A Weak Scattering Model for Tone Haystacking

Abstract

The scattering of sound by turbulence in a jet shear layer is considered. Spectral broadening or ‘haystacking’ is the process whereby the turbulent, timevarying inhomogeneities in the ∞ow scatter tonal sound flelds, which decreases the level of the incident tone, but increases the broadband level around the frequency of the tone. The scattering process is modelled analytically, using high-frequency asymptotic methods and a weak-scattering assumption. Analytical models for the far-fleld spectral density of the scattered fleld are derived for two cases: (1) any polar angle including inside the cone of silence; (2) polar angles outside the cone of silence. At polar angles outside the cone of silence, the predictions from the two models are very similar, but using the second model it is considerably simpler to evaluate the far-fleld spectral density. Simulation results are compared to experimental data, albeit only at a polar angle of 90 ‐ . The model correctly predicts the behaviour of the scattered fleld as a function of jet velocity and tone frequency. Also simulations at other polar angles and a parametric study are presented. These simulations indicate how the ‘haystacking’ is predicted to vary as a function of the polar angle, and also as a function of the characteristic length, time and convection velocity scales of the turbulence contained in the jet shear layer. Spectral broadening is a phenomenon whereby a tonal sound fleld interacts with a random time-varying scattering medium, with the result that power is lost from the tone and distributed into a broadband fleld around the tone frequency. Spectral broadening has been observed in far-fleld measurements of turbine tones, and to a lesser extent, fan tones radiated from the rear of a turbofan engine. The efiect is caused by the interaction of the tones radiated from the engine exhaust duct with the turbulence in the jet shear layers. Turbulent jet shear layers are formed between the hot core jet and cold bypass streams, and also between the bypass and ∞ight streams. Sound radiated from the exhaust propagates through these turbulent shear layers, and owing to the unsteady nature of turbulent ∞ow, this can scatter sound over a range of frequencies. The resulting scattered broadband fleld, known colloquially as a ‘haystack’, can be measured well above the jet-noise broadband at some engine conditions. In the context of this work, when the proportion of scattered energy is small relative to the energy that remains in the tone, this is termed ‘weak scattering’. An example of the spectrum from a tonal fleld which has undergone ‘weak’ spectral broadening is shown in flgure 1, which is taken from the experimental work of Candel, Guedel, & Julienne. 1 The level of the tone is around 20dB above that of the haystacks. However, spectral broadening can lead to the disappearance of the tone itself, replaced by a broadband hump. In the context of this work, this would be termed ‘strong scattering’.