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

TL;DR

The paper investigates Mack's second-mode instabilities in a Mach 6 hypersonic boundary layer using a first-principles DSMC approach, validated against slip-flow theory and linear stability predictions. By coupling PSD analyses with Dynamic Mode Decomposition, it resolves multiple, spatially coherent second-mode waves and demonstrates that growth occurs strictly within LST-identified unstable regions. The study further demonstrates frequency-selective interaction with an acoustic vibrating surface (AVS), where forcing at $f\approx300$ kHz amplifies disturbances while forcing at $f\approx500$ kHz dampens them, illustrating potential kinetic-level control of laminar-turbulent transition. Overall, the work establishes DSMC as a capable tool for analyzing and potentially controlling high-Re hypersonic boundary-layer instabilities from first principles.

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.

Figures (18)

• Figure 1: Computational workflow: (a) Boundary layer flow and probes and AVS placement, (b) time-series probe data of power spectral density (PSD) spectral analysis of DSMC time-accurate temperature data, and (c) flowfield snapshots of fluctuating DSMC streamwise velocity to be used in modal decomposition.
• Figure 2: Extraction of wavelengths of traveling waves from DMD modes.
• Figure 3: Slip velocity and temperature jump profiles along the surface from the DSMC solution.
• Figure 4: Compressible Blasius boundary-layer profiles and generalized inflection point.
• Figure 5: Comparison of DSMC results with the compressible Blasius solution at Mach 5.85, freestream temperature 52 K, freestream velocity 858 m/s, Prandtl number 0.72, and wall temperature 300 K.