Nonlinear indirect combustion noise for compact supercritical nozzle flows

In this paper, indirect combustion noise generated by the acceleration of entropy perturbations through a supercritical nozzle is investigated in the nonlinear regime and in the low-frequency limit (quasi-static hypothesis). This work completes the study of Huet and Giauque (Journal of Fluid Mechanics 733 (2013) 268–301) for nonlinear noise generation in nozzle flows without shock and particularly focuses on shocked flow regimes. It is based on the analytical model of Marble and Candel for compact nozzles (Journal of Sound and Vibration 55 (1977) 225–243), initially developed for excitations in the linear regime and rederived here for nonlinear perturbations. Full nonlinear analytical solutions are provided in the absence of shock as well as second-order analytical expressions when a shock is present in the diffuser. An analytical evaluation of the shock displacement inside the nozzle caused by the forcing is proposed and maximum possible forcings to avoid unchoke and ‘over-choke’ are discussed. The accuracy of the second-order model and the nonlinear contributions to the generated waves are then addressed. This model is found to be very accurate for the generated entropy wave with negligible nonlinear contributions. Nonlinearities are more visible, but still limited, for the downstream acoustic wave for large inlet Mach numbers. Analytical developments are validated thanks to comparisons with numerical simulations.