Compressible turbulent boundary layers over prism-shaped roughness: simulation and modeling

High-speed vehicles experience a highly challenging environment, where compressibility and aerodynamic heating influence mechanical and thermal loads. These driving factors can be greatly affected by the detrimental effect of distributed surface imperfections and roughness, which may be a subsidiary of the presence of a thermal protection system, or may arise from unforeseen events such as atmospheric hazards, such as ice particles impacting the surface. In the context of high-speed flows, it is not clear whether the theories developed for incompressible turbulence apply, and the literature on the subject is scarce. This study builds on this research gap to shed light on multiple aspects concerning the interaction between compressible turbulence and roughness. In particular, by conducting DNS of unprecedented size of supersonic TBLs, we present a two-fold analysis on both the spatial evolution of the flow and the local turbulence statistics in the rough region. Results are compared among different cases varying the Mach number (from 2 to 4), wall temperature condition (cold wall and adiabatic), and surface geometry (variations of prism-shaped roughness elements). We also offer possible implications for wall modeling, with an a priori analysis of drag and heat transfer predictions.