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Symmetry vs Wedge vs HP equation

VVenkatesh Sundaresan10 Jan 2020
CFDMATLAB

The main aim of this challenge is to write a MATLAB code which generates block mesh file for angles 10,25 and 45 degrees. Then solve them using the IcoFoam folder in openfoam and then compare velocity profiles at different length of pipe.

Parameters:

Working Fluid: Water

Reynolds Number(Re) : 2100

Wedge Angle: 2.5 degree

Diameter : 0.004m

Density : 997kg/m3

Absolute Viscosity(mu) : 1e-3Pa.s

Calculation:

Kinematic Viscosity(nu) = Absolute Viscosity/(Density) = 1e-6

Length of Pipe for fully developed flow = `0.05*Diameter*Reynolds Number` = 0.41m

Average Velocity = `Re*nu/D` = 0.52658m/s

Maximum Velocity = 2*Average Velocity = 1.05319m/s

Pressure drop in pipe flow = `(32*mu*v_(avg)*L)/D^2`=442.327N/m2

Kinematic Pressure = Pressure Drop/Density = 0.4423658m2/s2

MATLAB CODE FOR BLOCKMESH FILE: 

clear all 
close all
clc

%Inpit parameters
L = 0.5;
theta = 45;
d = 0.004;
r = d/2;
nx = 400;
ny = 50;
nz =1;


bd = fopen('blockMeshDictfinal','w');

fprintf(bd,'FoamFile\n{\n');
fprintf(bd,'%12s \t 2.0;\n','version');
fprintf(bd,'%11s \t ascii;\n','format');
fprintf(bd,'%10s \t dictionary;\n','class');
fprintf(bd,'%11s \t blockMeshDict;\n','object');
fprintf(bd,'}\n');
line8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //';
fprintf(bd,'%s\n\n',line8);

fprintf(bd,'convertToMeters 1;\n\n');

fprintf(bd,'vertices\n');
fprintf(bd,'(\n');
fprintf(bd,'\t (%d %d %d)\n',0,0,0); % point 0
fprintf(bd,'\t (%d %d %d)\n',0,r*cosd(theta/2),r*sind(theta/2)); % point 1
fprintf(bd,'\t (%d %d %d)\n',0,r*cosd(theta/2),-r*sind(theta/2)); % point 2
fprintf(bd,'\t (%d %d %d)\n',L,0,0);  % Pont 3
fprintf(bd,'\t (%d %d %d)\n',L,r*cosd(theta/2),r*sind(theta/2)); % point 4
fprintf(bd,'\t (%d %d %d)\n',L,(r*cosd(theta/2)),-r*sind(theta/2)); % point 5
fprintf(bd,');\n\n');

fprintf(bd,'blocks\n');
fprintf(bd,'(\n');
fprintf(bd,'     hex ( 0 3 5 2 0 3 4 1) (%d %d %d)',nx,ny,nz);
fprintf(bd, ' SimpleGrading (1 0.2 1)\n\n');
fprintf(bd,');\n\n');

fprintf(bd,'edges\n(\n\tarc %d %d (%d %d %d)\n',1,2,0,r,0);
fprintf(bd,'\tarc %d %d (%d %d %d)\n',4,5,L,r,0);
fprintf(bd,');\n\n');

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

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

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

fprintf(bd,'\t back\n');
fprintf(bd,'\t{\n');
fprintf(bd,'\t\t type wedge;\n');
fprintf(bd,'\t\t faces\n');
fprintf(bd,'\t\t (\n');
fprintf(bd,'\t\t\t (5 3 0 2)\n');
fprintf(bd,'\t\t );\n');
fprintf(bd,'\t}\n');

fprintf(bd,'\t front\n');
fprintf(bd,'\t{\n');
fprintf(bd,'\t\t type wedge;\n');
fprintf(bd,'\t\t faces\n');
fprintf(bd,'\t\t (\n');
fprintf(bd,'\t\t\t (3 4 1 0)\n');
fprintf(bd,'\t\t );\n');
fprintf(bd,'\t}\n');

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

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

BLOCK MESH DICT FILE FOR ANGLE 45 DEGREE:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
     version 	 2.0;
     format 	 ascii;
     class 	 dictionary;
     object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	 (0 0 0)
	 (0 1.847759e-03 7.653669e-04)
	 (0 1.847759e-03 -7.653669e-04)
	 (5.000000e-01 0 0)
	 (5.000000e-01 1.847759e-03 7.653669e-04)
	 (5.000000e-01 1.847759e-03 -7.653669e-04)
);

blocks
(
     hex ( 0 3 5 2 0 3 4 1) (500 50 1) SimpleGrading (1 0.1 1)

