Computational identification and Stuart-Landau modeling of collective dynamical behaviors of octuple laminar diffusion flame oscillators

Annular combustion chambers, consisting of multiple flame nozzles, are commonly used in gas turbine engines, particularly in aircraft engines and industrial power generation systems. In the study, we proposed a novel approach to the problem of annular combustion with emphasis on the collective dynamical behaviours that its individuals do not have. A series of circular arrays of octuple flickering laminar buoyant diffusion flames were investigated computationally and theoretically. Five distinct dynamical modes, such as the merged, in-phase, rotation, flickering death, partially flickering death, and anti-phase modes, were computationally identified and interpreted from the perspective of vortex dynamics. These modes were classified into three regimes. A unified regime diagram was obtained in terms of the normalized flame frequency f/f₀ and the combined parameter (α−1)Gr^1/2, where α=l/D is the ratio of the flame separation distance l to the flame nozzle size D and Gr is the Grashof number. The bifurcation transition between the in-phase and anti-phase regimes occurs at (α−1)Gr^1/2=655±55, where flames present the totally or partially flickering death. In addition, a Stuart-Landau model with a nearest neighbor time-delay coupling was utilized to reproduce the general features and collective modes of the octuple oscillator flame systems.