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  1. Home/
  2. Dipakv Virkarwe/
  3. Comparison of Wedge BC VS Symmetry BC VS Hagen poiseuille Equation

Comparison of Wedge BC VS Symmetry BC VS Hagen poiseuille Equation

Title: comparison of Symmetry BC vs Wedge BC vs HP equation Objective 1. To obtaine the result from solving the Hagen Poisuelle\'s equation 2.To obtain results for the pipe flow with symmetry BC 3.Write a Matlab program that takes an angle as input and generates a blockMesh file for the given angle. 4. To change the wedge…

  • CFD

  • Dipakv Virkarwe

    updated on 13 Feb 2020

Title: comparison of Symmetry BC vs Wedge BC vs HP equation

Objective

1. To obtaine the result from solving the Hagen Poisuelle\'s equation

2.To obtain results for the pipe flow with symmetry BC

3.Write a Matlab program that takes an angle as input and generates a blockMesh file for the given angle.

4. To change the wedge angle 10, 25, 45 degree for symmetry Boundary condition.

Theory

   In previous challange i got the result for wedge boundary condition , so here now we just made change of symmetry boundary condition instead of wedge boundary condition in Matlab code & prepared the blockMeshDict file, and this file will be use to get the result. 

   By change of wedge angle 10, 25, 45 degree for symmetry Boundary condition in Matlab code & generated blockMeshDict fiile is used for get the result.

So, to paste all the matlab code & blockMeshDict file for diffrent wedge angle , here i have paste the all code for only wedge 45 degree angle.

 

Matlab code at 45 Degree wedge angle for symmetry BC 

close all 
clear all 
clc

% given data
Re=2100;             % Reynold No.
mu=0.89e-3;          % Dynamic viscosity
D=0.020;             % Diameter of pipe D=20mm
R=(D/2);            % Raduis of pipe
rho=997 ;            % Density of water
Le= (0.06*Re*D);     % Entry lenght of pipe
L= Le+0.3 ;          % Length of pipe
theta=45;             
 % writing the  header part for blockMeshDict file in Matlab
h1=\'/*--------------------------------*- C++ -*----------------------------------*\\\';
h2=\'  =========                 |\';                                               
h3=\'  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox\';
h4=\'   \\\\    /   O peration     | Website:  https://openfoam.org\';
h5=\'    \\\\  /    A nd           | Version:  7\';
h6=\'     \\\\/     M anipulation  |\';
h7=\'\\*---------------------------------------------------------------------------*/\';
h8=\'FoamFile\';
h9=\'{\';
h10=\'    version     2.0;\';
h11=\'    format      ascii;\';
h12=\'    class       dictionary;\';
h13=\'    object      blockMeshDict;\';
h14=\'}\';
h15=\'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\';

conv=\'convertToMeters 1;\';
v0=[0 0 0];
v1=[0 R*cosd(theta/2)  R*sind(theta/2)];
v2=[0 R*cosd(theta/2) -R*sind(theta/2)];
v3=[L 0 0];
v4=[L R*cosd(theta/2) R*sind(theta/2)];
v5=[L R*cosd(theta/2) -R*sind(theta/2)];
block=\'hex (0 3 5 2 0 3 4 1) (300 10 1) simpleGrading (1 1 1)\';
inlet=\'(0 1 2 0)\';
outlet=\'(3 5 4 3)\';
top=\'(1 4 5 2)\';
front=\'(0 3 4 1)\';
back=\'(0 2 5 3)\';
axis=\'(0 3 3 0)\';
s1=blanks(4);
s2=blanks(7);
s3=blanks(11);
s4=blanks(3);

