Week 8 - Simulation of a backward facing step in OpenFOAM
Solving the simulation of an incompressible-laminar-viscous flow through the backward facing step geometry.
performing 2 case studies as described below and comparing the results.
Case 1 - Simulate the flow without using any grading factor (i.e., GF = 1)
Case 2 - Simulate the flow with grading factor of 0.2. The cells should be finer near the walls (including the step wall).
The typical approach adopted to performing numerical simulation in Open FOAM involves the following steps:
- Identifying the tutorial in the 'FOAM_TUTORIALS' folder that contains the appropriate governing equations relevant to the physics of the flow for the given problem. A typical file structure of an Open FOAM tutorial consists of the below mentioned directories and files:
- A 'system' directory with the 'controlDict’, 'fvSchemes’ and 'fvSolution' files used for specifying the numerical schemes and solution procedure along with control on the simulation run properties. Additionally, for the given numerical problem, a file by the name 'blockMeshDict’ mentions the creation of different blocks representing the geometry as well as its mesh properties.
- A 'constant’ directory that contains a 'polyMesh' directory outlining the various aspects of the mesh such as 'boundary', 'points', 'faces', etc., and a file that defines the physical properties, in this case, 'physicalProperties' specifying the value of kinematic viscosity.
- A time directory, usually called the '0' directory that consists of files representing the different fields or fluid flow properties with values as required at the start of simulation run.
- Copying the now identified tutorial folder from the 'FOAM_TUTORIALS' folder to the 'FOAM_RUN' folder, specifically created to allow simulation run of Open FOAM numerical simulation cases, with either the same name or preferably a name relevant to the geometry to be discretized.
- Replacing the geometry and boundary list of the pre-existing tutorial with the geometry and boundary list pertaining to the given problem and defining mesh parameters with regards to the flow physics, in this case by updating the 'blockMeshDict' file.
- Updating the fields' files present inside the '0' directory viz., 'U' and 'p', with the boundary list as specified in the 'blockMeshDict' file and appropriate values at the relevant boundary to ensure the given numerical problem has the right boundary conditions and that the solution would be correctly produced.
- Updating the 'controlDict' file, in this case the 'deltaT' parameter with value that take into consideration domain specific attributes such as length of the domain in the direction of flow, fluid flow velocity and avoiding violation of Courant-Friedrichs-Lewy Condition or the CFL number by limiting its mean and maximum value during simulation run.
Mesh specification:
- Number of cells along the x direction (longer dimension) = 200
- Number of cells along the longer y direction = 20;
Boundary conditions and specifications:
The domain specifications are provided in below shown fig.
Fig. 1.1
To get the above geometry we have to edit the blockMeshDict file which is available in system folder of cavity-test setup.
We have to create the sectioned/splitted geometry to solve the problem.
Geometry Creation:
Let us consider creating the geometry using 5 blocks as shown in the figure below
Fig. 1.2
The isometric view for the above fig. 1.2
Now let’s, start indexing the Vertices on the Back side of the Blocks, since Open Foam uses C++ programming, we start the index from “0”. (The Numbering of the vertices can be varied according to your comfort)
Similarly, the indexing for the frontside of the Blocks are,
To View the Bigger Picture,
Finally, to define the blocks, we need to specify the right order of vertex indices.
1.Inlet: (Type patch)
The faces that contribute to inlet boundary are shown above. If we are looking at these faces from the outside, the definition of inlet boundary will be in counter-clockwise direction,
(0 11 14 3)
(3 14 16 5)
2.Outlet: (Type patch)
Similarly, we have 3 faces contributing to the outlet boundary condition. Since we are viewing the faces from outside, hence the definition of the outlet boundary will be in counter-clockwise direction,
(9 8 19 20)
(8 7 18 19)
(7 6 17 18)
Now for the other boundary look at the images below and repeat the steps to define the boundaries.
3.Front & Back: (Type empty)
4.No Slip walls: (Type wall)
After defining the boundaries correctly, to check if you have given defined them correctly, execute the blockMesh command in the terminal. Now open paraFoam, select all the patches and click apply. You will now be able to see the boundary conditions that have been applied to the geometry.
CASE 1 : Simulation of flow without using grading factor i.e (GF = 1).
