Excitation of non-modal perturbations in hypersonic boundary layers by freestream forcing: shock-fitting harmonic linearised Navier-Stokes approach

Abstract: In this paper, we study the receptivity of non-modal perturbations in hypersonic boundary layers over a blunt wedge subject to freestream vortical, entropy and acoustic perturbations. Due to the absence of the Mack-mode instability and the rather weak entropy-layer instability, the non-modal perturbation is considered as the dominant factor triggering transition. This is a highly intricate problem, given the complexities arising from the presence of the bow shock, entropy layer, and their interactions with oncoming disturbances. To tackle this challenge, we develop a novel numerical tool, the shock-fitting harmonic linearized Navier-Stokes (SF-HLNS) approach, which offers a comprehensive investigation on the dependence of the receptivity efficiency on the nose bluntness and properties of the freestream forcing. The numerical findings suggest that the non-modal perturbations are more susceptible to freestream acoustic and entropy perturbations compared to the vortical perturbations, with the optimal spanwise length scale being comparable with the downstream boundary-layer thickness. Notably, as the nose bluntness increases, the receptivity to the acoustic and entropy perturbations intensifies, reflecting the transition reversal phenomenon observed experimentally in configurations with relatively large bluntness. In contrast, the receptivity to freestream vortical perturbations weakens with increasing bluntness. Additionally, through the SF-HLNS calculations, we examine the credibility of the optimal growth theory (OGT) on describing the evolution of non-modal perturbations. Its accuracy in predicting the early-stage evolution and the energy amplification proves to be unreliable. Given its high-efficiency and high-accuracy nature, the SF-HLNS approach shows great potential as a valuable tool for conducting future research on hypersonic blunt-body boundary-layer transition.