Flow over a Backward-Facing Step (BFS) using Converge CFD
Flow over a Backward-Facing Step (BSF) using Converge CFD
Objective
The objective of this project is to simulate a Backward Facing Step using Converge CFD for three different mesh sizes and compare the results between them.
The different base mesh sizes are-
- Case 1: dx=2e-3m, dy=2e-3m, dz=2e-3m
- Case 2: dx= 1.5e-3m, dy=1.5e-3m, dz=1.5e-3m
- Case 3: dx= 1e-3m, dy=1e-3m, dz=1e-3m
Although the above objective is the primary specified purpose of this project, the project is also about learning the case set up in CONVERGE CFD. The Backward-Facing Step is considered by most as the ideal canonical separated flow geometry because of its single fixed separation point and wake dynamics unperturbed by the downstream disturbances. Therefore, it is also important to learn about flow simulation over a BFS.
Backward-Facing Step (BSF)
A Backward Facing Step is a representative model for separation flows. It can be widely applied in engine flows, vehicles (cars, boat), heat transfer systems, condensers, aerodynamic flows (airfoil, spoiler, high attack angle process) and even the flow around buildings, etc. Depending on the BFS geometric design, inlet and outlet conditions, turbulent intensity, as well as heat transfer conditions, the flow separation occurs after a simple stage and introduces a separation bubble formation, evolution and re-attachment process.
It is a basic model involving the most important features of a separated flow- a free shear flow separation, vortex generation, and re-attachment.
The Backward-Facing Step is also called as “ sudden expansion flows”, “back-step flow”, “circular expanding flow” or “diverging channel”. It is an important model for separation flows across wide range of Reynolds numbers.
A BFS includes an inflow of uniform velocity, laminar or turbulent, from a channel to a step on either side or both sides, with a step height of ‘h’. The flow field is divided into four regions as shown in the figure above, namely- separated shear layer, the recirculation region under the shear layer, the reattachment region, and the attached/ recovery region.
The large separation vortices occur in the backward step region, with small vortex in the corner. As instabilities occur, the vortices in the shear layer roll up and pair with the adjacent vortices to form coherent structure. The vortices trigger recirculation. Then, due to the presence of adverse pressure gradient in the wake of the step, the free shear layer reattaches at the bottom wall.
Pre-Processing
Case Set-up
It will be beyond the scope of this report to explain all the settings selected; therefore, only important settings are mentioned here.
Application:
- General Flow
Materials:
- Predefined Mixtures: Air, select Reaction Mechanism
Simulation Parameters
- Run Parameters>Solver> Pressure-based steady solver
- Start time: 0 cycles
- End time: 15000 cycles
- Initial time-step: 1e-6 s
- Minimum time step: 1e-6 s
- Maximum time step: 1 s
Initial Conditions & Events
Regions and Initialization
- Add>rename to Volumetric region
- Pressure: 101325 Pa
- Species> Air: O2=0.23, N2=0.77
Boundary Conditions
It is a good practice to define boundary conditions after Initial conditions and events.
- Inlet: Inflow 110325 Pa Air
- Outlet: Outflow 101325 Pa Air
- Top-bottom-walls: Wall
- Front 2D: TWO_D
- Back 2D: TWO_D
Base Grid:
This is where inputs are given to create mesh for the analysis. As described in the objective following inputs are given and changed after each run to create the mesh in dx, dy and dz directions-
- Case-1 (2.0e-3, 2.0e-3, 2.0e-3)
- Case-2 (1.5e-3, 1.5e-3, 1.5e-3)
- Case-3 (1.0e-3, 1.0e-3, 1.0e-3)
Fixed Embedding
Fixed embedding is used to refine the mesh around the desired regions. In this case, the regions of interests are the inner walls of the channel. Therefore, the the fixed embedding is applied with the scale of 1 and 1 embedded layer.
Output files:
Time interval to write 3D output data files- 1000.0 cycles
This means that after every 1000 cycles, 3D output data files will be written and saved. Since we are running the simulation for 15000 cycles, we shall have 15 3D output data files.
Running the Simulation
Once the preprocessing is done, the input files are exported and saved. This allows to use external solvers, in this case Cygwin, to solve the problem using these input files.
The command for the Cygwin to execute the solving process is shown below-
mpiexec.exe -n 2 converge.exe logfile &
This command helps in solving the problem in parallel using 2 cores. I have defined 2 cores for solving in parallel based on my system configuration. This command also helps in solving the problem in background processes which can be verified by using Task Manager.
