Week 8 - BlockMesh Drill down challenge
Problem Definition:
1. To create a geometry given below by providing respective boundary names and conditions
2. Mesh
| Along x- axis | 200 |
| Along y-axis | 10 |
3. Observe the variation of velocity magnitude profile with change in grading factors 0.2, 0.5, 0.8. Measure the velocity profile at x = 0.085 m and represent using a line plot.
4. Contour plots of velocity and pressure.
Procedure:
a. Vertices of the geometry:
| point | Coordinates | Point | Coordinates |
| 0 | (0 0 0) | 11 | (0 0 1) |
| 1 | (80 0 0) | 12 | (80 0 1) |
| 2 | (80 5 0) | 13 | (80 5 1) |
| 3 | (0 5 0) | 14 | (0 5 1) |
| 4 | (80 10 0) | 15 | (80 10 1) |
| 5 | (0 10 0) | 16 | (0 10 1) |
| 6 | (200 10 0) | 17 | (200 10 1) |
| 7 | (200 5 0) | 18 | (200 5 1) |
| 8 | (200 0 0) | 19 | (200 0 1) |
| 9 | (200 -5 0) | 20 | (200 -5 1) |
| 10 | (80 -5 0) | 21 | (80 -5 1) |
The above tabular column contains coordinates for all the points starting from 0 to 21. Convert into meters by multiplying with 0.001.
b. Blocks:
The entire geometry is divided into 5 blocks each containing 8 vertices.
| Block number | Vertices |
| 1 | 0, 1, 2, 3, 11, 12, 13, 14 |
| 2 | 3, 2, 4, 5, 14, 13, 15, 16 |
| 3 | 2, 7, 6, 4, 13, 18, 17, 15 |
| 4 | 1, 8, 7, 2, 12, 19, 18, 13 |
| 5 | 10, 9, 8, 1, 21, 20, 19, 12 |
c. Meshing:
For the length of 80 mm '80' grid points are taken and for the length of 120 mm '120' grid points are taken along xaxis for all the blocks
Along y axis for each block ten grid points are taken.
Along z axis only one grid is taken because the problem being solved is 2D.
d. Mesh grading:
Mesh grading depends on grading factor(f) = `("end grid size")/("start grid size")`
if mesh grid size is less than 1 then end grid is smaller compared to starting grid, by using this concept fine mesh can be obtained at the walls.
e. boundary names:
| Boundary name | Faces |
| inlet | (14 3 0 11) (16 5 3 14) |
| outlet | (9 8 19 20) (8 7 18 19) (7 6 17 18) |
| Noslipwall | (15 4 5 16) (17 6 4 15) (12 1 10 21) (0 1 12 11) (10 9 20 21) |
| frontAndBack | (2 1 0 3) (4 2 3 5) (8 9 10 1) (7 8 1 2) (6 7 2 4) (12 13 14 11) (13 15 16 14) (20 19 12 21) (19 18 13 12) (18 17 15 13) |
BlockMeshDict file
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 0.001;
vertices
(
(0 0 0)
(80 0 0)
(80 5 0)
(0 5 0)
(80 10 0)
(0 10 0)
(200 10 0)
(200 5 0)
(200 0 0)
(200 -5 0)
(80 -5 0)
(0 0 1)
(80 0 1)
(80 5 1)
(0 5 1)
(80 10 1)
(0 10 1)
(200 10 1)
(200 5 1)
(200 0 1)
(200 -5 1)
(80 -5 1)
);
blocks
(
hex (0 1 2 3 11 12 13 14) (80 10 1) simpleGrading (0.2 5 1)
hex (3 2 4 5 14 13 15 16) (80 10 1) simpleGrading (0.2 0.2 1)
hex (2 7 6 4 13 18 17 15) (120 10 1) simpleGrading (5 0.2 1)
hex (1 8 7 2 12 19 18 13) (120 10 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
(
(14 3 0 11)
(16 5 3 14)
);
}
outlet
{
type patch;
faces
(
(9 8 19 20)
(8 7 18 19)
(7 6 17 18)
);
}
Noslipwall
{
type wall;
faces
(
(15 4 5 16)
(17 6 4 15)
(12 1 10 21)
(0 1 12 11)
(10 9 20 21)
);
}
frontAndBack
{
type empty;
faces
(
(2 1 0 3)
(4 2 3 5)
(8 9 10 1)
(7 8 1 2)
(6 7 2 4)
(12 13 14 11)
(13 15 16 14)
(20 19 12 21)
(19 18 13 12)
(18 17 15 13)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //In the blockMeshDict file all the information regarding mesh and geometry is present, here grading factors can be changed and also number of grid points can be changed as per requirement.
