We observe the transition from low-amplitude, seemingly random aperiodic fluctuations (combustion noise) to high-amplitude, periodic, limit cycle oscillations (thermoacoustic instability) via intermittency with increasing flow Reynolds number in a bluff-body stabilized turbulent combustor. Complex networks enable the possibility of visualizing the underlying dynamics and interaction between different components in the dynamical systems. We investigate this transition to thermoacoustic instability in a turbulent combustor using complex networks. Complex network theory is emerging very rapidly due to its applicability in a variety of fields. In this paper, unsteady pressure data which is indicative of the system dynamics in a thermoacoustic system is converted into complex networks using a visibility algorithm. We show that the complex network corresponding to combustion noise during the stable operation of the combustor exhibits scale-free behavior. The scale-free behavior of combustion noise disappears at the onset of thermoacoustic instability. We further show that thermoacoustic instability corresponds to a regular network. The transition from combustion noise to thermoacoustic instability is represented in the topology of the complex networks as a transition from complex scale-free structure to ordered regular structure.
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