be carried out while simulating for the entire pipe and by this we can save time due to axi-symmetry nature.

calculating analytical solution values for fluid flow:

Reynolds number: `Re=(rhoVavgD)/(mu)` `implies2100=(1000*Vavg*0.02)/(0.00091)impliesVavg=0.095m/s`
Maximum velocity at the centre : `Vmax=2*Vavg implies2*0.095=0.1911m/s`
hydrodynamic entrance length : `Le=0.06*Re*D implies0.06*2100*0.02implies2.52m`
Total length for profile Lt=3m
pressure drop across the pipe from Hp eqns : `Deltap=(32muVavgL)/(D^2)implies(32*0.0091*0.095*3)/(0.02^2)implies20.748kPa`
kinematic pressure difference : `DeltaPk=(Deltap)/(rho)=20.748/1000=0.020748`
velocity profile at any location wrt to radial direction: `u(r)=2Vavg(1-(r^2)/(R^2))`
kinematic viscosity `nu=mu/rho implies0.00091/1000implies0.00000091 m^2/s`

BlockmeshDict text file for thetha =10 degress:

clear all
close all
clc

%blockmesh file
Re=2100;
rho=1000;%kg/m^3
nu= 0.00091;%dynamic viscosity kine=dyna/rho
D=0.02;
r=D/2;
L_e = 0.06*Re*D;
L=3;
%hp eqns
v_avg = (r*nu)/(rho*D);
v_max = 2*v_avg;
dp = (32*nu*v_avg*L)/(D^2);%hagen poiseulles pressure drop
kinematic_p= dp/(rho);

th=10;
%meshing
mx=200;
my=40;
mz=1;
fx=1;%grading factor f
fy=0.2;
fz=1;

%vertices
v0=[0 0 0];
v1=[0 r*cosd(th/2) r*sind(th/2)];
v2=[0 r*cosd(th/2) -r*sind(th/2)];
v3=[3 0 0];
v4=[3 r*cosd(th/2) r*sind(th/2)];
v5=[3 r*cosd(th/2) -r*sind(th/2)];

header1='/*--------------------------------*- C++ -*----------------------------------*\'
header2=' =========             	|'
header3=' \\  	/   F ield     	| OpenFOAM: The Open Source CFD Toolbox'
header4='  \\	/   O peration 	| Website:  https://openfoam.org'
header5='   \\  /	A nd       	| Version:  8'
header6='	 \\/ 	M anipulation  |'
header7='\*---------------------------------------------------------------------------*/'
header8='FoamFile'
header9='{'
header11='version 	2.0;'
header12='format  	ascii;'
header13='class   	dictionary;'
header14='object  	blockMeshDict;'
header15='}'
header16='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'


f1=fopen('blockMeshDict','w')
fprintf(f1,'%sn',header1)
fprintf(f1,'%sn',header2)
fprintf(f1,'%sn',header3)
fprintf(f1,'%sn',header4)
fprintf(f1,'%sn',header5)
fprintf(f1,'%sn',header6)
fprintf(f1,'%sn',header7)
fprintf(f1,'%sn',header8)
fprintf(f1,'%sn',header9)
fprintf(f1,'%sn',header11)
fprintf(f1,'%sn',header12)
fprintf(f1,'%sn',header13)
fprintf(f1,'%sn',header14)
fprintf(f1,'%sn',header15)
fprintf(f1,'%sn',header16)

fprintf(f1,'convertToMeters 1;nn')

fprintf(f1,'verticesn')
fprintf(f1,'(n')
fprintf(f1,'t (%d %d %d)n',0,0,0)
fprintf(f1,'t (%d %d %d)n',0,r*cosd(th/2),r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',0,r*cosd(th/2),-r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',3,0,0)
fprintf(f1,'t (%d %d %d)n',3,r*cosd(th/2),r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',3,r*cosd(th/2),-r*sind(th/2))
fprintf(f1,');nn')

fprintf(f1,'blocksn')
fprintf(f1,'(n')
fprintf(f1,'t hex (0 3 5 2 0 3 4 1) (200 40 1) simpleGrading (1 0.2 1)')
fprintf(f1,');nn')

