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

KKaushal Kumar28 Feb 2023
CFDHTML

Aim: To study the effect of wedge angle and the Boundary Conditions on the simulation of an axisymmetric laminar flow in a cylindrical pipe.

Angles to test:

  • 10o
  • 25o
  • 45o

Wedge Boundary Condition:

Matlab code:

clear all
close all
clc

% Flow variables

rho = 1000;    % Density
mu = 0.00089;  % Dynamic Viscosity
nu = mu/rho;
re = 2100;     % Reynolds Number
d = 0.02;     % Dia of Pipe

alpha = 10;     % wedge angle <5
a = pi/4*d^2;
p = pi*d;       % wetted perimeter
d_h = 4*a/p;    % Hydraulic Dia of pipe 
r_h = d_h/2;    %Hydralic radius of pipe

v_avg = (re*mu)/(rho*d_h);     % Avg velocity 
v_max = 2*v_avg;               %Fully developed V max
tau_max = 2*mu*v_max/r_h;

l_e = 0.06*re*d_h;

l =l_e+0.18;        % Meters length of Pipe

%Daracy Friction factory --> for Laminar Circular pipe flow
f = 65/re;

%Haigen Poiseuille Eqn 

P = (32*mu*(l-l_e)*v_avg)/(d^2);
g = 9.81; 
h_loss = P/(rho*g); %head loss
P_kinematicPress = P/rho;
theta = 3; %3 degree wedge angle
r=r_h;


% Coordinates of the wedge

p0 = [0 0 0];
p1 = [0 r*cosd(alpha/2) r*sind(alpha/2)];
p2 = [0 r*cosd(alpha/2) -r*sind(alpha/2)];
p3 = [l 0 0];
p4 = [l r*cosd(alpha/2) r*sind(alpha/2)];
p5 = [l r*cosd(alpha/2) -r*sind(alpha/2)];

line1 ='/*--------------------------------*- C++ -*----------------------------------*\';
line2 = '  =========                 |';
line3 = '  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox';
line4 = '   \\    /   O peration     | Website:  https://openfoam.org';
line5 = '    \\  /    A nd           | Version:  10';
line6 = '     \\/     M anipulation  |';
line7 = '\*---------------------------------------------------------------------------*/';
line8 = 'FoamFile';
line9 = '{';
line10 = 'format      ascii;';
line11 = 'class       dictionary;';
line12 = 'object      blockMeshDict;';
line13 = '}';
line14 = '// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
line15 = '';
line16 = 'convertToMeters 1;';
line17 = 'vertices';
line18 = '(';
line19 = ');';


f1=fopen('blockMeshDict','w');
fprintf(f1,'%s\n',line1);
fprintf(f1,'%s\n',line2);
fprintf(f1,'%s\n',line3);
fprintf(f1,'%s\n',line4);
fprintf(f1,'%s\n',line5);
fprintf(f1,'%s\n',line6);
fprintf(f1,'%s\n',line7);
fprintf(f1,'%s\n',line8);
fprintf(f1,'%s\n',line9);
fprintf(f1,'\t %s \n',line10);
fprintf(f1,'\t %s \n',line11);
fprintf(f1,'\t %s \n',line12);
fprintf(f1,'%s\n',line13);
fprintf(f1,'%s\n',line14);
fprintf(f1,'%s\n',line15);


fprintf(f1,'%s\n\n',line16);
fprintf(f1,'%s\n',line17);
fprintf(f1,'%s\n',line18);

% Writing the vertices

fprintf(f1,'\t(%d %d %d)\n',p0(1), p0(2), p0(3));
fprintf(f1,'\t(%d %d %d)\n',p1(1), p1(2), p1(3));
fprintf(f1,'\t(%d %d %d)\n',p2(1), p2(2), p2(3));
fprintf(f1,'\t(%d %d %d)\n',p3(1), p3(2), p3(3));
fprintf(f1,'\t(%d %d %d)\n',p4(1), p4(2), p4(3));
fprintf(f1,'\t(%d %d %d)\n',p5(1), p5(2), p5(3));
fprintf(f1,'%s\n\n',line19);
% blocks
line20 = 'blocks';
line21 = '(';
line22 = 'hex (0 3 5 2 0 3 4 1) (200 50 1) simpleGrading (1 0.2 1)';
line23 = ');';
fprintf(f1,'%s\n',line20);
fprintf(f1,'%s\n',line21);
fprintf(f1,'\t%s\n',line22);
fprintf(f1,'%s\n\n',line23);

% Edges
arc1 = ' arc 2 1' ;
arc2 = 'arc 4 5';
fprintf(f1,'%s\n','edges');
fprintf(f1,'%s\n',line21);
fprintf(f1,'\t%s (%d %d %d)\n',arc1,0,r,0);
fprintf(f1,'\t%s (%d %d %d)\n',arc2,l,r,0);
fprintf(f1,'%s\n\n',line23);

