## Effect of Mesh Grading factor in a Backward Step Flow at a particular location

There are two core objectives of the project.

1. To create a backward step geometry by editing blockMeshDict file.
2. To study the effect of mesh grading on the velocity magnitude plot at particular location.

The geometry is predefined. To create the required geometry, the blockMeshDict file from cavity tutorial is edited. Below is the snippet of the file used for defining the geometry.

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     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 0.01 0)				//4
(0.08 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 0.001)				//11
(0.08 0 0.001)			//12
(0.08 0.005 0.001)			//13
(0 0.005 0.001)			//14
(0 0.01 0.001)			//15
(0.08 0.01 0.001)			//16
(0.2 0.01 0.001)			//17
(0.2 0.005 0.001)			//18
(0.2 0 0.001)			//19
(0.2 -0.01 0.001)			//20
(0.08 -0.01 0.001)			//21
);

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

edges
(
);

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

outlet
{
type patch;
faces
(
(9 8 19 20)
(8 7 18 19)
(7 6 17 18)
);
}
);

mergePatchPairs
(
);

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


This will create geometry with no mesh grading.

Flow Conditions

The fluid is taken to be water. The inlet speed is set to 0.05 m/s, this is done to achieve a laminar flow. icoFoam solver is used since it is a transient solver, the simulation is set to run up to the time of 1 second with a time stepping of 1e-3 s.

The simulation is run for four mesh type. The first one with zero grading, the others with 0.8, 0.5, 0.2 grading respectively at the walls. Simple grading is used in the Y direction and multi grading in the X direction, after the step. This is done to obtain decent mesh near the step.

Results

Mesh

Below are the images of the mesh in order of 0, 0.8, 0.5, 0.2 grading factors respectively.

Velocity Plot

The images are in the same order as above. (0, 0.8, 0.5, 0.2 grading factors)

From the images, it can be concluded that the grading factors affects the resolution of the vortex formed near the step.

It is clear after comparing the velocity magnitude plots.

Velocity Magnitude Line Plot.

For the plot, the data is extracted from location X = 0.085 m from the origin. The origin is the start of the small channel on the extreme left.

Again the order for the plot is same (viz 0, 0.8, 0.5, 0.2)

When the grading factor is 0.2, the velocity near the step from -0.008 to 0 is lower by 0.005 m/s from the rest of the plot. This is due to finer mesh generated due to the grading factor.

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