An advanced time approach for acoustic analogy predictions

Abstract

This paper deals with a new interpretation of the retarded time approach that is widely used in the prediction of acoustic fields from moving sources. A hierarchical inversion between the emission time and the reception time leads to advanced time approach. This consists in projecting the current status of a source in the observer time domain where the received signal is progressively built. The practical relevance of this methodology lies on two statements: no retarded time equations must be solved; an aerodynamic noise prediction can be processed parallelly to the aerodynamic computation. Theoretically, the advanced time approach differs from the retarded time approach only in one aspect. A signal emitted at a given instant by a point source, moving at subsonic as well as supersonic velocity, is received only one time by an observer moving at subsonic velocity. Consequently, only one value of the advanced time corresponds to a value of the emission time. The advanced time approach is herein applied to a retarded time solution of the Ffowcs Williams and Hawkings equation proposed by Farassat. The noise radiated by elementary acoustic sources in complex motion is then computed and checked against analytical solutions.