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We propose a mathematical model from physical principles to predict the soundgenerated in nozzles with dissipation. The focus is on the sound generated fromthe acceleration of temperature inhomogeneities (also known as entropy waves),which is referred to as indirect noise. First, we model the dissipation causedby flow recirculation and wall friction with a friction factor, which enablesus to derive quasi-one-dimensional equations from conservation laws. The modelis valid for both compact nozzles and nozzles with a spatial extent. Second,the predictions from the proposed model are compared against the experimentaldata available in the literature. Third, we compute the nozzle transferfunctions for a range of Helmholtz numbers and friction factors. It is foundthat the friction and the Helmholtz number have a significant effect on thegain/phase of the reflected and transmitted waves. The analysis is performedfrom subsonic to supersonic regimes (with and without shock waves). Theacoustic transfer functions vary significantly because of non-isentropiceffects and the Helmholtz number, in particular, in the subsonic-choked regime.Finally, we calculate the effect that the friction of a nozzle guide vane hason thermoacoustic stability. It is found that the friction and the Helmholtznumber can change thermoacoustic stability from a linearly stable regime to alinearly unstable regime. The study opens up new possibilities for the accurateprediction of indirect noise in realistic nozzles with implications on bothnoise emissions and thermoacoustic stability. nozzles with implications on bothnoise emissions and thermoacoustic stability.

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