Simulation of flow in a backward facing step using icoFoam solver using OpenFoam

AIM: To simulate the flow in a backward facing step using icoFoam solver and to create meshes with varing grading factors and comparing the results.

Mesh specification

1. Number of cells along the x direction (longer dimension) = 200
2. Number of cells along the y direction = 10
3. Use a graded mesh. Grading factor near all walls should be 0.2

Boundary condition specification

Follow the specifications that are provided in the following figure.

Procedure to Simulate:

1. Open the terminal window in linux OS.
2. Type 'tutorials' or 'tut' and tabspace (shortcut) once in the OpenFoam folder.
3. Once the above step is done, type "cd incompressible". This command opens the incompressible folder.
4. Now type "cd icoFoam". This loads the icoFoam folder.
5. To view the folders we type the command "ls" to view the files in the existing folder.
6. From this folder, we need to copy the cavity folder to a run folder that was created.
7. # Simulations are never to be run on the tutorial folder. This may hamper the preset values in this file. It would require reinstallation to recover these files.
8. Copying of the cavity folder is done by typing " cp -r cavity/ $FOAM_RUN/****.
9. Now once we have created a copy of this folder, we enter into it.
10. Post entering into the cavity folder, we can find the folders for the initial conditions, constants and system.
11. We enter into the system folder and edit the blockMeshDict using "gedit blockMeshDict"
12. The coordinates for the geometry are given as required and the file is then saved.
13. Similarly we edit the controlDict file as well as per the requirement of the problem and save it.
14. Once the above is done, we come back into the cavity directory using the command "cd .."
15. Now, we edit the initial conditions by entering into a folder 0.
16. Here, we edit the velocity and pressure as per the problem.
17. We now come back to the previous directory and run the command "blockMesh" in order to check for any descrepancies in the mesh formed.
18. To confirm the correctness, we use a command "checkMesh". If the mesh turns out to be correct, it returns Mesh ok message on the terminal else it notifies us the issue.
19. To view the figure, we type "paraFoam" in the terminal to view it.
20. Now to run the simulation, we type "icoFoam" and wait till the simulation ends.
21. Once this is done we can view the variation of the pressure and velocity in the paraview software by using the "paraFoam" command.

blockMeshDict code:

/*--------------------------------*- C++ -*----------------------------------*
  =========                 |
        /  F ield         | OpenFOAM: The Open Source CFD Toolbox
       /   O peration     | Website:  https://openfoam.org
      /    A nd           | Version:  8
     /     M anipulation  |
*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

convertToMeters 0.01;

vertices
(
    (0 0 0) //vertex 0
    (8 0 0) // vertex 1
    (8 0.5 0) //vertex 2
    (0 0.5 0) //vertex 3
    (0 1 0) //vertex 4
    (8 1 0) //vertex 5
    (20 1 0) //vertex 6
    (20 0.5 0)//vertex 7
    (20 0 0) //vertex 8
    (20 -1 0) //vertex 9
    (8 -1 0) //vertex 10
    
    (8 0 0.1) //vertex 11
    (0 0 0.1) //vertex 12 
    (0 0.5 0.1)// vertex13
    (8 0.5 0.1) //vertex 14
    (8 1 0.1) //vertex 15
    (0 1 0.1) //vertex 16
    (20 1 0.1) //vertex 17
    (20 0.5 0.1) //vertex18
    (20 0 0.1) //vertex19
    (20 -1 0.1) //vertex20
    (8 -1 0.1) //vertex21
    
    
);

blocks
 (
    hex (0 1 2 3 12 11 14 13) 
    (200 10 1) 
    simpleGrading (0.2 0.2 1)
    
    hex (3 2 5 4 13 14 15 16) 
    (200 10 1) 
    simpleGrading (0.2 0.2 1)
    
    hex (2 7 6 5 14 18 17 15) 
    (200 10 1) 
    simpleGrading (0.2 0.2 1)
    
    hex (1 8 7 2 11 19 18 14)
    (200 10 1) 
    simpleGrading (0.2 0.2 1)
    
    hex (10 9 8 1 21 20 19 11)
    (200 10 1) 
    simpleGrading (0.2 0.2 1)
 );

edges
(
);

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

mergePatchPairs
(
);

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

contolDict code:

/*--------------------------------*- C++ -*----------------------------------*
  =========                 |
        /  F ield         | OpenFOAM: The Open Source CFD Toolbox
       /   O peration     | Website:  https://openfoam.org
      /    A nd           | Version:  8
     /     M anipulation  |
*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         0.05;

deltaT          1e-05;

writeControl    timeStep;

writeInterval   20;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

Velocity code (U):

/*--------------------------------*- C++ -*----------------------------------*
  =========                 |
        /  F ield         | OpenFOAM: The Open Source CFD Toolbox
       /   O peration     | Website:  https://openfoam.org
      /    A nd           | Version:  8
     /     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 (1.5 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }

    front
    {
        type            empty;
    }
    
    back
    {
        type            empty;
    }
    
    topandbottomface
    {
        type            noSlip;
    }
}
}

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

Pressure code(p):

/*--------------------------------*- C++ -*----------------------------------*
  =========                 |
        /  F ield         | OpenFOAM: The Open Source CFD Toolbox
       /   O peration     | Website:  https://openfoam.org
      /    A nd           | Version:  8
     /     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            empty;
    }
    
    back
    {
        type            empty;
    }
    
    topandbottomface
    {
        type            zeroGradient;
    }
}

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

Profile of the backward step:

Profile of the Backward step for a mesh grade factor of 0.2:

Initial profile:

Grid (0.2):

Post Simulation:

Velocity profile:

Profile of the Backward step for a mesh grade factor of 0.5:

blocks
 (
    hex (0 1 2 3 12 11 14 13) 
    (200 10 1) 
    simpleGrading (0.5 0.5 1)
    
    hex (3 2 5 4 13 14 15 16) 
    (200 10 1) 
    simpleGrading (0.5 0.5 1)
    
    hex (2 7 6 5 14 18 17 15) 
    (200 10 1) 
    simpleGrading (0.5 0.5 1)
    
    hex (1 8 7 2 11 19 18 14)
    (200 10 1) 
    simpleGrading (0.5 0.5 1)
    
    hex (10 9 8 1 21 20 19 11)
    (200 10 1) 
    simpleGrading (0.5 0.5 1)
 );

Grid (0.5):

Post Simulation:

Velocity profile:

Profile of the Backward step for a mesh grade factor of 0.8:

blocks
 (
    hex (0 1 2 3 12 11 14 13) 
    (200 10 1) 
    simpleGrading (0.8 0.8 1)
    
    hex (3 2 5 4 13 14 15 16) 
    (200 10 1) 
    simpleGrading (0.8 0.8 1)
    
    hex (2 7 6 5 14 18 17 15) 
    (200 10 1) 
    simpleGrading (0.8 0.8 1)
    
    hex (1 8 7 2 11 19 18 14)
    (200 10 1) 
    simpleGrading (0.8 0.8 1)
    
    hex (10 9 8 1 21 20 19 11)
    (200 10 1) 
    simpleGrading (0.8 0.8 1)
 );

Grid (0.8):

Post Simulation:

Velocity profile:

Comparison of time taken VS grading factor

Grading Factor	Time taken
0.2	55.17
0.5	55.94
0.8	58.25

Inferences:

1. Time for execution for a meshing factor 0.2 was found to be least.
2. There is no significant changes in the plots observed. However there are minute changes in the plots when magnified.
3. The smoothest curve was obtained for a grading factor of 0.2.
4. On the whole, grading factor plays a minimal role in terms of solutions obtained for this case.