Abstract
A simplified theoretical model has been developed for describing transient ignition far downstream of a droplet with forced convection. The downstream velocity field is approximated by an analytic form pertaining to isothermal far-wake flow. The transient heating and evaporation of the droplet are treated using film theory; their effects on gas-phase temperature and species distributions are accounted for with integral conservation. Transport and chemical reaction are described with differential equations for mass and energy, together with the approximate analytic velocity field. The position of ignition and the ignition delay time are determined as when thermal runaway is reached in the calculations. For n-hexadecane droplets, ignition delay times and ignition positions have been calculated as a function of free-stream gas temperature, droplet diameter, velocity of the gas relative to the droplet, and initial temperature of the droplet. Numerical results agree well with experiment. The mechanism of convective droplet ignition is also discussed.