High sensitivity of indirect noise predictions in non-isentropic nozzles

In aircraft engine combustors, incomplete mixing and air cooling give rise to flow inhomogeneities. When accelerated through the nozzle guide vane downstream of the combustor, these inhomogeneities give rise to acoustic waves. This is commonly known as indirect combustion noise. When these sound waves are reflected off the outlet and travel upstream of the combustor, they can lead to thermoacoustic oscillations. To predict indirect noise, models proposed in the literature assume the frequency of impinging disturbances to be small (compact nozzle assumptions). However, in reality, the assumption might not hold; hence, a mismatch in the predicted and experimental results can be observed. First, we present a semi-analytical solution to a non-isentropic nozzle indirect noise model using asymptotic expansion. Second, we show that the indirect noise predictions are sensitive to a small change in the Helmholtz number for a nearly compact nozzle, especially in the subsonic flow regime. We also show the predictions become lesser sensitive as the non-isentropicity increases. This study highlights the importance of non-compact assumptions for the accurate prediction of indirect noise transfer functions and thermoacoustic instability in aeronautical gas turbines.