);

edges
(
	arc 1 2 (0 2.000000e-03 0)
	arc 4 5 (5.000000e-01 2.000000e-03 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)
		 );
	}
	 back
	{
		 type wedge;
		 faces
		 (
			 (0 2 5 3)
		 );
	}
	 front
	{
		 type wedge;
		 faces
		 (
			 (0 3 4 1)
		 );
	}
	 axis
	{
		 type empty;
		 faces
		 (
			 (0 3 3 0)
		 );
	}
);

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

NOTE: BY CHANGING VALUES FROM 45 TO 25 AND 10 WE CAN GET OTHER TWO BLOCKMESH FILE. IN ALL THREE BLOCKMESH FILES ONLY X, Y, Z CO-ORDINATES CHANGES REST ALL REMAIN CONSTANT

BLOCK MESH DICT FILE FOR ANGLE 25 DEGREE:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
     version 	 2.0;
     format 	 ascii;
     class 	 dictionary;
     object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	 (0 0 0)
	 (0 1.952592e-03 4.328792e-04)
	 (0 1.952592e-03 -4.328792e-04)
	 (5.000000e-01 0 0)
	 (5.000000e-01 1.952592e-03 4.328792e-04)
	 (5.000000e-01 1.952592e-03 -4.328792e-04)
);

blocks
(
     hex ( 0 3 5 2 0 3 4 1) (500 50 1) SimpleGrading (1 0.1 1)

);

edges
(
	arc 1 2 (0 2.000000e-03 0)
	arc 4 5 (5.000000e-01 2.000000e-03 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)
		 );
	}
	 back
	{
		 type wedge;
		 faces
		 (
			 (0 2 5 3)
		 );
	}
	 front
	{
		 type wedge;
		 faces
		 (
			 (0 3 4 1)
		 );
	}
	 axis
	{
		 type empty;
		 faces
		 (
			 (0 3 3 0)
		 );
	}
);

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

BLOCKMESH DICT FILE FOR ANGLE 10 DEGREE:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
     version 	 2.0;
     format 	 ascii;
     class 	 dictionary;
     object 	 blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
	 (0 0 0)
	 (0 1.992389e-03 1.743115e-04)
	 (0 1.992389e-03 -1.743115e-04)
	 (5.000000e-01 0 0)
	 (5.000000e-01 1.992389e-03 1.743115e-04)
	 (5.000000e-01 1.992389e-03 -1.743115e-04)
);

blocks
(
     hex ( 0 3 5 2 0 3 4 1) (500 50 1) SimpleGrading (1 0.1 1)

);

edges
(
	arc 1 2 (0 2.000000e-03 0)
	arc 4 5 (5.000000e-01 2.000000e-03 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)
		 );
	}
	 back
	{
		 type wedge;
		 faces
		 (
			 (0 2 5 3)
		 );
	}
	 front
	{
		 type wedge;
		 faces
		 (
			 (0 3 4 1)
		 );
	}
	 axis
	{
		 type empty;
		 faces
		 (
			 (0 3 3 0)
		 );
	}
);

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

INLET VELOCITY:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     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 (0.52658 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    
    axis
    {
        type            empty;
    }

    top
    {
       type            noSlip;
      
    }

    front
    {
        type            symmetry;
    }

    back
    {
        type            symmetry;
    }
}

INLET PRESSURE:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     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 0.44365;     
    }


    axis
    {
        type            empty;
    }

    top
    {
        type            zeroGradient;
    }

    front
    {
        type            symmetry;
    }

    back
    {
        type            symmetry;
    }
}

TRANSPORT PROPERTIES:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.0                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "constant";
    object      transportProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

nu              [0 2 -1 0 0 0 0] 1e-6;


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

OBSERVATIONS:

From the simulations velocity profiles for all three cases are same throughout the pipe as well it matches with the results calculated from the wedge-shaped model.

Fully developed flow occurs at the distance of 0.41m from inlet as calculated from Hagen poiseuille's equation. But the time taken to solve these three simulations are way higher than the time taken for simulation for running wedge shape pipe flow because of the angle used here (10,25 and 45 degrees)

Results obtained for 10 and 25 degrees are same as of 45 degree

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