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Influence of incidence angle on sound generation by airfoils interacting with high-frequency gusts

A theoretical model is developed for the sound generated when a convected vortical or entropic gust encounters an airfoil at non-zero angle of attack. The theory is based on a linearization of the Euler equations about the steady subsonic flow past the airfoil. High-frequency gusts, whose wavelengths are short compared to the airfoil chord, but long compared to the displacement of the mean-flow stagnation point from the leading edge, are considered. The analysis utilizes singular-perturbation techniques and involves four asymptotic regions. Local regions, which scale on the gust wavelength, are present at the airfoil leading and trailing edges. Behind the airfoil a ‘transition’ region, which is similar to the transition zone between illuminated and shadow zones in optical problems, is present. In the outer region, far away from the airfoil edges and wake, the solution has a geometric-acoustics form. The primary sound generation is found to be concentrated in the local leading-edge region. The trailing edge plays a secondary role as a scatterer of the sound generated in the leading-edge region. Parametric calculations are presented which illustrate that moderate levels of airfoil steady loading can significantly affect the sound field produced by airfoil–gust interactions.