Acoustic ray method derived with the concept of analogue gravity for the calculation of the sound field due to rotating sound sources

摘要

Acoustics in a moving fluid is a simple model of an analogue space-time. The analysis shows that the null geodesics of the metric g(mu nu) in that space-time correspond to the rays in the eikonal approximation of geometrical acoustics. The physical connection to general relativity is the propagation of sound along the null geodesics that corresponds to the propagation of a scalar field in a background gravitational field. In this framework, we derive a three-dimensional acoustic ray method in a rotating frame of reference and calculate an acoustic metric, acoustic rays, travel times, and amplitudes for the fluctuating part of the pressure. Further the application to rotating beamforming, i.e., localization and estimation of the strength of rotating sound sources with a microphone array, is presented. Analytical calculations are compared with the spherical harmonic series expansion method for the sound propagation in the rotating frame of reference. Two benchmark cases on rotating sound sources with generic time-data and measured time-data of an axial fan demonstrate its applicability to rotating beamforming. (C) 2020 The Authors. Published by Elsevier Ltd.