Effects of porous walls on supersonic/hypersonic boundary-layer instability

Abstract

The effects of porous walls on supersonic/hypersonic boundary-layer instability are investigated using theoretical and numerical approaches. The linear stability theory (LST) is utilized to examine the effects of admittance magnitude and phase on the first and second modes. Numerical simulations are performed to validate the theoretical predictions. Phase analysis is employed to study the mechanisms of the growth of the first and second modes. A design strategy of the ultrasonic absorptive coating (UAC) is also proposed to stabilize the first and second modes. The analyses based on the adiabatic or quasi-adiabatic wall show the stabilization and destabilization of the first and second modes depend on the wall admittance phase and are facilitated by the increase in the wall admittance magnitude. Moreover, the effects of porous walls on the first and second modes are independent of the wave-propagation angle. Both for the first and second modes, the fluctuating internal energy is dominated by the advection of perturbed thermal energy by mean flow in the vicinity of the critical layer and by the dilatation fluctuation near the wall. The growth rate of the second mode is determined by the contribution of the heat transport by the wall-normal velocity fluctuation to the fluctuation in the vicinity of the critical layer. While the growth rate of the first mode is associated with the energy exchange between the dilatation fluctuation and the internal energy fluctuation near the wall. Porous walls alter the phase of the wall-normal fluctuating velocity, which recasts the phase of the energy transport by the wall-normal velocity fluctuation. The design strategy of UAC focusing on the admittance magnitude and phase can provide quantitative requirements on the stabilization of the first and second modes. The designed UAC remarkably damps the second mode and meanwhile avoids aggravating the first mode in a supersonic flat-plate boundary layer.