Indirect noise in non-isentropic flows
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. Indirect noise is a large contributor to aircraft engine noise, therefore, it is an important aspect of the design of an aircraft engine. It is essential to model indirect noise because it can add to the thermoacoustic feedback and contribute to instabilities. Computationally efficient low-order acoustic models help to identify the noise transfer functions and to predict and control the effects of indirect noise.
On the one hand, most of the indirect noise models in the literature assume the flow to be isentropic. However, in real situations, the flow is non-isentropic because of losses due to factors such as viscosity and recirculation zones. Recent studies showed, because of flow dissipation, there is a mismatch in the theoretical predictions from isentropic models and experimental observations. Hence, for accurate modelling of indirect noise we need physics-based models that capture the effect of non-isentropicity. In the first part of this thesis, we focus on the indirect noise generated because of temperature inhomogeneities (commonly referred to as entropy noise). We propose a low-order model from physical principles to predict the sound generated in nozzles with dissipation. We parametrize dissipation using a friction factor. We show that the friction factor can be used as a global parameter to model the dissipation due to various factors averaged across the cross section. We analyse the effect of dissipation on the acoustics. We find that the friction and the Helmholtz number have a significant effect on the gain/phase of the reflected and transmitted waves. Furthermore, in the second part, we extend the work to the modelling of indirect compositional noise in multicomponent flows with dissipation. We validate the proposed model with the experimental data available in the literature for binary mixtures of four gases. We find a semi-analytical solution with path integrals, which provide an asymptotic expansion with respect to the Helmholtz number. In addition, we introduce a scaling factor to quickly estimate compositional noise transfer functions for any mixture using knowledge of one single-component gas transfer functions. Moreover, we qualitatively show that the friction factor and Helmholtz number can become key factors in determining thermoacoustic stability of a system.
On the other hand, recent large-eddy simulations of a realistic aeronautical com- bustion chamber revealed the presence of weakly chemically reacting perturbations at the exit of the combustor. However, the models in the literature for the prediction of indirect noise assume the flow to be chemically frozen. Hence, in the third part of this thesis, we focus on the effect of weakly reacting flows on the nozzle acoustics. We propose a low-order model to predict indirect noise in nozzle flows with weakly reacting compositional inhomogeneities. We identify the physical sources of sound, which generate indirect noise via two physical mechanisms: (i) chemical reaction generates compositional perturbations, thereby adding to compositional noise; and (ii) exothermic reaction generates entropy perturbations. We numerically compute the nozzle transfer functions for different frequency ranges (Helmholtz numbers) and reaction rates (Damköhler numbers) in subsonic flows with hydrogen and methane inhomogeneities. In all the analysed cases, we observe that both Damköhler num- ber and Helmholtz number affect the phase and magnitudes of the transmitted and reflected waves. Hence, they are important parameters in the determination of the thermoacoustic stability of a system. This thesis provides mathematical models and physical insights into entropy and compositional noise, which opens new possibilities to accurately predict indirect noise and instabilities in aeronautical gas turbines.