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Challenge

Week 11 - Simulation of Flow through a pipe in OpenFoam

MMayank Singh13 Mar 2023
CFDMATLABOPENFOAM

OBJECTIVE

Simulate an axi-symmetric flow across a pipe, applying wedge boundary condition with following parameters:

  • `R_e = 2100`
  • Wedge Angle < 5 degress
  • Pipe Diameter can be assumed

Validate the simulation using Hagen-Poiseuille's equations for fully developed flow.
Use MATLAB script to calculate relevant parameters and generate blockMeshDict file accordingly.

THEORY:

Hagen-Poiseuille Equation:

It is a physical law which gives the value of the pressure drop as a fluid in laminar flow, flows along a long cylindrical pipe of constant cross-section. It has the following assumptions:

  • The fluid is compressible and newtonian.
  • The flow is laminar
  • The pipe length of pipe is substabntially greater than its constant cross-section
  • There is no acceleration of fluid in pipe

Mathematically,

CODE:

Assuming Pipe Dia = 10mm, and Wedge Angle = 3 Degrees. Water at room temperature will be used as working fluid

Calculating Pre-requisite Parameters:

%% Pre-requisites:
% Given:
Re = 2100;    % Reynolds Number
theta = 3;    % Wedge Angle(Degrees)

% Taking Water as Working Fluid,
% Water Properties at room temperature:
rho = 997.13;   % Density (Kg/m^3)
mu = 8.91e-4;   % Dynamic Viscosity 
nu = mu/rho;    % Kinematic Viscoity

% Since the flow is Laminar, L/D = 0.06Re:
D = 10e-3;            % Assuming Pipe Dia = 10 mm
L = (0.06*Re*D)+0.1;  % Pipe Length with 0.1m buffer
r = D/2;

% Computing Velocity:
v = Re*nu/L;

% Flow Throw Time:
T = D/v;

% Pressure DIfference (Hagen-Poiseuille):
Q = v_max*pi*r^2;
delp = (8*mu*L*Q)/(pi*r^4);

% Shear Stress:
tau = mu*(v_max/r)

Generating BlockMeshDict:

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

% Unit Converter:
unit = 1;

% Geometry Vertices:
v0 = [0 0 0];
v1 = [r*sind(theta/2) r*cosd(theta/2) 0];
v2 = [-r*sind(theta/2) r*cosd(theta/2) 0];
v3 = [0 0 L];
v4 = [r*sind(theta/2) r*cosd(theta/2) L];
v5 = [-r*sind(theta/2) r*cosd(theta/2) L];

% Meshing and Local Coordinate System:
 block ='hex (0 0 1 2 3 3 4 5) (1 50 200) simpleGrading (1 0.5 1)';
arc1 ='arc 1 2';
arc2 ='arc 4 5';

% Boundary Flagging:
 inlet = '(0 0 2 1)';
 outlet = '(3 4 5 3)';
 front = '(0 1 4 3)';
 back = '(3 5 2 0)';
 wall =' (4 1 2 5)';
 axis =' (0 3 3 0)';

% BlockMeshDict Footer:
footer = '// ************************************************************************************************************************************************** //';

%% WRITING BLOCKMESHDICT:
% Open file:
fid = fopen('/home/cb/OpenFOAM/cb-10/run/pipeFlow/system/blockMeshDict','w');

% Write Header:
fprintf(fid,'%s\n\n',header);

% Write Unit Conversion:
fprintf(fid,'convertToMeters %d;\n\n',unit);

% Write Vertex Coordinates:
fprintf(fid,'vertices\n(\n');
fprintf(fid,'\t(%f %f %f)\n',v0);
fprintf(fid,'\t(%f %f %f)\n',v1);
fprintf(fid,'\t(%f %f %f)\n',v2);
fprintf(fid,'\t(%f %f %f)\n',v3);
fprintf(fid,'\t(%f %f %f)\n',v4);
fprintf(fid,'\t(%f %f %f)\n',v5);
fprintf(fid,');\n\n');

% Write Blocks:
fprintf(fid,'blocks\n(\n');
fprintf(fid,'\t%s\n',block);
fprintf(fid,');\n\n');

% Write Arcs:
fprintf(fid,'edges\n(\n');
fprintf(fid,'\tarc 1 2(%f %f %f)\n',[0 r 0]);
fprintf(fid,'\tarc 4 5(%f %f %f)\n',[L r 0]);
fprintf(fid,');\n\n');

% Write Boundaries:
fprintf(fid,'boundary\n(\n');

