Turbofan Aft Noise Predictions Based on Lilley's Wave Model

Abstract

To model the sound propagation through the discontinuous flow in a turbofan bypass configuration, a homogeneous linearized Lilley's equation is discretized in the frequency domain by using the Green's function discretization scheme. The main advantage of this third-order wave model, with respect to a conventional second-order model, is that it describes the refraction of an acoustic pressure field without restrictions on the ratio between the acoustic wavelength and the spatial nonuniformity scale of the mean flow. The resulting numerical model can be also applied in the vortex-sheet limit without any treatment of the wake shed from a trailing edge under sound excitation. Three-dimensional numerical solutions of the sound radiation from a bypass duct configuration are compared with analytical results available in the literature. Different cut-on duct modes are considered in the presence of different flow conditions, also including a developing mixing layer instead of an infinitesimal vortex sheet. The influence of an acoustically treated centerbody is also evaluated, as well as the noise scattering effects due to the presence of rigid splices on the afterbody. Additional key aspects of the present study are the use of a cylindrical formulation of the perfectly-matched-layer far-field condition, and the use of an iterative technique to solve the linear system without any observed occurrence of instability waves.