Multifractal analysis of flame dynamics during transition to thermoacoustic instability in a turbulent combustor

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.