Application of PDF mixing models to premixed flames with differential diffusion

Differential diffusion alters the balance of reaction and diffusion in turbulent premixed combustion, affecting the performance and emissions of combustion devices. Modelling combustion devices with Probability or Filtered Density Function (PDF or FDF) methods provides an exact treatment for the change in composition due to chemical reaction, while molecular mixing has to be modelled. Previous PDF molecular mixing models do not account for differential diffusion in a manner which satisfies realizability requirements. A new approach for treating differential diffusion, which ensures realizability, is proposed for pairwise-exchange mixing models in general, and applied in the Interaction by Exchange with the Mean (IEM) model of Dopazo [26], and in the Euclidean Minimum Spanning Tree (EMST) model of Subramaniam and Pope [5]. The new differential diffusion models are referred to as IEM-DD and EMST-DD respectively. Results from two and three-dimensional DNS of turbulent premixed methane–air combustion show that mixing rates and conditional statistics of species mass fractions depend on species diffusivities and the combustion regime. Zero-dimensional PDF model results obtained for the two-dimensional DNS case show that the EMST-DD model best reproduces the features that characterize differential diffusion in the DNS. The essential feature of the EMST-DD model, which accounts for its success in turbulent premixed combustion, is that differential mixing rates are imposed within a model which mixes locally in composition space