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Challenge

Study of effect of changing of boundary conditions : Symmetry vs Wedge vs HP equation on fluid parameters

SSwagat Padhan24 Mar 2021
CFD

Objective:

To study the effect of changing of boundary condition from wedge to symmetry. and check whether there is any deviation of parameters like pressure or velocity from theoretical equation.

Theory:

wedge boundary condition is used if the wedge angle is less than 5. while for wedge angle greater than 5 symmetry boundary condition is used. In this study i ran the simulation 3 times for different angle like 10 , 25 and 45 degree and calculate the parameters respectively. The initial conditions for each case of simulation are same. Only the difference is in the front and back boundary condition here symmetry boundary condition is used.

Pressure boundary condition:-

/*--------------------------------*- C++ -*----------------------------------*
| =========                 |                                                 |
| \      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \    /   O peration     | Version:  4.1                                   |
|   \  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \/     M anipulation  |                                                 |
*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 2 -2 0 0 0 0];

internalField   uniform 0;

boundaryField
{
         axis
	{
		 type empty;

	}
	 pipewall 
	{
		 type zeroGradient;

	}
	 	 
	 front
	{
		 type symmetry;

	}
	 back
	{
		 type symmetry;

	}
	 
	 inlet
	{
		 type zeroGradient;

	}
	 
	 outlet
	{
		 type fixedValue;
		 value uniform 10;


	 }
}

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

Velocity boundary conidition:-

/*--------------------------------*- C++ -*----------------------------------*
| =========                 |                                                 |
| \      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \    /   O peration     | Version:  4.1                                   |
|   \  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \/     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
{
         axis
	{
		 type empty;


	}
	 pipewall 
	{
		 type fixedValue;
		 value uniform (0 0 0);
	}
	 	 
	 front
	{
		 type symmetry;

	}
	 back
	{
		 type symmetry;

	}
	 
	 inlet
	{
		 type fixedValue;
		 value uniform (0.2107 0 0);

	}
	 
	 outlet
	{
		 type inletOutlet;
		 inletValue uniform (0.2107 0 0);
		 value uniform (0.2107 0 0);


	 }
}

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

Matlab Program:

1.) Program for wedge angle of 10 degree

clear all 
close all
clc

L = 2.1;
theta = 10;
r = 0.005;
a = 1
b = 0.2
c = 1
nx = 300
ny = 50
nz =1

line1='/*--------------------------------*- C++ -*----------------------------------*';
line2='| =========                 |                                                 |';
line3='| \      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |';
line4='|  \    /   O peration     | Version:  4.1                                   |';
line5='|   \  /    A nd           | Web:      www.OpenFOAM.org                      |';
line6='|    \/     M anipulation  |                                                 |';
line7='*---------------------------------------------------------------------------*/';

bmd = fopen('blockMeshDict','wt')
fprintf(bmd,'%sn',line1);
fprintf(bmd,'%sn',line2);
fprintf(bmd,'%sn',line3);
fprintf(bmd,'%sn',line4);
fprintf(bmd,'%sn',line5);
fprintf(bmd,'%sn',line6);
fprintf(bmd,'%sn',line7);

