Phil Dias Wedge Pipe Flow Pt 2

Introduction:

In this project the results from solving the Hagen-Poisuielle\'s equation, simulations using Symmetry Boundary condtion, and simulations using Wedge Boundary Conditions are compared. The Wedge boundary conditions is used to reduce computational time. Changes were made in the BlockMeshDict, veolicty, and pressure condition files.

BlockMeshDict:

/*--------------------------------*- 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 wedge;
		faces
		(
			(0 3 5 2)
		);
	}
	back
	{
		type wedge;
		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;


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

Boundary Conditions:

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            wedge;
    } 

     back
    {
        type            wedge;
    }

    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            wedge;
    } 

     back
    {
        type            wedge;
    }

    wall
    {
        type            zeroGradient;
    }

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

Results:

Wedge angle = 4deg (Wedge BC):

Wedge angle = 10deg (symmetry BC):

Wedge angle = 25deg (symmetry BC):

Wedge angle = 45deg (symmetry BC):

Conclusion:

The wedge BC replaced the symmetry BC was used to reduce execution time. It also recudes the amount of error when calculating velocity and pressure. Percent error of maximum velocity is reduced with an increase in wedge angle in the symmetry BC. The opposite effect is seen in pressure drop. Stable solution are attained in all wedge angles.