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Challenge

Week 12 - Symmetry vs Wedge vs HP equation

VVinay Omase5 Oct 2020

Aim: The objective of the given challenge is to find effect of symmetry boundary condition on the case that we have setup earlier with wedge boundary conditions. we are going to analyze the effect of symmetry boundary condition vs wedge boundary condition.

Approach: we have written a matlab program file to generate blockMeshdict file for given angle of 10,25 and 45 degree. The system directory and control directory remains same only change is in pressure(p),velocity(U) and blockMeshdict file i.e the wedge boundary condition at the front and back wall is changed to symmetry boundary condition.

Symmetry Boundary condition:

The symmetry boundary condition defines a mirror face/surface. It should only be used if the physical object or geometry and the expected flow field pattern of the developed solution are mirrored along that surface. By using this boundary condition, the domain can essentially be halved, reducing the time to achieve a solution.

The pressure and velocity files remains same only change is the boundary condition for front and back wall.

pressure Boundary conditions:

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

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

internalField   uniform 0;

boundaryField
{
    inlet
    {
        type            zeroGradient;
    }

    outlet
    {
        type            fixedValue;
        value           uniform 0;
    }

    axis
    {
        type            empty;
    }
    fixedWall
    {
        type            zeroGradient;
    }
    frontWall
    {
        type            symmetry;
    }
    backWall
    {
        type            symmetry;
    }
}

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

Velocity Boundary condition:

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

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

internalField   uniform (0 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.093 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }
    fixedWall
    {
        type            noSlip;
    }
    frontWall
    {
        type            symmetry;
    }
    backWall
    {
        type            symmetry;
    }
}

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

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       startTime;

startTime       0;

stopAt          endTime;

endTime         40;

deltaT          0.01;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

Transportdict 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    "constant";
    object      transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

     nu              [0 2 -1 0 0 0 0] 0.89e-06;  // Nu of water @ 30 degree celcius
//   nu              [0 2 -1 0 0 0 0] 1e-6;       // Nu of water @ 20 degree celcius
//   nu              [0 2 -1 0 0 0 0] 1.3e-6;   // Nu of water @ 10 degree celcius
   

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

Matlab program for Generating blockMeshdict:

Below file is for theta=10 degree.

clear all
close all
clc
%considered values
theta=10;
d=0.02;%in meters
r=0.01;%in meters
Re=2100;% reynolds number
L_e=Re*d*0.06;%hydrodynamic length of pipe
L_t=L_e+0.5;%total length of pipe


f1=fopen('blockMeshDict','w')

fprintf(f1,'%s','/*--------------------------------*- C++ -*----------------------------------*\');
fprintf(f1,'\n=========            |\n');
fprintf(f1, '\\\\      / F ield        | OpenFOAM: The Open Source CFD Toolbox\n');
fprintf(f1, ' \\\\    /  O peration    | Website: https://openfoam.org\n');
fprintf(f1, '  \\\\  /   A nd          | Version: 8\n');
fprintf(f1, '   \\\\/    M anipulation |\n');
fprintf(f1,'%s','\*---------------------------------------------------------------------------*/');
fprintf(f1,'\nFoamFile\n');
fprintf(f1,'\n{\n');
fprintf(f1,'version 2.0;\n');
fprintf(f1,'format ascii;\n');
fprintf(f1,'class dictionary;\n');
fprintf(f1,'object blockMeshDict;\n');
fprintf(f1,'\n}\n');
fprintf(f1,'%s','// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //');

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

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

%block
fprintf(f1,'\nblocks\n');
fprintf(f1,'(\n');
fprintf(f1,'\t hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.2 1 1)');
fprintf(f1,'\n\n);\n\n');

