  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.
