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Week 12 - Symmetry vs Wedge vs HP equation

VVivek Ramesh6 Nov 2020

Objective:- To simulate and analyze pipe flow using symmetry boundary condition

Matlab code to generate blockmesh dict file for any angle theta

clear all
close all
clc

d=0.02
r=d/2
mu=8.9e-4;
rho=1000;
nu=mu/rho;
Re=2100;
Lent=0.06*Re*d
L=Lent+0.3
vavg=Re*nu/(rho);
vmax=2*vavg;
deltaP=(8*vavg*mu*L)/(r^2);
kinP=deltaP/rho;

fprintf ("Enter theta for Wedge BC");
theta=input('Enter the angle : ');

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*/";
head1="/*--------------------------------*- C++ -*----------------------------------*\";
head2="  =========                 |                                                  ";
head3="  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox            ";
head4="   \\    /   O peration     | Website:  https://openfoam.org                   ";
head5="    \\  /    A nd           | Version:  8                                      ";
head6="     \\/     M anipulation  |                                                  ";
head7="\*---------------------------------------------------------------------------*/";
b4=blanks(4);
b8=blanks(8);
b12=blanks(12);
b16=blanks(16);
dict1="    version     2.0;";
dict2="    format      ascii;"
dict3="    class       dictionary;"
dict4="    object      blockMeshDict;";
dict5="// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //";
conv="convertToMeters  1;";
vertex1="vertices";
blocks1="hex (0 1 2 0 3 4 5 3) (50 1 200) simpleGrading (0.2 1 1)";
footer="// ************************************************************************* //"
f1=fopen('blockMeshDict.txt','w')
fprintf(f1,'%s\n',head1);
fprintf(f1,'%s\n',head2);
fprintf(f1,'%s\n',head3);
fprintf(f1,'%s\n',head4);
fprintf(f1,'%s\n',head5);
fprintf(f1,'%s\n',head6);
fprintf(f1,'%s\n',head7);

fprintf(f1,'FoamFile\n{\n');

fprintf(f1, '%s%s\n', b4,dict1);
fprintf(f1, '%s%s\n', b4,dict2);
fprintf(f1, '%s%s\n', b4,dict3);
fprintf(f1, '%s%s\n}\n', b4,dict4);
fprintf(f1, '%s%s\n', b4,dict5);

fprintf(f1, '%s\n',conv);

fprintf(f1, 'vertices\n(\n');
fprintf(f1, '%s(%d %d %d)\n', b4,v0(1),v0(2), v0(3));
fprintf(f1, '%s(%d %f %f)\n', b4,v1(1),v1(2), v1(3));
fprintf(f1, '%s(%d %f %f)\n', b4,v2(1),v2(2), v2(3));
fprintf(f1, '%s(%d %f %f)\n', b4,v3(1),v3(2), v3(3));
fprintf(f1, '%s(%d %f %f)\n', b4,v4(1),v4(2), v4(3));
fprintf(f1, '%s(%f %f %f)\n', b4,v5(1),v5(2), v5(3));

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

fprintf(f1, '\nblocks\n(\n');
fprintf(f1, '%s%s%\n', b4,blocks1);
fprintf(f1, ');\n');

fprintf(f1,'\nedges\n(\n');
fprintf(f1,'%sarc 1 2 (0 %0.3f 0)\n', b4,r);
fprintf(f1,'%sarc 4 5 (%0.2f %0.3f 0)\n', b4,L,r);
fprintf(f1,');\n');

fprintf(f1,'\nboundary\n(\n');
fprintf(f1,'%saxis\n%s{\n',b4,b4);
fprintf(f1,'%stype empty;\n',b8);
fprintf(f1,'%sfaces\n%s(\n',b8,b8);
fprintf(f1,'%s(0 3 3 0)\n%s);\n%s}\n',b12,b8,b4);

fprintf(f1,'%sinlet\n%s{\n', b4,b4);
fprintf(f1, '%stype patch;\n', b8);
fprintf(f1, '%sfaces\n%s(\n', b8,b8);
fprintf(f1, '%s(0 0 2 1)\n%s);\n%s}\n', b12,b8,b4 );

