Blockmesh analysis for Backward facing step

The simulation of the backward facing step is carried out using icoFoam solver in OpenFoam open source toolbox. The velocity profiles are analyzed for different mesh grid variations and the convergence graph is plotted for the below provided design.

fig1: Backward-facing step design

The simulation is done using icoFoam flow solver with an initial velocity of 1m/s and for the time varying from 0 to 0.1 sec for three different grading factors (0.2,0.5,0.8) near the wall. The standard mesh distribution along the x-direction is 200 cells and along y-direction is 10 cells.

Block mesh description:

The below link provides the files for blockmesh, time step and boundary conditions for pressure and velocity for all three different graded mesh.

https://drive.google.com/open?id=1vAH4JWYuEW4wSn6fbF5FTAsL2G9ytHLg

Representation of different Blockmesh

fig2: Blockmesh with 0.2 grad factor near the walls.

fig3: Blockmesh with 0.5 grad factor near the walls.

fig4: Blockmesh with 0.8 grad factor near the walls.

From fig2 to fig4 it can be observed that the as the grade factors are increased, the no of cells near the walls decreases. The code implementation is provided in the link which is mentioned at the start.

Result:

From the icoFoam solver, the simulation of the flow is carried out and the below table represents the time step, max courant no obtained for different mesh sizes.

Mesh grade	dt	Courant no max at the end time of 0.1s	Clock time to solve
0.2	1e-05	0.0909798	137 s
0.5	5e-05	0.272519	46 s
0.8	1e-04	0.438314	22 s

1. For different mesh, different dt are chosen. This is due to the fact for maintaining convergence which is obtained only when Courant no is less than 1.

2. It can be observed that, for the mesh grade of 0.8, the max courant no is at 0.4 for the end time of 0.1 sec. It can be analyzed that as the time is increased, the courant no may break above 1 and lead to divergence. But it can be controlled by dt. Since the time is constant for all the three different mesh, the dt is chosen according to the time from 0 to 0.1.

3. The below figure represents the simulation profile obtained after the time of 0.1 sec for all three different meshes.

fig5: Simulation result at time 0.1 sec

4. Since the result obtained is same for all the three meshes, it can be concluded that the solution is converged. But the convergence of the individual parameters for velocity and pressure is evaluated.

5. The convergence graphs are presented below for three different meshes which are evaluated using gnuplot.

fig6: Residual convergence for 0.2 grade mesh

fig7: Residual convergence for 0.5 grade mesh

fig8: Residual convergence for 0.8 grade mesh

6. From the convergence graphs, it can be observed that the 0.2 graded mesh has more accurate convergence than the 0.5 or 0.8 graded mesh. This is due to the fact that there are more cells near the walls for 0.2 graded mesh.

Velocity profile:

The velocity profile for all the three different mesh is compared. The velocity profile is obtained at a distance of 0.085m from the inlet along x direction. Below figure represent the velocity profile.

fig9: Velocity profile at x = 0.085m

It can be observed from the figure that the velocity profile does not vary much for the provided grading factors since all the three different mesh converges and provides a good result.