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Phil Dias Wedge Pipe Flow

PPhilippe Dias6 Sept 2019
CFD

Introduction:

This challenge simulates flow through a pipe using OpenFOAM. A wedge method is used to reduce computational time. Ocatve was used to generate the computational mesh for any wedge angle and grading scheme.

  • Working fluid: Water @ 25C
  • Reynold\'s Number: Re = 2100; Laminar
  • Kinematic viscosity: 8.917e-7 m^2/s
  • Pipe Diameter: 1 in
  • Entrance Length: Le = 0.06* Re* D
  • Density of Water: 1000 kg/m^3
  • Length to fully developed flow: L = Le + 0.3

since, `Re = (V*rho*D)/(mu)`

Therefore; V = 0.0738 m/s

Hagen-Poiseuille Equation:

`DeltaP = - (8*mu*L)/(R^2) U`

Octave Code:

clear all 
close all
clc

% Diameter (1\" pipe)
D = 0.0254;
R = D/2;

% Reynold\'s Number
Re = 2100;

% Entrance Length
Le = 0.06*Re*D;

% Total Length
L = 0.3 + Le;

% Assumed wedge angle 
theta = 4;

% Kinematic Viscosity of water @ 25C
nu = 8.917e-07;

% Inlet Velocity
u = (nu*Re)/D;

% 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)];


% Blockmesh File
f1 = fopen(\'blockMeshDict.txt\',\'w\');

fprintf(f1,\'%s \\r\\n\', \'\\*------------------------------------------*/\');
fprintf(f1, \' \\r\\n\');
fprintf(f1, \'FoamFile  \\r\\n{ \\r\\n\');
fprintf(f1, \'%16s %10s\\t 2.0; \\r\\n\', \'version\');
fprintf(f1, \'%12s \\t ascii; \\r\\n\', \'format\');
fprintf(f1, \'%11s \\t directory; \\r\\n\', \'class\');
fprintf(f1, \'12s \\t blockMeshDict;\\r\\n}\\r\\n\' , \'object\');
fprintf(f1, \'%s \\r\\n\', \'//************************************//\');

fprintf(f1, \'convertToMeters 1; \\r\\n\\r\\n\');
fprintf(f1, \'vertices\\r\\n(\\r\\n\');

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

fprintf(f1, \'blocks\\r\\n(\\r\\n\');
fprintf(f1, \'\\thex (0 3 4 1 0 3 5 2) (200 50 1)\');
fprintf(f1, \' simpleGrading (%d %d %d)\\r\\n\', 1,0.5,1);
fprintf(f1, \');\\r\\n\');

fprintf(f1, \'edges\\r\\n\\t(\\r\\n\');
fprintf(f1, \'\\t\\t arc %d %d (%d %d %d)\\r\\n\', 1,2,0,R,0);
fprintf(f1, \'\\t\\t arc %d %d (%d %d %d)\\r\\n\', 4,5,L,R,0);
fprintf(f1, \'\\t);\\r\\n\');

fprintf(f1, \'boundary\\r\\n(\\r\\n\');
% assign boundary conditions
fprintf(f1, \'\\tinlet\\r\\n\\t{\\r\\n\');
fprintf(f1, \'\\t\\ttype patch;\\r\\n\');
fprintf(f1, \'\\t\\tfaces\\r\\n\\t\\t(\\r\\n\');
fprintf(f1, \'\\t\\t\\t(0 2 1 0)\\r\\n\');
fprintf(f1, \'\\t\\t);\\r\\n\\t}\\r\\n\');

fprintf(f1, \'\\toutlet\\r\\n\\t{\\r\\n\');
fprintf(f1, \'\\t\\ttype patch;\\r\\n\');
fprintf(f1, \'\\t\\tfaces\\r\\n\\t\\t(\\r\\n\');
fprintf(f1, \'\\t\\t\\t(3 4 5 3)\\r\\n\');
fprintf(f1, \'\\t\\t);\\r\\n\\t}\\r\\n\');

