Planar shock-wave boundary-layer interaction

Semi-confined Flows

Underlying Flow Regime 3-32

Best Practice Advice

Key physics

The low frequency component (two orders of magnitude below the typical turbulent boundary layer frequencies) is an important feature of the interaction. It may be detected, for example, in the weighted power spectrum near the foot of the reflected shock wave.
Mean and turbulent flow properties show the presence of a shock-induced separation bubble.
For weak interaction cases the results for the spanwise periodic assumption compares favourably with experimental data.
With strong interactions and with sidewalls present the separated flow zones are highly three dimensional.

Numerical modelling issues

For weak interactions (here represented by the 8 degree shock generator) a periodic spanwise boundary condition may be used, but attention should be paid to the spanwise domain width. Good experience was obtained when the domain width was at least equal to the separation bubble length.
For strong interactions (here represented by a 9.5 degree shock generator) the full 3D domain corresponding to the experiment must be used.
Shock capturing should not be too dissipative. Both codes used here pay particular attention to minimising additional dissipation by using shock sensors in addition to basic shock-capturing techniques.
In LES with spanwise periodic boundary conditions attention needs to be placed in particular on the need for a sufficiently large domain size to capture both the mean flow and the low-frequency mode
Grid dependency studies showed that grid size and by inference sub grid scale model characteristics are secondary factors for cases where the viscous sublayer is correctly resolved (wall modelling was not employed)

Physical modelling

The full compressible Navier-Stokes equations for a Newtonian fluid with temperature-sensitive viscosity (e.g. using Sutherland's law) should be used.
Time-dependent inflow representations of turbulent boundary layers are recommended for LES, unless one is prepared to simulate a long entire transition process.
For DES inflow stimulation is necessary.

Application uncertainties

It should be checked that inflow mean and fluctuation specification has relaxed to an equilibrium turbulent boundary layer (judged for example by the mean and rms distribution).

Recommendations for future work

Explore sensitivity to a longer run of the turbulent boundary layer upstream of the interaction (while keeping the Reynolds number based on boundary layer thickness at the inviscid impingement point constant).
Further grid refinement studies are needed to determine the minimum grid requirements for good LES
Carry out LES with sidewalls to compare with SDES.

Contributed by: Jean-Paul Dussauge (*), P. Dupont (*) , N. Sandham (**), E. Garnier (***) — (*) Aix-Marseille Université, and Centre National de la Recherche Scientifique UM 7343, (**) University of Southampton, (***) ONERA/DAAP, Meudon, France