Eddy damped quasinormal Markovian theory for chemically reactive scalars in isotropic turbulence

The eddy damped quasinormal Markovian theory has been applied to the mixing of three scalars undergoing an isothermal, bimolecular chemical reaction of the form: A+B→C, with a reaction rate constant that is independent of the scalar concentrations. The model is an extension of the work by Vaithianathan, Ulitsky, and Collins [Proc. Combust. Inst. 29, 2139 (2002)] to allow for unequal initial molar concentrations of the reactant species and differences in the molecular diffusivities of the three scalars, thereby enabling the effect of differential diffusion to be studied. Comparisons of the model with results from direct numerical simulations are in good agreement for the low-order statistics considered here. The model also was used to explore the effect of the parameters (Reynolds number, Schmidt number, and Damköhler number) on the scalar statistics. The results show that differential diffusion effects decrease with increasing Reynolds number, as has been observed for nonreacting scalars. However, statistics involving the product species (e.g., cross correlation coefficients ρAC and ρBC) have the opposite trend with Damköhler number, which raises the question of the role of differential diffusion for the intermediate species in a turbulent flame, where the unity Lewis number assumption is often invoked on the basis of the high Reynolds number even though the Damköhler number too is quite large.