BlogFor BusinessTalk to a counsellor
CoursesIIT ProgramsPlacementsLog in
BlogFor Business
Talk to a counsellor
Challenge

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

NNikhil Kumar28 Oct 2022
CFDHTMLMATLAB

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 with HP equations.

Hagen-Poiseuille's law:

In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, is a physical law that gives 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:

ΔP=32μLVD2">ΔP = 32μLV/D^2

where,

ΔP">ΔP is the pressure drop.

μ">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.

Assumptions made:

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

PROCEDURE.

  • Will start with copying the cavity file from the tutorial 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 and pressure and 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.

  • Writing codes for wedge as wells as symmetry only for one angle i.e 25deg , rest everything will be same for both except the angles .
  • And i am generating the blockmeshdict file along with other files for every angles for both wedge and symmetry.

MATLAB CODE TO GENERATE blockMeshDict FILE for wedge boundary condition.

for angle = 25 deg.

clear all
close all
clc

% Inputs parameters

%Reynold's number
Re = 2100;

%Density
rho = 1000;

%Diameter (in m)
D = 0.02;

%Radius
R = D/2;

%Entry Length of the pipe
L_ent = 0.06*Re*D;

%viscosity (pa.s)
mu = 0.00089;

%Kinematic Viscosity
nu = mu/rho;

%Angle of wedge
theta = 25;

%Boundary conditions
v_avg = Re*nu/D;
v_max = 2*v_avg;
L_d = 0.3;
L = L_ent + L_d;
deltap = (8*v_avg*mu*L_d)/R^2;
deltap = deltap/rho;

%vertices cordinate
v0 = [0 0 0];  %point 0
v1 = [0 R*cosd(theta/2) -R*sind(theta/2)];  %point 1
v2 = [0 R*cosd(theta/2) R*sind(theta/2)];  %point 2
v3 = [L 0 0];  %point 3
v4 = [L R*cosd(theta/2) -R*sind(theta/2)]; %point 4
v5 = [L R*cosd(theta/2) R*sind(theta/2)]; %point 5

fileid = fopen('BlockMeshDict_wedge25','w')

fprintf(fileid,'FoamFile\n{\n\')
fprintf(fileid,'%12s \t 2.0;\n\','version')
fprintf(fileid,'%12s \t ascii;\n\','format')
fprintf(fileid,'%12s \t dictionary;\n\','class')
fprintf(fileid,'%12s \t blockMeshDict;\n\','object')
fprintf(fileid, '}\n\')

fprintf(fileid, 'vertices\n')
fprintf(fileid, '(\n')
fprintf(fileid, '\t(%s)\n', num2str(v0))
fprintf(fileid, '\t(%s)\n', num2str(v1))
fprintf(fileid, '\t(%s)\n', num2str(v2))
fprintf(fileid, '\t(%s)\n', num2str(v3))
fprintf(fileid, '\t(%s)\n', num2str(v4))
fprintf(fileid, '\t(%s)\n', num2str(v5))
fprintf(fileid, ');\n')

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

fprintf(fileid, 'edges\n')
fprintf(fileid, '(\n')
fprintf(fileid, '\t arc %d %d (%d %d %d)\n',1,2,0,R,0)
fprintf(fileid, '\t arc %d %d (%d %d %d)\n',4,5,L,R,0)
fprintf(fileid, ');\n')

fprintf(fileid, 'boundary\n')
fprintf(fileid, '(\n')
fprintf(fileid, '\t inlet \n')
fprintf(fileid, '\t {\n')
fprintf(fileid, '\t\t type patch;\n')
fprintf(fileid, '\t\t faces\n')
fprintf(fileid, '\t\t (\n')
fprintf(fileid, '\t\t\t (0 1 2 0)\n')
fprintf(fileid, '\t\t );\n')
fprintf(fileid, '\t }\n')

fprintf(fileid, '\t outlet\n')
fprintf(fileid, '\t {\n')
fprintf(fileid, '\t\t type patch;\n')
fprintf(fileid, '\t\t faces\n')
fprintf(fileid, '\t\t (\n')
fprintf(fileid, '\t\t\t (3 5 4 3)\n')
fprintf(fileid, '\t\t );\n')
fprintf(fileid, '\t }\n')

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

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

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

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

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


fclose(fileid)

