Sound power from a collection of monopoles with arbitrary coherence: Theory and application to aeroacoustic noise sources

Sound power is a fundamental characteristic of an acoustic source that is critical to developing radiation models. Current analytical methods for calculating sound power from a collection of monopoles either assume perfect coherence or incoherence. However, partially coherent sources are plentiful in structural acoustics and aeroacoustic applications. This paper expands the approach of Nelson, Curtis, Elliott, and Bullmore [(1987). J. Sound Vib. 116, 397-414], who calculated sound power due to mutual coupling between coherent sources, to allow for partially coherent interactions. This expression is used to find the sound power from quadrupole-like source configurations with varying degrees of coherence. When calculating the sound power, partially coherent interactions are limited by two factors: a coupling distance and the coherence length. A numerical example of a driven plate is used to demonstrate the regions where the partially coherent sound power is most applicable. It is shown that when the system coherence length is larger than about one wavelength, the sound power can be calculated assuming a fully coherent source. A final example is shown for the T-7A jet at MIL and AB engine conditions. Sound power spectra are created from an equivalent source model of partially coherent monopoles and compared to measured far-field spectra.