Converge CFD Simulation of Flow Over a Backward Facing Step

Converge CFD Simulation of Flow Over a Backward Facing Step

Objective:

• To perform a CFD simulation of flow over a Backward Facing Step (BSF) using Converge CFD for three different mesh sizes.
• To generate Pressure and Velocity contours for all three cases and make a comparison between them.
• To plot a graph of Pressure and Velocity across the length of the channel (X and Y direction)

Backward Facing Step (BFS):

Backward-Facing Step (BFS) flow is one representative model for separation flows, which can be widely seen in aerodynamic flows (airfoil, spoiler, high attack angle process), engine flows, condensers, vehicles (cars, boat), heat transfer systems, and even the flow around buildings, etc. The flow separation after a simple stage will introduce separation bubble formation, evolution and re-attachment process, which is dependent on the BFS geometric design, the inlet and outlet conditions, turbulent intensity, as well as heat transfer conditions. In the past decades, it has been widely studied by various theoretical, experimental and numerical methods. Backward-facing step (BFS) is arguably the most used and benchmarked geometry for numerical CFD and experimental flow analysis which involves laminar flow, recirculating turbulent flow and turbulence model verification in 2-D and 3-D.

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 a 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 a small vortex in the corner. As instabilities occur, the vortices in the shear layer roll-up and pair with the adjacent vortices to form a coherent structure. The vortices trigger recirculation. Then, due to the presence of an adverse pressure gradient in the wake of the step, the free shear layer reattaches at the bottom wall.

Geometry:

Pre-Processing:

Case Set-up:

General Flow

Materials:

Predefined Mixtures: Air

Simulation Parameters

Solver: Pressure-based steady solver

Mode: Full Hydronic

Start time: 0 cycles

End time: 15000 cycles

Initial time-step: 1e-6 s

Minimum time step: 1e-6 s

Maximum time step: 2.0 s

Regions and Initialization

Add Region

Pressure: 101325 Pa

Species: Air - O2 = 0.23, N2 = 0.77

Boundary Conditions

Inlet: Inflow 110325 Pa Air

Outlet: Outflow 101325 Pa Air

Top-bottom-walls: Wall

Front 2D: TWO_D

Back 2D: TWO_D

Base Grid: Mesh in dx, dy and dz directions-

Case-1 (2.0e-3, 2.0e-3, 2.0e-3) m

Case-2 (1.5e-3, 1.5e-3, 1.5e-3) m

Case-3 (1.0e-3, 1.0e-3, 1.0e-3) m

Fixed Embedding

Fixed embedding is used to refine the mesh around the desired regions. In this case, the regions of interest are the inner walls of the channel. Therefore, the fixed embedding is applied with a 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.

Meshing Model:

The total count of cells increases as we decrease the size of the element and we can see it from the above plot i.e. ‘Total_Cells Vs. Cycles’. As we see that case-3 has the highest number of cell count i.e. 5800 (approx.) followed by Case-2 i.e. 3200 (approx.) and case-1 i.e. 1950 (approx.). The finer mesh can capture the flow accurately as compared to coarse mesh and, the fixed embedding of scale 1 across top and bottom wall in the above cases helps us to capture the flow more accurately into that regions.

Results:

• Mass Flow Rate

• Velocity Contours

Case-3

• Velocity Plots (at X = 0.13m along Y-direction)

• Pressure Plots (along longitudinal direction i.e. X-direction)

Discussion:

• Flow in a BFS

The general characteristics of a BFS flow begin 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 (1^st white spot from the left side)

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 the reattachment zone (2^nd white spot on the right side). The reattachment length is the distance between the step and the reattachment point. This length is unsteady because of the inherent oscillatory motion of the shear layer, known as flapping.

These three regions, the shear layer region, recirculation region and reattachment zone as 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.

• Pressure Variation

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. The pressure is highest at the outlet.

Animation-Channel Flow-Backward Facing Step

Velocity Profile: https://www.youtube.com/watch?v=4Y-K1_o71sQ&feature=youtu.be

Pressure Profile: https://www.youtube.com/watch?v=n9c2r8mov2Y&feature=youtu.be

Conclusion:

1. The total cell count increases as the base grid size reduced.
2. The computational time increases as the total cell count increased.
3. The total computational time can be reduced by running the simulation using parallel processors.
4. Due to initial given boundary conditions, we get a disturbance in the plots initially but eventually, we can get a steady-state i.e. converged result.
5. The higher the number of total cell count, the more the number of cycles is required for simulation to get a steady-state condition.
6. The Mass is conserved. The addition of inlet and outlet mass flow rate results in zero.
7. The velocity near the outlet is less than the velocity at the inlet this is because first, the area of the channel increases as we move from inlet to outlet and second, there is a decrease in velocity at the recirculation regions i.e. near step edge.
8. The pressure is inversely proportional to the velocity and there is an increase in it at the recirculation regions.