Computational Identification and Stuart-Landau Modeling of Collective Dynamical Behaviors of Octuple Laminar Diffusion Flame Oscillators

Annular chambers, consisting of multiple flame nozzles, are frequently used in many industrial processes, for example, rocket engines and gas turbines. In the study, we proposed a novel approach to the problem of annular combustion with emphasis on the collective dynamical behaviors 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 mode, rotation, flickering death, partially flickering death, and anti-phase modes, were computationally identified and interpreted from the perspective of vortex dynamics. A unified regime diagram was obtained in terms of the normalized flame frequency f/f_0 and the combined parameter ({\alpha}-1)Gr^1/2, where {\alpha}=l/D is the ratio of the flame separation distance l to the flame nozzle diameter D and Gr is the Grashof number. The bifurcation transition from the in-phase mode and the anti-phase mode to the totally or partially flickering death occurs at ({\alpha}-1)Gr^1/2=655+-55. In addition, a Stuart-Landau model with a time-delay coupling was utilized to reproduce the general features and collective modes of the octuple oscillators flame systems.