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Challenge

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

AAshutosh Misra19 Oct 2022
CFDHTML

AIM

In this challenge you will simulate the same problem as in week 11 but by applying Symmetry Boundary Condition. You will do the simulation for the below mentioned angles using both symmetry and wedge boundary conditions and validate them with HP equations like you did in week 11 challenge.

Angles to test: 10,25,45(degrees)

Procedure

To create brockmeshdict file in matlab for symmetry and wedge boundary conditions, only the values of coordinates of vertices changes with respect to the values of theta.

The controldict file and transport properties is same for both boundary conditions.

For pressure and vecocity boundary condition script files, the boundary type should be changed for front and back faces depending on the boundary condition that we are choosing (symmetry/wedge).

Given below is the files for symmetry boundary condition (45 degree wedge angle)

Matlab code for creating blockmeshdict file

clear all
close all
clc

theta=45; %wedge angle
Re =2100;%Reynold's number
D =0.01;%Diameter
R =D/2;%Radius
Le =0.05*Re*D; %hydrodynamic entry length
L =Le+0.4; %Total length

%Temperature = 25degree celsius
mu =8.90*10^-4;  %Dynamic viscosity
rho =997;  %density
nu =8.9267*10^-7; %kinematic viscosity

V_avg =(Re*mu)/(rho*D); %average velocity
V_max =2*V_avg; %maximum velocity
delta_p =(32*mu*L*V_avg)/(D^2); %pressure drop
kinematic_pressure =delta_p/rho; %kinematic pressure


%Vertices
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)];






q1 ='/*--------------------------------*- C++ -*----------------------------------*\';
q2 ='  =========                 |';
q3 ='  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox';
q4 ='   \\    /   O peration     | Website:  https://openfoam.org';
q5 ='    \\  /    A nd           | Version:  9';
q6 ='     \\/     M anipulation  |';
q7 ='\*---------------------------------------------------------------------------*/';
q8 ='FoamFile';
q9 ='{';
q10 ='    format      ascii;';
q11 ='    class       dictionary;';
q12 ='    object      blockMeshDict;';
q13 ='}';
q14 ='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';


%creating the blockMeshDict file

f1 = fopen('blockMeshDict','w');
fprintf(f1,'%s\n',q1);
fprintf(f1,'%s\n',q2);
fprintf(f1,'%s\n',q3);
fprintf(f1,'%s\n',q4);
fprintf(f1,'%s\n',q5);
fprintf(f1,'%s\n',q6);
fprintf(f1,'%s\n',q7);
fprintf(f1,'%s\n',q8);
fprintf(f1,'%s\n',q9);
fprintf(f1,'%s\n',q10);
fprintf(f1,'%s\n',q11);
fprintf(f1,'%s\n',q12);
fprintf(f1,'%s\n',q13);
fprintf(f1,'%s\n',q14);
fprintf(f1,'\n');

fprintf(f1,'%s\n','convertToMeters 1;');
fprintf(f1,'\n');

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

fprintf(f1,'\t(%f %f %f)\n',v0(1),v0(2),v0(3));
fprintf(f1,'\t(%f %f %f)\n',v1(1),v1(2),v1(3));
fprintf(f1,'\t(%f %f %f)\n',v2(1),v2(2),v2(3));
fprintf(f1,'\t(%f %f %f)\n',v3(1),v3(2),v3(3));
fprintf(f1,'\t(%f %f %f)\n',v4(1),v4(2),v4(3));
fprintf(f1,'\t(%f %f %f)\n',v5(1),v5(2),v5(3));

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

%blocks
fprintf(f1,'%s\n','blocks');
fprintf(f1,'%s\n','(');
fprintf(f1,'\t%s\n','hex (0 3 5 2 0 3 4 1) (200 50 1) simpleGrading (1 0.3 1)');
fprintf(f1,'%s\n',');');
fprintf(f1,'\n');

%edges
fprintf(f1,'%s\n','edges');
fprintf(f1,'%s\n','(');
fprintf(f1,'\t%s\n','arc 1 2 (0.000000 0.005 0.000000)');
fprintf(f1,'\t%s\n','arc 4 5 (1.450000 0.005 0.000000)');
fprintf(f1,'%s\n',');');
fprintf(f1,'\n');

