A priori assessment of closures for scalar dissipation rate transport in turbulent premixed flames using direct numerical simulation

The scalar dissipation rate transport in both the corrugated flamelet and thin reaction zone regimes is studied using three-dimensional direct numerical simulation (DNS) databases for freely propagating statistically planar turbulent premixed flames. Both flames have comparable turbulent Reynolds number but the flame representing the corrugated flamelet combustion regime has a global Damköhler number, $Da>1$⁠, whereas the second flame representing the thin reaction zone regime has $Da<1$⁠. It is demonstrated that the turbulent transport of the scalar dissipation rate and its molecular diffusive transport have strong Da dependence. The contributions of dilatation rate, the turbulence-scalar interaction, the reaction-rate–scalar gradient interaction, and the dissipation processes have leading order contributions for both the flames. However, the turbulence-scalar interaction dissipates scalar gradients in the $Da>1$ flame, while it produces the scalar gradients in the $Da<1$ flame. Simple algebraic models for the contributions of the various processes noted above to the scalar dissipation rate evolution are proposed and their a priori assessment is carried out with respect to DNS data. These models explicitly have Da and the Karlovitz number Ka dependence, and thus, they can be viewed and used as unified models for both the corrugated flamelet and thin reaction zone regimes. Physical realizability of the modeled scalar dissipation rate transport equation is studied and the model constants obtained by using the DNS data sets are shown to satisfy the realizability condition.