Assessment of Subgrid-Scale Mixing Models for Large Eddy Simulation using the Filtered Density Function Approach

The solution of the filtered mass density function (FMDF) transport equation by stochastic Monte Carlo simulation is a promising approach for subgrid-scale (SGS) modeling in LES of turbulent reacting flows. One of the more challenging aspects of this approach is related to the accuracy of the SGS mixing model. Recent Reynolds-Averaged Navier-Stokes (RANS) computations have documented its current inability to predict the dynamics of flame extinction and reignition in moderate to high Reynolds number turbulent flames. This is partly related to the often made assumptions of a constant mechanical-to-scalar time scale ratio in the determination of mixing frequency and also neglecting the effect of chemical reactions on this time scale ratio.
In this study, we consider homogeneous incompressible turbulence and use the linear eddy model (LEM) to provide a surrogate DNS database for validation of several different mixing models for the joint scalar PDF as applied to two different, but related, problems. The first problem is a three-stream mixing problem and the second involves nonpremixed reactants undergoing a single-step, Arrhenius-type chemical reaction whose kinetic rate parameters were chosen such that extinction and reignition events occurred. The mixing models studied include Interaction by Exchange with the Mean (IEM), Modified Curl (MC), Euclidean Minimum Spanning Tree (EMST), and the method of Multiple Mapping Conditioning (MMC) in the context of pure mixing. Scatter plots, and joint PDFs, as well as scalar mean and rms, are presented to highlight differences among the models and LEM results related to the failure of the micromixing models to capture extinction and reignition events. Evidence is presented that this is directly related to the mixing frequency. To begin to address this, a recently developed model for the mixing time scale of reacting scalars, based on mapping closure methods, is applied to the mixing submodels and improvements are assessed.