Sound radiation by supersonic unstable modes in hypersonic blunt cone boundary layers. II. Direct numerical simulation

Abstract

Supersonic modes, previously thought to be insignificant due to their smaller amplitude than Mack’s traditional second mode, occur in hypersonic boundary layers when a disturbance travels supersonically with respect to the mean flow outside the boundary layer, causing outward-radiating acoustic waves. Very few previous studies perform Direct Numerical Simulation (DNS) of supersonic modes and instead rely on Linear Stability Theory (LST). This combined LST and DNS study investigates supersonic modes in Mach 5 flow over a blunt cold-wall cone. An LST analysis was performed in Paper I [C. P. Knisely and X. Zhong, “Sound radiation by supersonic unstable modes in hypersonic blunt cone boundary layers. I. Linear stability theory,” Phys. Fluids 31, 024103 (2019)], whereas DNS is the focus of Paper II. The overall goal is to determine the mechanism of supersonic modes and the conditions under which they exist. Compared to previous pure LST studies, DNS provides the advantage of making fewer limiting assumptions and can resolve interactions between modes. The results here indicate the excitation of supersonic modes via modal interactions not resolved with LST, suggesting the inadequacy of pure LST analyses concerning supersonic modes. Unsteady DNS results verified supersonic modes in the flow with wall-to-free-stream temperature ratio Tw/T∞ = 0.2, lending credence to the modes’ physical existence. However in the case of Tw/T∞ = 0.667, sound radiation was also found in DNS while LST predicted a stable supersonic mode. The mechanism for supersonic modes is attributed to a modal interaction between mode F1, mode S, and the slow acoustic spectrum. Therefore, it is necessary to perform combined LST and DNS studies of supersonic modes to reliably predict their presence and impact on transition to turbulence.