Instability of Hypersonic Boundary Layer on a Wall with Resonating Micro-Cavities

Abstract

Ultrasonically absorptive coatings (UAC) can stabilize the Mack second mode and thereby increase the laminar run on configurations where laminar-turbulent transition is second-mode dominated. Theory indicates that the stabilization effect can be essentially enhanced by increasing the UAC porosity. However, direct numerical simulations (DNS) showed that coatings having closely spaced grooves can trigger a new instability whose growth rate can be larger than that of Mack' second mode. The nature of the new instability is investigated theoretically and numerically. 2D linear DNS and stability analysis are performed for the temporally evolving boundary layer on a flat wall at the outer-flow Mach number 6. The wall is covered by UAC comprising equally-spaced spanwise grooves. It is shown that the new mode is associated with acoustic resonances in the grooves. Disturbance fields near mouths of resonating cavities are coupled such that the boundary-layer disturbance is decelerated and becomes unstable. To avoid this detrimental effect the coating should have sufficiently small porosity and/or narrow pores of sufficiently small aspect ratio. Restrictions on these parameters can be estimated using the linear stability theory with the impedance boundary conditions.