Investigating thermoacoustic instability mitigation dynamics with a Kuramoto model for flamelet oscillators

In this paper, we present experimental observations and phenomenological modeling of the intermittent dynamics that emerge while mitigating thermoacoustic instability by rotating the otherwise static swirler in a lean premixed, laboratory-scale combustor. Starting with a self-excited thermoacoustically unstable combustor, here we find that a progressive increase in swirler rotation rate does not uniformly decrease amplitudes of coherent, sinusoidal pressure or heat-release-rate oscillations. Instead, these oscillations emerge as high-amplitude bursts separated by low-amplitude noise in the signal. At increased rotational speeds, the high-amplitude coherent oscillations become scarce and their duration in the signal reduces. The velocity field from high-speed particle image velocimetry and simultaneous pressure and chemiluminescence data support these observations. Such an intermittent route to instability mitigation is reminiscent of the opposite transition implemented by changing the Reynolds number from a fully chaotic state to a fully unstable state. To model such dynamics phenomenologically, we discretize the swirling turbulent premixed flame into an ensemble of flamelet oscillators arranged circumferentially around the center body of the swirler. The Kuramoto model is proposed for these flamelet oscillators which is subsequently used to analyze their synchronization dynamics. The order parameter r, which is a measure of the synchronization between the oscillator phases, provides critical insights on the transition from the thermoacoustically unstable to stable states via intermittency. Finally, it is shown that the Kuramoto model for flamelet oscillator can qualitatively reproduce the time-averaged and intermittent dynamics while transitioning from the state of thermoacoustic instability to a state of incoherent noisy oscillations.