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Challenge

Week 12 - Symmetry vs Wedge vs HP equation

SSunny Sihag29 Jan 2021
CFD

This challange is the continuition of the Simulation of the flow through pipe in openFoam but the difference in this challange is that we have used the angle as 10deg, 25deg and 45deg for the wedge, and on the above of it the front and back face are of the type wedge and symmetry. So there are total 6 cases in this challange to solve.

The initial conditions are as similar to the previous one-

Diameter of pipe = 0.02m;

Length of Piper = 2.5m;

Density of Fluid = 997 `kg//m^3`;

Dynamic Viscosity of Fluid = 0.00089 Pa*sec

The whole problem is solved using icoFoam solver in Openfoam and the Blockmesh file is made automated in Matlab such that the user can have have ease to get results at different angles.

In this challange the velocity and pressure initials condoation are same for all cases of 3 wedge angles with symmetry condition and for all cases of 3 wedge angles with wedge condition.

  • Symmetry:
  1. Matlab code for 10 deg:
clear all
close all
clc


f1 = fopen('blockMeshDict.txt','w');

scale = 1;
theta = 10;
Re = 2100;
r = 0.01;
D=2*r;
l = 2.5;
nx = 25;
ny = 1;
nz =200;


fprintf(f1,'/*--------------------------------*-');
fprintf(f1,'C++ -*----------------------------------');
fprintf(f1,'\n');
fprintf(f1,'  =========                |\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,'---------------------------------------------------------------------------*/')
fprintf(f1,'\n');
fprintf(f1,'FoamFile\n');
fprintf(f1,'{\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');
fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ');
fprintf(f1,'* * * * * * * //\n');
fprintf(f1,'\n');
fprintf(f1,'convertToMeters %d;\n',scale);
fprintf(f1,'\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,'\t(%d %d %d)\n',0, 0, 0);
fprintf(f1,'\t(%d %d %d)\n',0,r*cosd(theta/2),r*sind(theta/2));
fprintf(f1,'\t(%d %d %d)\n',0,r*cosd(theta/2),-r*sind(theta/2));
fprintf(f1,'\t(%d %d %d)\n',l,0,0);
fprintf(f1,'\t(%d %d %d)\n',l,r*cosd(theta/2),r*sind(theta/2));
fprintf(f1,'\t(%d %d %d)\n',l,r*cosd(theta/2),-r*sind(theta/2));
fprintf(f1,');\n');
fprintf(f1,'\n');

fprintf(f1,'blocks\n');
fprintf(f1,'(\n');
fprintf(f1,'\thex (0 2 1 0 3 5 4 3) (%d %d %d) simpleGrading (1 1 1)\n',nx,ny,nz);
fprintf(f1,');\n');
fprintf(f1,'\n');


fprintf(f1,'edges\n')
fprintf(f1,'(\n');
fprintf(f1,'    arc 2 1 (%d %d %d)\n',0,r,0);
fprintf(f1,'    arc 5 4 (%d %d %d)\n',l,r,0);
fprintf(f1,');\n');
fprintf(f1,'\n');

fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
fprintf(f1,'    inlet\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type patch;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (0 2 1 0)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

fprintf(f1,'    outlet\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type patch;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (3 4 5 3)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

fprintf(f1,'    top\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type wall;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (1 2 5 4)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

fprintf(f1,'    front\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type symmetry;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (0 1 4 3)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

fprintf(f1,'    back\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type symmetry;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (0 3 5 2)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

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





fclose(f1)

Output is:

/*--------------------------------*-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 9.961947e-03 8.715574e-04)
	(0 9.961947e-03 -8.715574e-04)
	(2.500000e+00 0 0)
	(2.500000e+00 9.961947e-03 8.715574e-04)
	(2.500000e+00 9.961947e-03 -8.715574e-04)
);

blocks
(
	hex (0 2 1 0 3 5 4 3) (25 1 200) simpleGrading (1 1 1)
);

edges
(
    arc 2 1 (0 1.000000e-02 0)
    arc 5 4 (2.500000e+00 1.000000e-02 0)
);

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

mergePatchPairs
(
);

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

2. Pressure:

/*--------------------------------*- 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;	
    }

    top
    {
        type            zeroGradient;
    }
    front
    {
        type            symmetry;
    }
    back
    {
        type            symmetry;
    }
}