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

%boundary
fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
%inlet
fprintf(f1,'\t inlet\n');
fprintf(f1,'\t{\n');
fprintf(f1,'\t\t type patch;\n');
fprintf(f1,'\t\t faces\n');
fprintf(f1,'\t\t (\n');
fprintf(f1,'\t\t\t\t(%d %d %d %d)\n',0,2,1,0)
fprintf(f1,'\t\t );\n');
fprintf(f1,'\t}\n');
%outlet
fprintf(f1,'\t outlet\n');
fprintf(f1,'\t{\n');
fprintf(f1,'\t\t type patch;\n');
fprintf(f1,'\t\t faces\n');
fprintf(f1,'\t\t (\n');
fprintf(f1,'\t\t\t\t(%d %d %d %d)\n',3,4,5,3)
fprintf(f1,'\t\t );\n');
fprintf(f1,'\t}\n');
%axis
fprintf(f1,'\t axis\n');
fprintf(f1,'\t{\n');
fprintf(f1,'\t\t type empty;\n');
fprintf(f1,'\t\t faces\n');
fprintf(f1,'\t\t (\n');
fprintf(f1,'\t\t\t\t(%d %d %d %d)\n',0,3,3,0)
fprintf(f1,'\t\t );\n');
fprintf(f1,'\t}\n');
%fixedWall
fprintf(f1,'\t fixedWall\n');
fprintf(f1,'\t{\n');
fprintf(f1,'\t\t type wall;\n');
fprintf(f1,'\t\t faces\n');
fprintf(f1,'\t\t (\n');
fprintf(f1,'\t\t\t\t(%d %d %d %d)\n',1,2,5,4)
fprintf(f1,'\t\t );\n');
fprintf(f1,'\t}\n');
%frontWall
fprintf(f1,'\t frontWall\n');
fprintf(f1,'\t{\n');
fprintf(f1,'\t\t type symmetry;\n');
fprintf(f1,'\t\t faces\n');
fprintf(f1,'\t\t (\n');
fprintf(f1,'\t\t\t\t(%d %d %d %d)\n',0,3,5,2)
fprintf(f1,'\t\t );\n');
fprintf(f1,'\t}\n');
%backWall
fprintf(f1,'\t backWall\n');
fprintf(f1,'\t{\n');
fprintf(f1,'\t\t type symmetry;\n');
fprintf(f1,'\t\t faces\n');
fprintf(f1,'\t\t (\n');
fprintf(f1,'\t\t\t\t(%d %d %d %d)\n',0,1,4,3)
fprintf(f1,'\t\t );\n');
fprintf(f1,'\t}\n');
fprintf(f1,');\n');
fprintf(f1,'mergePatchPairs\n')
fprintf(f1,'(\n');
fprintf(f1,');\n');
fprintf(f1,'\n// ************************************************************************* //\n')




fclose(f1)

The above matlab file generates blockMeshdict file for angle 10 degree.

/*--------------------------------*- C++ -*----------------------------------*\
=========            |
\\      / F ield        | OpenFOAM: The Open Source CFD Toolbox
 \\    /  O peration    | Website: https://openfoam.org
  \\  /   A nd          | Version: 8
   \\/    M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile

{
version 2.0;
format ascii;
class dictionary;
object blockMeshDict;

}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

 convertToMeters 1;

vertices
(
	(0 0 0)
	(0 0.00996195 -0.000871557)
	(0 0.00996195 0.000871557)
	(3.02 0 0)
	(3.02 0.00996195 -0.000871557)
	(3.02 0.00996195 0.000871557)
);

blocks
(
	 hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.2 1 1)

);

edges
(
	 arc 1 2 (0 0.01 0)
	 arc 4 5 (3.02 0.01 0)


);

boundary
(
	 inlet
	{
		 type patch;
		 faces
		 (
				(0 2 1 0)
		 );
	}
	 outlet
	{
		 type patch;
		 faces
		 (
				(3 4 5 3)
		 );
	}
	 axis
	{
		 type empty;
		 faces
		 (
				(0 3 3 0)
		 );
	}
	 fixedWall
	{
		 type wall;
		 faces
		 (
				(1 2 5 4)
		 );
	}
	 frontWall
	{
		 type symmetry;
		 faces
		 (
				(0 3 5 2)
		 );
	}
	 backWall
	{
		 type symmetry;
		 faces
		 (
				(0 1 4 3)
		 );
	}
);
mergePatchPairs
(
);

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

Result:

Velocity=0.185142 m/s

blockMeshdict file for 25 degree :