% Boundary
line24 = 'Boundary';
line25 = '(';
line26 = 'Inlet';
line27 = '{';
line28 = '}';
line29 = ');';
inlet = '(0 1 2 0)';
outlet = '(3 5 4 3)';
fprintf(f1,'%s\n',line24);
fprintf(f1,'%s\n',line25);
fprintf(f1,'\t%s\n',line26);
fprintf(f1,'\t%s\n',line27);
fprintf(f1,'\t\t %s \n', 'type  patch;');
fprintf(f1,'\t\t %s \n', 'faces');
fprintf(f1,'\t\t %s \n', line25);
fprintf(f1,'\t\t\t %s \n', inlet);
fprintf(f1,'\t\t %s \n', line29);
fprintf(f1,'\t %s \n\n', line28);

% Outlet

fprintf(f1,'\t%s\n','Outlet');
fprintf(f1,'\t%s\n',line27);
fprintf(f1,'\t\t %s \n', 'type  patch;');
fprintf(f1,'\t\t %s \n', 'faces');
fprintf(f1,'\t\t %s \n', line25);
fprintf(f1,'\t\t\t %s \n', outlet);
fprintf(f1,'\t\t %s \n', line29);
fprintf(f1,'\t %s \n\n', line28);

% Walls
wall = '(2 1 4 5)';
fprintf(f1,'\t%s\n','fixedWalls');
fprintf(f1,'\t%s\n',line27);
fprintf(f1,'\t\t %s \n', 'type  wall;');
fprintf(f1,'\t\t %s \n', 'faces');
fprintf(f1,'\t\t %s \n', line25);
fprintf(f1,'\t\t\t %s \n', wall);
fprintf(f1,'\t\t %s \n', line29);
fprintf(f1,'\t %s \n\n', line28);

% Axis
Axis = '(0 3 3 0)';
fprintf(f1,'\t%s\n','axis');
fprintf(f1,'\t%s\n',line27);
fprintf(f1,'\t\t %s \n', 'type  wall;');
fprintf(f1,'\t\t %s \n', 'faces');
fprintf(f1,'\t\t %s \n', line25);
fprintf(f1,'\t\t\t %s \n', Axis);
fprintf(f1,'\t\t %s \n', line29);
fprintf(f1,'\t %s \n\n', line28);
fprintf(f1,'%s \n',');');
fprintf(f1,'\n');

%front
front=[1 0 3 4];
back=[0 2 5 3];
fprintf(f1,'\t%s\n','front');
fprintf(f1,'\t%s\n','{');
fprintf(f1,'\t\t%s\n','type wedge');
fprintf(f1,'\t\t%s\n','faces');
fprintf(f1,'\t\t%s\n','(');
fprintf(f1,'\t\t\t(%d %d %d %d)\n',front);
fprintf(f1,'\t\t%s\n',');');
fprintf(f1,'\t%s\n','}');

%back
fprintf(f1,'\t%s\n','back');
fprintf(f1,'\t%s\n','{');
fprintf(f1,'\t\t%s\n','type wedge');
fprintf(f1,'\t\t%s\n','faces');
fprintf(f1,'\t\t%s\n','(');
fprintf(f1,'\t\t\t(%d %d %d %d)\n',back);
fprintf(f1,'\t\t%s\n',');');
fprintf(f1,'\t%s\n','}');
fprintf(f1,'%s\n',');');

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

last_line = '// ************************************************************************* //';
fprintf(f1,'%s \n',last_line);
   
fclose(f1);

BlockmeshDict File

For wedge angle 10

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
	 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)
	(2.700000e+00 0 0)
	(2.700000e+00 9.961947e-03 8.715574e-04)
	(2.700000e+00 9.961947e-03 -8.715574e-04)
);

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

edges
(
	 arc 2 1 (0 1.000000e-02 0)
	arc 4 5 (2.700000e+00 1.000000e-02 0)
);

Boundary
(
	Inlet
	{
		 type  patch; 
		 faces 
		 ( 
			 (0 1 2 0) 
		 ); 
	 } 

	Outlet
	{
		 type  patch; 
		 faces 
		 ( 
			 (3 5 4 3) 
		 ); 
	 } 

	fixedWalls
	{
		 type  wall; 
		 faces 
		 ( 
			 (2 1 4 5) 
		 ); 
	 } 

	axis
	{
		 type  wall; 
		 faces 
		 ( 
			 (0 3 3 0) 
		 ); 
	 } 

); 

	front
	{
		type wedge
		faces
		(
			(1 0 3 4)
		);
	}
	back
	{
		type wedge
		faces
		(
			(0 2 5 3)
		);
	}
);
mergePatchPairs 
( 
 
); 
 

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

For wedge angle 25

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
	 format      ascii; 
	 class       dictionary; 
	 object      blockMeshDict; 
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	(0 0 0)
	(0 9.762960e-03 2.164396e-03)
	(0 9.762960e-03 -2.164396e-03)
	(2.700000e+00 0 0)
	(2.700000e+00 9.762960e-03 2.164396e-03)
	(2.700000e+00 9.762960e-03 -2.164396e-03)
);

