FLOW OVER A BACKWARD FACING STEP

by Ashraya Band

28^th June 28, 2019

Course: Advanced CFD for IC Engine Applications

Instructor : V.Sarangarajan

Introduction

Backward facing-step (BFS) has been a benchmark geometry for numerical and experimental turbulent flow study. Complex turbulent flow occurring in many engineering and industrial conditions that involve heat transfer; sudden expansion causing recirculating, flow separation, large pressure gradient, and mixing, recirculating flow. These can be represented in BFS geometry, both experimentally and numerically.

There are many geometrical aspects to a BFS, most of them being Non-Dimensional Parameters like Step Height, Upstream Height, Expansion ratio, and Total Length which are needed to be standardized.

This report aims to investigate the Flow of Air in the BFS and discuss variations in the Flow Parameters for different grid Sizes .

Literature Review

Backward-facing step is a simple geometry where the flow experiences several conditions described in Figure .

Figure 1. Flow Characteristics Over a BFS

This flow schematic is simplified to

Figure 2. Simplified representation of Flow over BFS

Upstream velocity at the inlet side, and downstream velocity at the outlet side. During this condition, the fluid may flow through the expansion zone when the height of the channel is increased. Recirculation vortexes occur at the inner side and get smaller up the reattachment point. Recirculation is mainly caused by unbalance forces and seen by the formation of rotational vortexes or forced vortexes. On BFS, the recirculation vortexes is highly dependent on edge step and height . At the end of the recirculation Zone , reattachment of the wake occurs. The reattachment length increases with increased expansion ratio . Generally, recirculation zone and reattachment point are frequently used as representative parameters of the flow on the BFS geometry.

Both recirculation zone and reattachment point are greatly influenced by the BFS geometry comprising step height (h), upstream height (H), and expansion ratio ((H+h)/H). The total length (L) tends to be insignificant if it is designed to be more than the minimum length.

Objective

To Simulate Air Flow through a Backward Facing Step for 3 different Mesh Sizes and Compare the Results.

Mesh Sizes to Compare:

Case 1: dx = dy = dz = 2e-3m

Case2: dx = dy = dz = 1.5e-3m

Case3: dx = dy = dz = 1.2e-3m

Approach

In order to setup a Simulation in Converge we have to Follow Steps:

_Pre Processing_

Setting up the Geometry :

We shall Create our Geometry with the help of Create option in the Geometry Tab by means of Create through Vertices .

-

Figure 3. Vertices Of One Face of the Geometry & triangles cretaed at one face of the geometry.

Then we shall loft the edges of our geometry along the open edges and Patch the Open Edges . Thus we get the geometry of BFS as depicted .

-

Figure 4. Lofted geometry

Figure 5. Patched Geometry

Setting up Boundaries:

For the Channel we need to set up 5 Boundary Conditions :

Inlet : Where the flow will enter, we have to select the 2 Triangles to setup the Initial BC.

Outlet: Where the flow shall exit

Top and Bottom Walls : The Walls of the Channel.

Front 2D

Back 2D

Figure 6 : Boundary determination

We have to group Boundaries into Volumetric Regions.

#Case Setup :

Application:Material

Since our case is of a normal form , Follow : General Flow-> Done.

Material

Gas Simulation

Global transport Parameters

Reaction Mechanism

Run Parameters:

Simulation Mode - Full Hydrodynamic

Gas Flow Solver - Compressible

Solver:

Since the flow is Simple and gets steady ie. It reaches a Pseudo Steady State , Therefore we use Steady Solver , in our case the Pressure Based Steady Solver .

Simulation Parameters:

For CFL we take the small value for CFL , for the larger value of CFL the solution might blow up .

Turbulence Model:

For the Turbulence we select RNG k Ꜫ.

Grid Control:

We set the Base Grid according to our Objective for 3 Cases.

Case 1: dx = dy = dz = 2e-3m

Case2: dx = dy = dz = 1.5e-3m

Case3: dx = dy = dz = 1.2e-3m

We select Fixed Embedding to refine the geometry at the walls by the scale of 1 and Embedded Layer 1.

Case Setup Complete :

All the check box has been checked , which means the Case has been setup Properly.

_Running the Simulation_

After setting up the Geometry Export the files to set up a Simulation in CYGWIN.

We navigate to the saved directory and run the simulation using the commands as depicted.

In my case , 4 processors are used .

After Successful Simulation convert the " post.out " files to " .case " files through ENSIGHT.

The " .case " files must be opened in ParaView to view the Simulation .

_Post – Processing_

The exported files can be visualized in the ParaView.

In the Converge Line Plotting we can visualize our data in the form of graphs , same is included for different cases .

