Reflection of acoustic wave in real atmosphere for hypersonic boundary layer control

Abstract

Some studies showed that an ultrasonically absorptive coating (UAC) can suppress the second instability thereby delay the transition of hypersonic boundary layer. A theoretical model is employed to analyze and compare the reflection behaviors of UAC cavities by keeping constant porosity φ and cavity aspect ratio AR. According to international standard atmosphere, the acoustic Reynolds number Re and Knudsen number Kn are estimated as functions of characteristic length and altitude. With respect to the characteristic length l = 150µm, the value of relevant Kn grows up to 0.03 at altitude h = 30km. Thus, the rarefaction effect in real atmosphere is then characterized by Kn. The existing data of direct numerical simulation (DNS) are used for initial validation of the theoretical model. The results from theory show that, the reflection coefficient decreases globally with increasing altitude due to the viscous effect for both of slit and pore. Additionally, at altitude h = 30km, the fluctuation of reflection coefficient decreases clearly as AR increases. In particular, the fluctuation of reflection coefficient of pore is smaller than slit. This phenomenon indicates that the dissipation caused by viscosity inside pore is enhanced. Furthermore, an acoustic physics qualification of the UAC energy extraction mechanism is introduced by performing a 2-D simulation based on finite element method (FEM). Specifically, the effect of the porosity on the top and bottom reflection is observed and discussed.