Stochastic Particle PDF Methods for Unresolved Fluctuations and Inter-Scale Couplings in LES of Turbulent Premixed Combustion

Transported probability density function (PDF) methods have emerged as a powerful approach for dealing with the influences of unresolved turbulent fluctuations in LES of turbulent reacting flows. PDF methods provide an effective resolution to the closure problems that arise from spatial filtering of terms that correspond to nonlinear point processes: in particular, the important chemical reaction source terms. PDF methods invoke no inherent assumptions regarding the regime of combustion. Stochastic Lagrangian particle methods are the predominant approach for implementing PDF methods, and offer advantages in dealing with subfilter-scale processes. In practice, hybrid Lagrangian particle/Eulerian mesh methods are used, where subfilter-scale fluctuations are treated using a particle-based representation while resolved-scale dynamics are treated using conventional Eulerian CFD. Here the focus is on issues that are especially important in premixed systems. That includes discussions of the fundamental level of closure (e.g., velocity-composition PDF versus composition PDF), the choice of thermochemical representation (e.g., progress variable/mixture fraction formulations versus reduced/skeletal/detailed chemical mechanisms), the modeling of molecular transport (the "mixing model"), and coupling of the subfilter-scale fluctuations with the resolved-scale dynamics. Tight coupling between molecular transport and chemistry is important in premixed systems. That includes accommodating flamelet regimes of combustion, and differential diffusion. There are also consistency issues that arise from the dual Lagrangian-Eulerian representation. Strategies that have been developed to address these issues, and to reduce the high computational cost of transported PDF methods, are discussed, including tradeoffs between accuracy and computational efficiency. The presentation concludes with a summary of key outstanding issues, and prospects for resolving those.