Reduction of Leading-Edge Noise by Tailored Turbulence Anisotropy

This paper investigates the effect of anisotropic turbulence on the generation of leading-edge aerofoil-turbulence interaction noise, and further considers the dual impact of anisotropy in conjunction with an acoustically compliant (porous) edge. Thin airfoil theory is used to model an aerofoil as a semi-infinite plate and the scattering of incoming turbulence is solved via application of the Wiener-Hopf technique. In the case of a compliant plate modelled as having an impedance boundary condition, a useful numerical formulation using the Maliuzhuinets function is presented. This theoretical solution encapsulates the diffraction problem for gust-airfoil interaction, and is integrated over a wavenumber-frequency spectrum to account for anisotropic incoming turbulence. We verify our model against anisotropic data obtained experimentally by placing a leading edge in the wake of a cylinder, then proceed to demonstrate potential noise reduction from implementing Robin boundary conditions and by exploiting the anisotropic turbulence spectrum.