Week 3: Flow over a backward facing step

Aim:

• The main aim of the project is to simulate the flow over Backward Facing step using CONVERGE CFD in which the simulation is setup with three different meshing parameters assigned with certain inlet and outlet parameters.

• dx = dy = dz =2e-3m
• dx = dy = dz =1.5e-3m
• dx = dy = dz =1.0e-3m (If this is too much for your PC, use 1.2e-3m)

• To display the mesh for different base grid sizes
• To show the pressure and velocity contours
• To plot the velocity, pressure and mass flow rate of different mesh grid sizes.

Introduction:

Flow separation and reattachment parameters are involved in many industrial applications. Some examples of these conditions are flow over an airfoil, in channel flow in which the area increases suddenly at certain locations.

These locations determine the mass transport properties of the flow. For this type of analysis the flow past the backward facing step is considered as a standard test case as numerical and experimental studies have been done on this issue.

This case became a practice for numeric validation for computational fluid dynamics because of its simplicity in geometry and flow diagnostic technique.

The flow through the channel which enters from the left which is inlet, when reaches the step due to the sudden expansion of the flow channels, the pressure gradient exists, by which the flow detaches and recirculation zone is formed.

A turbulent boundary layer encounters a sudden back step, causing the flow separation. Later the flow eventually reattaches to the bottom wall.

Geometry setup:

The geometry setup is done by the following steps.

• Open Converge studio software and create a new project.
• The geometry is created using Vertices. The vertices should be created to draw the Backward Facing step using the "Vertex" Command present in the Geometry dock. Geometry dock --> Create -->Vertex --> enter the co-ordinates.
• Total of 7 vertices are created for the geometry.

• The vertices are joined using " From three Vertices" command

• The front side of the geometry which is created is copied at an offset of -0.025 in the "Z" direction.

• These faces are attached by using the "Loft edge" command. This command is implemented by selecting the first face and second face individually.

• Forming Boundaries: To create the boundary regions click on Boundary-->Flag-->Click on the "+" symbol to create boundaries.
• The boundaries can be created in two ways. The first way is by entering the unique boundary id and boundary name manually. The second way is by using the "Create multiple boundaries" option which enables us to create multiple boundaries at once. A total of 5 boundaries are created for our case. After the boundaries are formed, it is named as inlet, outlet, Top-Bottom-walls, Front 2D, Back 2D respectively. While assigning the specific regions to the named boundaries we have to make sure that we have selected the desired region's triangle.
• The named boundaries are as follows,

• Then Click on the Normal Toggle option and click on any of the triangle which shows the normal opposite to the direction of the fluid flow and click apply.
• Then click on Options-->Visibility-->Geometry Bounding Box to create a boundary line across the geometry.
• TO ensure that the geometry is clean click on the Diagnosis tab and click Find option.
• All the parameters that got checked shows the green colour tick mark. 

Case Setup:

For setting the case for our model the following steps are done.

• Click on Case Setup--> Begin Case Setup option and a pop up window appears. In that choose Time-based, since we are solving for steady state channel flow setup.

• Then click on Materials which is present in the right side of the window that is case setup tree, uncheck the Reaction mechanism since there is no chemical reaction taking place in our flow case and select the Predefined mixtures as Air.

• Click on the Gas simulation and Global Transport parameter and retain the same values.
• Click on Species and then add O2 and N2.
• Click on Run Parameters and under the solver tab choose the solver as Steady-State Solver. Set the simulation mode to Full Hydrodynamic and the gas flow solver as compressible.
• Then under "Misc" tab check the Steady-state monitor and uncheck the use shared memory boxes.
• Then coming to Boundary Conditions click on Boundary--> Inlet -->Specify the inlet pressure value as 110325.0 Pa and select the predefined mixture as Air which contains N2 of 77% and O2 of 23% and then under the Temperature boundary condition choose specified value and allocate the temperature value with 300k.

• And at the Outlet assign the pressure value with 101325.0 Pa and add the species.
• Assign the Top-Bottom-Walls with the Boundary type as Wall and assign with no-slip condition.
• The Front 2D and Back 2D boundary regions are assigned as TWO_D.
• Then under the Simulation Parameter --> Run Parameters select the Steady-state monitor --> add config and then click on add option to add the variables to be monitored.

• The Monitor start display is a parameter that ensures that the simulation runs for a certain number of cycles before the variable can be monitored. This is especially useful in transient simulations when we want the solution to run for a particular amount of time before checking the convergence, if the steady state results are also required.
• Sample size denotes the number of cycles or seconds over which the variable is checked to see if the solutions have converged.
• Then under the Simulation Time Parameters assign the End time and look after the Maximum Convection CFL limit and assign with 1.

• Then click on Solver Parameters [Steady-state] --> Equations --> Pressure --> Make sure that the Preconditioner is set to None. Then under the Steady-state solver control assign the maximum convection CFL limit (final stage) to less than 1 --> Click on Validate --> Click on OK.
•  Then under the Initial conditions and Events --> Regions and Initialization --> add a region and rename it as Volumetric Region User Defined by using the F2 option

• Then under the physical models check the turbulence modelling and set with Reynolds Averaged Navier-Stokes (RANS) and set the turbulence model with RNG K-epsilon.

• Then in the Grid Control parameter --> Base Grid --> Enter the size of the grid.
• Then in the Grid control parameter check the "Fixed Embedding" option.
• Enter the values for fixed embedding.

• Then under Output/Post-Processing --> Post Variable Selection --> Add the Mass fraction with O2 and N2
• Then under the Output files --> Writing time intervals --> set the time interval for writing 3D output data files and time interval for writing restarting output.   

Mesh Refinement:

In this numerical simulation, mesh refinement was carried out by utilizing values for different mesh sizes, as described in the following table as part of each individual case setup and was entered into corresponding columns representing the 'base grid' sub option in the 'Grid Control' settings under the 'Case Setup' tree to compare the results obtained for the velocity magnitude values at the outer and pressure drop across the entire domain.

               

Case 1:-

In the case 1 the size of the mesh is assigned with 2e-3.

Mesh:-

Velocity Contour:-

Pressure Contour:-

Velocity Plot:-

Pressure Plot:-

Mass Flow Rate:-

Total Cell Count:-

Case 2:-

In the case 2 the size of the mesh is assigned with 1.5e-3.

Mesh:-

Velocity Contour:-

Pressure Contour:-

Velocity Plot:-

Pressure Plot:-

Mass Flow Rate:-

Total Cell Count:-

Conclusion:-

• Backward Facing step can help in analysing the physics near the boundary level.
• Flow separation create a wake region at the flow end which causes a recirculation region due to the adverse pressure gradient, creating turbulence and formation of eddies.
• With decrease in cell size the number of cells gets increase and vice versa. With decrease in cell size the simulation time increases.
• The refined mesh that is 0.001m shows the flow velocity clearly in velocity contour.
• The velocity and pressure are decreased in the recirculation region.