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

This paper reviews the basis of the beam former (BF) and polar correlation (PC) 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 BF method provides an image of the source PSD, whereas the PC method yields a ‘source strength’ which is an image of the axial wavenumber transform of the source CSD. However, the BF method can be generalised to provide an image of the source CSD. At first sight the generalised BF 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 CSD image information. For the same reasons, although the source PSD axial shape can be obtained with the conventional BF method, it cannot yield its absolute level for this type of source. The PC method yields a source strength axial distribution at each ‘reference’ microphone, which when integrated over the source length, yields the far-field PSD at that reference microphone. Therefore the PC 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