Noise generation by turbulent flow in ducts

Abstract
The aim of this work is to estimate the sound power generated by a turbulent flow in a duct from the knowledge of mean quantities which can be computed with a [MATH] turbulence model when only the plane wave can propagate, i.e., when the characteristic frequency of the turbulence is low. It does turn out to be possible for the simplest configuration of a duct free of internal obstruction. The result provides a prediction which gives rise to a U⁷ scaling law for the variation of the acoustic power. Nevertheless, there is no experimental data to compare our results with for this idealized configuration. That is why we tackled the problem of a duct obstructed by a diaphragm. Using conformal mapping and Matched Asymptotic Expansions, we have determined a two-dimensional Green's function which allow us to assess numerically the acoustic power. This case is more interesting because existing experimental data confirmed the U⁴ scaling law obtained by calculation for the acoustic power variation.