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Thermoacoustic instability is a result of the positive feedback between the acoustic pressure and the unsteady heat release rate fluctuations in a combustor. We apply the framework of the synchronization theory to study the coupled behavior of these oscillations during the transition to thermoacoustic instability in a turbulent bluff-body stabilized gas-fired combustor. Furthermore, we characterize this complex behavior using recurrence plots and recurrence networks. We mainly found that the correlation of probability of recurrence (CPR), the joint probability of recurrence (JPR), the determinism (DET), and the recurrence rate (RR) of the joint recurrence matrix aid in detecting the synchronization transitions in this thermoacoustic system. We noticed that CPR and DET can uncover the occurrence of phase synchronization state, whereas JPR and RR can be used as indices to identify the occurrence of generalized synchronization (GS) state in the system. We applied measures derived from joint and cross recurrence networks and observed that the joint recurrence network measures, transitivity ratio, and joint transitivity are useful to detect GS. Furthermore, we use the directional property of the network measure, namely, cross transitivity to analyze the type of coupling existing between the acoustic field (p′) and the heat release rate (q˙′) fluctuations. We discover a possible asymmetric bidirectional coupling between q˙′ and p′, wherein q˙′ is observed to exert a stronger influence on p′
than vice versa.
In practical combustion systems, a positive coupling between the acoustic field and the unsteady heat release rate fluctuations results in the occurrence of ruinously large amplitude acoustic oscillations, commonly referred to as the thermoacoustic instability. Recently, many studies have been conducted to investigate the transition to such instabilities from a state of combustion noise (stable state composed of low amplitude aperiodic oscillations) to thermoacoustic instability. As thermoacoustic instability is a result of coupled behavior between the acoustic pressure and the heat release rate, synchronization theory has been introduced to quantify the coupling between them. Pawar et al.25 have found that the periodic oscillations exhibited during the state of thermoacoustic instability are of two types, namely, weakly correlated and strongly correlated limit cycle oscillations. The difference between these states can be attributed to the extent of coupling that exists between the heat release rate and the acoustic oscillations in the system. Hence, it is important to characterize the synchronization transition to thermoacoustic instability in order to detect the occurrence of these dynamical states and also the directional dependence between these oscillations. We apply measures derived from recurrence plots and recurrence networks to detect the synchronization transition observed during the onset of thermoacoustic instability. Furthermore, we characterize the directional dependence between the acoustic field and the heat release rate fluctuations using measures derived from the cross recurrence networks constructed from their time series