fprintf(f1,'edgesn')
fprintf(f1,'(n')
fprintf(f1,'t arc 1 2 (0 0.01000 0)')
fprintf(f1,'t arc 4 5 (3 0.01000 0)')
fprintf(f1,');nn')

fprintf(f1,'boundaryn')
fprintf(f1,'(n')
fprintf(f1,'t inletn')
fprintf(f1,'t {n')
fprintf(f1,'t type patch;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 1 2 0)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t outletn')
fprintf(f1,'t {n')
fprintf(f1,'t type patch;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(3 5 4 3)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t topwalln')
fprintf(f1,'t {n')
fprintf(f1,'t type wall;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(1 4 5 2)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t frontn')
fprintf(f1,'t {n')
fprintf(f1,'t type symmetry;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 2 5 3)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t backn')
fprintf(f1,'t {n')
fprintf(f1,'t type symmetry;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 3 4 1)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t axisn')
fprintf(f1,'t {n')
fprintf(f1,'t type empty;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 3 3 0)')
fprintf(f1,');n')
fprintf(f1,'t }n')
fprintf(f1,');n')


fprintf(f1,'mergePatchPairs')
fprintf(f1,'t {n')
fprintf(f1,');nn')
fprintf(f1,'header16')

fclose(f1)

BlockmeshDict text file for thetha =25 degress:

clear all
close all
clc

%blockmesh file
Re=2100;
rho=1000;%kg/m^3
nu= 0.00091;%dynamic viscosity kine=dyna/rho
D=0.02;
r=D/2;
L_e = 0.06*Re*D;
L=3;
%hp eqns
v_avg = (r*nu)/(rho*D);
v_max = 2*v_avg;
dp = (32*nu*v_avg*L)/(D^2);%hagen poiseulles pressure drop
kinematic_p= dp/(rho);

th=25;
%meshing
mx=200;
my=40;
mz=1;
fx=1;%grading factor f
fy=0.2;
fz=1;

%vertices
v0=[0 0 0];
v1=[0 r*cosd(th/2) r*sind(th/2)];
v2=[0 r*cosd(th/2) -r*sind(th/2)];
v3=[3 0 0];
v4=[3 r*cosd(th/2) r*sind(th/2)];
v5=[3 r*cosd(th/2) -r*sind(th/2)];

header1='/*--------------------------------*- C++ -*----------------------------------*\'
header2=' =========             	|'
header3=' \\  	/   F ield     	| OpenFOAM: The Open Source CFD Toolbox'
header4='  \\	/   O peration 	| Website:  https://openfoam.org'
header5='   \\  /	A nd       	| Version:  8'
header6='	 \\/ 	M anipulation  |'
header7='\*---------------------------------------------------------------------------*/'
header8='FoamFile'
header9='{'
header11='version 	2.0;'
header12='format  	ascii;'
header13='class   	dictionary;'
header14='object  	blockMeshDict;'
header15='}'
header16='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'


f1=fopen('blockMeshDict','w')
fprintf(f1,'%sn',header1)
fprintf(f1,'%sn',header2)
fprintf(f1,'%sn',header3)
fprintf(f1,'%sn',header4)
fprintf(f1,'%sn',header5)
fprintf(f1,'%sn',header6)
fprintf(f1,'%sn',header7)
fprintf(f1,'%sn',header8)
fprintf(f1,'%sn',header9)
fprintf(f1,'%sn',header11)
fprintf(f1,'%sn',header12)
fprintf(f1,'%sn',header13)
fprintf(f1,'%sn',header14)
fprintf(f1,'%sn',header15)
fprintf(f1,'%sn',header16)

fprintf(f1,'convertToMeters 1;nn')

fprintf(f1,'verticesn')
fprintf(f1,'(n')
fprintf(f1,'t (%d %d %d)n',0,0,0)
fprintf(f1,'t (%d %d %d)n',0,r*cosd(th/2),r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',0,r*cosd(th/2),-r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',3,0,0)
fprintf(f1,'t (%d %d %d)n',3,r*cosd(th/2),r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',3,r*cosd(th/2),-r*sind(th/2))
fprintf(f1,');nn')

