A weak-scattering model for tone haystacking caused by sound propagation through an axisymmetric turbulent shear layer

摘要

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". Spectral broadening causes substantial difficulties in determining the relative importance of various sources of turbo-fan engine noise, as it scatters sound generated by tonal sources across a wide frequency range. This obscures the importance of some key sources of tone noise by apparently reducing their prominence, the resultant broadband noise being often difficult to attribute. Recently a new analytical solution has been derived to predict weak spectral broadening of a tone radiated through a circular jet. In this paper, validation of the weak scattering model is presented. A key aspect of the modelling 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. Results obtained using three different cross-correlation functions are compared. These include cross-correlation functions which have been developed using the theory for homogeneous isotropic turbulence or using the theory for homogeneous axisymmetric turbulence. In particular, 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 to the results calculated using correlation functions based on the theory for three-dimensional homogeneous isotropic turbulence.