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Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation

CChinnaiyan B5 Apr 2022
CFD

Objective:

  • To simulate an axis-symmetric laminar flow through the constant cross- sectional of the pipe by applying the symmetry boundary condition.
  • To simulating for the mentioned angles i.e for 10,25,45 degrees using both symmetry and wedge boundary conditions and validate them HP equations.         

Entrance length:

      The length of the entrance is the distance that fluid travels after entering a pipe before the full development of the flow. Entrance length refers to the length of the entry region, where effects from the pipe's interior wall spread as an expanding boundary layer into the flow. when the boundary layer extends to fill the entire pipe, the flow grows into a fully developed flow where the flow characteristics no longer change with increased distance along the pipe. To define a variety of flow conditions, there are many different entrance lengths. 

                      

Hydrodynamic entrance length: 

       The hydrodynamic entrance region refers to the area of a pipe where fluid entering a pipe develops a velocity profile due to viscous forces spreading from a pipe's interior wall. This region has a non-uniform flow. The fluid enters a pipe at a constant speed, so fluid partice in the layer in contact with the pipe's surface come to a complete stop because of the no-slip rule. The layer in contact with the pipe surface is resistant to the acceleration of neighbouring layers due to viscous forces within the fluid, creating a velocity profile. To keep the mass true, the speed of the fluid layers in the center of the pipe increases to compensate for the reduced speed of the fluid layers near the surface of the pipe. It creates a gradient of velocity across the pipe cross- section.

      Entry length for Laminar flow is Le= 0.006*Re*D

      To do the simulation we need to find properties using some variables. Those are Hagen Poiseuille equations.

Variables:

       Diameter, D=0.004

       Radius,r=0.002

       Radial Distance,R=0 to r

       Dynamic viscosity, mu= 0.00089 N/m^2

       Density, rho=997 kg/m^3

       Reynolds number, Re=2100

Hagen Poiseuille's Law:

       In non ideal fluid dynamics, Hagen-poiseuille equation is a physical law that gives pressure drop in an incompressible and newtonian fluid in a laminar flow through a long cylinder pipe of constant cross section.

Formulas:

       Average velocity  V_avg= (Re.mu)/(rho.D)

       Maximum velocity V_max= 2*V_avg

       Pressure Difference △P=(8*mu*L*V_avg)/r^2

       Kinematic pressure difference △Pk= △P/rho

       Shear stress =(2*mu*V_max*R)/r^2

Procedure:

  •  Will start with copying the cavity file from the tutoria to the FOAM_RUN folder.
  • In the run folder only we are going to simulate and whatever we want to do the changes in the blockMeshDict file, Pressure , Velocity files and ControlDict files we will be doing here.
  • Creating the block in the OpenFoam here we are creating the wedge after making the required changes in the blockMeshDict file to check the geometry run the blockMesh command.
  • After creating the wedge assign the boundary conditions, and also sitting the simulation end time and time-step in such a way that the courant number should be less than 0.5 and also in the transportproperties enter the kinematic viscosity.
  • RUN the simulation using the icoFoam solver after calculating the time needed for the fluid to travel from inlet to outlet.
  • After the simulation, use paraFoam to view the flow inside the wedge and use plot over line command to plot the velocity and shear stress changes at a point after the hydrodynamical entry region so that we analyse the fully developed region of the fluid.
  • Use Matlab to parse the blockMeshDict so that the same file can be used for any wedge values.

Matlab code to Generate blockMeshDict file for wedge boundary condition:

clear all 
close all
clc
%reynolds number
Re=2100;
%The diameter of pipe
D=0.02;
%The Entry length of pipe
L=0.06*Re*D;
%The total length of pipe
L_p=L+0.5;
%The Radius of pipe
r=D/2;
%Angle of wedge 
theta=input('Enter the value of the wedge angle=');
%Dynamic viscosity
mu=0.89e-3;
%Density
rho=997;

