Performance of transported PDF mixing models in a turbulent premixed flame

Abstract

Modeling of premixed turbulent flames is challenging due to the effects of strong turbulence-chemistry interaction. In the transported probability density function (TPDF) methods, chemical reactions are treated exactly, while molecular mixing needs to be modeled. In the present study, the performance of three widely used mixing models, namely the Interaction by Exchange with the Mean (IEM), Modified Curl (MC), and Euclidean Minimum Spanning Tree (EMST) models, are assessed using direct numerical simulation (DNS) data of a lean premixed hydrogen–air slot jet flame simulated at Sandia. The DNS provides initial conditions and time varying input quantities, including the mean velocity, turbulent diffusion coefficient, and scalar mixing rate for the TPDF simulations. A number of progress variable definitions are explored, as well as the commonly used constant mechanical-to-scalar mixing timescale model. It is found that the EMST model provides the best prediction of the flame structure and flame propagation speed out of the models tested. The IEM model implies a qualitatively incorrect conditional mean and RMS diffusion rate, while the MC model can qualitatively capture the conditional mean diffusion rate. Only the EMST model can accurately predict the conditional mean diffusion rate for this flame, which can be attributed to its enforcement of mixing that is local in composition space. Finally, a parametric study on the mechanical-to-scalar timescale ratio is performed. It is found that the optimal choice for the timescale ratio varies by a factor of 2 for the two DNS cases study, despite the cases having the same configuration. Therefore, this commonly used approach does not appear to be viable for turbulent premixed flames and further attention to mixing timescale models for reactive scalars is merited.