Flow over a backward facing step

Abstract
In this project, flow over a backward step was simulated in CONVERGE Studio, and compared the results of three different mesh grid size. The project was then post-processed in ParaView to understand the result visually. CYGWIN was use to run the simulation commands and convert files for the post-processing.

Introduction
Backward-Facing Step (BFS) is the frequently used and benchmarked geometry to validate new theory or results in Computational Fluid Dynamics (CFD). Another reason why BFS is widely use is due to the large number of available numerical and experimental data.

Method
The geometry was created in Converge Studio using vertex and triangles. There is no standarize geometry dimensions for BFS, as long as the geometry is acceptable, as shown in Figure 1.

FIGURE 1 Geometry of Backward-Facing Step in Converge Studio.

Case Set-up
Application: General Flow
Materials: Default
Simulation Paramenters: Pressure base steady-solve (Run parameters), 15000 cycle (Time parameters)
Boundary Conditions:

• One Y-Z plane as INLET with 110,325 Pascal pressure.
• One Y-Z plane as OUTLET with 101,325 Pascal pressure.
• Both X-Y plane as WALLS.
• Both X-Z plane as TWO_D

Regions and Initialization: User define region is assigned to all boundary flag to create volumetric region. Oxygen and Nitrogen is defined as species.
Physical Models: Default
Base Grid: Given as follow with fixed embedding

• Case 1: dx=dy=dz = 2E-4m
• Case 2: dx=dy=dz = 1.5E-4m
• Case 3: dx=dy=dz = 1.0E-4

Output/Post Processing: Default

Results and Discussion
Figure 2 shows the velocity vector at the last cycle. As seen from the figure, there is a vortices after the backward step. This is due to the adverse pressure gradient. After initial conditions, the flow flows from high pressure to low pressure in the middle, which is favorable pressure gradient, as seen in Figure 3.2. However, after the backward step, the flow has to flow from low pressure to high pressure, which is unfavorable, thus, adverse pressure gradient forces the flow to go backward creating seperation.

FIGURE 2.1 Case 1 Velocity vector at last cycle.

FIGURE 2.2 Case 2 Velocity vector at last cycle.

FIGURE 2.3 Case 3 Velocity vector at last cycle.

FIGURE 3.1 Case 1 Pressure contour at last cycle.

FIGURE 3.2 Case 2 Pressure contour at last cycle.

FIGURE 3.3 Case 3 Pressure contour at last cycle.

FIGURE 4.1 Case 1 Velocity contour at last cycle.

FIGURE 4.2 Case 2 Velocity contour at last cycle.

.FIGURE 4.3 Case 3 Velocity contour at last cycle.

FIGURE 5.1 Case 1 Velocity plot at last cycle.

FIGURE 5.2 Case 2 Velocity plot at last cycle.

FIGURE 5.3 Case 3 Velocity plot at last cycle.

FIGURE 6.1 Case 1 Mass Flow Rate at last cycle.

FIGURE 6.2 Case 2 Mass Flow Rate at last cycle.

FIGURE 6.3 Case 3 Mass Flow Rate at last cycle.

FIGURE 7.1 Case 1 Pressure plot at last cycle.

FIGURE 7.2 Case 2 Pressure plot at last cycle.

FIGURE 7.3 Case 3 Pressure plot at last cycle.

From Figure 5 - 7, it is obersved that simulation reaches steady-state fairly quickly (approximately after 5,000 cycle every output parameter has reach steady state). As stated earlier, the initial condition washed out and simulation reach steady state. As shown in Figure 7, static pressure at outlet is lower than inlet, however, after 500 cycles the static pressure of outlet is greater than inlet which causes recirculation region near the bottom of step.

FIGURE 8.1 Case 1 Rank cell plot.

FIGURE 8.2 Case 2 Rank cell plot.

FIGURE 8.3 Case 3 Rank cell plot.

FIGURE 9.1 Case 1 Mesh grid size.

FIGURE 9.2 Case 2 Mesh grid size.

FIGURE 9.3 Case 3 Mesh grid size.

Conclusion
In conclusion, the simulation successfully showcase the flow behavior in a Backward-Facing step. Post-processing the simulation, it was observed that adverse pressure gradient was developed after initial conditions which causes the flow to seperate and form a vortex in the recirculation region.