MATLAB CODE TO GENERATE blockMeshDict FILE for symmetry boundary condition.

for angle = 25deg.

clear all
close all
clc

% Inputs parameters

%Reynold's number
Re = 2100;

%Density
rho = 1000;

%Diameter (in m)
D = 0.02;

%Radius
R = D/2;

%Entry Length of the pipe
L_ent = 0.06*Re*D;

%viscosity (pa.s)
mu = 0.00089;

%Kinematic Viscosity
nu = mu/rho;

%Angle of wedge
theta = 25;


%Boundary conditions
v_avg = Re*nu/D;
v_max = 2*v_avg;
L_d = 0.3;
L = L_ent + L_d;
deltap = (8*v_avg*mu*L_d)/R^2;
deltap = deltap/rho;

%vertices cordinate
v0 = [0 0 0];  %point 0
v1 = [0 R*cosd(theta/2) -R*sind(theta/2)];  %point 1
v2 = [0 R*cosd(theta/2) R*sind(theta/2)];  %point 2
v3 = [L 0 0];  %point 3
v4 = [L R*cosd(theta/2) -R*sind(theta/2)]; %point 4
v5 = [L R*cosd(theta/2) R*sind(theta/2)]; %point 5

fileid = fopen('BlockMeshDict_symmetry25','w')
fprintf(fileid,'FoamFile\n{\n\')
fprintf(fileid,'%12s \t 2.0;\n\','version')
fprintf(fileid,'%12s \t ascii;\n\','format')
fprintf(fileid,'%12s \t dictionary;\n\','class')
fprintf(fileid,'%12s \t blockMeshDict;\n\','object')
fprintf(fileid, '}\n\')
fprintf(fileid, 'vertices\n')
fprintf(fileid, '(\n')
fprintf(fileid, '\t(%s)\n', num2str(v0))
fprintf(fileid, '\t(%s)\n', num2str(v1))
fprintf(fileid, '\t(%s)\n', num2str(v2))
fprintf(fileid, '\t(%s)\n', num2str(v3))
fprintf(fileid, '\t(%s)\n', num2str(v4))
fprintf(fileid, '\t(%s)\n', num2str(v5))
fprintf(fileid, ');\n')

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

fprintf(fileid, 'edges\n')
fprintf(fileid, '(\n')
fprintf(fileid, '\t arc %d %d (%d %d %d)\n',1,2,0,R,0)
fprintf(fileid, '\t arc %d %d (%d %d %d)\n',4,5,L,R,0)
fprintf(fileid, ');\n')

fprintf(fileid, 'boundary\n')
fprintf(fileid, '(\n')
fprintf(fileid, '\t inlet \n')
fprintf(fileid, '\t {\n')
fprintf(fileid, '\t\t type patch;\n')
fprintf(fileid, '\t\t faces\n')
fprintf(fileid, '\t\t (\n')
fprintf(fileid, '\t\t\t (0 1 2 0)\n')
fprintf(fileid, '\t\t );\n')
fprintf(fileid, '\t }\n')

fprintf(fileid, '\t outlet\n')
fprintf(fileid, '\t {\n')
fprintf(fileid, '\t\t type patch;\n')
fprintf(fileid, '\t\t faces\n')
fprintf(fileid, '\t\t (\n')
fprintf(fileid, '\t\t\t (3 5 4 3)\n')
fprintf(fileid, '\t\t );\n')
fprintf(fileid, '\t }\n')

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

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

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

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

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


fclose(fileid)

Blockmeshdict File for wedge with angle = 25deg.

FoamFile
{
     version 	 2.0;
      format 	 ascii;
       class 	 dictionary;
      object 	 blockMeshDict;
}
vertices
(
	(0  0  0)
	(0    0.009763  -0.0021644)
	(0    0.009763   0.0021644)
	(2.82           0           0)
	(2.82    0.009763  -0.0021644)
	(2.82    0.009763   0.0021644)
);
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 (2.820000e+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 for the same.

