A mathematical analysis of the ignition of a polydisperse spray/air mixture by an infinite surface heated in a pulsed manner is presented. In contrast to previous work in the literature, the entire history of the ignition process is accounted for starting from the flame-embryo progenitor stage, through the thermal runaway stage to the final flame propagation stage. For tractability at the current stage, the chemical kinetics is taken to be that of a single global reaction. The spray is modeled using the sectional approach and the influence of fuel spray characteristics on ignition is determined. Good agreement was found between the theoretical predictions and full numerical simulations. Delay in ignition due to the build-up of vapor from the fuel droplets as well as heat loss to the droplets for evaporation are found to play a significant role under certain operating conditions. Comparison between the critical energy flux and the initial spray polydispersity revealed small differences for larger values of the pulse duration but more significant minor differences for smaller pulse durations. Despite these seemingly minor differences, it was shown that the initial spray polydispersity can have a critical influence on whether flame ignition will occur or fail, even for sprays having the same initial SMD.
Theory of Stagnation-Point Spray Flame Ignition