Week 3: Flow over a backward facing step

In this report, I will be simulating a channel flow in a domain of the dimensions: 0.1m long, 0.1m tall and the wideness of the domain is infinity (the flow does not vary across the z axis) for 3 different mesh sizes.

Geometry Creation

The geometry can either be created manually using converge or it can also be imported from another CAD software, in my case I imported the simple geometry.

This is the final geometry seen in converge

Case Setup

Now, on to the case setup tab:

Application Type

Materials: Gas Simulation, Global Transport Parameters and Reaction Mechanisms were set to default. In species, O2 and N2 were added.

Simulation Parameters

Note: a maximum convection CFL limit is required else the solution will never form.

Boundary Conditions

Inlet: 110325.0 Pa

Outlet: 101325.0 Pa

Top ,Lower and Bottom walls: No-Slip, zero normal gradient

Front and Back: TWO_D

Initial Conditions

Physical Models

Turbulence was checked as vortices are formed due to turbulence, also RNG k-epsilon was chosen as the model.

Grid Control

This is the step were sizes of each element is provided. 3 sizes were used in this analysis, they are:

• dx = dy = dz =2e-3 m
• dx = dy = dz =1.5e-3 m
• dx = dy = dz =1.0e-3 m

Another option, fixed embedding was enabled for this simulation to ensure more cells are used for processing near the walls

Output/Post Processing

The time interval for writing 3D input files can be changed later on to obtain atleast 100 files, depeneding on when the solution converges.

Now, our case setup is complete. The files will be exported into a folder using the Files Export tool (File -> Export->Export input files)

In total 12 files were exported, these are:

These files contain all the necessary information for the simulation.

Running the Simulation

1. Open cygwin

2. Navigate to directory where case files were exported

3. Run the following command

mpiexec.exe -n 4 "C:\Program Files\Convergent_Science\CONVERGE\3.0.16\bin\intelmpi\converge.exe" restricted </dev/null> logfile.txt &

This will take a while, you can view the progress in task manager. CPU usage is usually maxed out.

Once CPU usage drops from 100%, the output files are generated. To view them in paraview, we must export them to a format which is supported by paraview.

Go to 3D-post processing in converge,

Post-Processing

In Paraview

Import these files into paraview

The required plots/animation are generated

In converge

Go to Line plotting, select the case folder and plots can be viewed

Outputs and Plots for each Case

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

This is the Grid Control values used for this case:

1. Velocity and Pressure Contours

These were taken in paraview.

Inlet Pressure is higher at the enterance of the channel, as expected due to the boundary condition. It then sharply drops in the region around the backward step and then increases slightly towards the outlet of the domain.

Velocity plot is as expected as well. Flow is initially pseudo-laminar before the backward step, then it becomes turbulent. A low velocity zone is observed just below the flow near the step. This is caused by vortices. The flow is the lowest near the walls (due to boundary layer effect) and increases gradually, the maximum value of velocity is seen at the center of the domain. After the step, the flow dissipates due to its turbulent nature

This shows the velocity distribution across the domain at the outlet, this shows a flow which is developing to turbulent flow, from laminar. The distribution is not smooth because of the number of cells used for this case (which is very low). Maximum velocity is around 50m/s

2. Mesh

This was taken in paraview.

The mesh is less fine as grid spacing is relatively high for this case. Also, we can notice the mesh sizes are smaller near the walls, this is because of the earlier "Fixed Embedding" option under Grid Control.

3. Velocity, Pressure, MassFlowRate and Cell Count Plots

This was taken in converge -> Line plotting

Velocity at the inlet is negative since flow enters the domain is considered negative, while velocity at the outlet is positive. The abosolute values of the velocities differ so much because, at the inlet where the area of the domain is lower, velocity magnitude is faster. At the outlet, where area is larger so the flow is more spread across the area. The velocities initially start from 0 and slowly approach the true value as the solution nears the true value.

Pressure at the inlet stays constant because of the boundary condition, and outlet pressure actually increases slightly to compensate for mass conservation.

Mass flow rate at the inlet is negative since flow enters the domain is considered negative, while mass flow rate at the outlet is positive. Both masses' abosolute values are roughly the same throughout the simulation showing that mass conservation is followed. The masses initially start from 0 and slowly approach the true value as the solution nears the true value.

Cellcount, all values remain constant as expected, the total cell count is 1943, and number of cells solved by each core is also seen.

5. Animation

https://youtu.be/N4Vj7-DFq2M

The domain appears pixelated due to the low number of cells used for this case, vortices formation can be seen as the flow moves over the backward step, the flow before the step is pseudo-laminar and transforms to turbulent while the velocity decreases as area increases.

