Analysis of spatial-temporal dynamics of cool flame oscillation phenomenon occurred around a fuel droplet array by using variational auto-encoder

Abstract

Cool flame oscillation of a fuel droplet array in high-temperature air was numerically simulated by using a droplet vaporization/spontaneous ignition numerical model. The time series data of temperature and chemical species spatial distributions were obtained. The data were used to train a Variational Auto-Encoder (VAE) that reduces the dimension of the data. The cool flame oscillation phenomenon was mapped as the trajectory onto a phase plane spanned by two latent variables obtained by the VAE. The oscillation phenomenon was investigated by using the distribution patterns derived by the VAE that distinguishes the temperature and the species states. Proper orthogonal decomposition was carried out on the decoder output of the VAE. The oscillation mechanism was investigated by the spatial eigenfunctions (mode maps). The temporal eigenfunctions of the three dominant modes were shown onto the trajectory of the plane. The correlation among physical variable distributions was evaluated to investigate the cool flame dynamics. From the above investigation, the plane was confirmed to distinguish the physical states, for the trajectory did not intersect during the oscillation. The plane was treated as a state space. The physical phenomena associated with each mode were identified from the mode maps and the temporal eigenfunctions. The phase in which the associated phenomenon arises was identified by checking the temporal eigenfunctions along with the trajectory. The mechanism of the oscillation was discussed with the correlation diagrams.