BlockMeshDict :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
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 0.001) //11
(0.08 0 0.001) //12
(0.08 0.005 0.001) //13
(0 0.005 0.001) //14
(0.08 0.01 0.001) //15
(0 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 4 5 14 13 15 16) (80 5 1) simpleGrading (1 1 1)
hex (2 7 6 4 13 18 17 15) (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
(
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)
);
}
upperWalls
{
type wall;
faces
(
(5 16 15 4)
(4 15 17 6)
);
}
lowerWalls
{
type wall;
faces
(
(0 1 12 11)
(10 9 20 21)
(10 21 12 1)
);
}
frontAndBack
{
type empty;
faces
(
(3 2 1 0)
(5 4 2 3)
(4 6 7 2)
(2 7 8 1)
(1 8 9 10)
(11 12 13 14)
(14 13 15 16)
(13 18 17 15)
(12 19 18 13)
(21 20 19 12)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //Added the vertices, blocks simpleGradings, boundary conditions.
ControlDict :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application icoFoam;
startFrom startTime;
startTime 0;
stopAt endTime;
endTime 0.5;
deltaT 0.001;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Here the time step took as 0.001 to satisfy the courant number condition.
Velocity File :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
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 (0.5 0 0);
}
outlet
{
type zeroGradient;
}
upperWalls
{
type noSlip;
}
lowerWalls
{
type noSlip;
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //Pressure File :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
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;
}
upperWalls
{
type zeroGradient;
}
lowerWalls
{
type zeroGradient;
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //SurfacewithEdges :
Simple block of surfecewithedges
Velocity Profile :
The velocity flow in a meshed block
Pressure file :
The meshing of pressure in block.
Velocity and Pressure plot :
The magnitude of velocity prifile with stable condition and the pressure profile with constant mesh.
CASE 2 : Simulation of flow with 0.2 Grading Factor.
BlocckMeshDict File :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
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 0.001) //11
(0.08 0 0.001) //12
(0.08 0.005 0.001) //13
(0 0.005 0.001) //14
(0.08 0.01 0.001) //15
(0 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 (0.2 5 1)
hex (3 2 4 5 14 13 15 16) (80 5 1) simpleGrading (0.2 0.2 1)
hex (2 7 6 4 13 18 17 15) (120 5 1) simpleGrading (5 0.2 1)
hex (1 8 7 2 12 19 18 13) (120 5 1) simpleGrading (5 5 1)
hex (10 9 8 1 21 20 19 12) (120 10 1) simpleGrading (5 5 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)
);
}
upperWalls
{
type wall;
faces
(
(5 16 15 4)
(4 15 17 6)
);
}
lowerWalls
{
type wall;
faces
(
(0 1 12 11)
(10 9 20 21)
(10 21 12 1)
);
}
frontAndBack
{
type empty;
faces
(
(3 2 1 0)
(5 4 2 3)
(4 6 7 2)
(2 7 8 1)
(1 8 9 10)
(11 12 13 14)
(14 13 15 16)
(13 18 17 15)
(12 19 18 13)
(21 20 19 12)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //Added the vertices, blocks simpleGrading (GF = 0.2), boundary conditions.
ControlDict File :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application icoFoam;
startFrom startTime;
startTime 0;
stopAt endTime;
endTime 0.5;
deltaT 1e-3;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //Here the time step taken as 1e-3 to satisfy courant number condition.
Velocity File :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
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 (0.5 0 0);
}
outlet
{
type zeroGradient;
}
upperWalls
{
type noSlip;
}
lowerWalls
{
type noSlip;
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //Pressure File :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
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;
}
upperWalls
{
type zeroGradient;
}
lowerWalls
{
type zeroGradient;
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //Pressure File :
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 10
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
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;
}
upperWalls
{
type zeroGradient;
}
lowerWalls
{
type zeroGradient;
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //Simulations we get from above files
SimpleSurface :
Simple surfece block for mesh.
Velocity Profile :
The velocity profile with block Mesh at located poits of 0.085 section location to flow.
Plots of Velocity and pressure :
The velocity profile with small variation of stable condition and constant pressure profile.
As the above plots of velocity profile it shows the velocity at section of 0.085 with GF = 1, the profile is smooth curved at 0.015 time step.
And at GF = 0.2 with same 0.085 section of profile the velocity prifile is shows the unstable than first velocity profile.
The pressure profile in both the cases is maintained constant.
CONCLUSION :
As change of Grading Facor 1 to 0.2 the velocity profile is finer to understand the profile with time step.
The meshing of pressure is constant till the end of block.
At ovarall change of simple grading the mesh size is approximately same.