%boundary
fprintf(f1,'%s\n','boundary');
fprintf(f1,'%s\n','(');
fprintf(f1,'\t%s\n','inlet');
fprintf(f1,'\t%s\n','{');
fprintf(f1,'\t\t%s\n','type patch;');
fprintf(f1,'\t\t%s\n','faces');
fprintf(f1,'\t\t%s\n','(');
fprintf(f1,'\t\t\t%s\n','(0 1 2 0)');
fprintf(f1,'\t\t%s\n',');');
fprintf(f1,'\t%s\n','}');
fprintf(f1,'\n');

fprintf(f1,'\t%s\n','outlet');
fprintf(f1,'\t%s\n','{');
fprintf(f1,'\t\t%s\n','type patch;');
fprintf(f1,'\t\t%s\n','faces');
fprintf(f1,'\t\t%s\n','(');
fprintf(f1,'\t\t\t%s\n','(3 4 5 3)');
fprintf(f1,'\t\t%s\n',');');
fprintf(f1,'\t%s\n','}');
fprintf(f1,'\n');

fprintf(f1,'\t%s\n','axis');
fprintf(f1,'\t%s\n','{');
fprintf(f1,'\t\t%s\n','type empty;');
fprintf(f1,'\t\t%s\n','faces');
fprintf(f1,'\t\t%s\n','(');
fprintf(f1,'\t\t\t%s\n','(0 3 3 0)');
fprintf(f1,'\t\t%s\n',');');
fprintf(f1,'\t%s\n','}');
fprintf(f1,'\n');

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

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

fprintf(f1,'\t%s\n','top');
fprintf(f1,'\t%s\n','{');
fprintf(f1,'\t\t%s\n','type wall;');
fprintf(f1,'\t\t%s\n','faces');
fprintf(f1,'\t\t%s\n','(');
fprintf(f1,'\t\t\t%s\n','(1 2 5 4)');
fprintf(f1,'\t\t%s\n',');');
fprintf(f1,'\t%s\n','}');
fprintf(f1,'\n');

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

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

blockMeshDict file

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    object      blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	(0.000000 0.000000 0.000000)
	(0.000000 0.004619 0.001913)
	(0.000000 0.004619 -0.001913)
	(1.450000 0.000000 0.000000)
	(1.450000 0.004619 0.001913)
	(1.450000 0.004619 -0.001913)
);

blocks
(
	hex (0 3 5 2 0 3 4 1) (200 50 1) simpleGrading (1 0.3 1)
);

edges
(
	arc 1 2 (0.000000 0.005 0.000000)
	arc 4 5 (1.450000 0.005 0.000000)
);

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

	outlet
	{
		type patch;
		faces
		(
			(3 4 5 3)
		);
	}
	
	axis
	{
		type empty;
		faces
		(
			(0 3 3 0)
		);
	}

	front
	{
		type symmetry;
		faces
		(
			(0 2 5 3)
		);
	}

	back
	{
		type symmetry;
		faces
		(
			(0 3 4 1)
		);
	}

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

)
mergePatchPairs
(
);

controlDict file

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         14;

deltaT          0.001;

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:  9
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "constant";
    object      transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

nu              [0 2 -1 0 0 0 0] 8.9267e-07;


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

Velocity boundary condition

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     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 (0.1875 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    
    axis
    {
        type            empty;
    }

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

}

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

Pressure boundary condition

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  9
     \\/     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;
    }
    
    axis
    {
        type            empty;
    }
    
    front
    {
        type            symmetry;
    }

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

}

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

Results

For Symmetry boundary condition

Wedge angle -10 degree

Wedge angle - 25 degree

Wedge angle - 45 degree

For Wedge boundary condition

Wedge angle - 10 degree

Wedge angle - 25 degree

Wedge angle - 45 degree

Numerical results

Vavg=Vavg= 0.1875 m/s

Vmax=Vmax= 0.3749m/s

τ=τ= 0.13346 Nm2Nm2

Conclusion

From the results it is clear that for symmetry and wedge boundary conditions the plots are almost similar and the values are close to the analytical solution.

The execution time is higher for symmetry boundary condition than for wedge boundary condition.

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