%Hagen poiseuille flow equation
v_avg = (Re*mu)/(rho*D);
v_max =2*(v_avg);
del_p = (8*mu*L_p*v_avg)/(r^2);
kinematic_p=del_p/rho;


header1='/*--------------------------------*- C++ -*----------------------------------*\'
header2= ' =========                 |'
header3='  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox'
header4='   \\    /   O peration     | Website:  https://openfoam.org'
header5='    \\  /    A nd           | Version:  9'
header6= '     \\/     M anipulation  |'
header7='\*---------------------------------------------------------------------------*/'
f1 = fopen('blockMeshDictWed','w')
fprintf(f1, '%s\n', header1)
fprintf(f1, '%s\n', header2)
fprintf(f1, '%s\n', header3)
fprintf(f1, '%s\n', header4)
fprintf(f1, '%s\n', header5)
fprintf(f1, '%s\n', header6)
fprintf(f1, '%s\n', header7)

fprintf(f1, 'FoamFile\n{\n')
fprintf(f1, '%12s \t ascii;\n','format')
fprintf(f1, '%12s \t dictionary;\n','class')
fprintf(f1, '%12s \t blockMeshDict;\n','object')
fprintf(f1, '}\n')
header8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'
fprintf(f1, '%s\n\n',header8)

fprintf(f1, 'convertToMeters 1;\n\n')

fprintf(f1, 'vertices\n')
fprintf(f1, '(\n')
fprintf(f1, '\t (%d %d %d)\n',0,0,0)
fprintf(f1, '\t (%d %d %d)\n',0,r*cosd(theta/2),r*sind(theta/2))
fprintf(f1, '\t (%d %d %d)\n',0,r*cosd(theta/2),-r*sind(theta/2))
fprintf(f1, '\t (%d %d %d)\n',L_p,0,0)
fprintf(f1, '\t (%d %d %d)\n',L_p,r*cosd(theta/2),r*sind(theta/2))
fprintf(f1, '\t (%d %d %d)\n',L_p,r*cosd(theta/2),-r*sind(theta/2))
fprintf(f1, ');\n\n')

fprintf(f1, 'blocks\n')
fprintf(f1, '(\n')
fprintf(f1, '\t hex (0 3 5 2 0 3 4 1) (%d %d %d)',300,30,1)
fprintf(f1, 'SimpleGrading (1 0.1 1)\n\n')
fprintf(f1, ');\n\n')

fprintf(f1, 'edges\n')
fprintf(f1, '(\n')
fprintf(f1, '\t arc %d%d(%d %d %d)\n',1,2,0,r,0)
fprintf(f1, '\t arc %d%d(%d %d %d)\n',4,5,L_p,r,0)
fprintf(f1, ');\n\n')

fprintf(f1, 'boundary\n')
fprintf(f1, '(\n')
fprintf(f1, '\t inlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t typepatch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 1 2 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t outlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t typepatch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (3 5 4 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t top \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wall;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (1 4 5 2)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t front \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wedge;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 4 1)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t back \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wedge;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 2 5 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t axis \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type empty;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 3 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '); \n\n')

fprintf(f1, 'mergePatchPairs\n')
fprintf(f1, '(\n')
fprintf(f1, ');\n')

header9='// ************************************************************************* //'
fprintf(f1, '%s\n',header9)

fclose(f1)

blockMeshDict File for 45 degree:

/*--------------------------------*- 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 9.238795e-03 3.826834e-03)
	 (0 9.238795e-03 -3.826834e-03)
	 (3.020000e+00 0 0)
	 (3.020000e+00 9.238795e-03 3.826834e-03)
	 (3.020000e+00 9.238795e-03 -3.826834e-03)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (300 30 1) SimpleGrading (1 0.1 1)

);

edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (3.020000e+00 1.000000e-02 0)
);

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

mergePatchPairs
(
);
// ************************************************************************* //

ControlDict File

/*--------------------------------*- 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         3;

deltaT          1e-3;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

transportproperties

/*--------------------------------*- 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] 8.9256e-07;


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

Pressure file:

