Scattering of Mack modes by solid-porous junctions in hypersonic boundary layers

Abstract

Porous coating is regarded as an effective control strategy to delay the laminar-turbulent transition in hypersonic boundary layers, whose effects include not only the successive distortion of the Mack-mode growth rate but also the scattering effect appearing at the junctions between the solid and porous walls. The present paper focuses particularly on the latter mechanism by employing the harmonic linearized Navier-Stokes approach, which is confirmed to be sufficiently accurate as compared to the results obtained by direct numerical simulations. A transmission coefficient is introduced to quantitatively characterize the scattering effect, which is define as the ratio of the Mack-instability amplitude downstream of the junction to that upstream. For a solid-to-porous junction, the scattering effect leads to a stabilization of the majority of the second mode but destabilizes slightly the first mode. In contrast, the porous-to-solid junction plays the opposite role. The overall effect of a finite-length porous panel requires a combined consideration of the Mack-mode-growth-rate distortion and the scattering effect of the two junctions at both boundaries of the panel, which shows a critical frequency separating the destabilizing and stabilizing frequency bands. Additionally, a decrease in the wall temperature leads to an enhanced scattering effect on the Mack modes.