Graphs and Discussions:

• Mesh : obtained for different cases

Case 1: dx = dy = dz = 2e-3m

Case2: dx = dy = dz = 1.5e-3m

Case3: dx = dy = dz = 1.2e-3m

Figure 7 : Mesh Size

Explanation:

It can be clearly seen in the mesh above for the 3 cases that the more we decrese the grid size the number of cells increases in our geometry .

At the walls we can see the Fixed Embedding which is the refining of geometry at the boundaries.

_____

Below ,the plot shows the number of Total cells required for the simulation by the Processors , in our case 4 Processors.

• Total Cell Count:

Case 1: dx = dy = dz = 2e-3m

Count - 83253

Case2: dx = dy = dz = 1.5e-3m

Count - 142272

Case3: dx = dy = dz = 1.2e-3m

Count-222916

Figure 7: Total Cell Counts

Explanation:

Count Case 1- 83253 , Count Case 2- 142272, Count Case 3- 222916

we can see that as the grid gets more fine the number of cells required to compute or complete the simulation increases with the decrease in base grid .

• Velocity Contour :

Case 1: dx = dy = dz = 2e-3m

Case2: dx = dy = dz = 1.5e-3m

Case3: dx = dy = dz = 1.2e-3m

Figure 8 :Velocity Contour

Explanation:

As the grid gets fine we obtain a smoother and more detailed contour of Velocity . The boundaries can be clearly seen , the vortex are more visible with refined mesh .

Glyph :

Figure 9 : Glyph Mode

The above diagram is a glyph mode in ParaView which shows the direction of vectors - Velocity , we can observe that in the Upstream area- the flow is uniform (ref Fig 2) , In the DownStream Area the Recirculation can be observed at the Step (The Velocity Vector's Recirculates ) and the vortex formed gradually get shredded .

• Velocity Profile :

Case 1: dx = dy = dz = 2e-3m

Case2: dx = dy = dz = 1.5e-3m

Case3: dx = dy = dz = 1.2e-3m

Figure 10 : Velocity Profile

Explanation: In the above Velocity Graph we observe that the velocity curve is drops initially , this is because of the recirculation at the step where the velocity drops due to vortex formation . then the velocity increases and again drops due to shear at wall.

• Pressure Counter :

Case 1: dx = dy = dz = 2e-3m

Case2: dx = dy = dz = 1.5e-3m

Case3: dx = dy = dz = 1.2e-3m

Figure 11: Presuure Contour

Explanation:

As it can be seen that the Pressure drops and increases (Observe the color hue and compare with the scale) mostly at the step and other region where it displays the vortex .

With finer grid we get more detailed view of the pressure variance .

• Total & Static Pressure Graph at Inlet /Outlet Boundary

Case 1: dx = dy = dz = 2e-3m

Total__:

Static_:

Case2: dx = dy = dz = 1.5e-3m

Total_:

Static_:

Case3: dx = dy = dz = 1.2e-3m

Total_:

Static_:

Figure 12 : Pressure graph at Boundary Inlet and Outlet

Explanation:

We observe that the Pressure is fluctuating at respective boundary ie because of the pressure drop at step ( recirculation region ) vortex formation and shear near the wall .

• Mass Flow Rate at Inlet /Outlet Boundary

Case 1: dx = dy = dz = 2e-3m

Case2: dx = dy = dz = 1.5e-3m

Case3: dx = dy = dz = 1.2e-3m

Figure 13 : Mass Flow rate graph at Boundary Inlet and Outlet

Explanation:

Above we observe the law of conservation of Mass ie the mass entering and leaving are same , there is disturbance which due to the fact that there is sudden opening in the channel .

• Velocity at Inlet/Outlet Boundary

Case 1: dx = dy = dz = 2e-3m

Case2: dx = dy = dz = 1.5e-3m

Case3: dx = dy = dz = 1.2e-3m

Figure 13 : Velocity graph at Boundary Inlet and Outlet

Explanation:

Here we observe the fluid velocity at respective Boundary i.e Inlet and Outlet . We observe certain fluctuation over the cycles which is due to the fact that the fluid experiences vortex formation where the velocity drops and also at the walls the velocity drops or is negligible . Over the period of cycles the velocity becomes stable.

Conclusion:

With the help of Backward Facing Step Geometry we were able to analyse the variations in Velocity . Mass Flow rate , Pressure . This becomes significant at the step where Recircualtion and Vortex Formation occurs . We observed the law of conservation of mass , the mass entering and leaving ws same .

As we increase the number of cells by decreasing the grid size we get accurate results but the computation time increases .

More analysis can be done for different turbulence model .

.