PII: S0010-2180(08)00050-3

Abstract

A joint mixture fraction–enthalpy probability density function (PDF) is proposed for the simulation of turbulent spray flames. The PDF transport equation is deduced and modeled. The interaction-by-exchange-with-the-mean (IEM) model that has been developed for gas-phase flows is extended to describe molecular mixing in nonreactive and reactive spray flows. The joint PDF transport equation is solved by a hybrid finite-volume and Lagrangian Monte Carlo method. Standard spray and turbulence models are used to describe the gas phase and the liquid phase. A turbulent methanol/air spray flame is simulated using the present method. Detailed chemistry is implemented through the spray flamelet model. The precalculated spray flamelet library for methanol/air combustion comprises 23 species and 168 elementary reactions. Thus, the model is capable of predicting the formation of radicals and of pollutants. Different values for the model constant Cϕ in the IEM model are tested. The numerical results for the gas velocity, the gas temperature, and the mass fraction of methanol vapor are compared with experimental data in the literature. Good agreement with experiment is obtained when Cϕ=2.0. Marginal PDFs of mixture fraction, enthalpy, and gas temperature are presented. The computed PDFs of mixture fraction are compared with the presumed standard β function and modified β function. The results show that the standard β function fails to reproduce bimodal shapes observed in transported PDF computation, while the modified β function, fits the computed PDFs very well. Moreover, joint PDFs of mixture fraction and enthalpy are presented and analyzed. The enthalpy and mixture fraction are strongly correlated. The samples that deviate from the linear correlation are due to the energy consumption of local spray evaporation.