Application of the two-phase filtered density function approach for LES of a 2D droplet laden turbulent mixing layer

In this study, the two-phase velocity-scalar filtered density function transport equation for large eddy simulation is considered in the limit of a continuum-dispersed phase two-phase flow. For a sufficiently small dispersed particulate phase, all quantities conditionally filtered within the dispersed phase may be disregarded leaving only terms conditionally filtered on the phase interface. These conditionally surface- filtered terms account for phase-coupling between the dispersed and continuum phases of the flow. Closure models are presented and implemented for a two-phase system consisting of a water droplet laden 2d temporally developing mixing layer. Marginal FDF transport equations are presented for each phase and a statistically equivalent set of Ito stochastic differential equations (SDE) are derived from each marginal FDF equation. Simulations are conducted via a full stand-alone Lagrangian particle Monte-Carlo method with closure models to account for sub-grid scale (SGS) mixing and inter-phase conversion processes. The effect of variable Stokes number on turbulent dispersion of evaporating and non-evaporating droplets is discussed.