Simulation of Flow through a pipe in OpenFoam(Wedge BC).

Comparative Analysis of Symmetry and wedge Boundary condition and its validation with Hagon-Poiseuille Equations.

The matlab code for all the above conditions remains the same except changing angle theta. The simulation is first performed with wedge boundary condition replacing symmetry boundary conditions. The simulation time with wedge boundary condition is less compared to symmetry boundary condition, but limitation with wedge BC is that we can not go beyond 5 degree of theta angle.

The Boundary conditions are:

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  6
     \\/     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            wedge;
    }
    back
    {
        type            wedge;
    }
    top
    {
        type            zeroGradient;
    }
    axis
    {
        type            empty;
    }
}

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

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  6
     \\/     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 (0.0672 0 0);
    }

    outlet
    {
        type            zeroGradient;

    }

    front
    {
        type            wedge;
    }
    back
    {
        type            wedge;
    }
    top
    {
        type            noSlip;
    }
    axis
    {
        type            empty;
    }
}

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

The symmetry conditions are used for other different angles, so to avoid repetition MATLAB code is not presented below. I feel that result comparison is most important part of this challenge, so I am presenting those directly.

Velocity Profiles:

1. Wedge

2. Symmetry_10Degrees

3. Symmetry_25Degrees

3. Symmetry_45Degrees

Result Table:

Sr. No.	Parameter	Wedge	Symmetry_10	Symmetry_25	Symmetry_45
1	Velocity	0.13321	0.133232	0.133346	0.133588
	error	0.8854	0.869	0.78422	0.6042
2	Pressure	0.5555	0.55777	0.58099	0.64329
	error	1.078	1.481	4.38734	13.64

Observations:

1. The parabolic profile is maintained irrespective of the angle of wedge.

2. The velocity is almost constant with all the wedge angles.

3. Error is decreasing with the wedge angle.

4. Pressure drop is increasing with wedge angle.

5. Wedge boundary condition instead of symmetry saves the simulation time.