Multi-modal effects on indirect noise induced by turbulent entropy fields

Planar entropy waves are commonly assumed for predicting indirect combustion noise. However, the non-planar and turbulent nature of flows found in most practical combustors challenges this assumption. In the present paper, we examine the indirect noise generated by non-planar and turbulent entropy fields through subsonic nozzles. Firstly, we introduce a new transfer function framework that accounts for the contribution of non-planar Fourier modes of the entropy field to the indirect noise spectra. When applied to a turbulent flow field, this method demonstrates a significant improvement in spectral predictions compared with a conventional approach that only considers the planar mode. Secondly, simulations show that non-planar Fourier modes become significant above a threshold frequency $f_{thresh}$ , found in the mid- to high-frequency range. This contribution of non-planar modes is explained by two-dimensional shear effects that distort the entropy waves. A scaling relation that uses residence times along streamlines is developed for $f_{thresh}$ , showing good agreement with simulation results. Finally, we show that the indirect noise from non-planar entropy modes found in aviation combustors can be significant at frequencies below 1 kHz, which might be relevant in situations of thermo-acoustic instabilities coupled to indirect noise.