Mathematical modeling of turbulent non-premixed piloted-jet flames with local extinctions

Abstract

Flamelet modeling of highly stretched jet flames is combined with the use of conditional moment closuresecond-order closure procedures to evaluate a pdf, p ˜ ( θ | η ) , of the reaction progress variable, θ, that is conditioned upon a value of the mixture fraction η. Through the use of a probability of burning function. P h , the model expresses the effects of strain rate and localized flame quenching. The product of this function and another term embodying the relevant laminar flamelet source term from a flamelet library, together with p ˜ ( θ | η ) , yields the required mean turbulent source term. Both heat release rate and the formation rate of species are dealt with in this way. It was found appropriate and convenient to use the k-ω model, with a kinematic eddy viscosity, for the flow turbulence. The overall model is applied to those experimental piloted-jet methane/air flames of Barlow and Frank, in which there are pronounced extinctions and reignitions. Velocity vectors and spatial contours of mean mixture fraction, mean volumetric heat release rate, and mean strain rate clearly show the essential structures of the flames. As the flow rate increases, so does the extent of the penetration of the region of high strain rates into that of flammable mixtures. This creates localized regions of reduced mean heat release rate in which localized extinctions might be anticipated, due to the strain rate being high and the mixture being less reactive. These locations are confirmed by experiments, as is the predicted extent of the flames. There is generally good agreement between predicted and measured mean temperatures, mean mixture fractions, and mass fractions of CH 4 , O 2 , and H 2 O. Agreement is less satisfactory for transient species. Possible limitations of the model are discussed.