/*--------------------------------*- 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
{
    inlet
    {
        type            zeroGradient;
    }

    outlet
    {
        type            fixedValue;
        value           uniform 1.0073;
    }

    axis
    {
        type            empty;
    }
    top
    {
        type            zeroGradient;
    }
    front
    {
        type           wedge;
    }
    back
    {
        type           wedge;
    }
}
// ************************************************************************* //

 Velocity File:

/*--------------------------------*- 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 (0.4686 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.4686 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }
    top
    {
        type            fixedValue;
        value           uniform (0 0 0);
    }
    front
    {
        type           wedge;
    }
    back
    {
        type           wedge;
    }
}

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

Outputs for 45 degree wedge angle

blockMeshDict File for 25 degree:

/*--------------------------------*- 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 9.762960e-03 2.164396e-03)
	 (0 9.762960e-03 -2.164396e-03)
	 (3.020000e+00 0 0)
	 (3.020000e+00 9.762960e-03 2.164396e-03)
	 (3.020000e+00 9.762960e-03 -2.164396e-03)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (300 30 1) SimpleGrading (1 0.1 1)

);

edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (3.020000e+00 1.000000e-02 0)
);

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

mergePatchPairs
(
);
// ************************************************************************* //

Outputs for 25 degree wedge angle

blockMeshDict File for 10 degree:

/*--------------------------------*- 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 9.961947e-03 8.715574e-04)
	 (0 9.961947e-03 -8.715574e-04)
	 (3.020000e+00 0 0)
	 (3.020000e+00 9.961947e-03 8.715574e-04)
	 (3.020000e+00 9.961947e-03 -8.715574e-04)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (300 30 1) SimpleGrading (1 0.1 1)

);

edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (3.020000e+00 1.000000e-02 0)
);

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

mergePatchPairs
(
);
// ************************************************************************* //

Outputs for 10 degree wedge angle

Matlab code to Generate blockMeshDict file for symmetry boundary condition:

clear all 
close all
clc
%reynolds number
Re=2100;
%The diameter of pipe
D=0.02;
%The Entry length of pipe
L=0.06*Re*D;
%The total length of pipe
L_p=L+0.5;
%The Radius of pipe
r=D/2;
%Angle of wedge 
theta=input('Enter the value of the wedge angle=');
%Dynamic viscosity
mu=0.89e-3;
%Density
rho=997;

%Hagen poiseuille flow equation
v_avg = (Re*mu)/(rho*D);
v_max =2*(v_avg);
del_p = (8*mu*L_p*v_avg)/(r^2);
kinematic_p=del_p/rho;


header1='/*--------------------------------*- C++ -*----------------------------------*\'
header2= ' =========                 |'
header3='  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox'
header4='   \\    /   O peration     | Website:  https://openfoam.org'
header5='    \\  /    A nd           | Version:  9'
header6= '     \\/     M anipulation  |'
header7='\*---------------------------------------------------------------------------*/'
f1 = fopen('blockMeshDictwe','w')
fprintf(f1, '%s\n', header1)
fprintf(f1, '%s\n', header2)
fprintf(f1, '%s\n', header3)
fprintf(f1, '%s\n', header4)
fprintf(f1, '%s\n', header5)
fprintf(f1, '%s\n', header6)

fprintf(f1, '%s\n', header7)

fprintf(f1, 'FoamFile\n{\n')
fprintf(f1, '%12s \t ascii;\n','format')
fprintf(f1, '%12s \t dictionary;\n','class')
fprintf(f1, '%12s \t blockMeshDict;\n','object')
fprintf(f1, '}\n')
header8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'
fprintf(f1, '%s\n\n',header8)

fprintf(f1, 'convertToMeters 1;\n\n')

