Week 11 - Simulation of Flow through a pipe in OpenFoam

/*--------------------------------*- 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 0.1;

vertices
(
(0.000000 0.0000 0.00000) // origin
(0.000000 0.009994 -0.000349) //1
(0.000000 0.009994 0.000349) //2

(2.520000 0.00000 0.000000)//3

2.520000 0.009994 -0.000349)//4
2.520000 0.009994 0.000349) //5
);

blocks
(
hex (0 1 2 0 3 4 5 3) (50 1 200) simpleGrading (0.4 1 1)
);

edges
(

arc 1 2 ( 0 0.01 0)

arc 4 5 (2.52 0.01 0)
);

boundary
(
axis
{
type empty;
faces
(
(0 3 3 0)
);
}
inlet
{
type patch;
faces
(
(0 1 2 0)
);
}
frontAndBack
{
type empty;
faces
(
(0 3 2 1)
(4 5 6 7)
);
}
);

mergePatchPairs
(
);

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

/*--------------------------------*- 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 10;

deltaT 0.01;

writeControl timeStep;

writeInterval 10;

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 Transport properties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

nu [0 2 -1 0 0 0 0] 8.9268e-07;

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

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

inlet
{
type zeroGradient;
}

Velocity:

/*--------------------------------*- 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
{
movingWall
{
type fixedValue;
value uniform (10 0 0);
}

fixedWalls
{
type noSlip;
}

frontAndBack
{
type empty;
}
}

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

RESULTED GEOMETRY CREATED BY BLOCKMESHDICT:

VELOCITY DISTRIBUTION RESULT BY APPLYING INITIAL AND BOUNDARY CONDITION

VELOCITY DISTRIBUTION ALONG THE LENGHT OF THE PIPE(FULLY DEVELOPED PROFILE)

Simulation Graph:

velocity profile at the inlet

SHEAR STRESS:

shear stress can be calculated `tau = mu((du)/(dr))`

where tau = shear stress

mu = viscosity

du/dr = velocity gradient

CALCULATING SHEAR STRESS NUMERICALLY

%%calculating shear stress

r = linspace(-0.01,0.01,100);

for i = 1:length(r)

tau(i) = 2*mu*u_max*abs(r(i)))/R^2;

end

plot(r,tau,'linewidth',3)

grid on

xlabel('Radius of pipe in meters')

ylabel(''shear stress in pascal)

legend('shear stress of profile')

SHEAR STRESS GRAPH FROM MATLAB

the open flow results are tabulated as:

Results Hagen poisueuille equation wedge angle 4

CFL number mean - 0.076

CFL number max - 0.304875

clock time - 141s

execution time - 114.63s

Umax 0.1875 0.16 m/s

CONCLUSION:

• The velocity profile is plotted at varying distances from the inlet of the pipe.
• The velocity at a distance-0.01 from the inlet seems to be slow and stable around the center of the pipe which shows that the velocity is gradually developing. It suddenly becomes zero at the wall because of the no slip condition.
• The velocity profile at a distance of -0.5 -1 -2.52 is parabolic in nature because the velocity profile moves to the hydrodynamically fully developed region.
• The shear stress plot is plotted as shown above.
• The irregularities can be observed in the shear stress profile is because of the 'finite volume method. At nodes intersection the value of shear stress increases, this can be reduced by increasing the number of grid points which in turn will increase the computational time.
• The above table shows that the velocity profile calculated numerically is equal to the HP equation with an error of 0.0275.
• The simulation is done for wedge angle 4" but the values will be the same when the simulation is performed for the wedge angle 2", 3" since the flow is steady, incompressible.