On the transition of four flames types of auto-ignited iso-octane droplet cloud

This study is motivated by the multi-stage ignition behavior of isooctane droplet clouds suggested by its chemical kinetics studies. A series of 1D numerical simulations and theoretical analyses were conducted to investigate auto-ignition phenomena. Four distinct flame structures, i.e. simple, two-stage, bilayer, and complicated, were identified, corresponding to two ignition modes: cool ignition alone and cool ignition followed by hot ignition. The resulting regime diagram in the T_a–G_ig space exhibits an inverted S-shaped boundary separating the presence and absence of hot ignition, indicating that increasing ambient temperature does not always promote ignition near the flammability limit of isooctane droplet cloud. To explain this non-monotonic behavior, we proposed two Damköhler numbers. In the 700 ∼ 900 K range, hot ignition is triggered by fuel accumulation near the cool flame due to faster chemistry than droplet vaporization, described by a droplet-scale Damköhler number (Da_d). In the 1000 ∼ 1500 K range, radical buildup from the convergence of cool and warm flame initiates hot ignition, which is governed by a cloud-scale Damköhler number (Da_c) comparing reaction and diffusion timescales. Additionally, in non-igniting cases, the cloud radius was observed to decrease nearly linearly, despite each droplet inside the cloud following the d²-law. This led to the development of a conduction-driven vaporization model for droplet cloud, enabling accurate prediction of cloud lifetime in hot environments.