Influence of airfoil nose radius on sound generated by gust interactions

The sound radiated by interaction of a short wavelength gust (k much greater than 1) with a symmetric thin airfoil is analyzed. The theory is based on a linearization of the Euler equations about the subsonic mean flow past the airfoil. The sound generation mechanism is found to be concentrated in a local region surrounding the parabolic nose of the airfoil; the size of this local region scales on the gust wavelength. Airfoil thickness produces terms of relative order O(sq rt S) in the far field sound, where S is a Strouhal number based on the airfoil nose radius. At low Mach numbers, entropy gusts generate much less sound than vorticity gusts. However, for O(1) Mach numbers and moderate values of S, entropy and vorticity gusts produce similar sound levels.