We study the spatio-temporal dynamics of high-frequency combustion instability in a model single-element rocket combustor using an acoustic energy flux-based spatial network. The acoustic energy source collapses by the formation of small communities with weak connection when the flame edge is attached to the injector rim. In contrast, large communities with strong connection are formed in the shear layer between the oxygen and hydrogen jets when the flame edge is detached from the injector rim, which has a significant impact on driving combustion instability. The switching between the attachment and detachment of the flame edge during combustion instability can be explained by the spectral-clustering-based transition network constructed from the pressure and flow velocity of the hydrogen jet at the injector exit, and the temperature near the injector rim.

This study numerically examines the gravitational effect on the nonlinear dynamics of a buoyant turbulent flame utilizing analytical methods based on complex networks and dynamical systems. A dense (sparse) network structure is formed in the near (far) field in low gravity, as shown by the degree and cluster coefficient in the spatial network. The global dynamics of the vertical flow velocity fluctuations in the intermittent luminous zone is synchronous with that of the temperature fluctuations in low gravity. The synchronized state disappears as the gravity level is increased, leading to a desynchronized state. These behaviors are clearly identified by the symbolic recurrence plots.

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