Analytical and experimental investigation into the effects of leading-edge radius on gust-aerofoil interaction noise

Abstract

This paper investigates the effects of local leading-edge geometry on unsteady aerofoil interaction noise. Analytical results are obtained by extending previous work for parabolic leading edges to leading edges of the form for . Rapid distortion theory governs the interaction of an unsteady vortical perturbation with a rigid aerofoil in compressible steady mean flow that is uniform far upstream. For high-frequency gusts interacting with aerofoils of small total thickness this allows a matched asymptotic solution to be obtained. This paper mainly focusses on obtaining the analytic solution in the leading-edge inner region, which is the dominant term in determining the total far-field acoustic directivity, and contains the effects of the local leading-edge geometry. Experimental measurements for the noise generated by aerofoils with different leading-edge nose radii in uniform flow with approximate homogeneous, isotropic turbulence are also presented. Both experimental and analytic results predict that a larger nose radius generates less overall noise in low-Mach-number flow. By considering individual terms in the analytic solution, this paper is able to propose reasons behind this result.