% Writing blockMeshDict file
f1=fopen(\'blockMeshDict.txt\',\'w\');
fprintf(f1,\'%s\\n\',h1);
fprintf(f1,\'%s\\n\',h2);
fprintf(f1,\'%s\\n\',h3);
fprintf(f1,\'%s\\n\',h4);
fprintf(f1,\'%s\\n\',h5);
fprintf(f1,\'%s\\n\',h6);
fprintf(f1,\'%s\\n\',h7);
fprintf(f1,\'%s\\n\',h8);
fprintf(f1,\'%s\\n\',h9);
fprintf(f1,\'%s\\n\',h10);
fprintf(f1,\'%s\\n\',h11);
fprintf(f1,\'%s\\n\',h12);
fprintf(f1,\'%s\\n\',h13);
fprintf(f1,\'%s\\n\',h14);
fprintf(f1,\'%s\\n\',h15);
fprintf(f1,\'\\n\');
fprintf(f1,\'%s\\n\',conv);
fprintf(f1,\'\\n\');
fprintf(f1,\'%s\\n\',\'vertices\');
fprintf(f1,\'%s\\n\',\'(\');
fprintf(f1,\'%s(%d %d %d)\\n\',s1,v0(1),v0(2),v0(3));
fprintf(f1,\'%s(%d %d %d)\\n\',s1,v1(1),v1(2),v1(3));
fprintf(f1,\'%s(%d %d %d)\\n\',s1,v2(1),v2(2),v2(3));
fprintf(f1,\'%s(%d %d %d)\\n\',s1,v3(1),v3(2),v3(3));
fprintf(f1,\'%s(%d %d %d)\\n\',s1,v4(1),v4(2),v4(3));
fprintf(f1,\'%s(%d %d %d)\\n\',s1,v5(1),v5(2),v5(3));
fprintf(f1,\'%s\\n\',\');\');
fprintf(f1,\'\\n\');
fprintf(f1, \'%s\\n\',\'blocks\');
fprintf(f1,\'%s\\n\',\'(\');
fprintf(f1,\'%s %s\\n\',s4,block);
fprintf(f1,\'\\n\');
fprintf(f1,\'%s\\n\',\');\');
fprintf(f1,\'\\n\');
fprintf(f1,\'%s\\n\',\'edges\');
fprintf(f1,\'%s\\n\',\'(\');
fprintf(f1,\'%s %s %d %d (%d %d %d)\\n\',s4,\'arc\',1,2,0,R,0);
fprintf(f1,\'%s %s %d %d (%d %d %d)\\n\',s4,\'arc\',4,5,L,R,0);
fprintf(f1,\'%s\\n\',\');\');
fprintf(f1,\'\\n\');
fprintf(f1,\'%s\\n\',\'boundary\');
fprintf(f1,\'%s\\n\',\'(\');
fprintf(f1,\'%s %s\\n\',s4,\'inlet\');
fprintf(f1,\'%s %s\\n\',s4,\'{\');
fprintf(f1,\'%s %s\\n\',s2,\'type patch;\');
fprintf(f1,\'%s %s\\n\',s2,\'faces\');
fprintf(f1,\'%s %s\\n\',s2,\'(\');
fprintf(f1,\'%s (%d %d %d %d)\\n\',s3,0,1,2,0);
fprintf(f1,\'%s %s\\n\',s2,\');\');
fprintf(f1,\'%s %s\\n\',s4,\'}\');
fprintf(f1,\'%s %s\\n\',s4,\'outlet\');
fprintf(f1,\'%s %s\\n\',s4,\'{\');
fprintf(f1,\'%s %s\\n\',s2,\'type patch;\');
fprintf(f1,\'%s %s\\n\',s2,\'faces\');
fprintf(f1,\'%s %s\\n\',s2,\'(\');
fprintf(f1,\'%s (%d %d %d %d)\\n\',s3,3,5,4,3);
fprintf(f1,\'%s %s\\n\',s2,\');\');
fprintf(f1,\'%s %s\\n\',s4,\'}\');
fprintf(f1,\'%s %s\\n\',s4,\'top\');
fprintf(f1,\'%s %s\\n\',s4,\'{\');
fprintf(f1,\'%s %s\\n\',s2,\'type wall;\');
fprintf(f1,\'%s %s\\n\',s2,\'faces\');
fprintf(f1,\'%s %s\\n\',s2,\'(\');
fprintf(f1,\'%s (%d %d %d %d)\\n\',s3,1,4,5,2);
fprintf(f1,\'%s %s\\n\',s2,\');\');
fprintf(f1,\'%s %s\\n\',s4,\'}\');
fprintf(f1,\'%s %s\\n\',s4,\'front\');
fprintf(f1,\'%s %s\\n\',s4,\'{\');
fprintf(f1,\'%s %s\\n\',s2,\'type symmetry;\');
fprintf(f1,\'%s %s\\n\',s2,\'faces\');
fprintf(f1,\'%s %s\\n\',s2,\'(\');
fprintf(f1,\'%s (%d %d %d %d)\\n\',s3,0,3,4,1);
fprintf(f1,\'%s %s\\n\',s2,\');\');
fprintf(f1,\'%s %s\\n\',s4,\'}\');
fprintf(f1,\'%s %s\\n\',s4,\'back\');
fprintf(f1,\'%s %s\\n\',s4,\'{\');
fprintf(f1,\'%s %s\\n\',s2,\'type symmetry;\');
fprintf(f1,\'%s %s\\n\',s2,\'faces\');
fprintf(f1,\'%s %s\\n\',s2,\'(\');
fprintf(f1,\'%s (%d %d %d %d)\\n\',s3,0,2,5,3);
fprintf(f1,\'%s %s\\n\',s2,\');\');
fprintf(f1,\'%s %s\\n\',s4,\'}\');
fprintf(f1,\'%s %s\\n\',s4,\'axis\');
fprintf(f1,\'%s %s\\n\',s4,\'{\');
fprintf(f1,\'%s %s\\n\',s2,\'type empty;\');
fprintf(f1,\'%s %s\\n\',s2,\'faces\');
fprintf(f1,\'%s %s\\n\',s2,\'(\');
fprintf(f1,\'%s (%d %d %d %d)\\n\',s3,0,3,3,0);
fprintf(f1,\'%s %s\\n\',s2,\');\');
fprintf(f1,\'%s %s\\n\',s4,\'}\');
fprintf(f1,\'%s\\n\',\');\');
fprintf(f1,\'\\n\');
fprintf(f1,\'%s\\n\',\'mergePatchPairs\');
fprintf(f1,\'%s\\n\',\'(\');
fprintf(f1,\'%s\\n\',\');\');
h16=\'// ************************************************************************* //\';
fprintf(f1,\'%s\\n\',h16);
fclose(f1);