fprintf(f1,'blocksn')
fprintf(f1,'(n')
fprintf(f1,'t hex (0 3 5 2 0 3 4 1) (200 40 1) simpleGrading (1 0.2 1)')
fprintf(f1,');nn')

fprintf(f1,'edgesn')
fprintf(f1,'(n')
fprintf(f1,'t arc 1 2 (0 0.01000 0)')
fprintf(f1,'t arc 4 5 (3 0.01000 0)')
fprintf(f1,');nn')

fprintf(f1,'boundaryn')
fprintf(f1,'(n')
fprintf(f1,'t inletn')
fprintf(f1,'t {n')
fprintf(f1,'t type patch;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 1 2 0)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t outletn')
fprintf(f1,'t {n')
fprintf(f1,'t type patch;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(3 5 4 3)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t topwalln')
fprintf(f1,'t {n')
fprintf(f1,'t type wall;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(1 4 5 2)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t frontn')
fprintf(f1,'t {n')
fprintf(f1,'t type symmetry;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 2 5 3)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t backn')
fprintf(f1,'t {n')
fprintf(f1,'t type symmetry;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 3 4 1)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t axisn')
fprintf(f1,'t {n')
fprintf(f1,'t type empty;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 3 3 0)')
fprintf(f1,');n')
fprintf(f1,'t }n')
fprintf(f1,');n')


fprintf(f1,'mergePatchPairs')
fprintf(f1,'t {n')
fprintf(f1,');nn')
fprintf(f1,'header16')

fclose(f1)

BlockmeshDict text file for thetha =45 degrees:

clear all
close all
clc

%blockmesh file
Re=2100;
rho=1000;%kg/m^3
nu= 0.00091;%dynamic viscosity kine=dyna/rho
D=0.02;
r=D/2;
L_e = 0.06*Re*D;
L=3;
%hp eqns
v_avg = (r*nu)/(rho*D);
v_max = 2*v_avg;
dp = (32*nu*v_avg*L)/(D^2);%hagen poiseulles pressure drop
kinematic_p= dp/(rho);

th=45;
%meshing
mx=200;
my=40;
mz=1;
fx=1;%grading factor f
fy=0.2;
fz=1;

%vertices
v0=[0 0 0];
v1=[0 r*cosd(th/2) r*sind(th/2)];
v2=[0 r*cosd(th/2) -r*sind(th/2)];
v3=[3 0 0];
v4=[3 r*cosd(th/2) r*sind(th/2)];
v5=[3 r*cosd(th/2) -r*sind(th/2)];

header1='/*--------------------------------*- C++ -*----------------------------------*\'
header2=' =========             	|'
header3=' \\  	/   F ield     	| OpenFOAM: The Open Source CFD Toolbox'
header4='  \\	/   O peration 	| Website:  https://openfoam.org'
header5='   \\  /	A nd       	| Version:  8'
header6='	 \\/ 	M anipulation  |'
header7='\*---------------------------------------------------------------------------*/'
header8='FoamFile'
header9='{'
header11='version 	2.0;'
header12='format  	ascii;'
header13='class   	dictionary;'
header14='object  	blockMeshDict;'
header15='}'
header16='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'


f1=fopen('blockMeshDict','w')
fprintf(f1,'%sn',header1)
fprintf(f1,'%sn',header2)
fprintf(f1,'%sn',header3)
fprintf(f1,'%sn',header4)
fprintf(f1,'%sn',header5)
fprintf(f1,'%sn',header6)
fprintf(f1,'%sn',header7)
fprintf(f1,'%sn',header8)
fprintf(f1,'%sn',header9)
fprintf(f1,'%sn',header11)
fprintf(f1,'%sn',header12)
fprintf(f1,'%sn',header13)
fprintf(f1,'%sn',header14)
fprintf(f1,'%sn',header15)
fprintf(f1,'%sn',header16)

