Large eddy simulation of two separated hypersonic shock/turbulent boundary layer interactions

A large eddy simulation (LES) method employing a one-coefficient dynamic mixed model is used to generate data of two separated hypersonic shock/turbulent boundary layer interactions. The first of these is a Mach 7.2 turbulent boundary layer at Re-theta = 3300 over a 33 degrees ramp. The second is a Mach 9.1 turbulent boundary layer at Re-theta = 8000 over a 34 degrees ramp. We document the mean flow statistics including Reynolds stresses, turbulent amplification, turbulent kinetic energy budget, anisotropy tensor invariants, wall pressure distribution, skin friction, and wall heat transfer. Various modeling assumptions typically used in engineering applications such as the Reynolds Analogy Factor, constant turbulent Prandtl number, and Strong Reynolds Analogies are assessed for these conditions. The documentation of the two-dimensional time-averaged flow statistics of these two datasets is the main focus of this article, however, we first demonstrate the reliability of our LES method by simulating both a separated supersonic compression ramp flow and an attached hypersonic compression ramp flow and comparing to existing direct numerical simulation (DNS) data. An excellent comparison of mean flow profiles, turbulence amplification factors, spectral content, and the state of separation is achieved. The practicality of the LES over the DNS method is also emphasized by the typical factor of 32 reduction in grid size as well as a numerical time step increase of three times the DNS. Additional grid size reduction might be possible. A discussion on the accuracy of the mixed model in comparison to the eddy viscosity model is included. We found that at Mach 7, omitting the scale-similar contribution in the subgrid-scale models of shear stress and heat flux resulted in as much as a 32% increase in the separation length and 10% decrease in shear layer spreading rate.