Imaging of directional distributed noise sources

This study relates to the acoustic imaging of noise sources that are distributed and strongly directional, such as in turbulent jets. The goal is to generate high-resolution noise source maps with self-consistency, i.e., their integration over the extent of the noise source region gives the far-field pressure auto-spectrum for a particular emission direction. Self-consistency is possible by including a directivity factor in the formulation of the source cross-spectral density. The resulting source distribution is based on the complex coherence, rather than the cross-spectrum, of the measured acoustic field. For jet noise, whose spectral nature changes with emission angle, it is necessary to conduct the measurements with a narrow-aperture array. Three coherence-based imaging methods were applied to a Mach 0.9 turbulent jet: delay-and-sum beamforming; deconvolution of the beamformer output; and direct spectral estimation that relies on minimizing the difference between the measured and modeled coherences of the acoustic field. The delay-and-sum beamforming generates noise source maps with strong spatial distortions and sidelobes. Deconvolution leads to a five-fold improvement in spatial resolution and significantly reduces the intensity of the sidelobes. The direct spectral estimation produces maps very similar to those obtained by deconvolution. The coherence-based noise source maps, obtained by deconvolution or direct spectral estimation, are similar at small and large observation angles relative to the jet axis.