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Gas turbine combustors are susceptible to thermoacoustic instability, which manifests as large amplitude periodic oscillations in acoustic pressure and heat release rate. The transition from a stable operation characterized by combustion noise to thermoacoustic instability in turbulent combustors has been described as an emergence of order (periodicity) from chaos in the temporal dynamics. This emergence of order in the acoustic pressure oscillations corresponds to a loss of multifractality in the pressure signal. In this study, we investigate the spatiotemporal dynamics of a turbulent flame in a bluff-body stabilized combustor during the transition from combustion noise to thermoacoustic instability. During the occurrence of combustion noise, the flame wrinkles due to the presence of small-scale vortices in the turbulent flow. On the other hand, during thermoacoustic instability, large-scale coherent structures emerge periodically. These large-scale coherent structures roll up the wrinkled flame surface further and introduce additional complexity in the flame topology. We perform multifractal analysis on the flame contours detected from high-speed planar Mie scattering images of the reactive flow seeded with non-reactive tracer particles. We find that multifractality exists in the flame topology for all the dynamical states during the transition to thermoacoustic instability. We discuss the variation of multifractal parameters for the different states. We find that the multifractal spectrum oscillates periodically during the occurrence of thermoacoustic instability at the time scale of the acoustic pressure oscillations. The loss of multifractality in the temporal dynamics and the oscillation of the multifractal spectrum of the spatial dynamics go hand in hand.

Gas turbine engines are prone to the phenomenon of thermoacoustic instability, which is highly detrimental to their components. Recently, in turbulent combustors, it was observed that the transition to thermoacoustic instability occurs through an intermediate state, known as intermittency, where the system exhibits epochs of ordered behaviour, randomly appearing amidst disordered dynamics. We investigate the onset of intermittency and the ensuing self-organization in the reactive flow field, which, under certain conditions, could result in the transition to thermoacoustic instability. We characterize this transition from a state of disordered and incoherent dynamics to a state of ordered and coherent dynamics as pattern formation in the turbulent combustor, utilizing high-speed flame images representing the distribution of the local heat release rate fluctuations, flow field measurements (two-dimensional particle image velocimetry), unsteady pressure and global heat release rate signals. Separately, through planar Mie scattering images using oil droplets, the collective behaviour of small scale vortices interacting and resulting in the emergence of large scale coherent structures is illustrated. We show the emergence of spatial patterns using statistical tools used to study transitions in other pattern forming systems. In this paper, we propose that the intertwined and highly intricate interactions between the wide spatio-temporal scales in the flame, the flow and the acoustics are through pattern formation.

Thermoacoustic instability is the result of a positive coupling between the acoustic field in the duct and the heat release rate fluctuations from the flame. Recently, in several turbulent combustors, it has been observed that the onset of thermoacoustic instability is preceded by intermittent oscillations, which consist of bursts of periodic oscillations amidst regions of aperiodic oscillations. Quantitative analysis of the intermittency route to thermoacoustic instability has been performed hitherto using the pressure oscillations alone. We perform experiments on a laboratory-scale bluff-body-stabilized turbulent combustor with a backward-facing step at the inlet to obtain simultaneous data of acoustic pressure and heat release rate fluctuations. With this, we show that the onset of thermoacoustic instability is a phenomenon of mutual synchronization between the acoustic pressure and the heat release rate signals, thus emphasizing the importance of the coupling between these non-identical oscillators. We demonstrate that the stable operation corresponds to desynchronized aperiodic oscillations, which, with an increase in the mean velocity of the flow, transition to synchronized periodic oscillations. In between these states, there exists a state of intermittent phase synchronized oscillations, wherein the two oscillators are synchronized during the periodic epochs and desynchronized during the aperiodic epochs of their oscillations. Furthermore, we discover two different types of limit cycle oscillations in our system. We notice a significant increase in the linear correlation between the acoustic pressure and the heat release rate oscillations during the transition from a lower-amplitude limit cycle to a higher-amplitude limit cycle. Further, we present a phenomenological model that qualitatively captures all of the dynamical states of synchronization observed in the experiment. Our analysis shows that the times at which vortices that are shed from the inlet step reach the bluff body play a dominant role in determining the behaviour of the limit cycle oscillations.

Thermoacoustic systems with a turbulent reactive flow, prevalent in the fields of power and propulsion, are highly susceptible to oscillatory instabilities. Recent studies showed that such systems transition from combustion noise to thermoacoustic instability through a dynamical state known as intermittency, where bursts of large-amplitude periodic oscillations appear in a near-random fashion in between regions of low-amplitude aperiodic fluctuations. However, as these analyses were in the temporal domain, this transition remains still unexplored spatiotemporally. Here, we present the spatiotemporal dynamics during the transition from combustion noise to limit cycle oscillations in a turbulent bluff-body stabilized combustor. To that end, we acquire the pressure oscillations and the field of heat release rate oscillations through high-speed chemiluminescence ($CH^{\ast }$) images of the reaction zone. With a view to get an insight into this complex dynamics, we compute the instantaneous phases between acoustic pressure and local heat release rate oscillations. We observe that the aperiodic oscillations during combustion noise are phase asynchronous, while the large-amplitude periodic oscillations seen during thermoacoustic instability are phase synchronous. We find something interesting during intermittency: patches of synchronized periodic oscillations and desynchronized aperiodic oscillations coexist in the reaction zone. In other words, the emergence of order from disorder happens through a dynamical state wherein regions of order and disorder coexist, resembling a chimera state. Generally, mutually coupled chaotic oscillators synchronize but retain their dynamical nature; the same is true for coupled periodic oscillators. In contrast, during intermittency, we find that patches of desynchronized aperiodic oscillations turn into patches of synchronized periodic oscillations and vice versa. Therefore, the dynamics of local heat release rate oscillations change from aperiodic to periodic as they synchronize intermittently. The temporal variations in global synchrony, estimated through the Kuramoto order parameter, echoes the breathing nature of a chimera state.