Extinction of stretched spray flames with nonunity Lewis numbers in a stagnation-point flow

The extinction of stretched premixed flames under the influence of dilute fuel sprays is studied using activation energy asymptotics. A completely prevaporized mode and a partially prevaporized mode of flame propagation are identified. Three parameters for flame extinction in the analysis consist of the mass fraction of liquid fuel and the initial droplet size of the spray, indicating the internal heat loss and heat gain for rich and lean sprays, respectively, and the flow stretch coupled with Lewis number (Le) that intensifies and weakens the burning strength of the Le<1 and Le>1 flame, respectively. The study presents sample calculations on lean ethanol-spray flames (Le>1), rich ethanol-spray flames (Le>1), and rich methanol-spray flames (Le<1). Results show that the burning intensity of a spray flame with Le>1 is weakened by the flow stretch: however, it is enhanced (further reduced) when the lean (rich) spray has a larger amount of liquid fuel loading or a smaller initial droplet size. It is generally found that the external heat loss associated with the flow stretch dominates the trend for flame extinction. The coupling effects of flow stretch and internal heat gain result in that there exists flame flashback instead of flame extinction for rich methanol-spray flames (Le<1).