A weak-scattering model for turbine-tone haystacking

Abstract

Noise and emissions are critical technical issues in the development of aircraft engines. This necessitates the development of accurate models to predict the noise radiated from aero-engines. Turbine tones radiated from the exhaust nozzle of a turbofan engine propagate through turbulent jet shear layers which causes scattering of sound. In the far-field, measurements of the tones may exhibit spectral broadening, where owing to scattering, the tones are no longer narrow band peaks in the spectrum. This effect is known colloquially as ‘haystacking’. In this article a comprehensive analytical model to predict spectral broadening for a tone radiated through a circular jet, for an observer in the far field, is presented. This model extends previous work by the authors which considered the prediction of spectral broadening at far-field observer locations outside the cone of silence. The modelling uses high-frequency asymptotic methods and a weak-scattering assumption. A realistic shear layer velocity profile and turbulence characteristics are included in the model. The mathematical formulation which details the spectral broadening, or haystacking, of a single-frequency, single azimuthal order turbine tone is outlined. In order to validate the model, predictions are compared with experimental results, albeit only at polar angle equal to 90°. A range of source frequencies from 4 to 20 kHz, and jet velocities from 20 to 60 ms−1, are examined for validation purposes. The model correctly predicts how the spectral broadening is affected when the source frequency and jet velocity are varied.