Revisiting the frozen gust assumption through the aeroacoustic scattering of wavepackets by a semi-infinite plate

Abstract

This paper presents an analytic solution for the aerodynamic noise generated by a traveling wavepacket passing near the edge of a rigid semi-infinite flat plate. The solution is derived in the time domain for a wavepacket of either constant or spatially-varying wavenumber, for which novel closed-form expressions are obtained for the incident and scattered sound fields. The case of a varying wavepacket constitutes a surrogate model for turbulent flow distortions caused by the edge region and its geometry. This modeling approach permits a relaxation of the frozen gust assumption that is commonly used in the analytical prediction of trailing-edge noise, whereby the local vorticity is assumed to be unaffected by the edge. Our results shed light on the role that spatial variations of the vortical field near the trailing edge have on the incident and scattered sound contributions to the acoustic far field. In particular, we find that the wavenumber modification has a significant effect on the incident field but not on the scattered field amplitude. However, the phase difference between the incident and scattered fields depends strongly on the spatial variation in the wavepacket wavenumber, which leads to a variation in the sound level and directivity of the total pressure field.