Mechanism of stabilization of porous coatings on unstable supersonic mode in hypersonic boundary layers

Abstract

This study clarifies the fundamental mechanism by which porous coatings suppress the supersonic mode instability in the hypersonic boundary layer (BL) by using Doak's momentum potential theory. The independent energy budget equations for vortical, acoustic, and thermal components of instabilities are derived. Data from direct numerical simulations of Mach 6.0 flat plate flows on a solid wall and porous coatings are then analyzed. By decomposing the momentum density into vortical, acoustic, and thermal components, the source terms and fluxes are studied based on their corresponding energy corollaries. The results demonstrate the role of different components in the generation and transport of the total fluctuation enthalpy (TFE) and the way in which the fluctuation energy is transferred between components. In the case of the solid wall, the oscillating disturbance on the BL consists of acoustic and vortical components. Near the critical layer, the positive acoustic source and energy transferred from the vortical component are primary energy producers for acoustic fluxes. Then, the TFE is transported outward by the acoustic component, which leads to “sound radiation” in the supersonic mode. In the case of the porous coating, the positive vortical source near the surface of the plate is suppressed significantly. Less vortical energy is transported to the critical layer, and thus less vortical energy is transformed into acoustic energy. Acoustic energy is eventually exhausted due to energy loss in the outward transport of the TFE, and “sound radiation” disappears from the porous coating.