fprintf(bmd,'FoamFilen{n');
fprintf(bmd,'%12s t 2.0;n','version');
fprintf(bmd,'%11s t ascii;n','format');
fprintf(bmd,'%10s t dictionary;n','class');
fprintf(bmd,'%11s t blockMeshDict;n','object');
fprintf(bmd,'}n');
line8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
fprintf(bmd,'%snn',line8);
fprintf(bmd,'convertToMeters 1;nn');
fprintf(bmd,'verticesn');
fprintf(bmd,'(n');
fprintf(bmd,'t (%d %d %d)n',0,0,0); % point 0
fprintf(bmd,'t (%d %d %d)n',L,0,0);  % Pont 1
fprintf(bmd,'t (%d %d %d)n',L,r*cosd(theta/2),r*sind(theta/2)); % point 2
fprintf(bmd,'t (%d %d %d)n',0,r*cosd(theta/2),r*sind(theta/2)); % point 3
fprintf(bmd,'t (%d %d %d)n',0,r*cosd(theta/2),-r*sind(theta/2)); % point 4
fprintf(bmd,'t (%d %d %d)n',L,(r*cosd(theta/2)),(-r*sind(theta/2))); % point 5
fprintf(bmd,');nn');
fprintf(bmd,'blocksn');
fprintf(bmd,'(n');
fprintf(bmd,'     hex ( 0 1 5 4 0 1 2 3) (%d %d %d)',nx,ny,nz);
fprintf(bmd, ' SimpleGrading (%d %d %d)nn',a,b,c);
fprintf(bmd,');nn');
fprintf(bmd,'edgesn(ntarc %d %d (%d %d %d)n',4,3,0,r,0);
fprintf(bmd,'tarc %d %d (%d %d %d)n',5,2,L,r,0);
fprintf(bmd,');nn');
fprintf(bmd,'boundaryn(n');
fprintf(bmd,'t inletn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type patch;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,0,3,4);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t outletn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type patch;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',1,5,2,1);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t backn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type symmetry;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,4,5,1);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t frontn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type symmetry;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,1,2,3);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t axisn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type empty;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,1,1,0);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t pipewall n');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type wall;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',3,2,5,4);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,');nn');
fprintf(bmd,'mergePatchPairsn(n');
fprintf(bmd,');n');
line9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
fprintf(bmd,'%sn',line9);
fclose(bmd)

The above program will generate the following blockMeshDict file for simulation.

/*--------------------------------*- C++ -*----------------------------------*
| =========                 |                                                 |
| \      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \    /   O peration     | Version:  4.1                                   |
|   \  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \/     M anipulation  |                                                 |
*---------------------------------------------------------------------------*/
FoamFile
{
     version 	 2.0;
     format 	 ascii;
     class 	 dictionary;
     object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	 (0 0 0)
	 (2.100000e+00 0 0)
	 (2.100000e+00 4.980973e-03 4.357787e-04)
	 (0 4.980973e-03 4.357787e-04)
	 (0 4.980973e-03 -4.357787e-04)
	 (2.100000e+00 4.980973e-03 -4.357787e-04)
);

blocks
(
     hex ( 0 1 5 4 0 1 2 3) (300 50 1) SimpleGrading (1 2.000000e-01 1)

);

edges
(
	arc 4 3 (0 5.000000e-03 0)
	arc 5 2 (2.100000e+00 5.000000e-03 0)
);

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

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

Result 1:

the velocity and pressure are calculated from the above simulation

velocity: 0.4151 m/s, at 1.05 metre from entrance of length.

Pressure: 0.0722 (kinematic Pressure)

2.) Program for wedge Angle of 25 degree.

clear all 
close all
clc

L = 2.1;
theta = 25;
r = 0.005;
a = 1
b = 0.2
c = 1
nx = 300
ny = 50
nz =1

line1='/*--------------------------------*- C++ -*----------------------------------*';
line2='| =========                 |                                                 |';
line3='| \      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |';
line4='|  \    /   O peration     | Version:  4.1                                   |';
line5='|   \  /    A nd           | Web:      www.OpenFOAM.org                      |';
line6='|    \/     M anipulation  |                                                 |';
line7='*---------------------------------------------------------------------------*/';

bmd = fopen('blockMeshDict','wt')
fprintf(bmd,'%sn',line1);
fprintf(bmd,'%sn',line2);
fprintf(bmd,'%sn',line3);
fprintf(bmd,'%sn',line4);
fprintf(bmd,'%sn',line5);
fprintf(bmd,'%sn',line6);
fprintf(bmd,'%sn',line7);

