Receptivity of a supersonic jet due to acoustic excitations near the nozzle lip

Abstract

In this paper, we present an analytical model aimed at investigating the generation of instability waves by upstream-propagating acoustic disturbances near the nozzle lip of a supersonic jet. This is related to the receptivity process of the screech feedback loop [1]. Our focus is on rectangular nozzles of high aspect ratios, therefore, we utilize a planar model. Specifically, we consider an asymptotic form of the acoustic wave resulting from the interaction between the downstream-propagating instability waves and shock waves. This acoustic wave reaches the nozzle lip and excites new shear-layer instability waves, whose solution is obtained using the Weiner-Hopf technique. We factor the kernel of the Weiner-Hopf equation using asymptotic expansions, and obtain a closed-form scattered field. We then impose the Kutta condition at the nozzle lip to derive the dispersion relation for the triggered instability wave, and obtain a transfer function that describes the nozzle receptivity to the acoustic disturbance. Based on this transfer function, we establish a phase condition for the resonance loop of the jet screech.