Flow over Backward Facing Step

OBJECTIVE

The objective of this study is to set up flow simulation within a 2D backward facing step and understand the dependency of grid size on simulation time and results. The project includes the key results for three simulations setups based on the three different grid sizes given below in the table

Case	Grid Size, dx (m)	Grid Size, dy (m)	Grid Size, dz (m)
Case 1:	dx = 2.0e-4 m;	dy = 2.0e-4 m;	dz = 2.0e-4 m
Case 2:	dx = 1.5e-4 m;	dy = 1.5e-4 m;	dz = 1.5e-4 m
Case 3:	dx = 1.0e-4 m;	dy = 1.0e-4 m;	dz = 1.0e-4 m

The simulation process includes three major steps:

1. Preprocessing

1.1. Geometry Import

1.2. Diagnosis

1.3. Boundary Flagging

1.4. Case Setup

2. Solving

3. Post Processing

3.1. Mesh

3.2. Plots (Mass Flow, Pressure, Velocity, Iteration Error)

3.3. Velocity Gradient Plot

3.4. Contours (Velocity, Pressure)

PROCEDURE:

The procedure followed for setting up the simulation is provided below

1. Preprocessing

1.1. Geometry Import

The geometry provided was imported by dragging and dropping the file in the converge studio window

Fig: Geometry (All dimension are in m)

1.2. Diagnosis: The diagnosis tool helps in identifying the different problems in the geometry.

The Diagnosis tool looks for the following geometric issues

a. Intersection: Highlights number of triangles with piercing inbetween adjacent two triangles

b. Nonmanifold Vertices: Checks for number vertex which are being shared between two triangles

c. Open Edge: This highlights the number of edges of a triangle which not shared by any other triangle

d. Normal Orientation: This highlights the number of traingles whose normal vector is not pointing towards the interior of fluid domain

e. Isolated Triangles: This checks for the number of triangle surrounded by any neighbouring triangles that have different boundary ID number

Goto Diagnostics Dock>Find>

Since all the problem traingles are green ticked it means there are no issues in the geometry

1.3. Boundary Flagging:

a. Goto Boundary>Flag>Create a New Boundary>Create Multiple Boundary>Enter 5 in "Number of Multiple Boundaries"

b. Selected the triangles at different faces and assign to respective boundaries as per the provide below

1.4. Case Setup:

a. Clicked on "Begin case Setup" and entered the value provided below

Settings	Values to be Entered
Application	General Flow
Material	Select Air (predefined mixture) Gas simulation>No Change Global Transport Paramters>No Change
Simulation Parameters	Run Paramters> Pressure-based steady solver Simulation Time Parameter> Start Time: 0 End time: 15000 cycles Initial time step: 1.0e-6 s Minimum time step: 1.0e-6 s Maximum time step: 2.0 s Solver Parameters> No Change
Boundary Conditions	Inlet> Boundary Type- INFLOW>Pressure Boundary Condition>Specified Value (DI)-110325 Pa> Species Boundary Condition> Air Outlet>Boundary Type-OUTFLOW>Pressure Boundary Condition>Specified Value (DI)-101325 Pa>Species>Backflow>Air Back>Boundary Type-TWO_D Front>Boundary Type-TWO_D TopBottomWall>Boundary Type-WALL>Velocity Boundary Condition>Wall Motion Type-Stationary>Law of Wall>Temperature Boundary Condition>Law of Wall>300k Assign Region 0 to all the boundaries
Initial Conditions & Events	Regions and Initialization Add region>"Region 0" Enter Pressure value:101325Pa Enter Temperature: 300K Species: Add Air
Physical Models	Turbulence Modeling-RNG-K Eplison is selected
Grid Controls	Enter the grid values for (dx, dy, dz) as per the case 1 dx = 2.0e-4 m, dy = 2.0e-4 m, dz = 2.0e-4 m similarly for Case 2 & 3 the following values were used sequentially Case 2: dx = 1.5e-4 m; dy = 1.5e-4 m; dz = 1.5e-4 m Case 3: dx = 1.0e-4 m; dy = 1.0e-4 m; dz = 1.0e-4 m Activate Fixed Embedding from the menu Fixed Embedding-Add Embedding>Entity Type-Boundary Boundary Type- TopBottomWall Mode>PERMANENT Scale> Enter a value of 1 Ember Layer>Enter a value of 1
Output/Post Processing	Post Variable Selection>No change
Output Files	Time Interval for writing 3D output data files: 100 cyc Time Interval for writing text output: 1.0 cyc Time Interval for restarting output: 1000 cyc

After this all the input files was imported to a seperate folder. Converge creates .txt files which contains all the values entered while setting up the case for respective settings done above. These input files will be processed by converge using Message Passing Interface (MPI) standard

