Block Mesh Drill down Using Open Foam

OBJECTIVE :

       The objective of the project is to create a backward facing step using icoFoam solver to stimulate it, the analysis of the transient solver for incompressible under which cavity is used to create the vertices, blocks & boundary for the facing step. Openfoam case file is manipulated to get the required result. The variation of the result by varying the mesh size using the simplegrading option is studied and explained.

PROBLEM DESCRIPTION :

      The fluid flow analysis has to be performed in the cavity under icoFoam. The solver used icoFoam, normally used for low reynold number, incompressible flows.

      The mesh size have to be changed 0.2, 0.5, 0.8 such that a finer mesh is created at the inlet & outlet. The velocity @ 0.085 is to be calculated for different simple grading size. Variation of the velocity for each grid size are plotted. Number of cells along X axis is 200 & Number of cells along Y axis is 10, since it is 2D flow Z axis is not considered & mesh value is taken as 1.

BOUNDARY CONDITIONS :

       Inlet velocity = 2m/s.

       Exit pressure is atmospheric.

       A fully developed flow at the exit.

       No slip condition to be used at the top & bottom surface.

Procedure

      The copy a the cavity is taken in the FOAM RUN folder to execute the command. The blockMeshDict under system folder is used to change value of vertices & blocks. To view geometry created, clear out all the entries inside the boundary section of blockMeshDict file and execute the blockMesh command in the terminal, now open paraview to view it.

8

blockMeshDict File the simple grading is set at 0.8.

inlet - left side.

outlet - right side.

noslip - top & bottom side.

front & back - remaining sides.

/*--------------------------------*- 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 0.01;

vertices
(
    (0 0 0) //point 0
    (8 0 0) //point 1
    (8 0.5 0)//point 2
    (0 0.5 0)//point 3
    (8 1 0)//point 4
    (0 1 0)//point 5
    (20 1 0)//point 6
    (20 0.5 0)//point 7
    (20 0 0)//point 8
    (20 1 0)//point 9
    (8 -1 0)//point 10

    (0 0 0.1)//point 11
    (8 0 0.1)//point 12
    (8 0.5 0.1)//point 13
    (0 0.5 0.1)//point 14
    (8 1 0.1)//point 15
    (0 1 0.1)//point 16
    (20 1 0.1)//point 17
    (20 0.5 0.1)//point 18
    (20 0 0.1)//point 19
    (20 -1 0.05)//point 20
    (8 -1 0.05)//point 21
);


blocks
(
     hex (0 1 2 3 11 12 13 14) (80 10 1) simplegrading (0.8 0.8 1)
     hex (3 2 4 5 14 13 15 16) (80 10 1) simplegrading (0.8 0.8 1)
     hex (2 7 6 4 13 18 17 15) (120 10 1) simplegrading (1.25 0.8 1)
     hex (1 8 7 2 12 19 18 13) (120 10 1) simplegrading (1.25 0.8 1)
     hex (10 9 8 1 21 20 19 12) (120 10 1) simplegrading (1.25 0.8 1)

);

edges
(
);

boundary
(
 inlet
    {
        type patch;
        faces
        (
            (3 0 11 14)
            (3 14 16 5)
        );
    }
    outlet
    {
        type patch;
        faces
        (
            (9 8 19 20)
            (8 7 18 19)
            (7 6 17 18)
        );
    }

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

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

ControlDict file :

The simulation is set to start from zero to end at 5. The time step is selected as 2e-4 to have the CFL no < 1. CFL no = u * dt/dx

dt = time step. 

u = velocity. 

dx = difference in x axis step.

/*--------------------------------*- 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;
    location    \"system\";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         5;

deltaT          2e-4;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

PRESSURE INITIAL CONDITIONS :

The pressure value @ outlet is set to atmospheric pressure since the pressure at outlet boundary is also equal the atmosperic pressure the gauge pressure value is set at zero.

/*--------------------------------*- 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;
    }
    
    noslipwalls
    {
        type            zeroGradient;
    }
}


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

VELOCITY INITIAL CONDITIONS :

The velocity @ inlet is set to 2 m/s & noslip condition is set at top & bottom walls so the velocity is not equal to zero.

/*--------------------------------*- 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 (2 0 0);  
    }

    outlet
    {
        type            zeroGradient;
    }

    frontAndBack
    {
        type            empty;
    }
    
    noslipwalls
    {
        type            noSlip;
    }
}

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

IcoFoam command is used to run the post processor for this program. Then to open paraview paraFoam command is used.  The wire frame option is used to capture the figure, then click on the filters, expand the data analysis group to choose plot over line option. To extract the plot data to an Excel file, click the file option in the toolbar and select the “Export Scene” option & name the output document and save it.

GRADING FACTOR

Depending the mesh size to be created the value in the simple grading is changed.

simple grading f = size of end cell/ size of start cell. This is used to refine the mesh at certain locations, we need to find value @ diatance of 0.085 from the inlet Depending the grading value of the simplegrading is changed in the blockMeshDict file.

1. 0.2

The wireframe view of the figure :

2. 0.5

3. 0.8

4. 1

Line Plot

The slice command is used to cut the part along plane so make it a 2D part & line over plot command is used to make to velocity plot.

Grading Factor - 0.2

Grading Factor - 0.5

Grading Factor - 0.8 

Velocity @ 0.085 from Inlet :

Grading Factor                        Velocity value                              Time taken(sec)

       0.2                                          1.346                                            192                     

       0.5                                          1.354                                            203

       0.8                                          1.368                                            212

Inference :

      From the plot of the various grading value we can see that the variation in the value is very less when compared to the simple grading change. Time taken to run the simulation is more for grade mesh @ 0.8 when compared to the other. Since the shape of the figure is very simple so mesh doesn\'t affect the values but however more finer the mesh the better will be the results & time to converge is also more for finer mesh so the plot @ 0.8 is smooth than the other mesh grade.The mesh nodes are more @ 0.085m where the step region starts flow enter the larger area & dip in the velocity due to the increase in flow area which follows continuity equation (a*v = constant, since it is incompressible flow density is not considered) . Magnitude of velocity was highest near the inlet above 2m/s the simulation results were for 1750 iterations. The maximum value of the CFL number increases as the grading factor decreases. It is excepted value since the distance between adjacent cell decreases at certain portion of the flow but the mean value of the CFL number is almost same for all grading factors. The accurate results are produced @ 0.2 grading factor this is due the higher number nodes in that region. 

REFERENCE :

1. https://www.openfoam.com/documentation/user-guide/

2. http://foam.sourceforge.net/docs/Guides-a4/OpenFOAMUserGuide-A4.pdf