Theory of vaporization and ignition of a droplet cloud in the field of a vortex

This paper presents an analytical study of the vaporization and ignition of a droplet ring and a droplet cloud of fuel immersed in the field of a circular vortex. The model considers the motion of the ring or cloud as induced by the vortical motion of the gas. The vaporization and in particular the transient variation of the gas-phase fuel mass fraction at the center of the vortex is obtained by means of the Green's function approach. The ignition phenomenon, which occurs at the vortex center, is treated by large-activation-energy asymptotics. The equation governing the perturbation temperature and thus the ignition is affected by three parameters: a Damköhler number and two dimensionless numbers resulting from the vaporization of the fuel. Results showing the influence of these three parameters are presented, indicating the conditions under which ignition can occur.