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       latestTime; // startTime

startTime       0;

stopAt          endTime;

endTime         25;

deltaT          0.02;

writeControl    runTime; //timeStep - it will print an output file every writeInterval*deltaT
			 //runTime - writes an output file every specified writeInterval sec
writeInterval   0.5;

purgeWrite      10; // 0 - it retain all the output folders

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     | 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
{
   outlet
    {
        type            fixedValue;
        value           uniform 0;
    }

    inlet
    {
        type            zeroGradient;
    }
    top
    {
        type            zeroGradient;
    }
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
    axis
    {
        type            empty;
    }
}

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

Velocity file

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0.0934 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.0934 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    top
    {
        type            noSlip;
    }
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
    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] 8.9e-7;


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

BlockmeshDict and other files for symmetry with angle = 25deg.

Blockmeshdict file

FoamFile
{
     version 	 2.0;
      format 	 ascii;
       class 	 dictionary;
      object 	 blockMeshDict;
}
vertices
(
	(0  0  0)
	(0    0.009763  -0.0021644)
	(0    0.009763   0.0021644)
	(2.82           0           0)
	(2.82    0.009763  -0.0021644)
	(2.82    0.009763   0.0021644)
);
blocks
(
	 hex (0 3 4 1 0 3 5 2) (300 30 1) SimpleGrading (1 0.1 1)

);
edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (2.820000e+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
(
);

ControlDict file

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       latestTime; // startTime

startTime       0;

stopAt          endTime;

endTime         25;

deltaT          0.02;

writeControl    runTime; //timeStep - it will print an output file every writeInterval*deltaT
			 //runTime - writes an output file every specified writeInterval sec
writeInterval   0.5;

purgeWrite      10; // 0 - it retain all the output folders

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     | 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
{
   outlet
    {
        type            fixedValue;
        value           uniform 0;
    }

    inlet
    {
        type            zeroGradient;
    }
    top
    {
        type            zeroGradient;
    }
    front
    {
        type            symmetry;
    }
    back
    {
        type            symmetry;
    }
    axis
    {
        type            empty;
    }
}

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

velocity file

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0.0934 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.0934 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    top
    {
        type            noSlip;
    }
    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] 8.9e-7;


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

Similarly , blockmeshdict and other files for other angles of wedges and symmetry are as follows.

for wedge = 10deg.

BlockMeshdict File

FoamFile
{
     version 	 2.0;
      format 	 ascii;
       class 	 dictionary;
      object 	 blockMeshDict;
}
vertices
(
	(0  0  0)
	(0   0.0099619 -0.00087156)
	(0   0.0099619  0.00087156)
	(2.82           0           0)
	(2.82   0.0099619 -0.00087156)
	(2.82   0.0099619  0.00087156)
);
blocks
(
	 hex (0 3 4 1 0 3 5 2) (300 30 1) SimpleGrading (1 0.1 1)

);
edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (2.820000e+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:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       latestTime; // startTime

startTime       0;

stopAt          endTime;

endTime         25;

deltaT          0.02;

writeControl    runTime; //timeStep - it will print an output file every writeInterval*deltaT
			 //runTime - writes an output file every specified writeInterval sec
writeInterval   0.5;

purgeWrite      10; // 0 - it retain all the output folders

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     | 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
{
   outlet
    {
        type            fixedValue;
        value           uniform 0;
    }

    inlet
    {
        type            zeroGradient;
    }
    top
    {
        type            zeroGradient;
    }
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
    axis
    {
        type            empty;
    }
}

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

Velocity File

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0.0934 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.0934 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    top
    {
        type            noSlip;
    }
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
    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] 8.9e-7;


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

For wedge with angle = 45deg.

BlockMeshdict file

FoamFile
{
     version 	 2.0;
      format 	 ascii;
       class 	 dictionary;
      object 	 blockMeshDict;
}
vertices
(
	(0  0  0)
	(0   0.0092388  -0.0038268)
	(0   0.0092388   0.0038268)
	(2.82           0           0)
	(2.82   0.0092388  -0.0038268)
	(2.82   0.0092388   0.0038268)
);
blocks
(
	 hex (0 3 4 1 0 3 5 2) (300 30 1) SimpleGrading (1 0.1 1)

);
edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (2.820000e+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:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       latestTime; // startTime

startTime       0;

stopAt          endTime;

endTime         25;

deltaT          0.02;

writeControl    runTime; //timeStep - it will print an output file every writeInterval*deltaT
			 //runTime - writes an output file every specified writeInterval sec
writeInterval   0.5;

purgeWrite      10; // 0 - it retain all the output folders

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     | 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
{
   outlet
    {
        type            fixedValue;
        value           uniform 0;
    }

    inlet
    {
        type            zeroGradient;
    }
    top
    {
        type            zeroGradient;
    }
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
    axis
    {
        type            empty;
    }
}