ControlDict file
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application icoFoam;
startFrom startTime;
startTime 0;
stopAt endTime;
endTime 0.3;
deltaT 0.0002;
writeControl timeStep;
writeInterval 200;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //In controlDict file start time, end time, time step(deltaT) and others can be changed for a given problem to maintain the courant number < 1.
Courant number plays very important role while running icoFoam for maintaining accuracy and stability courant number must be less then 1
Courant number `C_0 = (deltat|U|)/(deltax)`
Therefore courant number depends on time step, velocity, grid size and by varying these one can maintain courant number less than 1.
initial conditions are not varied to observe changes by varing grading factor and comparing with results of no mesh grading.
f. Initial and boundary conditions for velocity and pressure
For velocity:-
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ 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 0 0);
}
outlet
{
type zeroGradient;
}
Noslipwall
{
type noSlip;
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //For Kinematic Pressure:-
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ 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;
}
Noslipwall
{
type zeroGradient;
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //Results:
I. For simple grading (1 1 1)
| Variable | Value set to |
| Thermal diffusivity | 0.001 |
| time step(deltaT) | 3e-4 |
| t start | 0 |
| t end | 0.3 |
| U_initial | 1 m/s |
Here the maximum value of CFL for last time step is found to be 0.544112
1. Mesh obtained:
In the above mesh no mesh grading is done.
2. Plot over line showing variation of velocity magnitude wrt width at x = 0.085 m for no mesh grading.
Here the variation of velocity profile is calculated from bottom to top. ie . point 1 at the bottom (0.085, -0.01, 0) and point 2 is at the top (0.085, 0.01, 0)
3. Contour plots of velocity and pressure for no mesh grading.
Here as expected velocity at the centre is maximum and decrease to zero at the walls because of no slip condition.
Here pressure at the inlet is high and as the fluid flows though the pipe pressure gradually decreases and finally reaches to atmospheric pressure (zero gauge pressure) at the outlet.
II. For grading factor f = 0.2
Here grading factor is introduced to create a finer mesh at the walls and code in the blockMeshDict file is varied respctively.
| Variable | Value set to |
| Thermal diffusivity | 0.001 |
| time step(deltaT) | 2e-4 |
| t start | 0 |
| t end | 0.3 |
| U_initial | 1 m/s |
Here maximum CFL for the final time step is found to be 0.755528.
1. Mesh:
Here it can be clearly seen to be refined at the walls, so one can observe changes in results due to mesh grading.
2. Plot over line showing variation of velocity magnitude wrt width at x = 0.085 m for grading factor = 0.2.
Here one can observe the variation of results compared to no mesh grading (I.2) here clear results are obtained between 0.005 to 0.008 but when no mesh grading is done there was increase in peak value and graph started to parabolically increase after width = 0.008, because of lack of mesh refinement.
3. Contour plots of velocity magnitude and Kinematic pressure for mesh grading factor = 0.2
Vector plot:
From the vector plot it can be seen that there is changes in the direction of velocity at the backward facing step. so, in the graph one can observe small velocity magnitude at the bottom.
III. For mesh grading factor = 0.5
| Variable | Value set to |
| Thermal diffusivity | 0.001 |
| time step(deltaT) | 2e-4 |
| t start | 0 |
| t end | 0.3 |
| U_initial | 1 m/s |
Here the maximum value of CFL for the last time step is found to be 0.4645
1. Mesh
One can observe that by increasing the mesh grading factor from 0.2 to 0.5 there is decrease in mesh refinement at the walls.
2. Plot over line showing variation of velocity magnitude wrt width at x = 0.085 m for grading factor = 0.5:
3. Contour plots of velocity and kinematic pressure for mesh grading factor = 0.5:
IV. For mesh grading factor = 0.8
| Variable | Value set to |
| Thermal diffusivity | 0.001 |
| time step(deltaT) | 2e-4 |
| t start | 0 |
| t end | 0.3 |
| U_initial | 1 m/s |
Here the maximum value of CFL for the last time step is found to be 0.388754
1. Mesh:
2. Plot over line on Variation of velocity magnitude wrt width for mesh grading factor = 0.8
3. contour plot of velocity magnitude and kinematic pressure for mesh grading factor = 0.8
Conclusion:
From the above result we can conclude that for mesh grading factor = 0.2 one can obtain good results as there is sudden decrease in velocity near the walls and tending to zero at the walls due to no slip condition. so, by mesh refinement at the walls correct plots can be obtained and results will be realistic.
when the plot over line graphs are compared it can be seen that with increase in mesh grading from 0.2 to 1 it is difficult to capture the values at the bottom wall because of lack of refinement.
Also by varying mesh grading factor from 0.2 to 1 slight changes in contour plots can be observed especially in velocity contour plot at the walls.
Mesh grading factor of 0.2 is recommended for this case is recommended but needed to be carefully chosen to get realistic results because by using mesh grading factor end grid size is reduced and also start grid size is increased.