A mathematical model for the interaction of anisotropic turbulence with a rigid leading edge

Abstract

This paper investigates the effect of anisotropic turbulence on generating leading-edge aerofoil–turbulence interaction noise. Thin aerofoil theory is used to model an aerofoil as a semi-infinite plate, and the scattering of incoming turbulence is solved via the Wiener–Hopf technique. This theoretical solution encapsulates the diffraction problem for gust–aerofoil interaction and is integrated over a wavenumber–frequency spectrum to account for general incoming anisotropic turbulence. We develop a novel axisymmetric wavenumber–frequency model that captures the wall-normal variation in turbulence characteristics, differing from previous approaches. Then, the method of Gaussian decomposition, in which the generalised spectra are approximated through the weighted sum of individual Gaussian eddy models, is applied to fit the turbulence model to experimental data. Comparisons with experimental data show good agreement for a range of anisotropic ratios.