Numerical Analysis of Wall Temperature Similarity in Hypersonic Boundary-Layer Transition Experiments

A numerical analysis of boundary-layer stability over the cone–cylinder–flare geometry is conducted at Mach 6 and a Reynolds number of [Formula: see text] in order to investigate the role of wall-to-recovery temperature ratio similarity in hypersonic boundary-layer transition. The study compares typical flight conditions with wind-tunnel experiments to assess differences caused by the missing wall-temperature similarity parameter. A second wind-tunnel case with a cooled wall is studied as a potential solution to attain Mach, Reynolds, and wall-to recovery temperature similarity with flight. Global stability and resolvent analysis are employed to characterize the dominant global and convective instabilities. The results indicate that the global bubble modes are strongly destabilized by the wall cooling. Regarding the convective modes, Mach and Reynolds number similarities alone are insufficient to replicate the linear transition mechanisms observed during hypersonic flight. In wind-tunnel conditions, both the first and second modes contribute to transition, whereas mainly the second mode is amplified in flight conditions. The third case incorporating wall-to-recovery temperature ratio similarity demonstrates that the inclusion of this parameter allows for the successful reproduction of the linear mechanisms at play in the transition process in flight conditions, even at low stagnation temperatures. These findings emphasize the critical role of wall-to-recovery temperature ratio effects in hypersonic boundary-layer transition studies and the challenges associated with replicating flight conditions in ground-test campaigns.