Sound Generation in Multicomponent Nozzle Flows With Dissipation

Low emission aircraft engines burn in a lean regime, which makes the combustor susceptible to unsteady combustion. Along with improper mixing and air cooling, the unsteady combustion process gives rise to flow inhomogeneities. The acceleration of these inhomogeneities in the nozzle downstream of the combustor generates indirect combustion noise. If the acoustic waves that are reflected off the nozzle are sufficiently in phase with the heat released by the flame, thermoacoustic instabilities can occur. The generation and transmission of sound through the nozzle guide vane are typically modeled with a compact and isentropic nozzle model. Because the flow is non-isentropic due to losses from wall friction and recirculation zones, in the literature, a mismatch is observed between experimental and theoretical predictions in subsonic-choked regimes. In this work, we propose a low-order physical model to predict indirect noise in a multicomponent nozzle flow with dissipation using conservation laws whilst modeling non-isentropicity using a friction factor. The model is generalized for finite-length (non-compact) arbitrary geometry nozzles. We show that the friction factor can account for wall friction and two (or three) dimensional effects, such as flow recirculation in a cross-averaged sense. We analyze the model numerically for both subsonic and supersonic nozzles, emphasizing the importance of non-isentropic and non-compact assumptions with compositional inhomogeneities. Further, we show the effect of the nozzle geometry. The results are validated with existing experimental data from the literature.