Nonlinear dynamics of spray combustion oscillations in a back-step combustor

We numerically study the nonlinear dynamics and driving mechanism of spray combustion oscillations in a back-step combustor using the complex network and machine learning. We mainly apply two methods: (i) the ordinal partition transition network in combination with the pseudo-periodic surrogate data method [Small et al., Physical Review Letters, vol. 87, p. 188101, 2001] and (ii) the causality analysis [Sugihara et al., Science, vol. 338, p. 496, 2012] to the spatiotemporal data during combustion oscillations obtained by large-eddy simulation [Kitano et al., Combust. Flame, vol. 170, p. 63, 2016; Pillai et al., Combust. Flame, vol. 220, p. 337, 2020]. The ordinal partition transition network entropy for the original data does not coincide with those for the pseudo-periodic surrogate data. This indicates that the dynamic behavior of spray combustion oscillations represents a deterministically chaotic state. The causal analysis based on a random forest [Leng et al., Chaos, vol. 29, p. 093130, 2019] shows that the flow velocity inside the combustor strongly affects the evaporation rate fluctuations of fuel droplets, which in turn drives the heat release rate fluctuations. This directional coupling has a significant impact on the driving of spray combustion oscillations with low-dimensionally chaotic dynamics.