Sound radiation by supersonic unstable modes in hypersonic blunt cone boundary layers. I. Linear stability theory

Abstract

There has been renewed interest in supersonic modes in hypersonic boundary layers, which have been previously thought to be insignificant due to their smaller amplitudes than Mack’s traditional second mode. Supersonic modes are associated with an unstable second mode synchronizing with the slow acoustic spectrum, causing sound to radiate outwards from the boundary layer. Because supersonic modes have not been observed experimentally, the majority of previous investigations either relied on Linear Stability Theory (LST) to study supersonic modes on a flat plate or observed them in the context of other research objectives. This two-part study uses a combined LST and Direct Numerical Simulation (DNS) approach to investigate the mechanism of supersonic modes in Mach 5 flow over a blunt cold-wall cone with thermochemical nonequilibrium effects. Paper I focuses on LST with new shock boundary conditions, whereas Paper II [C.P. Knisely and X. Zhong, “Sound radiation by supersonic unstable modes in hypersonic blunt cone boundary layers. II. Direct numerical simulation,” Phys. Fluids 31, 024104 (2019)] focuses on DNS with the overall goal of investigating the impact of supersonic modes on transition. LST results indicate that supersonic modes exist in the flow with wall-to-free-stream temperature ratio Tw/T∞ = 0.2 and create an abnormal growth pattern. However, supersonic modes were not shown to exist using LST in the case with Tw/T∞ = 0.667. Subsequent DNS analysis in Paper II shows supersonic modes in the Tw/T∞ = 0.667 case, although they are significantly weaker than the second mode and are unlikely to lead to transition. Understanding the mechanism of supersonic modes can yield more accurate transition location predictions leading to improved estimates for drag and heat transfer to the vehicle.