Phased array transformation methods to estimate non-compact jet noise source characteristics

Abstract

This paper reviews the basis of the beamformer and polar correlation phased array methods and shows that these provide different information about axially distributed, non-compact noise sources, which nevertheless satisfy a simple integral relationship. The conventional beamformer method provides an image of the source power or auto spectral density, whereas the polar correlation method yields a ‘source strength’ which is an image of the axial wavenumber transform of the source cross-spectral density. However, the beamformer method can be generalised to provide an image of the source cross-spectral density. At first sight, the generalised beamformer method is therefore more useful for diagnostic purposes but the results presented here suggest that the combined effects of resolution and source convection place serious limitations on the source cross-spectral density image information. For the same reasons, although the source power or auto spectral density axial shape can be obtained with the conventional beamformer method, it cannot yield its absolute level for this type of source. The polar correlation method yields a source strength axial distribution at each ‘reference’ microphone, which when integrated over the source length, yields the far-field power or auto spectral density at that reference microphone. Therefore, the polar correlation source strength is arguably the more relevant quantity to measure when determining what proportion of the sound at a particular microphone position comes from each region of the jet axis, as a function of radiation angle.