/*--------------------------------*- C++ -*----------------------------------*\
=========            |
\\      / F ield        | OpenFOAM: The Open Source CFD Toolbox
 \\    /  O peration    | Website: https://openfoam.org
  \\  /   A nd          | Version: 8
   \\/    M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile

{
version 2.0;
format ascii;
class dictionary;
object blockMeshDict;

}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

 convertToMeters 1;

vertices
(
	(0 0 0)
	(0 0.00976296 -0.0021644)
	(0 0.00976296 0.0021644)
	(3.02 0 0)
	(3.02 0.00976296 -0.0021644)
	(3.02 0.00976296 0.0021644)
);

blocks
(
	 hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.2 1 1)

);

edges
(
	 arc 1 2 (0 0.01 0)
	 arc 4 5 (3.02 0.01 0)


);

boundary
(
	 inlet
	{
		 type patch;
		 faces
		 (
				(0 2 1 0)
		 );
	}
	 outlet
	{
		 type patch;
		 faces
		 (
				(3 4 5 3)
		 );
	}
	 axis
	{
		 type empty;
		 faces
		 (
				(0 3 3 0)
		 );
	}
	 fixedWall
	{
		 type wall;
		 faces
		 (
				(1 2 5 4)
		 );
	}
	 frontWall
	{
		 type symmetry;
		 faces
		 (
				(0 3 5 2)
		 );
	}
	 backWall
	{
		 type symmetry;
		 faces
		 (
				(0 1 4 3)
		 );
	}
);
mergePatchPairs
(
);

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

Result:

Velocity=0.18525 m/s

blockMeshdict file for 45 degree :

/*--------------------------------*- C++ -*----------------------------------*\
=========            |
\\      / F ield        | OpenFOAM: The Open Source CFD Toolbox
 \\    /  O peration    | Website: https://openfoam.org
  \\  /   A nd          | Version: 8
   \\/    M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile

{
version 2.0;
format ascii;
class dictionary;
object blockMeshDict;

}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

 convertToMeters 1;

vertices
(
	(0 0 0)
	(0 0.0092388 -0.00382683)
	(0 0.0092388 0.00382683)
	(3.02 0 0)
	(3.02 0.0092388 -0.00382683)
	(3.02 0.0092388 0.00382683)
);

blocks
(
	 hex (0 1 2 0 3 4 5 3) (50 1 300) simpleGrading (0.2 1 1)

);

edges
(
	 arc 1 2 (0 0.01 0)
	 arc 4 5 (3.02 0.01 0)


);

boundary
(
	 inlet
	{
		 type patch;
		 faces
		 (
				(0 2 1 0)
		 );
	}
	 outlet
	{
		 type patch;
		 faces
		 (
				(3 4 5 3)
		 );
	}
	 axis
	{
		 type empty;
		 faces
		 (
				(0 3 3 0)
		 );
	}
	 fixedWall
	{
		 type wall;
		 faces
		 (
				(1 2 5 4)
		 );
	}
	 frontWall
	{
		 type symmetry;
		 faces
		 (
				(0 3 5 2)
		 );
	}
	 backWall
	{
		 type symmetry;
		 faces
		 (
				(0 1 4 3)
		 );
	}
);
mergePatchPairs
(
);

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

Result:

Velocity=0.18547 m/s

Results:

Boundary condition's wedge B.C (4⁰) symmetry B.C(10⁰) symmetry B.C(25⁰) symmetry B.C(45⁰)
Courant number 0.424914 0.425437 0.429897 0.441784
Execution time 1582.14 1791.17 1820.6 1672.97
Velocity (analytical) 0.185143 0.185142 0.18525 0.18547
Velocity (numerical) 0.18746
Error 0.002317 0.002318 0.00221 0.00199

Conclusion:

1) Wedge boundary condition require minimum amount of execution time as it contains less amount of cells as compared to symmetric boundary condition.

2) With symmetry B.C the error in velocity value decreases eith increase in wedge angle as no of cells increses we get more accurate value but at the expense of time required for execution.

3) Courant number increases with increase in wedge angle.

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