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

TL;DR

This paper develops a physical model to predict indirect noise generated by entropy waves in non-isentropic nozzles, analyzing the effects of dissipation, flow regimes, and friction on acoustic transfer functions and stability.

Contribution

It introduces a new mathematical model based on physical principles that accounts for dissipation and predicts transfer functions across various flow regimes, including shock presence.

Findings

Friction and Helmholtz number significantly influence wave reflection and transmission.

The model accurately predicts experimental data for different nozzle configurations.

Friction effects can alter thermoacoustic stability from stable to unstable regimes.

Abstract

We propose a mathematical model from physical principles to predict the sound generated in nozzles with dissipation. 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 from conservation laws. The model is valid for both compact nozzles and nozzles with a spatial extent. Second, the predictions from the proposed model are compared against the experimental data available in the literature. Third, 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. The analysis is performed from subsonic to supersonic regimes (with and without shock waves). The acoustic transfer functions vary significantly because of non-isentropic effects and the Helmholtz number, in particular, in the subsonic-choked regime. 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. nozzles with implications on both noise emissions and thermoacoustic stability.