Stability of Temporally Evolving Supersonic Boundary Layers over Micro-Cavities for Ultrasonic Absorptive Coatings

Abstract

Ultrasonic absorptive coatings, consisting of regularly-spaced arrays of micro-cavities, have previously been shown to effectively damp second-mode instability for the purpose of delaying transition in hypersonic boundary layers. However, previous simulations and stability analysis have used approximate porous-wall boundary conditions. Here we investigate the feasibility of using direct numerical simulation to directly compute the hypersonic boundary layer including the micro-cavities. In order to keep the problem computationally tractable, we restrict our attention to the two-dimensional case (which is relevant since the second-mode is initially two dimensional), and we show that temporally evolving layers display qualitatively similar behavior to spatially developing boundary layer and instabilities. We validate the numerical method by comparing the simulation results to temporal linear stability analysis of the (frozen) velocity and temperature profiles from the direct numerical simulation. Two-dimensional linear simulations of the boundary layer on a flat plate and over a porous coating are performed, and it is shown that the presence of the cavities attenuates the instability waves, as expected from theory.