Thermoacoustic instabilities: Should the Rayleigh criterion be extended to include entropy changes?
نویسندگان
چکیده
The Rayleigh criterion (which measures the correlation between pressure and heat release) is the standard tool used to investigate and predict combustion instabilities both in experimental and numerical studies. However, the Rayleigh term is just one of the terms appearing in the acoustic energy equation. The recent development of Large Eddy Simulations (LES) for combustion chambers allows to completely close the budget and analyze all terms in this equation. This task leads to unexpected difficulties and requires some basic work since multiple definitions of the energy of fluctuations in a reacting compressible flow can be derived. The objective of this paper is to revisit the theoretical derivations of the fluctuation energy equations. Two forms of energy are defined: the first one is the classical acoustic energy (AE) introduced by various authors [1− 3]. The second one is the fluctuation energy (FE) presented by Chu [4]. Both equations are rederived in a compact manner starting from full non-linear forms. It is shown that the classical Rayleigh criterion naturally appears as the source term of the AE equation while the FE form leads to a different criterion stating that temperature and heat release must be in phase for the instability to be fed by the flame/acoustics coupling. The FE form also integrates the fluctuations of three variables (pressure, velocity and entropy) while the AE form uses only pressure and velocity perturbations. It is shown that only the FE form should be used in flames, in contradiction with many present studies performed for combustion instabilities.
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