Sound radiation from sources close to a corner in supersonic flow

Abstract

Scattering of sound waves by the sharp edges of a wing or blade arises in many practical situations in aeroacoustics, and can have a very significant effect on the radiation reaching an observer in the far field. In this paper, the practically important case of supersonic motion is considered, and we aim to extend previous work by including effects arising from the presence of the blade/wing tip. We therefore first consider the unsteady field produced by the interaction between a single point source located at a finite distance from the trailing edge of a rigid quarter plane in supersonic flow, and analyse both the resulting unsteady lift on the quarter plane and the radiation reaching the far field. The flow is seen to be crucially dependent on the way in which the source Mach cone intersects the quarter plane; in particular, the amplitudes of the unsteady lift and the radiation are seen to take maximum values when only the trailing edge is illuminated by the source, and are rather smaller when both the trailing edge and the side edge are illuminated. Our point-source solution is then used to investigate the radiation from turbulence lying in the vicinity of the corner, and we see that amplification occurs for those eddies lying within a wavelength of the edges, as originally discovered by Ffowcs Williams and Hall (1970). It is also seen that the side-edge amplification is significantly greater than that provided by the trailing edge, leading to the conclusion that the noise generated by turbulent flow near a supersonic blade or wing would be dominated by eddies lying close to the tip on the wavelength scale.