Optimal disturbances and growth patterns in hypersonic blunt-wedge flow

Abstract

In hypersonic boundary layers, the optimal disturbance is notably caused by normal-mode instabilities, such as Mack second mode. However, recent experimental and numerical efforts have demonstrated the dominance of nonmodal growth in hypersonic flows with the presence of moderate nose bluntness. In this study, resolvent analysis and parabolized stability equation analysis are performed to investigate the instabilities over a blunt-tip wedge. Main parameters include Mach number 5.9, unit Reynolds number 91.5 × 106/m, half wedge angle 5°, and nose radii ranging from 2.54 mm to 15.24 mm. Two novel growth patterns of travelling waves are identified to compete, whose nature is the intersection of the energy gain of optimal and sub-optimal disturbances. Pattern A with large spanwise wavelengths has the signature of slow energy amplification over a long distance which concentrates in the entropy layer. By contrast, pattern B with relatively small spanwise wavelengths presents rapid transient growth inside the boundary layer. A systematic study is performed on the growth/attenuation mechanism of disturbance patterns and the effects of wall temperature and nose radius. Wall cooling is found to be an alternative control strategy aimed at nonmodal instabilities. The receptivity to slow acoustic waves is considered when the effect of bluntness is studied. An estimated amplitude response favorably reproduces the reversal-like phenomenon. The lift-up/Orr mechanism analysis provides an explanation of energy growth for nonmodal responses.