Numerical Simulation and Theoretical Analysis on Boundary-Layer Instability Affected by Porous Coating

Abstract

The effect of porous coating on the instability of a Mach 5.92 flat-plate boundary layer is investigated by a combination of numerical simulation and theoretical analysis. It is motivated by Fedorov et al.’s experimental and theoretical studies considering the effect of an ultrasonically absorptive coating on hypersonic boundary-layer stability [1] and our previous numerical simulations on hypersonic boundary-layer receptivity [2, 3] . The steady base flow is obtained by solving compressible Navier-Stokes equations with a combination of a fifth-order shock-fitting method and a second-order total variation diminishing (TVD) scheme. Stability simulations consist of two steps: 1. periodic disturbances corresponding to single boundary layer wave (mode F or mode S) are superimposed on steady base flow at a cross-section of the boundary layer to show spatial development of the wave; 2. porous coating, modelled by pressure oscillation related wall blowing-suction, is used downstream of the superimposed wave to investigate its effect on boundary-layer instability. Stability characteristics of the hypersonic boundary layer are analyzed by linear stability theory. The numerical results show that porous coating only has local effects on the spatial developments of mode S and mode F. In case of mode S, porous coating destabilizes the Mack first mode whereas it stabilizes the Mack second mode. All the six cases of stability simulations show a larger peak amplitude of mode S, which means destabilization of the Mack first mode is quite significant. In case of mode F, all three cases of stability simulations show that mode F changes to mode S near the synchronization point and mode F is generally stabilized in porous region