Turbulent Flow over a Backward-Facing Step (3D)

Description of the case

The figure below shows the geometry of the test case you will run in this tutorial.

Geometry of the step

Fluid Properties

Property	Value
\(\rho\)	\(2 kg.m^{-3}\)
\(\mu\)	\(5.10^{-5} kg.m^{-1}.s^{-1}\)

Boundary Conditions

Location	Condition
Inlet	\(U_0=1 m.s^{-1}\)
Outlet	\(P_0=0\)

with \(Re=\frac{U_0 H_{inlet} \rho}{\mu} = \frac{1 \times 1 \times 2}{5.10^{-5}} = 40000\)

Tutorial setup

First, go to an empty directory and copy the base TrioCFD test case from which we will start: Marche3D

triocfd -copy Marche3D && cd Marche3D

Open the datafile Marche3D.data in a text editor of your choice.

Notice that we use a Pb_Hydraulique_Turbulent problem with Navier_Stokes_Turbulent equation, which has a modele_turbulence keyword for the turbulence.

Modifying the test case

Start by making some changes in the file Marche3D.data:

• Modify the fluid characteristics for a calculation at Reynolds number \(Re = 50000\):
  • this is done in the block fluide_incompressible.
  • For example, use \(\rho = 1 kg.m^{-3}\) and \(\mu = 2.10^{-5} kg.m^{-1}.s^{-1}\).
• Change the turbulence model for a subgrid Smagorinsky model with standard wall law:
  • replace sous_maille by sous_maille_smago.
  • Look into the Keyword Reference Manual to find the keywords and the parameters that you can tweak.
• Change the convection scheme to quick. This happens in the block convection of the equation. amont is currently used.
• In the Post_processing block, add format lata to ease visualization with visit.
• Postprocess the fields velocity, pressure, vorticity and turbulent viscosity at the nodes (som) and elements (elem).
  • only vorticity should be missing

Running and visualizing the simulation

Now, you can run the calculation:

triocfd Marche3D

Have a look at the postprocessed fields using visit.

Using a RANS turbulence model

This next part of the tutorial will guide you toward using a RANS turbulence model with TrioCFD, starting from the previous LES simulation. This is fairly hard to do by yourself. The detailed instructions should cover everything, but the complete solution is given afterwards.

Edit the file Marche3D.data again, to change the turbulence model for a RANS k-epsilon model.

• You need to replace sous_maille_smago by k_epsilon.
  • In the k_epsilon block, you will need to add several keywords:
  • The transport_equation keyword is mandatory. You must specify transport_equation transport_k_epsilon { ... }
  • Inside the transport_k_epsilon block, you must specify the convection and diffusion schemes (see the corresponding keyword blocks in the Keyword Reference Manual).
  • Then, you also need to define the boundary_conditions:
    • For that, you can copy the ones from Navier_Stokes_Turbulent above and do some slight adaptations.
    • Replace Paroi_Fixe with paroi to use the wall law.
    • In the 2 SortieXXX boundaries, replace frontiere_ouverte_pression_imposee with frontiere_ouverte k_eps_ext. This boundary condition expects a field with two components (for k and eps). Replace Champ_Front_Uniforme 1 0. with Champ_Front_Uniforme 2 0. 0.. It is used on this equation to let k and eps leave through the boundary, but in case of reentering flow, force the entering values of k and eps.
    • For the Entree, use frontiere_ouverte_k_eps_impose, which takes a field with 2 components again, and choose pertinent values of k and eps (not 0 or nothing will happen).
  • Finally, you need to specify initial_conditions. You can also copy the one from Navier_Stokes_Turbulent above. Here, you need to initialize the field k_Eps (probably with the same values as in the Entree boundary).

Now, you can run the test case again and visualize the results.

Solution for the RANS model

modele_turbulence k_epsilon {
    transport_equation transport_k_epsilon {
            convection { amont }
            diffusion { }
 
            boundary_conditions
            {
                Bas1 paroi
                Haut1 paroi
                Haut2 paroi
                Haut3 paroi
                Bas2 paroi
                Gauche paroi
                Bas3 paroi
                Sud1 paroi
                Nord1 paroi
                Sud2 paroi
                Nord2 paroi
                Sud3 paroi
                Nord3 paroi
                Sud4 paroi
                Nord4 paroi
                Sud5 paroi
                Nord5 paroi
                SortieBasse frontiere_ouverte k_eps_ext Champ_Front_Uniforme 2 0. 0.
                SortieHaute frontiere_ouverte k_eps_ext Champ_Front_Uniforme 2 0. 0.
                Entree frontiere_ouverte_k_eps_impose Champ_Front_Uniforme 2  0.405 7.73
            }
 
            initial_conditions
            {
                k_Eps Champ_Uniforme 2 0.405 7.73 # taken from another test case, may not be pertinent #
            }
    }
    TURBULENCE_PAROI loi_standard_hydr
}