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

Velocity File

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0.0934 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.0934 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    top
    {
        type            noSlip;
    }
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
    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] 8.9e-7;


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

SYMMETRY

for angle = 10deg

Blockmeshdict file

FoamFile
{
     version 	 2.0;
      format 	 ascii;
       class 	 dictionary;
      object 	 blockMeshDict;
}
vertices
(
	(0  0  0)
	(0   0.0099619 -0.00087156)
	(0   0.0099619  0.00087156)
	(2.82           0           0)
	(2.82   0.0099619 -0.00087156)
	(2.82   0.0099619  0.00087156)
);
blocks
(
	 hex (0 3 4 1 0 3 5 2) (300 30 1) SimpleGrading (1 0.1 1)

);
edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (2.820000e+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
(
);

Controldict file

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       latestTime; // startTime

startTime       0;

stopAt          endTime;

endTime         25;

deltaT          0.02;

writeControl    runTime; //timeStep - it will print an output file every writeInterval*deltaT
			 //runTime - writes an output file every specified writeInterval sec
writeInterval   0.5;

purgeWrite      10; // 0 - it retain all the output folders

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     | 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
{
   outlet
    {
        type            fixedValue;
        value           uniform 0;
    }

    inlet
    {
        type            zeroGradient;
    }
    top
    {
        type            zeroGradient;
    }
    front
    {
        type            symmetry;
    }
    back
    {
        type            symmetry;
    }
    axis
    {
        type            empty;
    }
}

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

Velocity File

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0.0934 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.0934 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    top
    {
        type            noSlip;
    }
    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] 8.9e-7;


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

For angle = 45 deg

symmetry

Blockmeshdict file

FoamFile
{
     version 	 2.0;
      format 	 ascii;
       class 	 dictionary;
      object 	 blockMeshDict;
}
vertices
(
	(0  0  0)
	(0   0.0092388  -0.0038268)
	(0   0.0092388   0.0038268)
	(2.82           0           0)
	(2.82   0.0092388  -0.0038268)
	(2.82   0.0092388   0.0038268)
);
blocks
(
	 hex (0 3 4 1 0 3 5 2) (300 30 1) SimpleGrading (1 1 1)

);
edges
(
	 arc 1 2 (0 1.000000e-02 0)
	 arc 4 5 (2.820000e+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
(
);

Controdict FIle

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       latestTime; // startTime

startTime       0;

stopAt          endTime;

endTime         25;

deltaT          0.02;

writeControl    runTime; //timeStep - it will print an output file every writeInterval*deltaT
			 //runTime - writes an output file every specified writeInterval sec
writeInterval   0.5;

purgeWrite      10; // 0 - it retain all the output folders

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     | 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
{
   outlet
    {
        type            fixedValue;
        value           uniform 0;
    }

    inlet
    {
        type            zeroGradient;
    }
    top
    {
        type            zeroGradient;
    }
    front
    {
        type            symmetry;
    }
    back
    {
        type            symmetry;
    }
    axis
    {
        type            empty;
    }
}

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

Velocity file

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0.0934 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.0934 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    top
    {
        type            noSlip;
    }
    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] 8.9e-7;


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

RESULTS

for plotting the results its better to make a table for comparison for both the symmetry and wedge with all the given angles i.e 10deg , 25deg and 45deg.

This is the comparison table plot for the pressure contour of both the wedges and the symmetry.

ANGLES WEDGE SYMMETRY
10 degrees
25 degrees
45 degrees

now compariosn of velocity contours

ANGLES WEDGE SYMMETRY
10 degrees
25 degrees
45 degrees

COMPARISON OF PROFILES

SHEAR STRESS PROFILES

ANGLES WEDGE SYMMETRY
10 DEGREES
25 DEGREES
45 DEGREES

COMPARISON OF VELOCITIES PROFILE

ANGLES WEDGE SYMMETRY
10 DEGREES
25 DEGREES
45 DEGREES

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 important role in terms of accuracy in the result

Your portfolio, next

Ship work like this
in your own course.

Talk to a career counsellor

Free 20-minute call. We'll map the right course to where you want to work.

By submitting you agree to our Terms and Privacy Policy.