% inlet
fprintf(fid,'\t%s\n','inlet');
fprintf(fid,'\t%s\n','{');
fprintf(fid,'\t\t%s\n','type patch;');
fprintf(fid,'\t\t%s\n','faces');
fprintf(fid,'\t\t%s\n','(');
fprintf(fid,'\t\t\t%s\n',inlet);
fprintf(fid,'\t\t%s\n',');');
fprintf(fid,'\t%s\n','}');

% outlet
fprintf(fid,'\t%s\n','outlet');
fprintf(fid,'\t%s\n','{');
fprintf(fid,'\t\t%s\n','type patch;');
fprintf(fid,'\t\t%s\n','faces');
fprintf(fid,'\t\t%s\n','(');
fprintf(fid,'\t\t\t%s\n',outlet);
fprintf(fid,'\t\t%s\n',');');
fprintf(fid,'\t%s\n','}');

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

% wall
fprintf(fid,'\t%s\n','pipewall');
fprintf(fid,'\t%s\n','{');
fprintf(fid,'\t\t%s\n','type wall;');
fprintf(fid,'\t\t%s\n','faces');
fprintf(fid,'\t\t%s\n','(');
fprintf(fid,'\t\t\t%s\n',wall);
fprintf(fid,'\t\t%s\n',');');
fprintf(fid,'\t%s\n','}');

% front wedge:
fprintf(fid,'\t%s\n','front');
fprintf(fid,'\t%s\n','{');
fprintf(fid,'\t\t%s\n','type wedge;');
fprintf(fid,'\t\t%s\n','faces');
fprintf(fid,'\t\t%s\n','(');
fprintf(fid,'\t\t\t%s\n',front);
fprintf(fid,'\t\t%s\n',');');
fprintf(fid,'\t%s\n','}');

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

% Footer:
fprintf(fid,'%s \n','mergePatchPairs');
fprintf(fid,'%s \n','(');
fprintf(fid,'%s \n',');');
fprintf(fid,'\n');
fprintf(fid,'%s \n',footer);

% Close File:
fclose(fid);

OPENFOAM INPUTS:

BlockMeshDict:

/*--------------------------------*- 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
(
	(0.000000 0.000000 0.000000)
	(0.000131 0.004998 0.000000)
	(-0.000131 0.004998 0.000000)
	(0.000000 0.000000 1.270000)
	(0.000131 0.004998 1.270000)
	(-0.000131 0.004998 1.270000)
);

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

edges
(
	arc 1 2(0.000000 0.005000 0.000000)
	arc 4 5(1.270000 0.005000 0.000000)
);

boundary
(
	inlet
	{
		type patch;
		faces
		(
			(0 0 2 1)
		);
	}
	outlet
	{
		type patch;
		faces
		(
			(3 4 5 3)
		);
	}
	axis
	{
		type empty;
		faces
		(
			 (0 3 3 0)
		);
	}
	pipewall
	{
		type wall;
		faces
		(
			 (4 1 2 5)
		);
	}
	front
	{
		type wedge;
		faces
		(
			(0 1 4 3)
		);
	}
	back
	{
		type wedge;
		faces
		(
			(3 5 2 0)
		);
	}
);
mergePatchPairs 
( 
); 

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

ControlDict:

/*--------------------------------*- 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         0.5;

deltaT          1e-2;

writeControl    timeStep;

writeInterval   10;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

physicalProperties:

/*--------------------------------*- 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    "constant";
    object      physicalProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

nu              [0 2 -1 0 0 0 0] 8.9356e-07;


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

U:

/*--------------------------------*- 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 0 0.1879);
    }

    outlet
    {
        type                zeroGradient;
    }
    

    pipewall
    {
        type		    noSlip;
    }

    axis
    {
        type                empty;
    }

    front
    {
        type                wedge;
    }

    back
    {
        type                wedge;
    }
}

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

P:

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

    pipewall
    {
        type            zeroGradient;
    }

    axis
    {
        type            empty;
    }

    front
    {
        type            wedge;
    }

    back
    {
        type            wedge;
    }
}
// ************************************************************************* //

RESULTS:

Velocity Profile:

Pressure:

Shear Stress:

COMPARISON OF RESULTS:

RESULTS Pressure Max Velocity Shear Stress
Analytical Results 0.1460 0.3758 0.1570
Simulation Results 0.11 0.28 0.2

CONCLUSION:

We see certain deviation from the analytical results which is typical for such a simplified case. The Hagen-Poiseuille flow has been successfully studied.

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