Lagrangian Mixing Models for Turbulent Combustion: Review and Prospects

Compared to other simulation approaches utilized for modeling turbulent reacting flows with detailed chemistry, probability density function (PDF) methods offer several advantages. This is because the changes in fluid composition due to convection and reaction processes can be treated exactly. PDF methods require however closure models for the mixing process representing the transport of the PDF owing to molecular diffusion. Over the years several mixing models with different degrees of complexity have been developed. A review of the main Lagrangian mixing models for turbulent combustion developed so far is presented in this work. This review includes models where the composition of a particle changes (i) essentially independently of the composition associated with the other particles, and (ii) through direct interaction with other particles. The main advantages and shortcomings of the mixing models reviewed are highlighted accordingly. Because Lagrangian Monte Carlo techniques are usually used for solving PDF transport equations, a particular emphasis is put on their corresponding particle implementation. The mixing models review is preceded by a section highlighting the mathematical formulation associated with the use of PDF methods for turbulent reacting flows. In the last part of the article both comparative results of mixing models performance and prospects for the mixing models are discussed. Despite the effort that has been devoted to the development of more capable mixing models, currently there is no mixing model presenting all desirable characteristics. Even more, there are significant differences in the results obtained when different mixing models are utilized, especially when higher order scalar statistics are accounted for. Therefore work still needs to be carried out in order to develop a mixing model satisfying all desirable characteristics expected from these models. Several avenues can be further explored in order to achieve this goal. These potential routes include those accounting for spatial scalar structures and both scalar length and turbulent frequency scales distributions. Other approaches based on competitive mixing, manifold-based features and Lagrangian coherent structures have also the potential to further improve upon existing mixing models. The development of a sound mixing model will allow eventually removing one of the largest sources of modeling uncertainty in PDF-based computations.