The Supersonic Mode and the Role of Wall Temperature in Hypersonic Boundary Layers with Thermochemical Nonequilibrium Effects

Abstract

There has been a renewed interest in studying the stability of the supersonic mode in hypersonic boundary layers. The supersonic mode, sometimes also referred to as the spontaneous radiation of sound, is associated with an unstable Mack's second mode synchronizing with the slow acoustic spectrum, causing the disturbance to travel upstream supersonically relative to the meanflow outside the boundary layer. Recent theoretical results have shown the possibility of the supersonic mode existing in hot-wall flows, which is contrary to decades of research on the supersonic mode suggesting it is an artifact of hypersonic cold-wall (Tw/T∞ < 1) flows. The flow conditions leading to the supersonic mode have not been thoroughly and systematically investigated. As a result, it is unknown whether or not the supersonic mode can become the dominant boundary layer instability over the traditional second mode. This work uses thermochemical nonequilibrium Direct Numerical Simulation (DNS) along with thermochemical nonequilibrium Linear Stability Theory (LST) to replicate the flow conditions used in the theoretical study to obtain a more complete investigation of the supersonic mode in both hot-wall and cold-wall flow conditions. The purpose is to analyze the effect of wall temperature on the supersonic mode at high-enthalpy conditions. The simulation is Mach 10 flow over a 1mm nose radius axisymmetric cone 1 meter in length. LST results indicate that the supersonic mode does not exist in neither the hot-wall nor the cold-wall flows, however unsteady DNS results indicate the presence of the spontaneous radiation of sound in both cases, going against LST predictions. Further FFT analysis indicated that this sound radiation was an artifact of the interaction between an unstable subsonic mode S, stable supersonic mode F1, and the slow acoustic spectrum. The supersonic mode found in the cold-wall case had a significantly higher magnitude than the hot-wall case, demonstrating that a colder wall produces a stronger supersonic mode. Additionally, the magnitude of the supersonic mode in the cold-wall case was higher than the magnitude of the traditional second mode and could impact transition unexpectedly if not accounted for.

Significant Supersonic Modes and the Wall Temperature Effect in Hypersonic Boundary Layers

“…where U is the state vector of conserved quantities, W is the source terms, and F j and G j are the inviscid and viscous flux vectors, respectively. For further details of the governing equations and thermochemical model, see the work of Knisely and Zhong [28][29][30] and Mortensen [37].…”

“…Therefore, few studies have been performed directly analyzing the supersonic mode, although it has been encountered in many other studies [14,[17][18][19][20][21][22][23]. Even with the recent resurgence in interest in the supersonic mode sparked by Bitter and Shepherd [24], most studies [25][26][27][28][29][30] have shown a weaker supersonic mode than the traditional second mode. However, based on Edwards and Tumin's [27] finding of the supersonic mode on a hot wall with chemical effects, the effect of wall temperature on the supersonic mode in thermochemical nonequilbrium flow must be reevaluated.…”

Impact of Thermochemical Nonequilibrium Effects on the Supersonic Mode in Hypersonic Boundary Layers

“…There has been a resurgence of interest in studying the supersonic mode due to its presence and large amplification in some unexpected flow conditions. 24,26,27 However, the impact of thermochemical nonequilibrium effects on the stability of the supersonic mode is not fully understood. This study used Direct Numerical Simulation (DNS) with both thermochemical nonequilibrium and frozen flow models as mean flow inputs to Linear Stability Theory (LST) solvers.…”

“…This phenomenon may be attributed to the real gas effect and may have been overlooked in previous simulations assuming chemical equilibrium. Later in 2018, Knisely and Zhong 26 and Mortensen 27 showed the supersonic mode can have a higher growth rate than the traditional second mode under certain conditions, demonstrating the importance of investigating this mechanism.…”