fprintf(f1, 'vertices\n')
fprintf(f1, '(\n')
fprintf(f1, '\t (%d %d %d)\n',0,0,0)
fprintf(f1, '\t (%d %d %d)\n',0,r*cosd(theta/2),r*sind(theta/2))
fprintf(f1, '\t (%d %d %d)\n',0,r*cosd(theta/2),-r*sind(theta/2))
fprintf(f1, '\t (%d %d %d)\n',L_p,0,0)
fprintf(f1, '\t (%d %d %d)\n',L_p,r*cosd(theta/2),r*sind(theta/2))
fprintf(f1, '\t (%d %d %d)\n',L_p,r*cosd(theta/2),-r*sind(theta/2))
fprintf(f1, ');\n\n')

fprintf(f1, 'blocks\n')
fprintf(f1, '(\n')
fprintf(f1, '\t hex (0 3 5 2 0 3 4 1) (%d %d %d)',300,30,1)
fprintf(f1, 'SimpleGrading (1 0.1 1)\n\n')
fprintf(f1, ');\n\n')

fprintf(f1, 'edges\n')
fprintf(f1, '(\n')
fprintf(f1, '\t arc %d%d(%d %d %d)\n',1,2,0,r,0)
fprintf(f1, '\t arc %d%d(%d %d %d)\n',4,5,L_p,r,0)
fprintf(f1, ');\n\n')

fprintf(f1, 'boundary\n')
fprintf(f1, '(\n')
fprintf(f1, '\t inlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t typepatch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 1 2 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t outlet \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t typepatch;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (3 5 4 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t top \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type wall;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (1 4 5 2)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t front \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type symmetry;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 4 1)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t back \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type symmetry;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 2 5 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t axis \n')
fprintf(f1, '\t {\n')
fprintf(f1, '\t\t type empty;\n')
fprintf(f1, '\t\t faces\n')
fprintf(f1, '\t\t (\n')
fprintf(f1, '\t\t\t (0 3 3 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '); \n\n')

fprintf(f1, 'mergePatchPairs\n')
fprintf(f1, '(\n')
fprintf(f1, ');\n')

header9='// ************************************************************************* //'
fprintf(f1, '%s\n',header9)

fclose(f1)

blockMeshDict File for 10 degree:

/*--------------------------------*- 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 9.961947e-03 8.715574e-04)
	 (0 9.961947e-03 -8.715574e-04)
	 (3.020000e+00 0 0)
	 (3.020000e+00 9.961947e-03 8.715574e-04)
	 (3.020000e+00 9.961947e-03 -8.715574e-04)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (300 30 1) SimpleGrading (1 0.1 1)

);

edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (3.020000e+00 1.000000e-02 0)
);

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

mergePatchPairs
(
);
// ************************************************************************* //

Outputs for 10 degree symmetry

blockMeshDict File for 25 degree:

/*--------------------------------*- 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 9.762960e-03 2.164396e-03)
	 (0 9.762960e-03 -2.164396e-03)
	 (3.020000e+00 0 0)
	 (3.020000e+00 9.762960e-03 2.164396e-03)
	 (3.020000e+00 9.762960e-03 -2.164396e-03)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (300 30 1) SimpleGrading (1 0.1 1)

);

edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (3.020000e+00 1.000000e-02 0)
);

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

mergePatchPairs
(
);
// ************************************************************************* //

Outputs for 25 degree symmetry

blockMeshDict File for 45 degree:

/*--------------------------------*- 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 9.238795e-03 3.826834e-03)
	 (0 9.238795e-03 -3.826834e-03)
	 (3.020000e+00 0 0)
	 (3.020000e+00 9.238795e-03 3.826834e-03)
	 (3.020000e+00 9.238795e-03 -3.826834e-03)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (300 30 1) SimpleGrading (1 0.1 1)

);

edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (3.020000e+00 1.000000e-02 0)
);

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

mergePatchPairs
(
);
// ************************************************************************* //

Outputs for 45 degree symmetry

Shear stress chart:

Conclusion:

      We can observe there is no much change in the maximum velocities. The only difference observed is execution time a little high than type-wedge. While the angle increases the error in the maximum velocity is decreased. Though there is not much difference between analytical and numerical results and also with increasing the angle of the wedge, The courant number is slightly increasing. we can say that the symmetric boundary condition plays an impoartant role in terms of accuracy in the result.  

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