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Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation

AAthiyaman R13 Mar 2021
CFDMATLAB

In the last project, flow through a pipe was simulated and results were presented for wedge boundary conditions. In this project, the working environment is kept the same as the previous one. Instead of the wedge boundary, the symmetry boundary is used in this project.

MATLAB SCRIPT

clear all
close all
clc

% The Reynolds number
Re = 2100
% The Diameter of pipe
D = 0.015
% The Entry length of pipe
L =0.06*Re*D
% The total length of pipe
L_p = L+0.945
% Radius of pipe
r = D/2
% Angle of wedge 
theta = 10
% Dynamic viscosity
mu = 0.89e-3
% Density 
rho = 997

% Hagen poiseuille flow equations
v_avg = (Re*mu)/(rho*D)
v_max = 2*(v_avg)
del_p = (8*mu*L_p*v_avg)/(r^2)
kinematic_p = del_p/rho

% calculating shear stress
R = linspace(-r,r,1000)

for i = 1:length(R)
    tau(i) = 2*mu*v_max*(abs(R(i)))/r^2
end

plot(R,tau)
xlabel('Radius')
ylabel('Shear stress')
grid on
legend ('Shear stress')


header1='/*----------------------------------*- C++ -*------------------------------------*\'
header2='   =========                 |                                                    ' 
header3='   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox      '
header4='    \\    /   O peration     | Website:  https://openfoam.org                 '
header5='     \\  /    A nd           | Version:  8                                 '
header6='      \\/     M anipulation  |                                                  '
header7='\*----------------------------------------------------------------------------------*/'

f1 = fopen('blockMeshDict.txt','w')
fprintf(f1, '%s\n', header1)
fprintf(f1, '%s\n', header2)
fprintf(f1, '%s\n', header3)
fprintf(f1, '%s\n', header4)
fprintf(f1, '%s\n', header5)
fprintf(f1, '%s\n', header6)
fprintf(f1, '%s\n', header7)

fprintf(f1, 'FoamFile\n{\n')
fprintf(f1, '%12s \t 2.0;\n','version')
fprintf(f1, '%12s \t ascii;\n','format')
fprintf(f1, '%12s \t dictionary;\n','class')
fprintf(f1, '%12s \t blockMeshDict;\n','object')
fprintf(f1, '}\n')
header8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'
fprintf(f1, '%s\n\n',header8)


fprintf(f1, 'convertToMeters 1;\n\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_p,0,0)
fprintf(f1, '\t (%d  %d %d)\n',L_p,r*cosd(theta/2),r*sind(theta/2))
fprintf(f1, '\t (%d  %d %d)\n',L_p,r*cosd(theta/2),-r*sind(theta/2))
fprintf(f1, ');\n\n')


fprintf(f1, 'blocks\n')
fprintf(f1, '(\n')
fprintf(f1, '\t hex (0 3 5 2 0 3 4 1) (%d %d %d)',300,30,1)
fprintf(f1, ' SimpleGrading (1 0.1 1)\n\n')
fprintf(f1, ');\n\n')

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_p,r,0)
fprintf(f1, ');\n\n')

fprintf(f1, 'boundary\n')
fprintf(f1, '(\n')
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 (0 1 2 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')


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 (3 5 4 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')


fprintf(f1, '\t top\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 (1 4 5 2)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t front\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 (0 3 4 1)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

fprintf(f1, '\t back\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 (0 2 5 3)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')

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 (0 3 3 0)\n')
fprintf(f1, '\t\t );\n')
fprintf(f1, '\t }\n')
fprintf(f1, '); \n\n')

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

header9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //'
fprintf(f1, '%s\n',header9)

fclose(f1)

BlockMeshDict 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;
      object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	 (0  0 0)
	 (0  0.00747146 0.000653668)
	 (0  0.00747146 -0.000653668)
	 (2.835  0 0)
	 (2.835  0.00747146 0.000653668)
	 (2.835  0.00747146 -0.000653668)
);

blocks
(
	 hex (0 3 5 2 0 3 4 1) (300 30 1) SimpleGrading (1 0.1 1)

);

edges
(
	 arc 1 2 (0 0.0075 0)
	 arc 4 5 (2.835 0.0075 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:

/*--------------------------------*- 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         5;

deltaT          0.01;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

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 0.0449;
    }

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

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

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 (0.125 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }
    
    top
    {
    	type		 noSlip;
    }
    
    front
    {
    	type		 symmetry;
    }
    
    back
    {
    	type 		 symmetry;
    	}
}

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

TransportProperties:

/*--------------------------------*- 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] 8.917e-7;


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

For symmetry 10^o:

For symmetry 25^o:

For symmetry 45^o:

CONCLUSIONS:

1. SYMMETRY BOUNDARY CONDITION IS MORE ACCURATE THAN WEDGE BOUNDARY CONDITION.

2. EXECUTION TIME IS GREATER FOR SYMMETRY BOUNDARY CONDITION THAN WEDGE BOUNDARY CONDITION.

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