Low-Order Modeling of Interacting Flames in an Annular Combustor: Mutual Coupling and Synchronization within a Stochastic Environment

Interacting flames in continuous combustion systems can exhibit complex nonlinear dynamics, particularly under the influence of inherent stochastic fluctuations. In this study, we adopt a low-order modeling approach to capture the essential features of mutual coupling and synchronization in such systems. Specifically, we investigate the behavior of two flames in an annular combustor operating within a stochastic environment and subject to external acoustic forcing. Experimental measurements reveal the emergence of asymmetric limit-cycle oscillations, indicating localized lock-in. To interpret these dynamics, we adopt a Van der Pol-type low-order model comprising two coupled self-sustained oscillators, each subjected to both stochastic excitation and sinusoidal forcing. The model illustrates how local synchronization with the external signal—mediated by coupling strength—governs the onset of high-amplitude oscillations. Through system identification using experimental data, we demonstrate that enhanced coupling alone can induce a bifurcation toward self-excited dynamics without requiring changes in intrinsic flame properties. This combined experimental and modeling approach offers a predictive framework for analyzing flame–flame interactions and lock-in phenomena in practical combustion systems.