2. Solving:

For running the simulation, Cygwin tool was used instead of converge studio interface. Cygwin is a POSIX-compatible API which is based on command prompt is used to run the simulation

Steps:

a. Navigated to the folder location containing the input files

b. Enter the command> mpiexec.exe -n 2 converge.exe </dev/null> logfile &

c. Enter the command> taif -f logfile

d. After the simulation is over. Went back to converge studio>Post-Processing 3D

e. Enter Case Name>"Test", Change the File Type to Paraview VTK in-line binary format

d. Enter the address for the output files>Select all files>Select all Cell Variables>click on Convert

e. After the conversion of the post files to the binary output, open the Test.vtm (group file) file in Paraview

3. Post-Processing:

3.1. Meshing:

Fig: Cell Count (Case 1, 2 & 3)

Fig: Case 1: Mesh View

Fig: Case 2: Mesh View

Fig: Case 3: Mesh View

3.2. Plots

Iteration Error Plots

Fig: Case 1: Iteration Error Plots

Fig: Case 2: Iteration Error Plots

Fig: Case 3: Iteration Error Plots

Inference: The above graphs depict the error values in the calculation of Momentum, Energy and Pressure. The smoothening of the graph towards the end of cycle time represent that the solutions are converged

Mass Flow Rate Plots

Fig: Case 1: Mass Flow Rate Plots

Fig: Case 2: Mass Flow Rate Plots

Fig: Case 3: Mass Flow Rate Plots

Inference: From the above the graphs it can be said that the mass is conserved, i.e., the magnitude of inlet mass flow rates and outlet mass flow rates are alternate in nature

Velocity Plots

Fig: Case 1: Velocity Plots

Fig: Case 2: Velocity Plots

Fig: Case 3: Velocity Plots

Inference: The graphs above represent the velocities at inlet and outlet, towards the end of the cycle the fluctuations reduces as the solution gets converged. The positive inlet velocity vector and negative outlet velocity vector showcases the law of conservation of mass

Pressure Plots

Fig: Case 1: Pressure Plots

Fig: Case 2: Pressure Plots

Fig: Case 3: Pressure Plots

Inference: The pressure at inlet is constant thorughout the iteration cycle, however, at the outlet the magnitude of pressure is near to 101500 Pa at the initiation however at around 2000 cycle, the pressure reaches around 103500 Pa and thereafter remains steady as the flow gets converged.

Temperature Plots

Fig: Case 1: Temperature Plots

Fig: Case 2: Temperature Plots

Fig: Case 3: Temperature Plots

Inference: The plots showcases the temperature at inlet and outlet, the temperature at inlet reduces from 300k to 290.3k as the cycle progresses. The outlet temperature however first increases to 304.5k, then reduces to 290k, and finally reaches a steady value of 297.5k after the flow gets converged. The temperature fluctuations occur due to the drop in velocity as the area expands after the step, due to which temperature reduces and as the flow gets converged, the temperature reaches the steady state.

3.3. Velocity Gradient Plots (Along Y+)

Fig: Case 3: Velocity Gradient (Y Direction: Output 1)

Fig: Case 3: Velocity Gradient (Y Direction: Output 2)

Fig: Case 3: Velocity Gradient (Y Direction: Output 3)

Note: X=0.130 (Red Graph), 0.170 (Blue Graph), 0.230 (Green Graph)

Inference: To understand the velocity gradient along the y direction, three vertical line probes were constructed at X=(0.130, 0.170, 0.230) and the above plots were generated at output 1,2 & 3 (output 1, 2 & 3 were recorded during the flow initiation, developing and steady state). The plots generated showcases the velocity profiles with the

3.4. Contours:

Fig: Velocity and Pressure Contour Plot (Case 3-Output 1)

Fig: Velocity and Pressure Contour Plot (Case 3-Output 2)

Fig: Velocity and Pressure Contour Plot (Case 3-Output 3)

Note: Similar contours were achieved for case 2 and case 3, but with greater resolutions

Inference: During the flow initiation, at the position after the step, flow circulation is observed. The blue pressure glyphs showcases the lowering in the pressure at step area and as due to this, the air parcel proceeding this, experiences gradual increase in the pressure. The low pressure (pink glyphs) can also be observed proceeding from figures 1 (output1: observed near the step) to figure 3 (output 3: after the step).

Animation Link:

Key Conclusions

1.With the decrease in grid size the total cell increases and the flow profile becomes more refined as more number of the equations are solved

2. The magnitude of velocity reduces at the step area due to sudden expansion in the area of flow, as per continuity of flow equation which results to flow separation. This results to reduction in pressure and generates vortices due to recirculation.