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

SSathiya V23 Jul 2023
CFDMATLAB

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

Hagen-Poiseuille's law:

Hagen–Poiseuille law defines the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross-section. The pressure drop is given by:

where,

ΔP is the pressure drop.

μ is the dynamic viscosity.

L is the length of the pipe.

V is the velocity.

At the entrance, the flow is said to be in the hydrodynamic entrance region where the velocity profile gradually takes the shape of a parabola from a straight line.

As soon as the parabolic velocity profile becomes steady the flow is said to be in its fully developed state. Normally Hagen Poiseuille's Equation is applicable for a fully developed flow which helps us to calculate the pressure loss.

Let,

Geometry: Axisymmetric.

Reynolds number: 2100.

Working fluid: Water.

Diameter of the pipe: 0.02 m.

Dynamic viscosity(μ)=0.89x10^-3 Pas

Kinematic viscosity(ν)=0.8927x10^-6 m^2/s

theta=10, 25, 45

Average velocity

V_avg=Reμ/ρD m/s

Maximum velocity

V_max=2⋅Vavg m/s

Pressure drop

ΔP=32μLV/d^2 pa

kinematic pressure drop = ΔP/ρ

PROCEDURE

- Copying the cavity file from the tutorial to the FOAM_RUN folder.

- Updating the blockMeshDict file and pressure and velocity files and controlDict files.

- Creating the block in the OpenFoam

- After creating the wedge assigning the boundary conditions, 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.

- Running 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: (Wedge BC)

clear all
close all
clc

Re=2100; 
rho=997;  
D=0.02; 
r=D/2; 
mu=0.89*10^-3;  
v=0.88927*10^-6; 
theta=input('Enter the value of the wedge angle= ')
L_h=0.06*Re*D; 

L=L_h+0.5;
% Analytical solutions 
V_avg=(Re*mu)/(rho*D);  
V_max=2*V_avg;   
P_drop=(32*mu*L*V_avg)/D^2;  
P_kinematic=(P_drop)/rho;  


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)]


% BlockMeshDict FILE

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='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';

% opening the file
f1=fopen('blockMeshDict_parsedNEW.txt','wt');

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,'%s \n',H8);
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,'%s \n',H15);
fprintf(f1,'\n');

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

fprintf(f1,'%s \n','vertices');
fprintf(f1,'%s \n','(');
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v0(1),v0(2),v0(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v1(1),v1(2),v1(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v2(1),v2(2),v2(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v3(1),v3(2),v3(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v4(1),v4(2),v4(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v5(1),v5(2),v5(3));
  
fprintf(f1,'%s \n',');');

fprintf(f1,'%s \n','blocks');
fprintf(f1,'%s \n','(');
fprintf(f1,'%s %s \n',blanks(5),'hex (0 2 1 0 3 5 4 3) (20 1 200) simpleGrading (1 1 1)');
fprintf(f1,'%s \n',');');

fprintf(f1,'%s \n','edges');
fprintf(f1,'%s \n','(');
fprintf(f1,'arc 1 2 (%f %f %f) \n',0,r,0);
fprintf(f1,'arc 4 5 (%f %f %f) \n',L,r,0);
fprintf(f1,'%s \n',');');