fprintf(bmd,'FoamFilen{n');
fprintf(bmd,'%12s t 2.0;n','version');
fprintf(bmd,'%11s t ascii;n','format');
fprintf(bmd,'%10s t dictionary;n','class');
fprintf(bmd,'%11s t blockMeshDict;n','object');
fprintf(bmd,'}n');
line8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
fprintf(bmd,'%snn',line8);
fprintf(bmd,'convertToMeters 1;nn');
fprintf(bmd,'verticesn');
fprintf(bmd,'(n');
fprintf(bmd,'t (%d %d %d)n',0,0,0); % point 0
fprintf(bmd,'t (%d %d %d)n',L,0,0);  % Pont 1
fprintf(bmd,'t (%d %d %d)n',L,r*cosd(theta/2),r*sind(theta/2)); % point 2
fprintf(bmd,'t (%d %d %d)n',0,r*cosd(theta/2),r*sind(theta/2)); % point 3
fprintf(bmd,'t (%d %d %d)n',0,r*cosd(theta/2),-r*sind(theta/2)); % point 4
fprintf(bmd,'t (%d %d %d)n',L,(r*cosd(theta/2)),(-r*sind(theta/2))); % point 5
fprintf(bmd,');nn');
fprintf(bmd,'blocksn');
fprintf(bmd,'(n');
fprintf(bmd,'     hex ( 0 1 5 4 0 1 2 3) (%d %d %d)',nx,ny,nz);
fprintf(bmd, ' SimpleGrading (%d %d %d)nn',a,b,c);
fprintf(bmd,');nn');
fprintf(bmd,'edgesn(ntarc %d %d (%d %d %d)n',4,3,0,r,0);
fprintf(bmd,'tarc %d %d (%d %d %d)n',5,2,L,r,0);
fprintf(bmd,');nn');
fprintf(bmd,'boundaryn(n');
fprintf(bmd,'t inletn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type patch;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,0,3,4);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t outletn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type patch;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',1,5,2,1);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t backn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type symmetry;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,4,5,1);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t frontn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type symmetry;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,1,2,3);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t axisn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type empty;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,1,1,0);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t pipewall n');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type wall;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',3,2,5,4);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,');nn');
fprintf(bmd,'mergePatchPairsn(n');
fprintf(bmd,');n');
line9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
fprintf(bmd,'%sn',line9);
fclose(bmd)

the above program will generate the following blockMeshDict file

/*--------------------------------*- C++ -*----------------------------------*
| =========                 |                                                 |
| \      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \    /   O peration     | Version:  4.1                                   |
|   \  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \/     M anipulation  |                                                 |
*---------------------------------------------------------------------------*/
FoamFile
{
     version 	 2.0;
     format 	 ascii;
     class 	 dictionary;
     object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	 (0 0 0)
	 (2.100000e+00 0 0)
	 (2.100000e+00 4.881480e-03 1.082198e-03)
	 (0 4.881480e-03 1.082198e-03)
	 (0 4.881480e-03 -1.082198e-03)
	 (2.100000e+00 4.881480e-03 -1.082198e-03)
);

blocks
(
     hex ( 0 1 5 4 0 1 2 3) (300 50 1) SimpleGrading (1 2.000000e-01 1)

);

edges
(
	arc 4 3 (0 5.000000e-03 0)
	arc 5 2 (2.100000e+00 5.000000e-03 0)
);

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

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

Result 2:

after running the simulation for wedge angle of 25 degree. the velocity and pressure magnitude came out to be:

velocity: 0.4158 m/s

Pressure: 0.075 (Kinematic Pressure)

3.) Program for wedge angle of 45 degree.

clear all 
close all
clc

L = 2.1;
theta = 45;
r = 0.005;
a = 1
b = 0.2
c = 1
nx = 300
ny = 50
nz =1

line1='/*--------------------------------*- C++ -*----------------------------------*';
line2='| =========                 |                                                 |';
line3='| \      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |';
line4='|  \    /   O peration     | Version:  4.1                                   |';
line5='|   \  /    A nd           | Web:      www.OpenFOAM.org                      |';
line6='|    \/     M anipulation  |                                                 |';
line7='*---------------------------------------------------------------------------*/';

bmd = fopen('blockMeshDict','wt')
fprintf(bmd,'%sn',line1);
fprintf(bmd,'%sn',line2);
fprintf(bmd,'%sn',line3);
fprintf(bmd,'%sn',line4);
fprintf(bmd,'%sn',line5);
fprintf(bmd,'%sn',line6);
fprintf(bmd,'%sn',line7);

