Linear stability analysis of second-mode attenuation via porous carbon-matrix ceramics

Abstract

Effects of porous carbon-fiber-reinforced carbon-matrix ceramics (C/C) on the stability of second-mode waves on a 7°-half-angle cone were investigated for Reynolds numbers Rem=2.43×106–6.40×106 m−1 at the freestream Mach number of M∞=7.4, for both sharp and 2.5-mm-round nose tips. A broadband time-domain impedance boundary condition was used to model the effects of the C/C porosity on the flow dynamics leveraging direct ultrasonic benchtop experiments and homogenous absorber theory. A spectral linear stability solver based on orthogonal Laguerre functions, naturally vanishing in the free stream, was used to predict linear spatial growth rates, which are in agreement with independent pulsed axisymmetric direct-numerical simulations. The latter were carried out with the quasi-spectral viscosity closure—a dynamic quasi-spectral procedure capable of deactivating the sub-filter scale stresses in the absence of turbulent break down—verifying its suitability to carry out transitional calculations without affecting ultrasonic wave dynamics. The effectiveness of a porous C/C surface is shown to decrease drastically with static pressure and its presence is shown to decrease the second-mode growth rates in regions where it is unstable as well as increasing the attenuation rates in regions where it is stable.