fprintf(f1,'convertToMeters 1;nn')

fprintf(f1,'verticesn')
fprintf(f1,'(n')
fprintf(f1,'t (%d %d %d)n',0,0,0)
fprintf(f1,'t (%d %d %d)n',0,r*cosd(th/2),r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',0,r*cosd(th/2),-r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',3,0,0)
fprintf(f1,'t (%d %d %d)n',3,r*cosd(th/2),r*sind(th/2))
fprintf(f1,'t (%d %d %d)n',3,r*cosd(th/2),-r*sind(th/2))
fprintf(f1,');nn')

fprintf(f1,'blocksn')
fprintf(f1,'(n')
fprintf(f1,'t hex (0 3 5 2 0 3 4 1) (200 40 1) simpleGrading (1 0.2 1)')
fprintf(f1,');nn')

fprintf(f1,'edgesn')
fprintf(f1,'(n')
fprintf(f1,'t arc 1 2 (0 0.01000 0)')
fprintf(f1,'t arc 4 5 (3 0.01000 0)')
fprintf(f1,');nn')

fprintf(f1,'boundaryn')
fprintf(f1,'(n')
fprintf(f1,'t inletn')
fprintf(f1,'t {n')
fprintf(f1,'t type patch;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 1 2 0)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t outletn')
fprintf(f1,'t {n')
fprintf(f1,'t type patch;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(3 5 4 3)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t topwalln')
fprintf(f1,'t {n')
fprintf(f1,'t type wall;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(1 4 5 2)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t frontn')
fprintf(f1,'t {n')
fprintf(f1,'t type symmetry;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 2 5 3)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t backn')
fprintf(f1,'t {n')
fprintf(f1,'t type symmetry;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 3 4 1)')
fprintf(f1,');n')
fprintf(f1,'t }n')

fprintf(f1,'t axisn')
fprintf(f1,'t {n')
fprintf(f1,'t type empty;')
fprintf(f1,'t facesn')
fprintf(f1,'(n')
fprintf(f1,'(0 3 3 0)')
fprintf(f1,');n')
fprintf(f1,'t }n')
fprintf(f1,');n')


fprintf(f1,'mergePatchPairs')
fprintf(f1,'t {n')
fprintf(f1,');nn')
fprintf(f1,'header16')

fclose(f1)

BlockmeshDict file in openfoam for thetha=10:

/*--------------------------------*- 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)//v0
    (0 0.009968 0.000872)//v1
    (0 0.009968 -0.000872)//v2
    (3 0 0)//v3
    (3 0.009968 0.000872)//v4
    (3 0.009968 -0.000872)//v5
    
);

blocks
(
    hex (0 3 5 2 0 3 4 1) (200 40 1) simpleGrading (1 0.2 1)
);

edges
(
    arc 1 2 (0 0.01000 0)
    arc 4 5 (3 0.01000 0)
);

boundary
(
    inlet
    {
        type patch;
        faces
        (
            (0 1 2 0)
        );
    }
    outlet
    {
        type patch;
        faces
        (
            (3 5 4 3)
        );
    }
    topwall
    {
        type wall;
        faces
        (
            (1 4 5 2)
        );
    }
    front
    {
        type symmetry;
        faces
        (
            (0 2 5 3)
        );
    }
    back
    {
        type symmetry;
        faces
        (
            (0 3 4 1)
        );
     }
     axis
    {
        type empty;
        faces
        (
            (0 3 3 0)
        );
    }
);

mergePatchPairs
(
);

// ************************************************************************* //

BlockmeshDict file in openfoam for thetha=25;

/*--------------------------------*- 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)//v0
    (0 0.009763 0.002164)//v1
    (0 0.009763 -0.002164)//v2
    (3 0 0)//v3
    (3 0.009763 0.002164)//v4
    (3 0.009763 -0.002164)//v5
    