fprintf(bmd,'FoamFilen{n');
fprintf(bmd,'%12s t 2.0;n','version');
fprintf(bmd,'%11s t ascii;n','format');
fprintf(bmd,'%10s t dictionary;n','class');
fprintf(bmd,'%11s t blockMeshDict;n','object');
fprintf(bmd,'}n');
line8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
fprintf(bmd,'%snn',line8);
fprintf(bmd,'convertToMeters 1;nn');
fprintf(bmd,'verticesn');
fprintf(bmd,'(n');
fprintf(bmd,'t (%d %d %d)n',0,0,0); % point 0
fprintf(bmd,'t (%d %d %d)n',L,0,0);  % Pont 1
fprintf(bmd,'t (%d %d %d)n',L,r*cosd(theta/2),r*sind(theta/2)); % point 2
fprintf(bmd,'t (%d %d %d)n',0,r*cosd(theta/2),r*sind(theta/2)); % point 3
fprintf(bmd,'t (%d %d %d)n',0,r*cosd(theta/2),-r*sind(theta/2)); % point 4
fprintf(bmd,'t (%d %d %d)n',L,(r*cosd(theta/2)),(-r*sind(theta/2))); % point 5
fprintf(bmd,');nn');
fprintf(bmd,'blocksn');
fprintf(bmd,'(n');
fprintf(bmd,'     hex ( 0 1 5 4 0 1 2 3) (%d %d %d)',nx,ny,nz);
fprintf(bmd, ' SimpleGrading (%d %d %d)nn',a,b,c);
fprintf(bmd,');nn');
fprintf(bmd,'edgesn(ntarc %d %d (%d %d %d)n',4,3,0,r,0);
fprintf(bmd,'tarc %d %d (%d %d %d)n',5,2,L,r,0);
fprintf(bmd,');nn');
fprintf(bmd,'boundaryn(n');
fprintf(bmd,'t inletn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type patch;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,0,3,4);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t outletn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type patch;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',1,5,2,1);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t backn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type symmetry;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,4,5,1);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t frontn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type symmetry;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,1,2,3);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t axisn');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type empty;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',0,1,1,0);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,'t pipewall n');
fprintf(bmd,'t{n');
fprintf(bmd,'tt type wall;n');
fprintf(bmd,'tt facesn');
fprintf(bmd,'tt (n');
fprintf(bmd,'ttt (%d %d %d %d)n',3,2,5,4);
fprintf(bmd,'tt );n');
fprintf(bmd,'t}n');
fprintf(bmd,');nn');
fprintf(bmd,'mergePatchPairsn(n');
fprintf(bmd,');n');
line9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
fprintf(bmd,'%sn',line9);
fclose(bmd)

the aobve program will generate the following blockMeshDict file for simulation.

/*--------------------------------*- C++ -*----------------------------------*
| =========                 |                                                 |
| \      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \    /   O peration     | Version:  4.1                                   |
|   \  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \/     M anipulation  |                                                 |
*---------------------------------------------------------------------------*/
FoamFile
{
     version 	 2.0;
     format 	 ascii;
     class 	 dictionary;
     object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	 (0 0 0)
	 (2.100000e+00 0 0)
	 (2.100000e+00 4.619398e-03 1.913417e-03)
	 (0 4.619398e-03 1.913417e-03)
	 (0 4.619398e-03 -1.913417e-03)
	 (2.100000e+00 4.619398e-03 -1.913417e-03)
);

blocks
(
     hex ( 0 1 5 4 0 1 2 3) (300 50 1) SimpleGrading (1 2.000000e-01 1)

);

edges
(
	arc 4 3 (0 5.000000e-03 0)
	arc 5 2 (2.100000e+00 5.000000e-03 0)
);

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

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

Result 3:

After running the simulation the parameters like velocity and pressure are calculated and are as follows.

Velocity: 0.4174 m/s at 1.05 metre from the entrance of pipe

Pressure: 0.0836 (Kinematic Pressure)

Simulation Result.

Final Result:

Parameters 3 degree 10 degree 25 degree 45 degree
Velocity: 0.4159 0.4151 0.4158 0.4174
Pressure: 0.0716 0.0722 0.075 0.0836

Theoretical Result calculated using Hagen Poisuelle's equation.

velocity: 0.4214 m/s

pressure: 0.07107 (Kinematic Pressure)

Error:-

Parameters 3 degree 10 degree 25 degree 45 degree
velocity(Error) 0.013 0.014 0.013 0.009492
Pressure(Error) 0.0074 0.0015 0.0524 0.149

There is error when the wedge angle increases from 10 to 45 degree. but at the end of pipe i.e. at 2.1 metre the velocity in each case remains same i.e at 0.4206 m/s.

Conclusion

1. symmetry boundary condition is more accurate than wedge boundary condition.

2.execution time is greater for symmetry boundary condition than wedge boundary condition for the same computational mesh.

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