fprintf(f1, \'\\tfront\\r\\n\\t{\\r\\n\');
fprintf(f1, \'\\t\\ttype symmetry;\\r\\n\');
fprintf(f1, \'\\t\\tfaces\\r\\n\\t\\t(\\r\\n\');
fprintf(f1, \'\\t\\t\\t(0 3 5 2)\\r\\n\');
fprintf(f1, \'\\t\\t);\\r\\n\\t}\\r\\n\');

fprintf(f1, \'\\tback\\r\\n\\t{\\r\\n\');
fprintf(f1, \'\\t\\ttype symmetry;\\r\\n\');
fprintf(f1, \'\\t\\tfaces\\r\\n\\t\\t(\\r\\n\');
fprintf(f1, \'\\t\\t\\t(0 1 4 3)\\r\\n\');
fprintf(f1, \'\\t\\t);\\r\\n\\t}\\r\\n\');

fprintf(f1, \'\\ttop\\r\\n\\t{\\r\\n\');
fprintf(f1, \'\\t\\ttype wall;\\r\\n\');
fprintf(f1, \'\\t\\tfaces\\r\\n\\t\\t(\\r\\n\');
fprintf(f1, \'\\t\\t\\t(1 2 5 4)\\r\\n\');
fprintf(f1, \'\\t\\t);\\r\\n\\t}\\r\\n\');

fprintf(f1, \'\\taxis\\r\\n\\t{\\r\\n\');
fprintf(f1, \'\\t\\ttype empty;\\r\\n\');
fprintf(f1, \'\\t\\tfaces\\r\\n\\t\\t(\\r\\n\');
fprintf(f1, \'\\t\\t\\t(0 3 3 0)\\r\\n\');
fprintf(f1, \'\\t\\t);\\r\\n\\t}\\r\\n\');
fprintf(f1, \');\\r\\n\\r\\n\');

fprintf(f1, \'mergePatchPairs\\r\\n\\r\\n(\\r\\n);\');
fprintf(f1, \'// ************************************************** //\');

fclose(f1);

OpenFoam:

blockMesh Dict:

/*--------------------------------*- 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 0.0126923 -0.000443224)
	(0 0.0126923 0.000443224)
	(3.5004 0 0)
	(3.5004 0.0126923 -0.000443224)
	(3.5004 0.0126923 0.000443224)
);

blocks
(
	hex (0 3 4 1 0 3 5 2) (200 50 1) simpleGrading (1 0.5 1)
);

edges
	(
		 arc 1 2 (0 0.0127 0)
		 arc 4 5 (3.5004 0.0127 0)
	);

boundary
(
	inlet
	{
		type patch;
		faces
		(
			(0 2 1 0)
		);
	}
	outlet
	{
		type patch;
		faces
		(
			(3 4 5 3)
		);
	}
	front
	{
		type symmetry;
		faces
		(
			(0 3 5 2)
		);
	}
	back
	{
		type symmetry;
		faces
		(
			(0 1 4 3)
		);
	}
	top
	{
		type wall;
		faces
		(
			(1 2 5 4)
		);
	}
	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:  7  
     \\\\/     M anipulation  |
\\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    \"system\";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         20;

deltaT          0.01;

writeControl    timeStep;

writeInterval   10;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

transportProperties:

/*--------------------------------*- 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] 8.917e-07;


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

Velocity:

/*--------------------------------*- 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 0 0);

boundaryField
{
    inlet
    {
        type            fixedValue;
        value           uniform (0.073723 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

     front
    {
        type            symmetry;
    } 

     back
    {
        type            symmetry;
    }

    wall
    {
        type            noSlip;
    }

    axis
    {
        type            empty;
    }
}

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

Pressure:

/*--------------------------------*- 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;
    }

     front
    {
        type            symmetry;
    } 

     back
    {
        type            symmetry;
    }

    wall
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }
}
// ************************************************************************* //

Results:

The theoretical results are similar to the simulation results. For velocity, the theoretical and simulated results are 0.2104 m/s and 0.20877 m/s. For shear stress, the theoretical and simulated results are 4.21 Pa and 4.177 Pa. Both results show a percent error of less than 0.8%.

Conclusion:

It is deduced from the parabolic curve that the flow becomes fully developed after the entrance lenth. The theoretical results calculated using the Hagen-Poiseuille equation are near the results from the simulation.

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