Review of Lagrangian stochastic models for turbulent combustion

Predictive simulation of the combustion process in engine is crucial to understand the complex underlying physicochemical processes, improve engine performance, and reduce pollutant emissions. Key issues such as the physical modeling of the interaction between turbulence, chemistry and droplets, and the incorporation of the detailed chemistry in high-fidelity simulations of complex flows remain essential though challenging. This paper reviews the transported probability density function method for turbulent dilute spray flames in the dual-Lagrangian framework that shows potential to address some critical modeling issues. An overview is presented for the contributions made within the last decade or so for the three key ingredients for modeling the interaction between turbulence, chemistry and droplets, i.e., micro-mixing, subgrid dispersion and two-phase coupling. Then, various methods for detailed chemistry acceleration are reviewed to address the issue of high computational cost for its use in multidimensional simulations. Finally, some applications of the dual-Lagrangian method in both laboratory-scale and device-scale configurations are provided to demonstrate its capability as well as deficiency at the current stage. Some open modeling challenges are raised and recommended for further investigation. Graphic abstract