The FDF or LES/PDF method for turbulent two-phase flows

TL;DR

This paper introduces a new formalism for the filtered density function approach in LES simulations of turbulent polydispersed two-phase flows, based on Lagrangian quantities, enabling rigorous modeling and connections with other methods.

Contribution

The paper develops a Lagrangian-based formalism for FDF in LES of two-phase flows, linking it with SPH and probabilistic subgrid models.

Findings

Framework allows rigorous LES modeling of particle-laden flows.

Establishes connections between LES, FDF, and SPH methods.

Provides basis for probabilistic subgrid stochastic models.

Abstract

In this paper, a new formalism for the filtered density function (FDF) approach is developed for the treatment of turbulent polydispersed two-phase flows in LES simulations. Contrary to the FDF used for turbulent reactive single-phase flows, the present formalislm is based on Lagrangian quantities and, in particular, on the Lagrangian filtered mass density function (LFMDF) as the central concept. This framework allows modeling and simulation of particle flows for LES to be set in a rigorous context and various links with other approaches to be made. In particular, the relation between LES for particle simulations of single-phase flows and Smoothed Particle Hydrodynamics (SPH) is put forward. Then, the discussion and derivation of possible subgrid stochastic models used for Lagrangian models in two-phase flows can set in a clear probabilistic equivalence with the corresponding LFMDF.