fprintf(f1,'%swall\n%s{\n', b4,b4);
fprintf(f1, '%stype wall;\n', b8);
fprintf(f1, '%sfaces\n%s(\n', b8,b8);
fprintf(f1, '%s(2 5 4 1)\n%s);\n%s}\n', b12,b8,b4 );

fprintf(f1,'%soutlet\n%s{\n', b4,b4);
fprintf(f1, '%stype patch;\n', b8);
fprintf(f1, '%sfaces\n%s(\n', b8,b8);
fprintf(f1, '%s(3 4 5 3)\n%s);\n%s}\n', b12,b8,b4 );

fprintf(f1,'%sfront\n%s{\n', b4,b4);
fprintf(f1, '%stype symmetry;\n', b8);
fprintf(f1, '%sfaces\n%s(\n', b8,b8);
fprintf(f1, '%s(0 3 5 2)\n%s);\n%s}\n', b12,b8,b4 );
fprintf(f1,'%sback\n%s{\n', b4,b4);
fprintf(f1, '%stype symmetry;\n', b8);
fprintf(f1, '%sfaces\n%s(\n', b8,b8);
fprintf(f1, '%s(0 1 4 3)\n%s);\n%s}\n', b12,b8,b4 );
fprintf(f1,')\n');
fprintf(f1, '\nmergePatchPairs\n(\n);\n');

fprintf(f1,'%s',footer);
fclose(f1);

- Blockmesh dict file for 10 degrees

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |                                                  
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox            
   \\    /   O peration     | Website:  https://openfoam.org                   
    \\  /    A nd           | Version:  8                                      
     \\/     M anipulation  |                                                  
\*---------------------------------------------------------------------------*/
FoamFile
{
        version     2.0;
        format      ascii;
        class       dictionary;
        object      blockMeshDict;
}
    // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters  1;
vertices
(
    (0 0 0)
    (0 0.009962 -0.000872)
    (0 0.009962 0.000872)
    (2.820000e+00 0.000000 0.000000)
    (2.820000e+00 0.009962 -0.000872)
    (2.820000 0.009962 0.000872)
);

blocks
(
    hex (0 1 2 0 3 4 5 3) (50 1 200) simpleGrading (0.2 1 1));

edges
(
    arc 1 2 (0 0.010 0)
    arc 4 5 (2.82 0.010 0)
);

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

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

- Kinematic Pressure drop 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
{
    axis
    {
        type            empty;
    }

    inlet
    {
        type            zeroGradient;
    }

    wall
    {
        type            zeroGradient;
    }
    outlet
    {
        type            fixedValue;
        value           uniform 0.018072;
    }
    front
    {
        type            symmetry;
    }
    back
    {
        type            symmetry;
    }
}

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

- Initial 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 (0.0937312 0 0);

boundaryField
{
    axis
    {
        type            empty;
      
    }

    inlet
    {
        type            fixedValue;
        value           uniform (0.0937312 0 0);
    }

    wall
    {
        type            fixedValue;
        value           uniform (0 0 0);
    }
    outlet
    {
        type            zeroGradient;
        
    }
   front
    {
        type            symmetry;
        
    }
   back
    {
        type            symmetry;
        
    }
}

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

Results

- Wedge Angle 10

- Wedge Angle 25

-Wedge Angle 40

From the above plots we note that the profile for velocity and shear stress are on similar to the ones observed in wedge boundary condition. Differences however can be observed with regard to simulation time and accuracy. It is summarized in the below table

Wedge Angle (Symmetry Boumdary Condition) Courant Number max Velocity Max ClockTime Hagen Poisuelle Delta
10 0.341418 0.1851 632 0.1869 0.0018
25 0.34465 0.1854 478 0.1869 0.0015
40 0.35874 0.1859 348 0.1869 0.001
Wedge Angle Maximum Velocity Hagen Poisuelle Delta Time
2 0.185 0.1869 0.0019 382 (This is the correct value. Wrong value inserted in previous submission)
4 0.1851 0.1869 0.0018 260 This is the correct value. Wrong value inserted in previous submission)

CONCLUSION

- Symmetry Boundary condition produces more accurate results than wedge boundary condition

- In symmetry boundary conditon, higher the wedge angle, greater is the accuracy of the result.

- Symmetry boundary condition requires greater execution time that wedge boundary condition.

- Considering only symmetry, greater is the wedge angle, lower is the execution time.

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