Flow over a backward facing step.

Objective

To simulate the flow through a backward facing step with three base mesh sizes and post process the results using Paraview software.

Geometry

Geometry of a backward facing step.

Above geometry is checked for all the errors by running diagnosis over the geometry and then its flagged into different boundaries to further setup the case to run simualtion.

Boundary Flagging

Case setup

• It is a general flow case.
• Air is the pre-defined mixture used here.
• Simulation run parameters are pressure based steady-state solver, full hydrodynamic and compressible gas flow solver.
• Simulation time parameters:

start time : 0 cycles

end time : 15000 cycles

Initial time-step : 1e-6 sec

Minimun time-step : 1e-6 sec

Maximum time-step : 1 sec

• Boundary Condiitons :

Inlet boundary:It is assigned inflow boundary condition with inlet pressure of 110325 Pa

Outlet boundary:It is assigned outflow boundary condition with outlet pressure of 101325 Pa

Top and bottom boundaries :It is assigned with wall conditions.

Front and back boundaries :These are 2D boundaries. They are alloted 2D boundary condition as they are in the z-direction and along z-direction simulation won't be considered as we perform 2D simulation.

• Region and Initialization : Region 0 is the volumetric flow region assigned to all the boundaries. Only single boundary will be used in this case.
• Turbulence modelling : RNG k-ɛ
• Grid control :

Grid size: dx = dy = dz =2e-3m

dx = dy = dz =1.5e-3m

dx = dy = dz =1.0e-3m

Fixed embedding: Permanent embedding is given across top and bottom boundaries with a scale of 1 and 1 embed layer.

• Output Files: 3D data files were dumped every 100 cycles.

Meshing with embedding

• Base mesh: dx = dy = dz =2e-3m

• Base mesh: dx = dy = dz =1.5e-3m

• Base mesh: dx = dy = dz =1.0e-3m

As the base mesh size is reducing the mesh of the geometry is coarsening which will result in the increase of the number of cells. Due to more refined mesh more accurate line and contour plots can be obtained.The thick lines along the boundary of the geometry is the fixed embedding provided for top and bottom boundaries.

Results

Cell Count

• Base mesh: dx = dy = dz =2e-3m

• Base mesh: dx = dy = dz =1.5e-3m

• Base mesh: dx = dy = dz =1.0e-3m

Rank 0 and rank 1 are the cell count for two processors. Here the total number of cells keeps on increasing as the mesh size is reducing. As the meshing becomes more refined the number of cells increases.

Mass flow rate

• Base mesh: dx = dy = dz =2e-3m

• Base mesh: dx = dy = dz =1.5e-3m

• Base mesh: dx = dy = dz =1.0e-3m

The mass flow rate at the inlet is equal to the mass flow rate at the outlet. From the three plots it can be observed that initially the mass flow rate varies greatly but after aroung 4000 cycles it attains convergence and hence reaches steady state. As compared to mesh size of 2e-3m the curve is more smoother and accurate for mesh size of 1.0e-3m.

Velocity

• Base mesh: dx = dy = dz =2e-3m

Velocity at inlet and outlet.

Velocity contour plot.

• Base mesh: dx = dy = dz =1.5e-3m

Velocity at inlet and outlet.

Velocity contour plot.

• Base mesh: dx = dy = dz =1.0e-3m

Velocity at inlet and outlet.

Velocity contour plot.

Initially the velocity is very high,shown by the red region, as soon as it reaches the step the flow encounters a larger area and it seperates which leads to decrease in velocity which is depicted by blue region.

Eventually after some thousand of cycles the velocity reaches the steady state which can be seen in the line plots.The maximum velocity observed is 160m/s in first case and 150m/s in the second and third case.

Pressure

• Base mesh: dx = dy = dz =2e-3m

Static pressure at inlet and outlet.

Pressure contour plot.

• Base mesh: dx = dy = dz =1.5e-3m

Static pressure at inlet and outlet.

Pressure contour plot.

• Base mesh: dx = dy = dz =1.0e-3m

Static pressure at inlet and outlet.

Pressure contour plot.

Initially, the pressure increases and after the rise in the plot there is sudden fall in the pressure curve which indicates the effect of recirculation of the flow after encountering the step which can be observed by the low pressure regions formed downstream. Once the flow starts recirculationg in the low pressure region the pressure again increases which can be seen at the end of the pressure contour plot.This is the reason for the separation of flow.

With increase in meshing more detailed curve can be observed.Static pressure at the outlet remains constant throughout the simulation.

Glyph

• dx = dy = dz =2e-3m

• dx = dy = dz =1.5e-3m

• dx = dy = dz =1.0e-3m

Above are the plots showing flow vectors which help in better understanding of direction of flow through the geometry.These plots also show the recirculating regions which is shown by the recirculating vectors just after the flow encounters the step.

Velocity and pressure contour plots animation

• dx = dy = dz =2e-3m

• dx = dy = dz =1.5e-3m

• dx = dy = dz =1.0e-3m

Conclusion

From the above simualtion it is understood how the fluid flow is affected through the shapes which consists of sudden changes in their geometries.It is observed how the static pressure, velocity and vectors are affected when fluid flow suddenly encounters change in the geometry and flows into comparatively larger area.