Forced thermal ignition of a polydisperse fuel spray

A new mathematical model is presented for determining critical conditions for forced thermal ignition of an arbitrary polydisperse fuel spray/oxidant mixture. An asymptotic analysis is used to ascertain both the necessary initial applied temperature as well as the time needed to accumulate enough fuel vapor through droplet evaporation in order that thermal runaway, indicating ignition, should occur. The influence of the combined effect of heat loss due to evaporation and volumetric heat loss on critical ignition conditions is accounted for. The quenching distance is analyzed and found to match the expression used in the literature. It is demonstrated that, for practical purposes, even when volumetric heat loss alone does not prevent ignition, the presence of the fuel droplets can do so. The impact of liquid fuel-related parameters on ignition conditions is discussed in detail.