fprintf(f1,'%s \n','boundary');
fprintf(f1,'( \n');
fprintf(f1,'%s %s \n',blanks(5),'inlet');
fprintf(f1,'%s %s \n',blanks(5),'{');
fprintf(f1,'%s %s \n',blanks(10),'type patch;');
fprintf(f1,'           %s \n','faces');
fprintf(f1,'          %s \n','(');
fprintf(f1,'           (%d %d %d %d)\n',0, 1, 2, 0);
fprintf(f1,'          );\n');
fprintf(f1,'      }\n');
fprintf(f1,'      %s\n','outlet');
fprintf(f1,'      {\n');
fprintf(f1,'        %s\n','type patch;');
fprintf(f1,'         %s\n','faces');
fprintf(f1,'         (\n');
fprintf(f1,'            (%d %d %d %d)\n',3, 4, 5, 3);
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,'     %s\n','wedge_front');
fprintf(f1,'     {\n');
fprintf(f1,'         %s\n','type wedge;');
fprintf(f1,'         %s\n','faces');
fprintf(f1,'         (\n');
fprintf(f1,'             (%d %d %d %d)\n',2, 5, 3, 0);
fprintf(f1,'\n');            
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,'     %s\n','wedge_Back');
fprintf(f1,'     {\n');
fprintf(f1,'%s\n','         type wedge;');
fprintf(f1,'%s\n','         faces');
fprintf(f1,'         (\n');
fprintf(f1,'\n');            
fprintf(f1,'             (%d %d %d %d)\n',0, 3, 4, 1);
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,'     %s\n','top');
fprintf(f1,'     {\n');
fprintf(f1,'         %s\n','type wall;');
fprintf(f1,'         %s\n','faces');
fprintf(f1,'         (\n');
fprintf(f1,'             (%d %d %d %d)\n',1, 4, 5, 2);
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,'     %s\n','axis');
fprintf(f1,'     {\n');
fprintf(f1,'         %s\n','type empty;');
fprintf(f1,'         %s\n','faces');
fprintf(f1,'         (\n');
fprintf(f1,'             (%d %d %d %d)\n',0, 3, 3, 0);
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,' );\n');
fprintf(f1,'\n'); 
fprintf(f1,' %s\n','mergePatchPairs');
fprintf(f1,'(\n');
fprintf(f1,' );\n');
fprintf(f1,'\n'); 
fprintf(f1,' // ************************************************************************* //\n');


fclose(f1);

MATLAB CODE: (Symmetry BC)

clear all
close all
clc

Re=2100; 
rho=997;  
D=0.02; 
r=D/2; 
mu=0.89*10^-3; 
v=0.88927*10^-6; 
theta=input('Enter the value of the wedge angle= ')
L_h=0.06*Re*D; % hydrodynamic lenght 

L=L_h+0.5;

V_avg=(Re*mu)/(rho*D);  
V_max=2*V_avg;   
P_drop=(32*mu*L*V_avg)/D^2;  
P_kinematic=(P_drop)/rho;  

 
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)]


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='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';

f1=fopen('blockMeshDict_parsedNEW.txt','wt');

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,'%s \n',H8);
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,'%s \n',H15);
fprintf(f1,'\n');

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

fprintf(f1,'%s \n','vertices');
fprintf(f1,'%s \n','(');
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v0(1),v0(2),v0(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v1(1),v1(2),v1(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v2(1),v2(2),v2(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v3(1),v3(2),v3(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v4(1),v4(2),v4(3));
fprintf(f1,'%s (%f %f %f) \n',blanks(5),v5(1),v5(2),v5(3));
  
fprintf(f1,'%s \n',');');

fprintf(f1,'%s \n','blocks');
fprintf(f1,'%s \n','(');
fprintf(f1,'%s %s \n',blanks(5),'hex (0 2 1 0 3 5 4 3) (40 1 500) simpleGrading (1 1 1)');
fprintf(f1,'%s \n',');');

fprintf(f1,'%s \n','edges');
fprintf(f1,'%s \n','(');
fprintf(f1,'arc 1 2 (%f %f %f) \n',0,r,0);
fprintf(f1,'arc 4 5 (%f %f %f) \n',L,r,0);
fprintf(f1,'%s \n',');');

