An analytic solution for gust-aerofoil interaction noise including effects of geometry
An analytic solution is obtained for the sound generated by gust-aerofoil interaction for aerofoils with thickness, camber, and angle of attack. The model is based on the linearisation of the Euler equations about a steady subsonic flow, and is an extension of previous work which considered restrictive aerofoil geometries. Only high-frequency incident gusts are considered. The aerofoil thickness, camber, and angle of attack are such that the steady flow past the aerofoil is seen as a small perturbation to uniform flow. The method of matched asymptotic expansions is used to identify regions around the aerofoil where different processes govern the generation or propagation of sound. Key local regions at the leading and trailing edges of the aerofoil determine the generation of noise whilst transition regions along the rigid aerofoil surface, and outer regions away from the surface play key roles in the propagation of sound. The effects of varying thickness and camber angle are discussed, along with the effects of varying the radius of the leading edge.