Week 3: Flow over a backward facing step

Aim:

To simulate the turbulent flow of air in a backward-facing step for different base grid sizes and draw suitable conclusions.

Theory:

The separated flow generated as the fluid passes over a backward-facing step is of interest for a variety of reasons. First, separated flows produced by an abrupt change in geometry are of great importance in many engineering applications. Also, the backward-facing step is an extreme example of separated flows that occur in aerodynamic devices such as high-lift airfoils at large angles of attack. In these flows, separation may be created by a strong adverse pressure gradient rather than a geometric perturbation, but the flow topology is similar. Secondly, from a fundamental perspective, there is a strong interest in understanding instability and transition to turbulence in non-parallel open flows. Hence, transition mechanisms in parallel flows such as plane channels and pipes have received substantial attention.

The general characteristics of the backward-facing step flow begin with an upstream boundary layer separating at the step edge due to the adverse pressure gradient that develops into a thin shear layer. The size of the shear layer increases downstream. It consists of many vortices and further vortices start merging together to form larger vortices. The shear layer becomes the shear zone when the size of the shear layer increases due to vortices, and coherent structures. Finally, the separated flow attaches to the bottom of the BFS when a favorable pressure gradient is obtained. The point of reattachment is known as the reattachment point. The distance between the wall of the step and the reattachment point is known as the reattachment length. The location of the reattachment point is unsteady due to the inherent oscillatory motion of the shear layer. Hence, the reattachment zone is formed in which the reattachment point can be present. The turbulent structures in the shear layer entrain irrotational fluid outside the shear zone. This creates low-velocity circulation between the step wall and the shear zone. This leads to the formation of the recirculation zone. The recirculation zone is mainly comprised of a primary vortex in the center and a secondary vortex adjacent to the corner of the step.

Geometry:

• Creating a geometry using the creation tool of Converge Studio.
• Running diagnosis to check if there are any open edges or faces.
• Checking the orientation of Normals, The normal should be such that their orientation is pointing towards the fluid flow.

The length of the backward-facing channel is 0.272m, and the dimensions of the inlet and outlet are 0.01m and 0.02m respectively. Since we are performing a 2D simulation on the given backward-facing step, the length of the channel in the z-direction is not important. The faces of the geometry are given different names(inlet, outlet, front_2d, back_2d, and top_bottom) so that the boundary conditions can be provided easily.

Boundary Flagging:

The boundaries are flagged. The converge studio basically uses triangular blocks to create geometry, but here we used by angle method for boundary flagging.

• Inlet
• Outlet
• Top and Bottom Walls
• Front2D
• Back2D

Case Setup: 

• Application Type = Time-based
• Materials- Air
• Gas simulation is checked. The species are O2 and N2

Simulation Parameter:

In Run Parameters- two main things to be considered 

(a) Select the following solver settings.

Steady-State Monitor:

Simulation Parameters:

Solver Parameters[Steady-State]

Boundary Conditions:

Regions and Initialization:

Physical Models: Uncheck Turbulence Modeling in this Case.  

Grid Control:

Fixed Embedding:

Post Variable Selection:

Output Files:

• Once the case setup is complete all the input files are exported to a specific folder
• Then Cygwin is used to solve the inputs and once the simulation is complete converge converts the result data into a format that can be read by Paraview.
• Post-processing is done in Paraview.

Results:

Case1: mesh grid size= 2e-3m

Mesh:

Average velocity:

Total pressure:

Mass flow rate:

Case2: Mesh grid size= 1.5e-3m

Mesh:

Average velocity:

Total pressure:

Mass flow rate:

Case3: Mesh grid size= 1e-3m 

Mesh:

Average velocity:

Total pressure:

Mass flow rate:

Conclusions:

The flow simulation of air was performed on the backward-facing step for 3 different mesh sizes and the following conclusions can be drawn:

• The air flows from the inlet to the outlet. The velocity of air is higher at the inlet than at the outlet. This is because of the backward-facing step, which changes the geometry of the fluid domain.
• Due to the backward-facing step, there is a pressure drop near the step, this causes some fluid particles to flow in the reverse direction, which creates vortices. This can be clearly seen in the vector plot.
• With the increase in the number of grid elements, the solution obtained becomes more and more accurate. The flow properties are captured more accurately if the mesh is more refined. This is the reason for the introduction of embedded layers which improves the accuracy of the solution near the walls. In general, the smaller the element size, the more accurate is the solution obtained.
• With the increase in the number of cells, the solution becomes more accurate but the computation time increases considerably. Hence, the problem must be studied thoroughly before performing the simulation and it must be decided how much are we willing to compromise the accuracy of the solution to save resources.