fprintf(f1,'%s \n','boundary');
fprintf(f1,'( \n');
fprintf(f1,'%s %s \n',blanks(5),'inlet');
fprintf(f1,'%s %s \n',blanks(5),'{');
fprintf(f1,'%s %s \n',blanks(10),'type patch;');
fprintf(f1,'           %s \n','faces');
fprintf(f1,'          %s \n','(');
fprintf(f1,'           (%d %d %d %d)\n',0, 1, 2, 0);
fprintf(f1,'          );\n');
fprintf(f1,'      }\n');
fprintf(f1,'      %s\n','outlet');
fprintf(f1,'      {\n');
fprintf(f1,'        %s\n','type patch;');
fprintf(f1,'         %s\n','faces');
fprintf(f1,'         (\n');
fprintf(f1,'            (%d %d %d %d)\n',3, 4, 5, 3);
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,'     %s\n','wedge_front');
fprintf(f1,'     {\n');
fprintf(f1,'         %s\n','type symmetry;');
fprintf(f1,'         %s\n','faces');
fprintf(f1,'         (\n');
fprintf(f1,'             (%d %d %d %d)\n',2, 5, 3, 0);
fprintf(f1,'\n');            
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,'     %s\n','wedge_back');
fprintf(f1,'     {\n');
fprintf(f1,'%s\n','         type symmetry;');
fprintf(f1,'%s\n','         faces');
fprintf(f1,'         (\n');
fprintf(f1,'\n');            
fprintf(f1,'             (%d %d %d %d)\n',0, 3, 4, 1);
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,'     %s\n','top');
fprintf(f1,'     {\n');
fprintf(f1,'         %s\n','type wall;');
fprintf(f1,'         %s\n','faces');
fprintf(f1,'         (\n');
fprintf(f1,'             (%d %d %d %d)\n',1, 4, 5, 2);
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,'     %s\n','axis');
fprintf(f1,'     {\n');
fprintf(f1,'         %s\n','type empty;');
fprintf(f1,'         %s\n','faces');
fprintf(f1,'         (\n');
fprintf(f1,'             (%d %d %d %d)\n',0, 3, 3, 0);
fprintf(f1,'          );\n');
fprintf(f1,'     }\n');
fprintf(f1,' );\n');
fprintf(f1,'\n'); 
fprintf(f1,' %s\n','mergePatchPairs');
fprintf(f1,'(\n');
fprintf(f1,' );\n');
fprintf(f1,'\n'); 
fprintf(f1,' // ************************************************************************* //\n');


fclose(f1);

Symmetry BC Angle 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 
( 
      (0.000000 0.000000 0.000000) 
      (0.000000 0.009763 0.002164) 
      (0.000000 0.009763 -0.002164) 
      (3.020000 0.000000 0.000000) 
      (3.020000 0.009763 0.002164) 
      (3.020000 0.009763 -0.002164) 
); 
blocks 
( 
      hex (0 2 1 0 3 5 4 3) (40 1 500) simpleGrading (1 1 1) 
); 
edges 
( 
arc 1 2 (0.000000 0.010000 0.000000) 
arc 4 5 (3.020000 0.010000 0.000000) 
); 
boundary 
( 
      inlet 
      { 
           type patch; 
           faces 
          ( 
           (0 1 2 0)
          );
      }
      outlet
      {
        type patch;
         faces
         (
            (3 4 5 3)
          );
     }
     wedge_front
     {
         type symmetry;
         faces
         (
             (2 5 3 0)

          );
     }
     wedge_back
     {
         type symmetry;
         faces
         (

             (0 3 4 1)
          );
     }
     top
     {
         type wall;
         faces
         (
             (1 4 5 2)
          );
     }
     axis
     {
         type empty;
         faces
         (
             (0 3 3 0)
          );
     }
 );

 mergePatchPairs
(
 );

 // ************************************************************************* //
 
controlDict file

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2006                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       latestTime;

startTime       0;

stopAt          endTime;

endTime         30;

deltaT          0.005;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

Pressure file

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2006                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     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;
    }

    wedge_front
    {
        type            symmetry;
    }

    wedge_back
    {
        type            symmetry;
    }

    top
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }
}

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

Velocity file

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2006                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     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 (0.09373 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    top
    {
        type            noSlip;
    }

    wedge_front
    {
        type            symmetry;
    }

    wedge_back
    {
        type            symmetry;
    }

    axis
    {
        type            empty;
    }
}

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

Results:

