Modeling non-equilibrium effects in wall modeled les of high-speed flows

We explore the use of wall modeled large eddy simulation (WMLES) in the context of compressible flows with shock-induced separation. A novel feature of the non-equilibrium model used is that it doesn’t require the explicit generation of an auxiliary mesh. The nonequilibrium model has shown good results in all the regions where the boundary layer is attached and performed much better compared to the equilibrium model in separated regions. The bottleneck for these cases seems to be the use of an eddy viscosity model which is derived based on the assumption that the boundary layer is attached. The classic damping functions computed using the local friction velocity cause unphysical damping of eddy viscosity in separated regions. A modified algebraic model using a velocity scale based on the pressure gradient was tested on the shock-boundary layer interaction (SBLI) cases. This eddy viscosity was modeled such that it reverts to the classic mixing-length model in attached regions and does not excessively damp the eddy viscosity in separated regions. The modified eddy viscosity did lead to better skin-friction results in the separated region but it also led to a slight expansion of the separation bubble due to excessive eddy viscosity in the upstream region of the shock-interaction.