Case 2: dx = dy = dz =1.5e-3 m

This is the Grid Control values used for this case: 

1. Velocity and Pressure Contours

These were taken in paraview.

Inlet Pressure is higher at the enterance of the channel, as expected due to the boundary condition. It then sharply drops in the region around the backward step and then increases slightly towards the outlet of the domain.

Velocity plot is as expected as well. Flow is initially pseudo-laminar before the backward step, then it becomes turbulent. A low velocity zone is observed just below the flow near the step. This is caused by vortices. The flow is the lowest near the walls (due to boundary layer effect) and increases gradually, the maximum value of velocity is seen at the center of the domain. After the step, the flow dissipates due to its turbulent nature

This shows the velocity distribution across the domain at the outlet, this shows a flow which is developing to turbulent flow, from laminar. The distribution is not smooth because of the number of cells used for this case (which is very low). Maximum velocity is around 100m/s

2. Mesh

This was taken in paraview.

The mesh is relatively more fine as grid spacing is relatively low for this case. Also, we can notice the mesh sizes are smaller near the walls, this is because of the earlier "Fixed Embedding" option under Grid Control.

3. Velocity, Pressure, MassFlowRate and Cell Count Plots

This was taken in converge -> Line plotting

Velocity at the inlet is negative since flow enters the domain is considered negative, while velocity at the outlet is positive. The abosolute values of the velocities differ so much because, at the inlet where the area of the domain is lower, velocity magnitude is faster. At the outlet, where area is larger so the flow is more spread across the area. The velocities initially start from 0 and slowly approach the true value as the solution nears the true value.

Pressure at the inlet stays constant because of the boundary condition, and outlet pressure actually increases slightly to compensate for mass conservation.

Mass flow rate at the inlet is negative since flow enters the domain is considered negative, while mass flow rate at the outlet is positive. Both masses' abosolute values are roughly the same throughout the simulation showing that mass conservation is followed. The masses initially start from 0 and slowly approach the true value as the solution nears the true value.

Cellcount, all values remain constant as expected, the total cell count is 2994, and number of cells solved by each core is also seen.

5. Animation

https://youtu.be/vOdbYCL_iFs

The domain appears pixelated due to the low number of cells used for this case, vortices formation can be seen as the flow moves over the backward step, the flow before the step is pseudo-laminar and transforms to turbulent while the velocity decreases as area increases.

Case 3: dx = dy = dz =1.0e-3 m

This is the Grid Control values used for this case: 

The results of this case are interesting, it seems the solution is on the verge of instability as the velocities are quite high and the grid size is quite low as well. This causes the CFL number to cross 1.

1. Velocity and Pressure Contours

These were taken in paraview.

Inlet Pressure is higher at the enterance of the channel, as expected due to the boundary condition. It sharply increases near the backward step.  It then decreases slightly towards the outlet of the domain.

Flow velocity is so high in this case, the flow is turbulent throughout. A low velocity zone is observed just below the flow near the step. The flow does not dissapate due to the very high speeds, and hence flow seperation is minimal.

This shows the velocity distribution across the domain at the outlet, there are 2 distinct flows, one major flow of a peak velocity of about 120 m/s and a minor flow with a peak velocity of about 25m/s.

2. Mesh

This was taken in paraview.

The mesh is relatively fine as grid spacing is least for this case. Also, we can notice the mesh sizes are smaller near the walls, this is because of the earlier "Fixed Embedding" option under Grid Control.

3. Velocity, Pressure, MassFlowRate and Cell Count Plots

This was taken in converge -> Line plotting

Velocity at the inlet is negative since flow enters the domain is considered negative, while velocity at the outlet is positive. The abosolute values of the velocities differ so much because, at the inlet where the area of the domain is lower, velocity magnitude is faster. At the outlet, where area is larger so the flow is more spread across the area. The velocities initially start from 0 and slowly approach the true value as the solution nears the true value, the wobbleness of the values is due to impending instablity of the solution.

Pressure at the inlet stays constant because of the boundary condition, and outlet pressure actually increases slightly to compensate for mass conservation. The wobbleness of the values is due to impending instablity of the solution.

Mass flow rate at the inlet is negative since flow enters the domain is considered negative, while mass flow rate at the outlet is positive. Both masses' abosolute values are roughly the same throughout the simulation showing that mass conservation is followed. The masses initially start from 0 and slowly approach the true value as the solution nears the true value, the wobbleness of the values is due to impending instablity of the solution.

Cellcount, all values remain constant as expected, the total cell count is 1943, and number of cells solved by each core is also seen.

5. Animation

https://youtu.be/WhM0pRysTUI

The flow is turbulent throughout the entire video, since velocity is so high there is barely any seperation of flow.