Blockmesh

Velocity profile

Pressure profile

Symmetry BC Angle 10 deg

/*--------------------------------*- 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 
( 
      (0.000000 0.000000 0.000000) 
      (0.000000 0.009962 0.000872) 
      (0.000000 0.009962 -0.000872) 
      (3.020000 0.000000 0.000000) 
      (3.020000 0.009962 0.000872) 
      (3.020000 0.009962 -0.000872) 
); 
blocks 
( 
      hex (0 2 1 0 3 5 4 3) (40 1 500) simpleGrading (1 1 1) 
); 
edges 
( 
arc 1 2 (0.000000 0.010000 0.000000) 
arc 4 5 (3.020000 0.010000 0.000000) 
); 
boundary 
( 
      inlet 
      { 
           type patch; 
           faces 
          ( 
           (0 1 2 0)
          );
      }
      outlet
      {
        type patch;
         faces
         (
            (3 4 5 3)
          );
     }
     wedge_front
     {
         type symmetry;
         faces
         (
             (2 5 3 0)

          );
     }
     wedge_back
     {
         type symmetry;
         faces
         (

             (0 3 4 1)
          );
     }
     top
     {
         type wall;
         faces
         (
             (1 4 5 2)
          );
     }
     axis
     {
         type empty;
         faces
         (
             (0 3 3 0)
          );
     }
 );

 mergePatchPairs
(
 );

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

Results:

Blockmesh

Velocity profile

Pressure profile

Symmetry BC Angle 45 degrees

/*--------------------------------*- 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 
( 
      (0.000000 0.000000 0.000000) 
      (0.000000 0.009239 0.003827) 
      (0.000000 0.009239 -0.003827) 
      (3.020000 0.000000 0.000000) 
      (3.020000 0.009239 0.003827) 
      (3.020000 0.009239 -0.003827) 
); 
blocks 
( 
      hex (0 2 1 0 3 5 4 3) (40 1 500) simpleGrading (1 1 1) 
); 
edges 
( 
arc 1 2 (0.000000 0.010000 0.000000) 
arc 4 5 (3.020000 0.010000 0.000000) 
); 
boundary 
( 
      inlet 
      { 
           type patch; 
           faces 
          ( 
           (0 1 2 0)
          );
      }
      outlet
      {
        type patch;
         faces
         (
            (3 4 5 3)
          );
     }
     wedge_front
     {
         type symmetry;
         faces
         (
             (2 5 3 0)

          );
     }
     wedge_back
     {
         type symmetry;
         faces
         (

             (0 3 4 1)
          );
     }
     top
     {
         type wall;
         faces
         (
             (1 4 5 2)
          );
     }
     axis
     {
         type empty;
         faces
         (
             (0 3 3 0)
          );
     }
 );

 mergePatchPairs
(
 );

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

Results:

Blockmesh

Velocity profile

Pressure profile

Wedge BC Angle 10 deg

/*--------------------------------*- 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 
( 
      (0.000000 0.000000 0.000000) 
      (0.000000 0.009962 0.000872) 
      (0.000000 0.009962 -0.000872) 
      (3.020000 0.000000 0.000000) 
      (3.020000 0.009962 0.000872) 
      (3.020000 0.009962 -0.000872) 
); 
blocks 
( 
      hex (0 2 1 0 3 5 4 3) (40 1 500) simpleGrading (1 1 1) 
); 
edges 
( 
arc 1 2 (0.000000 0.010000 0.000000) 
arc 4 5 (3.020000 0.010000 0.000000) 
); 
boundary 
( 
      inlet 
      { 
           type patch; 
           faces 
          ( 
           (0 1 2 0)
          );
      }
      outlet
      {
        type patch;
         faces
         (
            (3 4 5 3)
          );
     }
     wedge_front
     {
         type wedge;
         faces
         (
             (2 5 3 0)

          );
     }
     wedge_back
     {
         type wedge;
         faces
         (

             (0 3 4 1)
          );
     }
     top
     {
         type wall;
         faces
         (
             (1 4 5 2)
          );
     }
     axis
     {
         type empty;
         faces
         (
             (0 3 3 0)
          );
     }
 );

 mergePatchPairs
(
 );

