Modeling scalar dissipation and scalar variance in LES: algebraic and transport equation closures

The scalar dissipation rate and the scalar variance are important modeling parameters in large eddy simulations (LES) of chemically reacting flows. Models for these quantities that are based on transport equations are theoretically preferable to algebraic models, but the closure of the subfilter terms in the transport equation approaches remains challenging. Here, two direct numerical simulation (DNS) data sets are used to analyze the performance of LES dissipation rate and variance models, and to propose a new closure. The first data set is the non-premixed auto-igniting C2H4 jet flame DNS performed by Yoo et al. (Proc. Comb. Inst., 2010). An LES of this case is run using both algebraic and transport equation models for the dissipation rate. It is shown that the algebraic models do not accurately describe the details of the dissipation and variance physics, motivating the examination of the subfilter closure models in the transport equation approach. Closure is addressed by introducing a new adapted dynamic approach to computing the most important subfilter model coefficient. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside primarily on the smallest length scales of the flow. The adapted closure is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Scalar variance modeling in the reacting jet DNS is also considered. It is shown that a transport equation model performs significantly better than the algebraic model, and that the closure of the relevant variance equation is sensitive to the predicted dissipation rate