Challenge

Week 11 - Simulation of Flow through a pipe in OpenFoam

KKamalesh Balasubramanian2 Aug 2022

Abstract

The flow through a pipe is the case of internal flow. The surface is the duct in the case of air, it is a pipe in the case of water. The flow is driven because of the pressure difference created by the pumps, air handling units, fans, etc. They find their major application refrigeration and air conditioning industries.

The fluid velocity changes from zero to wall and becomes maximum at the center. In fluid flow, it is preferred to take average velocity because it remains constant when the flow is incompressible and the cross-sectional area is constant.

Assumptions

The steady laminar incompressible flow of a fluid is taken.
There is no velocity in the radial direction.
There is no acceleration since the flow is steady.
Reynolds number for the laminar flow is 2100.
Only the wedge shape of the pipe is considered because the flow is axis-symmetric.
The equation governing the fluid flow is described by the Hagen-Poiseuille equation.

Hagen-Poiseuille equation

The assumptions of the equations are that the fluid is incompressible and Newtonian, the flow is laminar through a pipe of the constant cross-section of length that is longer than the diameter, and there is no acceleration of the fluid in the pipe.

The velocity profile remains unchanged in the hydrodynamically fully developed region, the shear stress at the wall also remains unchanged.

Hydrodynamically fully developed region `frac{delu(r,x)}{delx}=0`

which means `u=u(r)`

Observations based on Hagen-Poiseuille equation

Matlab coding and script for blockMeshDict file

The blockMeshDict file was directly shared and we were informed by Ashwanth that Matlab code is not required as there are time constraints as live sessions are being conducted.

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

// blockMesh parameterization

/* Geometrical Info */

D 0.004; // Diameter
r #calc "0.5*$D"; // Radius
angle 5; // Angle in degrees
theta #calc "degToRad($angle)"; // Angle in radians
Re 100; // Reynolds Number
Le #calc "0.06*$Re*$D"; // Entrance Length
L #calc "0.2 + $Le"; // Total length of pipe

/* Vertices Info */

xmin 0;
xmax $L;
ymax #calc "$r*cos($theta)";
zmax #calc "$r*sin($theta)";
zmin #calc "-$r*sin($theta)";

/* Mesh Info */

nx 10; // Cells along local X
ny 1; // Cells along local Y
nz 50; // Cells along local Z
gx 0.2; // SG along local X
gy 1; // SG along local Y
gz 1; // SG along local Z

convertToMeters 1;

vertices
(
($xmin 0 0) //0
($xmin $ymax $zmax) //1
($xmin $ymax $zmin) //2
($xmax 0 0) //3
($xmax $ymax $zmax) //4
($xmax $ymax $zmin) //5

);

blocks
(
hex (0 2 1 0 3 5 4 3) ($nx $ny $nz) simpleGrading ($gx $gy $gz)
);

edges
(
);

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

);

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 5;

deltaT 0.001;

writeControl timeStep;

writeInterval 500;

purgeWrite 0;

writeFormat ascii;

writePrecision 6;

writeCompression off;

timeFormat general;

timePrecision 6;

runTimeModifiable true;

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

Pressure 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 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 wedge; // symmetry
}

back
{
type wedge; // symmetry
}

wall
{
type zeroGradient;
}

axis
{
type empty;
}
}

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

Velocity 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 volVectorField;
object U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions [0 1 -1 0 0 0 0];

internalField uniform (0 0 0);

boundaryField
{
inlet
{
type fixedValue;
value uniform (0.0223169508525577 0 0);
}

outlet
{
type zeroGradient;
}

front
{
type wedge; // symmetry
}

back
{
type wedge; // symmetry
}

wall
{
type noSlip;
}

axis
{
type empty;
}

}

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

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] 8.9267803410231e-07;

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

Wedge profile of the pipe used in the blockMeshDict file