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

edges
(
	 arc 2 1 (0 1.000000e-02 0)
	arc 4 5 (2.700000e+00 1.000000e-02 0)
);

Boundary
(
	Inlet
	{
		 type  patch; 
		 faces 
		 ( 
			 (0 1 2 0) 
		 ); 
	 } 

	Outlet
	{
		 type  patch; 
		 faces 
		 ( 
			 (3 5 4 3) 
		 ); 
	 } 

	fixedWalls
	{
		 type  wall; 
		 faces 
		 ( 
			 (2 1 4 5) 
		 ); 
	 } 

	axis
	{
		 type  wall; 
		 faces 
		 ( 
			 (0 3 3 0) 
		 ); 
	 } 

); 

	front
	{
		type wedge
		faces
		(
			(1 0 3 4)
		);
	}
	back
	{
		type wedge
		faces
		(
			(0 2 5 3)
		);
	}
);
mergePatchPairs 
( 
 
); 
 

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

For wedge angle 45

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
	 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)
	(2.700000e+00 0 0)
	(2.700000e+00 9.238795e-03 3.826834e-03)
	(2.700000e+00 9.238795e-03 -3.826834e-03)
);

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

edges
(
	 arc 2 1 (0 1.000000e-02 0)
	arc 4 5 (2.700000e+00 1.000000e-02 0)
);

Boundary
(
	Inlet
	{
		 type  patch; 
		 faces 
		 ( 
			 (0 1 2 0) 
		 ); 
	 } 

	Outlet
	{
		 type  patch; 
		 faces 
		 ( 
			 (3 5 4 3) 
		 ); 
	 } 

	fixedWalls
	{
		 type  wall; 
		 faces 
		 ( 
			 (2 1 4 5) 
		 ); 
	 } 

	axis
	{
		 type  wall; 
		 faces 
		 ( 
			 (0 3 3 0) 
		 ); 
	 } 

); 

	front
	{
		type wedge
		faces
		(
			(1 0 3 4)
		);
	}
	back
	{
		type wedge
		faces
		(
			(0 2 5 3)
		);
	}
);
mergePatchPairs 
( 
 
); 
 

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

Control Dict File

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         50;

deltaT          0.01;

writeControl    timeStep;

writeInterval   200;

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:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    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; 
    }

    fixedWalls
    {
        type            wall;
    }

    axis
    {
        type            empty;
    }

    front
    {
        type            wedge;
    }

    back
    {
        type            wedge;
    }
}

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

Velocity

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    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 (0.0935 0 0); 
    }

    outlet
    {
        type            zeroGradient;
    }

    fixedWalls
    {
        type		noSlip;
	//type            fixedValue;
	//value		uniform (0 0 0);
    }

    axis
    {
        type            empty;
    }
    front
    {
        type            wedge;
    }

    back
    {
        type            wedge;
    }
}

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

Results:

For wedge angle 10

For wedge angle 25

For wedge angle 45

For Symmetry Boundary Condition:

BlockMesh Dict 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;
    object      blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *//
convertToMeters 1;

vertices
(
   (0 0 0)
	(0 9.762960e-03 2.164396e-03)
	(0 9.762960e-03 -2.164396e-03)
	(2.700000e+00 0 0)
	(2.700000e+00 9.762960e-03 2.164396e-03)
	(2.700000e+00 9.762960e-03 -2.164396e-03)
);

blocks
(

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

edges
(
   arc 1 2 (0 1e-02 0)
   arc 4 5 (2.7 1e-02 0)
);

boundary
(
    inlet
    {
        type patch;
        faces
        (
            (0 1 2 0)
        );
    }

    outlet
    {
        type patch;
        faces
        (
	    (3 5 4 3)
        );
    }

    fixedWalls
    {
        type wall;
        faces
        (
            (2 1 4 5)
        );
    }
   
    axis
    {
        type empty;
        faces
        (
            (0 3 3 0)
        );
    
    }
    
    front
    {
	type symmetry;
	faces
	(	
           (0 3 4 1)
	);
    }
    
    back
    {
   	type symmetry;
	faces
	(
           (0 2 5 3)
	);
    }
);

mergePatchPairs
(
);

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

Control Dict File

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         50;

deltaT          0.01;

writeControl    timeStep;

writeInterval   200;

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:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    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; 
    }

    fixedWalls
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }

    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:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    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 (0.0935 0 0); 
    }

    outlet
    {
        type            zeroGradient;
    }

    fixedWalls
    {
        type		noSlip;
	//type            fixedValue;
	//value		uniform (0 0 0);
    }

    axis
    {
        type            empty;
    }
    front
    {
        type            symmetry;
    }

    back
    {
        type            symmetry;
    }
}

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

For 10 deg angle

For 25 deg angle

For 45 deg angle

Conclusion:

Plot of shear stress and max velocity is plotted for both symmetry boundary condition as well as wedge boundary condition for various wedge angles.

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