Sound of transverse momentum fluxes in circular subsonic jets

Lighthill’s theory of aerodynamic sound is employed to model the acoustic far field of turbulent jets. The theory identifies the turbulence two-point statistics needed to compute the acoustic far-field. These statistics are obtained from hot wire measurements and a large eddy simulation, and the predicted acoustic far field is compared to microphone measurements. The acoustic far field is analysed for an observer at 90 degrees to the jet axis, where effects of the sound propagation through the mean flow can be ignored and source non-compactness effects are minimum (though not negligible). The theory shows how the acoustic spectrum is related to the cross-power spectral density of transverse momentum fluxes in the jet. The cross-power spectral density is written as power spectral density, coherence, and phase. Modelling the evolution of these three properties on the lipline of the jet enables the prediction of the acoustic far-field spectrum. The low-frequency range is underpredicted; but the level and decay of the spectrum at high-frequency is correctly predicted. The spectrum is shown to be proportional to St-5/3 at high-frequency for isothermal jets in the subsonic range (Mach number 0.5 to 1). This slope at high frequency is related to the quadrupolar efficiency of the source (which gives a factor of ∞ St4), the power spectral density (shown to be ∞ St-5/3) and the “spectrum” of length scales (shown to be ∞ St-1). Effects of source non-compactness due to turbulence convection are shown to be more significant than acoustic non-compactness and to be significant in most of the frequency range of interest. It is corroborated that modelling the evolution of turbulence two-point statistics in the jet plume and accounting for source non-compactness are key to model the sound radiated by turbulent jets