Spectral Broadening of Tonal Sound Propagating Through an Axisymmetric Turbulent Shear Layer

In aeroacoustics, spectral broadening refers to the scattering of tonal sound fields by turbulent shear layers, whereby the interaction of the sound with turbulent flow results in power lost from the tone and distributed into a broadband field around the tone frequency. Fan and turbine tone spectral broadening is known colloquially as "haystacking". Recently a new analytical model has been derived to predict weak spectral broadening of a tone radiated through a circular jet. A key part of the modeling is the choice of the two-point turbulent velocity cross-correlation function, which is used to provide a statistical description of the turbulence in the shear layer. A new cross-correlation function for an axisymmetric turbulent shear layer formed by a circular jet, based on the theory for homogeneous axisymmetric turbulence, has been developed. Validation results of weak-scattering calculated using this correlation function show better agreement with measurements when compared with the results calculated using a correlation function based on the theory for homogeneous isotropic turbulence.