A nonlinear model for indirect combustion noise through a compact nozzle

Abstract

AbstractThe present paper deals with the generation of sound by the passage of acoustic or entropy perturbations through a nozzle in the nonlinear regime and in the low-frequency limit. The analytical model of Marble and Candel for compact nozzles (J. Sound Vib., vol. 55, 1977, pp. 225–243), initially developed for excitations in the linear regime, is rederived and extended to the nonlinear domain. Full nonlinear and second-order models are written for both subcritical and supercritical nozzles in the absence of shock and a detailed methodology is provided for the resolution of the second-order system. The accuracy of the second-order model is assessed for entropy forcings. It is shown to be accurate for all waves, with the exception of the upstream generated wave for subcritical diverging geometries where higher-order nonlinear contributions cannot be neglected. In the context of indirect combustion noise, the phenomenon of regime change of the nozzle due to an incoming entropy fluctuation is also addressed. Regime change is related to a Mach number modification induced by temperature and velocity fluctuations. In the present study, it translates into a limitation of the maximum amplitude of the incoming entropy forcing. Such limitations are to be considered for subcritical nozzles with significant inlet or outlet Mach numbers, where the flow transition is observed even for very low-amplitude entropy excitations. With the constraint of those limitations, the analytical extended nozzle describing functions representing the full nonlinear response for indirect combustion noise are validated through detailed comparisons with numerical simulations.