Computational study of the spectral broadening of an acoustic tone by turbulence

Abstract

Spectral broadening results from the unsteady scattering of acoustic waves propagating across a region of turbulence. This phenomenon has been observed previously for an harmonic source radiating through the shear layer of a cold jet at low speed. The resulting spectra displayed a reduced tone peak surrounded by lateral bands, with changes in these bands levels and width depending on the source and flow parameters. In this paper, spectral broadening is studied numerically for a simple configuration, consisting of a monopole radiation scattered by a turbulent layer with a constant thickness and convected by a uniform mean velocity. The numerical method relies on a finite difference code solving the linearized Euler equations in the time domain. The turbulent layer is synthesized with a stochastic method based on the filtering of white noise to impose prescribed statistical properties to the turbulence. The turbulent fluctuations are then added to the steady mean flow to form an unsteady base flow around which the Euler equations are linearized. This introduces terms involving products between the turbulent and acoustic fluctuations which are responsible for the scattering. Such a numerical methodology allows to vary the properties of the turbulence generated for the chosen configuration such as the turbulent kinetic energy and the integral length scale. In this paper, the effects of several parameters such as the convection velocity and source frequency on the spectral broadening are studied. The trends deduced from the results can be compared to previous models and experimental data for a jet shear layer, and they can also be related to the trends observed in a previous study of the scattering of sound by a single convected vortex.

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