Sound generation by a supersonic aerofoil cutting through a steady jet flow

Abstract

This paper examines the sound generation process when a supersonic aerofoil cuts through a steady jet flow. It is shown that the principal sound is generated by the leading edge of the aerofoil when it interacts with the streaming jet. To the leading order in terms of the jet velocity, no trailing-edge sound is generated. This is not the result of the cancellation of a trailing-edge sound by that from vortex shedding through the imposition of the Kutta condition. Instead, the null acoustic radiation from the trailing edge is entirely because, to the leading order, there is no interaction between the trailing edge and the jet. The effect of the trailing edge is to diffract sound waves generated by the leading edge. It is shown that the diffracted field (as well as the incident field) is regular at the trailing edge and the issue of satisfying the Kutta condition does not arise during the diffraction process. Thus, there is no extra vortex shedding from the trailing edge owing to its interaction with the flow, apart from those resulting from the discontinuity across the aerofoil, generated by the flow-leading edge interaction. This is in sharp contrast to the case of subsonic aerofoils where the removal of the singularity in the diffracted field at the trailing edge through the imposition of the Kutta condition results in vortex shedding from the sharp edge and energy exchange between the sound field and the vortical wake.