Chaotic and linear statistics analysis in thermoacoustic instability detection

Recent experiments reveal that even simple thermoacoustic systems may exhibit nonlinear behavior, far more elaborate than period-1 limit cycle oscillations. Consequently, a new approach based on nonlinear dynamics is emerging besides conventional linear analysis to characterize unstable regimes in gas turbine combustors. This approach reducesor avoids the risk of misunderstanding the deterministic chaos, hidden in the measured signals also during stable combustion regimes, as stochastic noise. The gained information will be available to analytically formulate an index acting as the earliest warning signal of an impending oscillatory combustion instability. In light of this, we first apply the chaotic analisys to an unsteady thermoacoustic time series coming from a typical industrial combustor operated in a stability-to-humming/back-to-stability transition. Then, observing that the Rayleigh and extended Chu indices describe the instability as a linear-interaction-induced synchronization between heat release and flow disturbances, to account for nonlinear interactions, the chaotic synchronization theory is applied. In particular, the interdependence index E, a nonlinear causality detector, with no previous applications in combustion instability sensing, is proven to be more effective than linear analysis detectors, both in the early perception of self-sustained (chaotic or not) thermoacoustic oscillations and in gaining meaningful insight on unsteady combustor physics.