A Molecular Gas Dynamics Study of Hypersonic Boundary Layer Second Mack Mode Instabilities

TL;DR

This study uses DSMC simulations to analyze second-mode instabilities in hypersonic boundary layers, confirming theoretical predictions and demonstrating potential for flow control in high-speed aerodynamics.

Contribution

It applies DSMC to capture and analyze second-mode instabilities at hypersonic speeds, validating linear stability theory predictions and exploring flow control methods.

Findings

PSD analysis matches LST predicted frequencies

Wave packets confined within unstable regions

Flow control via surface vibration amplifies or dampens disturbances

Abstract

A flat-plate laminar boundary layer is simulated at Mach 6 and unit Reynolds number of 1.1e7 using the Direct Simulation Monte Carlo (DSMC) method to capture and analyze spontaneous second-mode instability growth. Power spectral density (PSD) analysis identifies dominant frequencies of 200-400 kHz, in line with linear stability theory (LST) predictions. Near-wall perturbations remain confined within the unstable regions known from linear theory. Dynamic mode decomposition (DMD) of unsteady flowfield snapshots reveals wave packets of spatially coherent modes having wavelengths and phase speeds characteristic of the acoustic second mode; their growth and decay occur exclusively within LST-predicted unstable bounds. Targeted interaction with these flow instabilities is demonstrated for an acoustic vibrating surface (AVS), where forcing at the unstable frequency of 300 kHz results in amplified waves downstream, while at the stable frequency of 500 kHz AVS-induced disturbances are damped. This further emphasizes the ability of the present kinetic simulations to capture and describe linear perturbations at high Reynolds numbers and suggests that DSMC will be a useful tool for understanding theoretically founded control of laminar-turbulent transition in hypersonic boundary layers.