(97a) Applied Filtered Density Function

The optimal means of capturing the detailed, unsteady physics of turbulent reacting flows, as it is now widely believed, is via large eddy simulation (LES). The challenge in LES is accurate and consistent modeling of the subgrid scale (SGS) quantities. The filtered density function (FDF) methodology; including its mass weighted form, the filtered mass density function (FMDF), has proven particularly effective for this purpose. The FDF is essentially the probability density function (PDF) of the SGS quantities. Therefore, it provides all the statistical information pertaining to these quantities.

In its stand-alone form, the FDF must account for the joint statistics of all the relevant physical variables. The most sophisticated FDF closure available to-date is the frequency-velocity-scalar FMDF (FVS-FMDF), and a simpler  version (VS-FMDF) which does not include the SGS frequency.  Hydrodynamic closure in incompressible, non-reacting flows has been successfully achieved via the velocity-FDF (V-FDF) and the one which has been utilized the most only considers the scalar field (S-FDF and S-FMDF). This is the most elementary form of FDF when it was first introduced.  Since then, the FDF has experienced widespread usage, and is now regarded as one of the most effective and popular means of LES worldwide. Some of the most noticeable contributions in FDF by others are in its basic implementation, fine-tuning of its sub-closures, and its validation via laboratory experiments.

In this chapter, a review is presented of modern advances in FDF modeling and simulation. These are primarily the development of new sub-closures in FDF transport, and construction of efficient solvers for this transport. With these developments, it is now possible to conduct LES of turbulent reactive flows in complex configurations. Examples are provided of recent FDF-based simulations with some speculation of  the type of complex flows to be simulated within the near future.