Supercritical bifurcations and nonlinear mode interactions of combustion instabilities in a centrally-staged swirl spray combustor

Centrally-staged combustors, characterized by a center pilot flame surrounded by an annual main stage flame, are widely used in modern aeroengines to achieve low NO_x emissions. However, due to the premixed combustion of the main stage, centrally-staged combustors are prone to combustion instability. This paper experimentally investigates the bifurcation behaviors and nonlinear dynamics of combustion instabilities in a centrally-staged swirl-stabilized combustor fueled by aviation kerosene fuel. The current study reveals that the swirling flame transitions from a stable state to a limit-cycle oscillation state either by increasing the overall equivalence ratio of the dome or by decreasing the fuel split ratio. This transition manifests as a supercritical Hopf bifurcation and is essentially governed by the main stage equivalence ratio. Synchronization between pressure and heat release rate fluctuations is found to occur when the main stage equivalence ratio surpasses a threshold, resulting in large-amplitude oscillations and ultra-harmonics that stem from nonlinear interactions. Bispectral mode decomposition is further employed to elucidate the nonlinear triadic interactions of the thermoacoustic system, successfully revealing the interaction routes among different modes. This analysis indicates that the triadic mode interactions predominately occur in the main flame region, while the pilot flame region is insignificant as long as the oscillation amplitude remains low. These findings provide a deeper understanding of the combustion instability in stratified swirling flames in general and contribute to the development of better strategies for controlling combustion instability in centrally-staged combustors in particular.