A modified coherent flame model to describe turbulent flame propagation in mixtures with variable composition

Abstract

Stratified direct-injection spark-ignition engines feature both large- and small-scale spatial variations in unburned mixture composition. Modifications of the coherent flame model (CFM) are proposed in the present study to account for the effects of variable mixture strength on the primary premixed flame, as well as for the formation of a secondary non-premixed reaction zone downstream of the premixed flame. The domain of validity of the present modifications is restricted to the case of small variations in mixture strength, without the additional complication of premixed flame extinction. The modeling strategy is based on previous results from direct numerical simulations as well as a theoretical analysis of a simplified problem by Kolmogorov, Petrovskii, and Piskunov (KPP). The KPP problem corresponds to a one-dimensional, turbulent flame propagating steadily into frozen turbulence and frozen fuel-air distribution, and it provides a convenient framework to test the modified CFM model. In this simplified but somewhat generic configuration, two radically different situations are predicted: for variations in mixture strength around mean stoichiometric conditions, unmixedness tends to have a net negative impact on the turbulent flame speed: in contrast, for variations in mixture strength close to the flammability limits, unmixedness tends to have a net positive impact on the turbulent flame speed. While featuring a restricted domain of validity, the proposed modifications to the CFM set the basis for future developments and are well suited in particular for an extension of the model to the case of combustion with occurrences of premixed flame extinction.