Analytical study of coherence between flame heat release and acoustic pressure fluctuations

A number of modeling and experimental studies have considered the role of direct combustion noise relative to other noise sources from aircraft engines. Indeed, in low Mach number flows, these analyses predict that direct combustion noise is dominant. This implies that the coherence between heat release fluctuations and far-field acoustic pressure should have near unity values. Relatively little coherence data exist, however, and the limited data sets show much lower broadband heat release-pressure coherence values- typically on the order of 0.1- 0.3. This implies that either direct combustion noise is the not the dominant noise production mechanism, that there is a problem with the measurement, or that additional confinement or near field effects reduce coherence. This study analytically considers the role of near-field effects on these reduced coherence values. The coherence between the globally integrated heat release rate and acoustic pressure fluctuations is analytically and numerically investigated. Asymptotic methods are applied to a canonical problem to investigate scaling laws. Finally, a Green's function approach is investigated as a method to study the effects of a confined boundary. These studies suggest that near-field effects do reduce coherence values but do not fully account for the values seen in experimental measurements. These results demonstrate that significant open questions exist today about the role of direct combustion noise.