Abstract
In this work, the dynamics of the pressure oscillations and flame behaviors in a premixed swirl-stabilized combustor were experimentally investigated. As equivalence ratio Φ varied between 0.55 and 1.35, five combustion states were distinguished based on the characteristics of the acoustic pressures and flame dynamics. The permutation entropy (PE) and proper orthogonal decomposition (POD) were used to analyze the fluctuating pressure signal complexities and spatial CH⁎ chemiluminescence images, respectively. The results showed that the magnitude of the PE was at a differentiable level. In addition, the POD modes exhibited distinguishable features when the system was in different combustion states. Further analyses of the state transitions indicated that the system underwent a supercritical Hopf bifurcation and a pair of fold bifurcations when Φ was in the lean condition. The state transition from quasi-periodic oscillation to limit-cycle oscillation was attributed to the movement of the flame location, which enhanced the coupling of the acoustics and combustion by reducing the phase difference between the pressure oscillations and heat release fluctuations. In addition, a hysteresis phenomenon was observed for the trajectory of the fluctuating pressure root-mean-square (RMS) value in the forward and backward processes of the equivalence ratio under the lean condition. A low-order model was used to capture the bifurcations; the theoretical results agreed well with the experimental data. As for the rich condition, a supercritical Hopf bifurcation was captured when the system switched between the dual-frequency oscillation mode and the rich stable state. Furthermore, the influence of combustion chamber length Lc on the combustion stability in relation to Φ was investigated. Parameter Lc was divided into steady and unsteady regions depending on whether the combustion system could reach limit-cycle oscillation. The PE was demonstrated to be effective in distinguishing the stable state and limit-cycle oscillation even for combustors of different lengths. Understanding the nonlinear dynamics by analyzing experimental data could be critical to developing models for the prediction and suppression of thermoacoustic instabilities.