Flow over a backwards facing step using openFoam
Objective: To simulate flow of a fluid over a backwards facing step.
A fluid of given viscosity is considered for flow over a backwards facing step with definite initial and boundary conditions.
We use the icoFoam solver available in openFoam for this simulation, for 10 seconds with a time step calculated keeping in check the value of the Courant number.
Problem: The geometry of the step is shown below with the boudnary conditions and dimensions. The flow simulated will be a 2-D flow, as the flow properties do not change in the z-direction.
The kinematic viscosity of the fluid is set to be 1e^-6.
The number of cells in the x-direction - 200
The number of cells in the y-direction - 10
The grading factor of the cells will be changed to different values to check for consistency and accuracy of solution.
Grading factor = (Size of last cell) / (Size of first cell). Grading factor is used to manipulate mesh quality.
The geomtry of the block is divided into different blocks.
blockmeshDict File:
/*--------------------------------*- 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) //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 0.1) //point 20
(8 -1 0.1) //point 21
);
blocks
(
hex (0 1 2 3 11 12 13 14) (200 10 1) simpleGrading (0.8 1.8 1)
hex (3 2 4 5 14 13 15 16) (200 10 1) simpleGrading (0.8 0.8 1)
hex (1 8 7 2 12 19 18 13) (200 10 1) simpleGrading (1.8 1.8 1)
hex (2 7 6 4 13 18 17 15) (200 10 1) simpleGrading (1.8 0.8 1)
hex (10 9 8 1 21 20 19 12) (200 10 1) simpleGrading (1.8 1.8 1)
);
edges
(
);
boundary
(
inlet
{
type patch;
faces
(
(0 11 14 3)
(3 14 16 5)
);
}
outlet
{
type patch;
faces
(
(9 8 19 20)
(8 7 18 19)
(7 6 17 18)
);
}
frontAndBack
{
type empty;
faces
(
(0 3 2 1)
(3 5 4 2)
(10 1 8 9)
(1 2 7 8)
(2 4 6 7)
(11 12 13 14)
(14 13 15 16)
(21 20 19 12)
(12 19 18 13)
(13 18 17 15)
);
}
Noslipwalls
{
type wall;
faces
(
(4 5 16 15)
(6 4 15 17)
(11 0 1 12)
(21 10 9 20)
(1 10 21 12)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //controlDict File
/*--------------------------------*- 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 10;
deltaT 0.01;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Velocity initial conditons
/*--------------------------------*- 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 (0.02 0 0);
}
outlet
{
type zeroGradient;
}
frontAndBack
{
type empty;
}
Noslipwalls
{
type noSlip;
}
}
// ************************************************************************* //Pressure initial conditions
/*--------------------------------*- 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;
}
Noslipwalls
{
type zeroGradient;
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //Grading factor of 0.2
The blockMeshdict file has to be edited to account for this grading factor. The changes in the blockMeshdict file are-
blocks
(
hex (0 1 2 3 11 12 13 14) (200 10 1) simpleGrading (0.2 1.2 1)
hex (3 2 4 5 14 13 15 16) (200 10 1) simpleGrading (0.2 0.2 1)
hex (1 8 7 2 12 19 18 13) (200 10 1) simpleGrading (1.2 1.2 1)
hex (2 7 6 4 13 18 17 15) (200 10 1) simpleGrading (1.2 0.2 1)
hex (10 9 8 1 21 20 19 12) (200 10 1) simpleGrading (1.2 1.2 1)
);The simulation is run from t=0 to t=10 seconds and the distributions of velocity and pressure at t=10 are shown.
Mesh:
Pressure distribution:
Velocity distribution:
Velocity distribution along the vertical direction at 0.085m from inlet:
Grading factor of 0.5:
The changes in the blockMeshdict file are-
blocks
(
hex (0 1 2 3 11 12 13 14) (200 10 1) simpleGrading (0.5 1.5 1)
hex (3 2 4 5 14 13 15 16) (200 10 1) simpleGrading (0.5 0.5 1)
hex (1 8 7 2 12 19 18 13) (200 10 1) simpleGrading (1.5 1.5 1)
hex (2 7 6 4 13 18 17 15) (200 10 1) simpleGrading (1.5 0.5 1)
hex (10 9 8 1 21 20 19 12) (200 10 1) simpleGrading (1.5 1.5 1)
);Mesh:
Pressure distribution:
Velocity distribution:
Velocity distribution along the vertical direction at 0.085m from inlet:
Grading factor of 0.8:
The changes in the blockMeshdict file are-
blocks
(
hex (0 1 2 3 11 12 13 14) (200 10 1) simpleGrading (0.8 1.8 1)
hex (3 2 4 5 14 13 15 16) (200 10 1) simpleGrading (0.8 0.8 1)
hex (1 8 7 2 12 19 18 13) (200 10 1) simpleGrading (1.8 1.8 1)
hex (2 7 6 4 13 18 17 15) (200 10 1) simpleGrading (1.8 0.8 1)
hex (10 9 8 1 21 20 19 12) (200 10 1) simpleGrading (1.8 1.8 1)
);
Mesh:
Pressure distribution:
Velocity distribution:
Velocity distribution along the vertical direction at 0.085m from inlet:
Conclusion:
Having a finer mesh gives a more accurate output of results, however, with negligible differences.