Effect of Porous Coating and its Location on Hypersonic Boundary Layer Waves

Abstract

In this paper, effect of porous coating and its location on the spatial developments of mode S and mode F in a Mach 5.92 flat-plate boundary layer is investigated by linear stability theory (LST) and direct numerical simulation (DNS). The current study is motivated by Fedorov et al.’s experimental and theoretical studies of the effect of an ultrasonically absorptive coating on hypersonic boundary-layer stability [1] and our previous numerical simulations on hypersonic boundary-layer stabilities [2, 3] . The mean flow is calculated 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. The stability characteristics of the hypersonic boundary layer is analyzed by LST. Stability simulations based on mean flow consist of three steps: 1. disturbances corresponding to a specific boundary layer wave (mode S or mode F) at a frequency of 100 kHz are introduced at the inlet of the computational domain to study its spatial development; 2. porous coating is used to investigate its effect on the spatial development of mode S and mode F; 3. multiple porous coatings are used to study the effect of porous coating location on the spatial development of mode S and mode F. The same theoretical model of porous coating as that in Fedorov et al.’s paper is used, i.e., porous coating is modelled by pressure perturbation related wall blowing-suction. For all the cases considered in current paper, porous coatings are located upstream of the corresponding synchronization point of mode S and mode F at x ∗ = 0.33184 m. The numerical results show that porous coating and its location have significant effects on the spatial developments of mode S and mode F. No matter which mode of mode S and mode F is introduced at the inlet, porous coating increases pressure perturbation amplitude downstream of the porous region. With the number of porous coatings increasing, pressure perturbation amplitude keeps increasing. In case of mode S, the effect of porous coating on mode S in porous region is not consistent. With the location of porous coating shifting from upstream to downstream, the effect of porous coating on mode S changes from destabilization to stabilization. In case of mode F, all cases show that mode F changes to mode S near the synchronization point and mode F is stabilized in porous region.