);

blocks
(
    hex (0 3 5 2 0 3 4 1) (200 40 1) simpleGrading (1 0.2 1)
);

edges
(
    arc 1 2 (0 0.01000 0)
    arc 4 5 (3 0.01000 0)
);

boundary
(
    inlet
    {
        type patch;
        faces
        (
            (0 1 2 0)
        );
    }
    outlet
    {
        type patch;
        faces
        (
            (3 5 4 3)
        );
    }
    topwall
    {
        type wall;
        faces
        (
            (1 4 5 2)
        );
    }
    front
    {
        type symmetry;
        faces
        (
            (0 2 5 3)
        );
    }
    back
    {
        type symmetry;
        faces
        (
            (0 3 4 1)
        );
     }
     axis
    {
        type empty;
        faces
        (
            (0 3 3 0)
        );
    }
);

mergePatchPairs
(
);

// ************************************************************************* //

BlockmeshDict file in openfoam for thetha=45;

/*--------------------------------*- 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)//v0
    (0 0.009239 0.003827)//v1
    (0 0.009239 -0.003827)//v2
    (3 0 0)//v3
    (3 0.009239 0.003827)//v4
    (3 0.009239 -0.003827)//v5
    
);

blocks
(
    hex (0 3 5 2 0 3 4 1) (200 40 1) simpleGrading (1 0.2 1)
);

edges
(
    arc 1 2 (0 0.01000 0)
    arc 4 5 (3 0.01000 0)
);

boundary
(
    inlet
    {
        type patch;
        faces
        (
            (0 1 2 0)
        );
    }
    outlet
    {
        type patch;
        faces
        (
            (3 5 4 3)
        );
    }
    topwall
    {
        type wall;
        faces
        (
            (1 4 5 2)
        );
    }
    front
    {
        type symmetry;
        faces
        (
            (0 2 5 3)
        );
    }
    back
    {
        type symmetry;
        faces
        (
            (0 3 4 1)
        );
     }
     axis
    {
        type empty;
        faces
        (
            (0 3 3 0)
        );
    }
);

mergePatchPairs
(
);

// ************************************************************************* //

Boundary conditions for velocity U and Pressure p:

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 (0.095 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    topwall
    {
        type            noSlip;
    }
    front
    {
        type            symmetry;
    }
    back
    {
        type            symmetry;
    }
    axis
    {
        type            empty;
    }
}

// ************************************************************************* //

pressure 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;
    }
    
    topwall
    {
        type            zeroGradient;
    }
    
    front
    {
        type            symmetry;
    }
    
    back
    {
        type            symmetry;
    }
    
    axis
    {
        type            empty;
    }
}


// ************************************************************************* //

Transport properties:

/*--------------------------------*- 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] 0.00000091;


// ************************************************************************* //

Mesh for wedge angle 10:

mesh for wedge angle 25:

Mesh for wedge angle 45:

Velocity distribution:

for wedge angle 10:

For wedge angle 25:

For wedge angle 45:

shear stress distribution for thetha=10,25,45:

comparison of Results:

thetha	Vmax(Hp eqn)	Vmax(openfoam)	max shear stress
4 (wedge)	0.1911m/s	0.1889m/s(approx)	0.034N/m^2
10 (symmetry)	0.1911m/s	0.1891m/s	0.0340 N/m^2
25 (symmetry)	0.1911m/s	0.1910m/s	0.0347N/m^2
45 (symmetry)	0.1911m/s	0.1911m/s	0.0347N/m^2

Conclusion and inferences:

There is a slight increase and decrease in Vmax while comparing the wedge angle 10 and 45.
The trend cant be compared but can be seen as the wegde angle increases the Vmax openfoam gives much accurate results.
The shear stress distribution is almost the same and the gradient makes a very slightest change to the shear stress from eqn `tau=mu(du)/(dr)`
The symmetry gives more accurate results then wedge
The computational time is more for symmetry bc when compared to wedge
The end time can be reduced in control dict to lessen the iteration and more or less gives similar results.
The time span and dx should be kept in mind for CFL condition.

Week 12 - Symmetry vs Wedge vs HP equation

Ship work like this
in your own course.

Talk to a career counsellor

Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.