On Lagrangian stochastic methods for turbulent polydisperse two-phase reactive flows

The purpose of the present paper is to provide a comprehensive account of Lagrangian stochastic methods for polydisperse two-phase reactive flows. In this work, the emphasis is put on the description of the dispersed phase and on one-particle probabilistic approaches to general non-homogeneous flows. This is a domain where significant progress has been achieved in the last decade and reporting on these advances brings out the current status of Lagrangian stochastic methods. A first objective of this paper is to recall the main aspects of the existing theoretical framework where developments are shown to be set in. A second objective is to clarify the physics contained in present stochastic models. To that effect, the presentation of the main aspects of the reference Langevin model as well as the detailed analysis of several applications covering a range of practical concerns reveal the actual possibilities of these modeling approaches. A third objective is to report on recent developments that open possibilities for Lagrangian stochastic methods, including for example first steps toward structure-based models, hybrid numerical formulations as well as new accounts of particle–particle interactions. Building on these results, a formalism is introduced in the last section for the extension of Lagrangian stochastic methods to particle-laden turbulent flows where the fluid flow is calculated with a Large Eddy Simulation. Finally, the research areas where work is still needed are outlined.