  Indirect noise is a significant contributor to aircraft engine noise, which
needs to be minimized in the design of aircraft engines. Indirect noise is
caused by the acceleration of flow inhomogeneities through a nozzle.
High-fidelity simulations showed that some flow inhomogeneities can be
chemically reacting when they leave the combustor and enter the nozzle (Giusti
et al., 2019). The state-of-art models, however, are limited to chemically
non-reacting (frozen) flows. In this work, first, we propose a low-order model
to predict indirect noise in nozzle flows with reacting inhomogeneities.
Second, 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. Third, we numerically
compute the nozzle transfer functions for different frequency ranges (Helmholtz
numbers) and reaction rates (Damk\"{o}hler numbers) in subsonic flows with
hydrogen and methane inhomogeneities. Fourth, we extend the model to supersonic
flows. We find that hydrogen inhomogeneities have a larger impact to indirect
noise than methane inhomogeneities. Both the Damk\"{o}hler number and the
Helmholtz number markedly influence the phase and magnitude of the transmitted
and reflected waves, which affect the sound generation and thermoacoustic
stability. This work provides a physics-based low-order model, which can open
new opportunities for predicting noise emissions and instabilities in
aeronautical gas turbines with multi-physics flows.
