Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor

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 ( $$ ), the joint probability of recurrence ( $$ ), the determinism ( $$ ), and the recurrence rate ( $$ ) of the joint recurrence matrix aid in detecting the synchronization transitions in this thermoacoustic system. We noticed that $$ and $$ can uncover the occurrence of phase synchronization state, whereas $$ and $$ 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 ( $$ ) and the heat release rate ( $$ ) fluctuations. We discover a possible asymmetric bidirectional coupling between $$ and $$ , wherein $$ is observed to exert a stronger influence on $$ than vice versa.