Comparative Analysis of Cool Flame Oscillation Occurred Around a Single Fuel Droplet and a Droplet Pair Using a Phase Space

Abstract

The cool flame oscillation occurred around a fuel droplet pair is compared with that around a single droplet. A Variational Auto-Encoder (VAE), a kind of deep neural network, was trained by data of these oscillations. The encoder part of the VAE reduces the data into three dimensions. The data is projected to trajectories in a phase space spanned by the three latent variables from the encoder. The submanifolds, on which the trajectory for each of the single droplet and the droplet pair case were mapped, were determined in the space to sample physical states represented by the distribution of temperature and species mass fraction. The difference distributions, derived by subtracting those of the single droplet from the droplet pair’s distribution, were used to identify the physical process during the cool flame oscillations. Distributions of temperature and mass fractions are sampled at different phases of the oscillation. Similar phenomena are located close together in the phase space, while different ones are located far apart in the space. From the difference distributions, we identified both the locations and the timing at which the temperature or the mass fractions is different for the droplet pair case compared with those of the single droplet.