 // ************************************************************************* //
 
controlDict file
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2006                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       latestTime;

startTime       0;

stopAt          endTime;

endTime         10;

deltaT          0.005;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


// ************************************************************************* //
 
Pressure file
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2006                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     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;
    }

    wedge_front
    {
        type            wedge;
    }

    wedge_back
    {
        type            wedge;
    }

    top
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }
}

// ************************************************************************* //
 
Velocity file
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  v2006                                 |
|   \\  /    A nd           | Website:  www.openfoam.com                      |
|    \\/     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 (0.09373 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    top
    {
        type            noSlip;
    }

    wedge_front
    {
        type            wedge;
    }

    wedge_back
    {
        type            wedge;
    }

    axis
    {
        type            empty;
    }
}

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

Results:

Blockmesh

Pressure profile

Velocity profile

Wedge BC Angle 25 deg

/*--------------------------------*- 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 
( 
      (0.000000 0.000000 0.000000) 
      (0.000000 0.009763 0.002164) 
      (0.000000 0.009763 -0.002164) 
      (3.020000 0.000000 0.000000) 
      (3.020000 0.009763 0.002164) 
      (3.020000 0.009763 -0.002164) 
); 
blocks 
( 
      hex (0 2 1 0 3 5 4 3) (40 1 500) simpleGrading (1 1 1) 
); 
edges 
( 
arc 1 2 (0.000000 0.010000 0.000000) 
arc 4 5 (3.020000 0.010000 0.000000) 
); 
boundary 
( 
      inlet 
      { 
           type patch; 
           faces 
          ( 
           (0 1 2 0)
          );
      }
      outlet
      {
        type patch;
         faces
         (
            (3 4 5 3)
          );
     }
     wedge_front
     {
         type wedge;
         faces
         (
             (2 5 3 0)

          );
     }
     wedge_back
     {
         type wedge;
         faces
         (

             (0 3 4 1)
          );
     }
     top
     {
         type wall;
         faces
         (
             (1 4 5 2)
          );
     }
     axis
     {
         type empty;
         faces
         (
             (0 3 3 0)
          );
     }
 );

 mergePatchPairs
(
 );

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

Results:

Blockmesh

Pressure profile

Velocity profile

Wedge BC Angle 45 deg

/*--------------------------------*- 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 
( 
      (0.000000 0.000000 0.000000) 
      (0.000000 0.009239 0.003827) 
      (0.000000 0.009239 -0.003827) 
      (3.020000 0.000000 0.000000) 
      (3.020000 0.009239 0.003827) 
      (3.020000 0.009239 -0.003827) 
); 
blocks 
( 
      hex (0 2 1 0 3 5 4 3) (40 1 500) simpleGrading (1 1 1) 
); 
edges 
( 
arc 1 2 (0.000000 0.010000 0.000000) 
arc 4 5 (3.020000 0.010000 0.000000) 
); 
boundary 
( 
      inlet 
      { 
           type patch; 
           faces 
          ( 
           (0 1 2 0)
          );
      }
      outlet
      {
        type patch;
         faces
         (
            (3 4 5 3)
          );
     }
     wedge_front
     {
         type wedge;
         faces
         (
             (2 5 3 0)

          );
     }
     wedge_back
     {
         type wedge;
         faces
         (

             (0 3 4 1)
          );
     }
     top
     {
         type wall;
         faces
         (
             (1 4 5 2)
          );
     }
     axis
     {
         type empty;
         faces
         (
             (0 3 3 0)
          );
     }
 );

 mergePatchPairs
(
 );

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

Results:

Blockmesh

Pressure profile

Velocity profile

Conclusion:

- Observed that there is no significant change in the maximum velocities.

- Noted that the execution time a little high than type-wedge.

- As the angle increases the error in the maximum velocity decreases.

- Eventhough the difference is very slight between analytical and numerical results, also with increasing the angle of the wedge, the Courant number is slightly increasing.

- One thing to note is that symmetric boundary condition plays an important role in terms of accuracy in the result.

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