A physical model for indirect noise in non-isentropic nozzles: Transfer functions and stability

We propose a mathematical model from physical principles to predict the sound generated in nozzles with dissipation and a finite spatial extent. The focus is on the sound generated from the acceleration of temperature inhomogeneities (also known as entropy waves), which is referred to as indirect noise. First, we model the dissipation caused by flow recirculation and wall friction with a friction factor, which enables us to derive quasi-one-dimensional equations. Second, we physically interpret the semi-empirical model by De Domenico et al, which is the model used in the literature to estimate indirect noise in non-isentropic nozzles. Third, the predictions from the proposed model are compared against the experimental data available in the literature. Fourth, we compute the nozzle transfer functions for a range of Helmholtz numbers and friction factors. It is found that the friction and the Helmholtz number have a significant effect on the gain/phase of the reflected and transmitted waves. Finally, we calculate the effect that the friction of a nozzle guide vane has on thermoacoustic stability. It is found that the friction and the Helmholtz number can change thermoacoustic stability from a linearly stable regime to a linearly unstable regime. The study opens up new possibilities for the accurate prediction of indirect noise in realistic nozzles with implications on both noise emissions and thermoacoustic stability.