Scaling Of Hypersonic Shock/Turbulent Boundary Layer Interactions

A separation length scaling method for shock/turbulent boundary layer interactions (STBLIs) is considered. A modification of the scaling method of Souverein et al. [J. Fluid Mech. 714, 505 (2013)] is introduced to account for heat transfer effects. As a further generalization of the model, a control volume analysis applied to a cylinder-with-flare geometry demonstrates that this axisymmetric geometry scales with the same parameters as the two-dimensional interactions. The current modified scaling is evaluated for a large range of STBLI conditions. A database of STBLI flows at Mach 2-3 has been collected from the available literature and includes both reflected shock and compression ramp data with various wall heat transfer conditions. A new Large Eddy Simulation database of Mach 7 and Mach 10 cold wall compression ramp flows with parametrically varying ramp angle is also utilized. In addition, the Mach 10 compression ramp experiments of Elfstrom [J. Fluid Mech. 53, 1 13 (1972)] as well as the Mach 10 cylinder-with-flare experiments of Coleman (Ph.D. thesis, University of London, 1973) and Brooks et al. (AIAA Paper No. 2017-3325, 2017) are included in the evaluation. It is shown that this new generalized scaling method results in a linear collapse of all incipiently separated STBLI data. No collapse is observed for fully separated interactions. Arguments for the physical mechanisms affecting the separation length scaling for the two STBLI regimes, incipient and fully separated, that are consistent with the data trends are presented. Namely, for incipient cases, the distribution of momentum in the incoming boundary layer is key to separation length scaling. In contrast, for fully separated cases, we postulate that the presence and strength of inviscid vortical structures significantly affects the separation length. Furthermore, we postulate how the distinct flow dynamics of the boundary layer and of the inviscid vortical structures mechanisms found in STBLI interplay and become dominant over the other.