An analytical model of sound refraction by the fuselage boundary layer for fan tone radiation from a turbofan aero-engine

The work presented in this paper is on the development and validation of an analytical-based model to predict scattering of fan tone noise from a turbofan engine by the airframe fuselage and refraction due to the presence of a boundary layer on the fuselage. The aim is to avoid numerical solutions to calculate sound propagation through the fuselage boundary layer which have been prevalent in previous work on this topic. The work presented here is a continuationof the work by the authors in which the 1/7th power-law boundary-layer velocity profile was replaced with a linear profile which enabled an analytical solution of the Pridmore-Brown equation. The work presented here offers an even simpler alternative solution by replacing the power-law profile with a step function. This approach once again leads to a far-field solution in terms of a Fourier series, and a near-field solution expressed in terms of a Fourier series and an inverse Fourier transform. The two approaches utilising a linear or step-function velocity profile are compared with each other, and against existing numerical results. The results show that for sufficiently thin boundary-layers both approaches can approximate a more realistic power-law boundary-layer profile, while the accuracy of the step-function solution appears to not deteriorate with thicker layers. A parametric study based on multi-modal simulations is performed with realistic operating and flight conditions. Predictions for boundary-layer shielding and the far-field polar directivity are generated with both linear and step-functio