Numerical and asymptotic Lilley equation solutions for the Goldstein jet-noise source model

Morfey, C.L., Tester, B.J. and Powles, C.J. (2007) Numerical and asymptotic Lilley equation solutions for the Goldstein jet-noise source model. In Proceedings of the 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference). American Institute of Aeronautics and Astronautics. pp. 1-28 .

Abstract

Far-field sound radiation from model sources in a jet shear layer has been calculated numerically using the stationary phase approximation. The jet column is modeled as an axisymmetric parallel shear flow, so jet spreading is neglected. For this simplified model, analytical predictions are provided in the low and high frequency limits, k0?<<1 and k0?>>1 (k0 = acoustic wavenumber; ? = shear layer thickness). The low-frequency analytic result matches the numerical prediction quite closely up to k0? = 1; it accounts quantitatively for the observed strong scattering of quadrupole radiation by the mean velocity and density profiles in the jet. Further work is required to establish bounds of validity for the stationaryphase approximation, and to assess available high-frequency (k0?>1) approximations for the cone of silence region.

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