Reverse design of ultrasonic absorptive coating for the stabilization of Mack modes

The effects of ultrasonic absorptive coating (UAC) admittance on the first and second modes in a high-speed boundary layer are analyzed using linear stability theory. It is shown that the growth rate of the first mode is increased as UAC admittance phase θ varies from 0.5π to π, whereas the second mode is amplified when θ tends to 0.5π and damped if θ ≥ 0.75π. The frequency range of the first mode is broadened when θ is in the vicinity of π, and the second mode shifts to low frequencies when θ < π. Moreover, the stabilization or destabilization effects on Mack modes, frequency band broadening, and frequency shifting are promoted by large UAC admittance magnitudes. Based on the requirements of the admittance phase and magnitude for the stabilization of Mack modes, a design strategy for UAC is proposed to stabilize the second mode in a wide frequency range with the first mode little amplified.