Alternate Designs of Ultrasonic Absorptive Coatings for Hypersonic Boundary Layer Control

Abstract

Numerical simulations of the linear and nonlinear two-dimensional Navier-Stokes equations are used to parametrically investigate hypersonic boundary layers over ultrasonic absorptive coatings consisting of a uniform array of rectangular pores (slots) with a range of porosities and pore aspect ratios. Based on our previous work, we employ a temporally evolving approximation appropriate to slowly-growing second-mode instabilities. We consider coatings operating in attenuative regimes where the pores are relatively deep and acoustic waves and second mode instabilities are attenuated by viscous effects inside the pores, as well as cancellation/reinforcement regimes with alternating regions of local minima and maxima of the coating acoustic absorption, depending on the frequency of the acoustic waves. The focus is on reinforcement cases which represent a worst case scenario (minimal second-mode damping). For all but one of the cases considered, the linear simulations confirm the results of linear instability theory that employs an approximate porous-wall boundary condition. A particular case with a relatively shallow cavities and very high porosity showed the existence of a shorter wavelength instability that is not predicted by theory. Finally, nonlinear simulations of the same cases led to the same conclusions as linear analysis; in particular, we did not observe any "tripping" of the boundary layer by small scale disturbances associated with individual pores.