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

3. Velocity:

/*--------------------------------*- 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 (0.09373 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    top
    {
        type            noSlip;
    }
    front
    {
        type            symmetry;
    }

    back
    {
        type            symmetry;
    }
}

// ************************************************************************* //
  • Wedge condition for 10 deg:
  1. Matlab code:
clear all
close all
clc


f1 = fopen('blockMeshDict.txt','w');

scale = 1;
theta = 10;
Re = 2100;
r = 0.01;
D=2*r;
l = 2.5;
nx = 25;
ny = 1;
nz =200;


fprintf(f1,'/*--------------------------------*-');
fprintf(f1,'C++ -*----------------------------------');
fprintf(f1,'\n');
fprintf(f1,'  =========                |\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,'---------------------------------------------------------------------------*/')
fprintf(f1,'\n');
fprintf(f1,'FoamFile\n');
fprintf(f1,'{\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');
fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ');
fprintf(f1,'* * * * * * * //\n');
fprintf(f1,'\n');
fprintf(f1,'convertToMeters %d;\n',scale);
fprintf(f1,'\n');
fprintf(f1,'vertices\n');
fprintf(f1,'(\n');
fprintf(f1,'\t(%d %d %d)\n',0, 0, 0);
fprintf(f1,'\t(%d %d %d)\n',0,r*cosd(theta/2),r*sind(theta/2));
fprintf(f1,'\t(%d %d %d)\n',0,r*cosd(theta/2),-r*sind(theta/2));
fprintf(f1,'\t(%d %d %d)\n',l,0,0);
fprintf(f1,'\t(%d %d %d)\n',l,r*cosd(theta/2),r*sind(theta/2));
fprintf(f1,'\t(%d %d %d)\n',l,r*cosd(theta/2),-r*sind(theta/2));
fprintf(f1,');\n');
fprintf(f1,'\n');

fprintf(f1,'blocks\n');
fprintf(f1,'(\n');
fprintf(f1,'\thex (0 2 1 0 3 5 4 3) (%d %d %d) simpleGrading (1 1 1)\n',nx,ny,nz);
fprintf(f1,');\n');
fprintf(f1,'\n');


fprintf(f1,'edges\n')
fprintf(f1,'(\n');
fprintf(f1,'    arc 2 1 (%d %d %d)\n',0,r,0);
fprintf(f1,'    arc 5 4 (%d %d %d)\n',l,r,0);
fprintf(f1,');\n');
fprintf(f1,'\n');

fprintf(f1,'boundary\n');
fprintf(f1,'(\n');
fprintf(f1,'    inlet\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type patch;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (0 2 1 0)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

fprintf(f1,'    outlet\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type patch;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (3 4 5 3)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

fprintf(f1,'    top\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type wall;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (1 2 5 4)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

fprintf(f1,'    front\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type wedge;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (0 1 4 3)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

fprintf(f1,'    back\n');
fprintf(f1,'    {\n');
fprintf(f1,'        type wedge;\n');
fprintf(f1,'        faces\n');
fprintf(f1,'        (\n');
fprintf(f1,'            (0 3 5 2)\n');
fprintf(f1,'        );\n');
fprintf(f1,'    }\n');

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





fclose(f1)

Output is:

/*--------------------------------*-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 9.961947e-03 8.715574e-04)
	(0 9.961947e-03 -8.715574e-04)
	(2.500000e+00 0 0)
	(2.500000e+00 9.961947e-03 8.715574e-04)
	(2.500000e+00 9.961947e-03 -8.715574e-04)
);

blocks
(
	hex (0 2 1 0 3 5 4 3) (25 1 200) simpleGrading (1 1 1)
);

edges
(
    arc 2 1 (0 1.000000e-02 0)
    arc 5 4 (2.500000e+00 1.000000e-02 0)
);

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

mergePatchPairs
(
);

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

2. pressure:

/*--------------------------------*- 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;	
    }

    top
    {
        type            zeroGradient;
    }
    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
}

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

3. velocity:

/*--------------------------------*- 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 (0.09373 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    top
    {
        type            noSlip;
    }
    front
    {
        type            wedge;
    }

    back
    {
        type            wedge;
    }
}

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

So now the values were used for 10 degree, 25 degree, 45 degree wedge and the results are:

  • 10 deg
  • Velocity along the length:

Velocity profile at 0.3 m

Velocity profile at 1.8 m

  • 25 degVelocity along the length:

Velocity profile at 0.3 m

Velocity profile at 1.8 m

  • 45 deg wedge
  • Velocity along the length:

Velocity profile at 0.3 m

Velocity profile at 1.8 m

Also the following observation table can be drawn:

10 deg 10 deg 25 deg 25 deg 45 deg 45 deg
Symmetric Wedge Symmetric Wedge Symmetric Wedge
U at 0.3 m 0.14115 0.14112 0.14207 0.14112 0.1447 0.14206
U at 1.8 m 0.17581 0.17581 0.17683 0.17581 0.17935 0.17683
Execution time(sec) 324.48 394.15 330.89 378.49 340.74 364.2

Following Observations can be drawn from the above results-

1. For all of the angles of geometry, The execution time is minimum for symmetry case.

2. The values in symmetry case are much closer to the actual ones.

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