When large simulations are being run, the logfile helps in saving all that data which can be retrieved to view in Notepad, in case the simulation crashes or the computer system shuts down abruptly, or just to view the results afterwards.
Results
Mesh
Case 1= 2.0e-3 m
Case 2= 1.5e-4 m
Case 3= 1e-4 m
Mass Flow Rate
Velocity Contours
Case 1=2.0e-3 m
Case 2=1.5e-3 m
Case 3= 1.0e-3 m
Pressure Contours
Case 1=2.03e-3 m
Case 2= 1.5e-3 m
Case 3= 1.0e-3 m
Total Cell Count
Velocity Plots
Case 1, at x=0.13 m
Case 2, at x=0.13 m
Case 3, at x=0.13 m
Pressure Plots
Case 1, in X direction
Case 2, in X direction
Case 3, in Y direction
Discussion and Conclusion
Flow in a BFS
Let’s look at what how flow occurs as obtained from the simulation. The general characteristics of a BFS flow begins when the upstream boundary layer separates at the step edge because extensive momentum diffusion occurs and an adverse pressure gradient is developed into a thin shear layer. Now because the shear layer contains amalgamated turbulent structure within, it grows as the flow progresses downstream.
The turbulent structures in the shear layer catch irrotational fluid from the non-turbulent region and this causes the formation of a low velocity recirculation in the region between the shear layer and the wall.
There is a primary vortex in the center and a secondary and small vortex in the corner of the step. As the entrained fluid creates a favorable pressure gradient, the shear layer curves down towards the wall. This point where the fluid impinges the wall is called reattachment zone.
The reattachment length is the distance between the step and the reattachment point. This length is unsteady because of inherent oscillatory motion of the shear layer, known as flapping.
These three regions, the shear layer region, recirculation region and reattachment zone in a whole comprise the important features of the BFS. Altering or controlling these regions can provide a desirable outcome such as, enhanced mixing characteristics, reduced drag, noise and vibrations. Hence it is imperative to understand the flow dynamics in the BFS.
Velocity Plots
The above velocity profile was plotted at four different distances in X direction- 0m, 0.13m, 0.18m, and 0.27m and covered the entre length of the Channel in Y direction.
It can bee seen that Velocity at x=0 is constant with no disturbances. It is obvious as the step has not reached yet. The velocity near the outlet is less than the velocity at inlet which can be seen when we compare the two (black at inlet, blue at outlet). This is also obvious as the area increases after step.
We know that pressure is inversely proportional to velocity. If the velocity decreases, pressure has increases. This can also be observed from the velocity and pressure contours.
But the most interesting part is between the length x=0.18 and x=0.27(outlet). The reattachment takes place in this region. The boundary layer recovers after reattaching. The reason we see negative velocity at x=0.18 is because that region is still very close to recirculation region. We can see that outlet velocity is that inlet, but it is not negative. This means that flow has recovered before outlet.
At x=0.13, this is region closest to the step and this is where flow separation occurs. Therefore, we see negative velocity (recirculation) at Y=0 and max velocity Y=0.014m, where flow separation occurs and shear layer.
Pressure Plots
Pressure profiles are plotted along the longitudinal direction. We can see a gradual drop in pressure from inlet until the step is reached. Velocity is constant until the step. But as soon as the step appears, there is a sudden flow separation and we can observe a steep rise in pressure. Pressure is highest at the outlet.
Total Cell counts
It is obvious now that as we decrease the base grid size, the total cell count increases. It is highest in case 3. The finer mesh can capture the flow accurately than a coarser mesh, but it is intensive on resources. Also, the fixed embedding could be increased to better capture the flow characteristics.
Mass conservation
We can observe that the mass conserved in all the cases as their sum will be equal to zero.
Animation- Flow over a Backward-Facing Step
References
- Chen, L., Asai, K., Nonomura, T., Xi, G. and Liu, T. (2018). A review of Backward-Facing Step (BFS) flow mechanisms, heat transfer and control. Thermal Science and Engineering Progress. [online] Available at: https://www.sciencedirect.com/science/article/abs/pii/S2451904918300167 [Accessed 1 May 2019].
- Rajasekaran, J. (2011). On the Flow Characteristics Behind a Backward-Facing Step and the Design of a New Axisymmetric Model for their study.