Computational Identification and Stuart-Landau Modeling of Collective Dynamical Behaviors of Octuple Laminar Diffusion Flame Oscillators (2312.02018v3)

Abstract: 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.