BlockmeshDict file at 45Degree  wedge angle for symmetry BC 

/*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     M anipulation  |
\\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
    (0 0 0)
    (0 9.238795e-03 3.826834e-03)
    (0 9.238795e-03 -3.826834e-03)
    (2.820000e+00 0 0)
    (2.820000e+00 9.238795e-03 3.826834e-03)
    (2.820000e+00 9.238795e-03 -3.826834e-03)
);

blocks
(
    hex (0 3 5 2 0 3 4 1) (300 10 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
(
);
// ************************************************************************* //

ControlDict file

/*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     M anipulation  |
\\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    \"system\";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         50;

deltaT          0.005;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

Transport Properties

/*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     M anipulation  |
\\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    \"constant\";
    object      transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

nu              [0 2 -1 0 0 0 0] 8.92e-7;


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

Intial condiion for Pressure file

/*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     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 0.018;
    }

    axis
    {
        type            empty;
    }
    
    top
    {
        type            zeroGradient;
    }

    front
    {
        type            symmetry;
    }

    back
    {
        type            symmetry;
    }
}

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

Intial condiion for Velocity file

/*--------------------------------*- C++ -*----------------------------------*\\
  =========                 |
  \\\\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\\\    /   O peration     | Website:  https://openfoam.org
    \\\\  /    A nd           | Version:  7
     \\\\/     M anipulation  |
\\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

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

internalField   uniform (0.0937 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.0937 0 0);
    }

    outlet
    {
        type            zeroGradient;
	
    }

    axis
    {
        type            empty;
    }
    
    top
    {
        type            noSlip;
    }

    front
    {
        type            symmetry;
    }

    back
    {
        type            symmetry;
    }
}

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

Result of Symmtery BC at 10 degree Wedge Angle

Mesh

\"messh\"

Velocity

\"v\"

Velocity At Entrance x=0.01m

\"v\"

Velocity at exit x= 2.81

\"v\"

Pressure Variation from X=0 to 2.82m

\"p\"

Result of Symmtery BC at 25 degree Wedge Angle

Mesh

\"m\"

Velocity Distribution

\"v\"

Velocity At Entrance x=0.01m

\"v\"

Velocity At Exit x=2.81m

\"v\"

Pressure Variation from X=0 to 2.82m

\"p\"

Result of Symmtery BC at 45 degree Wedge Angle

\"m\"

Velocity distribution

\"v\"

Velocity At Entrance x=0.01m

\"v\"

Velocity At Exit x=2.81m

\"v\"

From the above all graph its found that velocity is maximum at exit of pipe at x=2.81 & it velocity is get constant. At the entry region there is velocity is lower one due to higher kinematic pressure

Pressure Variation from X=0 to 2.82m

\"p\"

from the above graph it shows that as length of pipe increase in x-direction there is pressure is get it decrease  & its constant slope is created , so that there is velocity increase at exit of pipe.

Result table

Parameter

Wedge BC at 4

 

Symmetry BC at 10 

 

Symmetry BC at 25

Symmetry BC at 45

Max.Velocity by hagen poiseuille 

(Theoretical) in m/sec

0.1874

0.1874

0.1874

0.1874

Max.Velocity

(Computational)m/sec

0.1844

0.1842

0.1844

0.1843

Error in %

1.6

1.7

1.6

1.6

Execution time in sec

125.7

189.9

173.9

197.2

 

conclusion

1. As there is wedge angle increase there is error is get decreases ,so it means that result is nearly velocity is get increases & its reach to match the theoretical result of hagen poiseuille equation.

2. As there is wedge angle increase there is Execution time decrease , but for 45 angle it found that its increase.

3. Parabolic nature of flow is created for diffrent wedge angle.

4. Pressure diffrence is get decrase as wedge angle is increase.

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