BlockMesh Drill down challenge

Objective

The objective of the study is to simulate the flow through a backward facing step of the given diagram.

Mesh specification

Number of cells along the x direction (longer dimension) = 200

Number of cells along the y direction = 10

1) BlockMeshDict File:

/*--------------------------------*- 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       dictionary;
    object      blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 1;

vertices
(
    (0 0 0)//0
    (0.08 0 0)//1
    (0.08 0.005 0)//2
    (0 0.005 0)//3
    (0.08 0.01 0)//4
    (0 0.01 0)//5
    (0.2 0.01 0)//6
    (0.2 0.005 0)//7
    (0.2 0 0)//8
    (0.2 -0.01 0)//9
    (0.08 -0.01 0)//10
    (0 0 0.005)//11
    (0.08 0 0.005)//12
    (0.08 0.005 0.005)//13
    (0 0.005 0.005)//14
    (0.08 0.01 0.005)//15
    (0 0.01 0.005)//16
    (0.2 0.01 0.005)//17
    (0.2 0.005 0.005)//18
    (0.2 0 0.005)//19
    (0.2 -0.01 0.005)//20
    (0.08 -0.01 0.005)//21
   
);

blocks
(
    hex (0 1 2 3 11 12 13 14) (80 10 1) simpleGrading (0.2 0.2 1)
    hex (3 2 4 5 14 13 15 16) (80 10 1) simpleGrading (0.2 0.2 1)
    hex (2 7 6 4 13 18 17 15) (120 10 1) simpleGrading (2 0.2 1)
    hex (1 8 7 2 12 19 18 13) (120 10 1) simpleGrading (2 0.2 1)
    hex (10 9 8 1 21 20 19 12) (120 10 1) simpleGrading (2 0.2 1)
);

edges
(
);

boundary
(
    inlet
    {
        type patch;
        faces
        (
            (0 11 14 3)
            (3 14 16 5)
        );
    }
    outlet
    {
        type patch;
        faces
        (
            (7 6 17 18)
            (8 7 18 19)
            (20 9 8 19)
        );
    }
    frontAndBack
    {
        type empty;
        faces
        (
            (21 20 19 12)
            (11 12 13 14)
            (14 13 15 16)
            (12 19 18 13)
            (13 18 17 15)
            (0 3 2 1)
            (3 5 4 2)
            (2 4 6 7)
            (1 2 7 8)
            (10 1 8 9)
        );
    }
   topandbottom
    {
        type wall;
        faces
        (
            (4 5 16 15)
            (4 15 17 6)
            (11 0 1 12)
            (21 10 9 20)
            (1 10 21 12)
            
        );
    }
);

mergePatchPairs
(
);

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

2) Velocity

/*--------------------------------*- 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 (5 0 0);
    }

    outlet
    {
        type            zeroGradient;
       
    }

    frontAndBack
    {
        type            empty;
    }
   topandbottom
    {
        type            noSlip;
    }
}
// ************************************************************************* //

3) Pressure

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

    frontAndBack
    {
        type            empty;
    }
   topandbottom
    {
        type            zeroGradient;
    }
}

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

The mesh file for 0.2 grade is shown below.

Results:

The velocity profiles for ungrades, and for different grading systems is shown below.

1) ungraded (f=1)

2) 0.8 grade

3) 0.5 grade

4) 0.2 grade

Conclusions:

X axis provides the distance and the Y axis is the velocity.

The velocity was measured from 0.085 m from the inlet and the following graphs provides the information at that point.

As we can see from the above diagrams, all the graphs look similar in nature with a very small variation. But we can conclude that 0.2 grade mesh gives the accurate results as the mesh is finer as compared to that of 0.5 and 0.8 grade mesh.