On indirect noise in multicomponent nozzle flows

TL;DR

This paper models unsteady multicomponent nozzle flows to identify how compositional inhomogeneities generate indirect noise, revealing the roles of thermodynamic variables and flow gradients in sound production.

Contribution

It introduces a thermodynamic framework and mathematical solution for quantifying indirect noise sources in multicomponent nozzle flows, advancing understanding of aeroacoustic phenomena.

Findings

Compositional inhomogeneities induce sound via chemical potential and heat capacity variations.

Linear acoustic, entropy, and compositional perturbations evolve independently but couple through flow gradients.

Transfer functions for supersonic nozzles with methane-air inhomogeneities are computed.

Abstract

A one-dimensional, unsteady nozzle flow is modelled to identify the sources of indirect noise in multicomponent gases. First, from non-equilibrium thermodynamics relations, it is shown that a compositional inhomogeneity advected in an accelerating flow is a source of sound induced by inhomogeneities in the mixture (i) chemical potentials and (ii) specific heat capacities. Second, it is shown that the acoustic, entropy and compositional linear perturbations evolve independently from each other and they become coupled through mean-flow gradients and/or at the boundaries. Third, the equations are cast in invariant formulation and a mathematical solution is found by asymptotic expansion of path-ordered integrals with an infinite radius of convergence. Finally, the transfer functions are calculated for a supersonic nozzle with finite spatial extent perturbed by a methane-air compositional inhomogeneity. The proposed framework will help identify and quantify the sources of sound in nozzles with relevance, for example, to aeronautical gas turbines.