Directivity of acoustic emissions from wave packets to the far field

Abstract

We investigate the acoustic emission from wave packets to the far field. To this end, we develop a theory for one-and two-dimensional source fields in the shape of wave packets with Gaussian envelopes. This theory is based on an approximation to Lighthill's acoustic analogy for distant observers. It is formulated in the spectral domain in which a Gaussian wave packet is represented again by a Gaussian. This allows us to determine the directivity of the acoustic emission (e.g. superdirectivity and Mach waves) by simple geometric constructions in the spectral domain. It is shown that the character of the acoustic emission is mainly governed by the aspect ratio and the Mach number of the wave packet source. To illustrate the relevance of this theory we use it to study two prominent problems in subsonic jet aeroacoustics.

A study of Mach wave radiation using active control

“…Tam 1995;Avital, Sandham & Luo 1998;Obrist 2009;Tam 2009). The basic construction of this discussion has been that a single perturbation frequency should be broadened by the spatiotemporal variation of amplification in the jet.…”

Acoustic emissions from convected wave packets

“…1-3, 10, 12, and 15͒ used asymptotic matching to relate hydrodynamic instabilities of the shear flows to the acoustic far field. Other studies 6,9,16 determined the acoustic far field by solving an inhomogeneous wave equation in free space, while Haj-Hariri and Akylas 17 and Crighton and Huerre, 7 for instance, solved the homogeneous wave equation and introduced the acoustic source through inhomogeneous boundary conditions.…”

“…The present work is an extension of a paper on the acoustic emission from standing wave packets, 9 i.e., wave packets with a stationary envelope. This study developed a theoretical framework on the basis of a spectral formulation of Lighthill's acoustic analogy which was then used to explain various directivity patterns such as superdirectivity, bidirectivity, and Mach waves.…”

“…This is similar to the approach used by Huerre and Crighton, 6 Crighton and Huerre, 7 and Obrist. 9 On the one hand, this approach is somewhat abstract because it does not address the question how or where the wave packet source has originated. On the other hand, it allows a detailed discussion of the fundamental relationship between the properties of wave packet sources and their acoustic emission to the far field, e.g., the influence of the shape of the wave packet envelope on the directivity of the acoustic emission.…”

The separation of radiating and non-radiating near-field pressure fluctuations in supersonic jets

“…Following the prevailing analysis in recent publications (see for example [9][10][11]), these noise sources are modeled as spatially organized wavepackets of the near-field pressure fluctuations at discrete frequencies. Experimental measurements of the near-field pressure fluctuations have identified the wavepacket structures, and their predicted acoustic radiation showed favorable agreement with far-field noise measurements [12][13][14].…”