Study of Formulating Conserved Scalar Equations for Turbulent Reactive Flows with General Species Mass- Diffusion Coefficients for Utilization in Flamelet Models

The modeling of turbulent reactive flows is a subject of contemporary research. Current turbulent-reaction models cannot account for realistic complexities such as distinct species mass-diffusion coefficients. Under the assumption of a single, constant, mass-diffusion coefficient, a conserved-scalar equation is typically derived in turbulent reactive flows by taking the difference between chemical-species conservation equations having opposite reaction rates (in the sense that the reactant has an opposite reaction rate to the product), thereby creating an equation devoid of reaction terms. Assuming the reaction regions are very thin and are merely contorted by turbulence, chemistry and turbulence can be decoupled, and the evolving statistics of the conserved scalar describe the reaction progression. No such equation has yet been derived for distinct mass-diffusion coefficient cases where the single coefficient is now replaced by a full matrix. Considering that mass diffusion is responsible for reactants approaching at the molecular level and for reaction initiation, this lack of mathematical framework is very disturbing.