Direct combustion noise: Nearfield and non-compactness influences on pressure–heat release coherence

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There are several mechanisms through which turbulent flames produce sound. In low Mach number, unconfined flows, direct combustion noise – i.e., unsteady gas expansion generated by heat release fluctuations – is known to be a dominant contributor. This study is motivated by the fact that in the farfield, the coherence between spatially integrated heat release fluctuations from acoustically compact flames and direct combustion noise is unity. This suggests that the role of direct combustion noise relative to other sources can be ascertained from the value of the coherence. However, in practice it is difficult to fully satisfy the requirements to achieve a unity coherence, even in cases where direct combustion noise is the dominant noise source. This paper explores the contribution of noncompactness and nearfield effects on coherence. For the noncompactness part, while it is often the case that flames are small relative to a wavelength, they are never infinitesimally small. For the nearfield aspect, it is often not possible or practical to obtain farfield measurements, particularly in confined environments. This paper presents calculations that quantify how these noncompactness and nearfield effects influence coherence values. These calculations provide guidance on frequency ranges over which direct combustion noise will lead to near-unity coherence values, as well as required distances and optimal angles for acoustic instrumentation.Novelty and significance statementThis study presents a theoretical study on the coherence between heat release rate and acoustic pressure fluctuations, which has been mostly overlooked in prior literature. To the extent of the author’s knowledge, this is the first attempt that identify and investigate the inconsistencies between traditional theory and experimental literature on coherence. Results have implications for our previous understanding of the relationship between the heat release rate fluctuations and direct noise, aiding in future studies on combustion noise.