On the quenching of premixed flames by water sprays: Influences of radiation and polydispersity

Abstract

We analyze the process of premixed flame extinguishment by water sprays, as analytically as possible. Our main assumptions are as follows. o 1. Combustion is sustained by an overall Arrhenius reaction that yields water and carbon dioxide as products. 2. The activation energy is large. 3. The flame is planar and steady. 4. The water spray is polydispersed and viewed as a continuous medium exchanging heat and water vapor with the gas phase. 5. Combustion products and vaporized water radiate toward the surroundings according to the optically thin approximation. 6. Relistic emissive properties are retained. 7. Both phases have the same local velocity Using activation energy asymptotics and tabulations of two auxilliary functions, we obtain a relationship between the fractional changes in burning rate, the initial amount and size distribution of water droplets, and the gas properties/composition. This enables one to determine in a simple way how the burning velocity varies with the mixture strength and the spray properties. This is first illustrated in the case of monodisperse sprays, then of bimodal droplet-size distributions, for methane/air-like flames. In general, the amount of water needed to preclude flame propagation cannot be expressed in terms of such a simple moment of the droplet-size distribution as Sauter's diameter. The theory could be easily adapted to account for kinetic quenching.