Modelling effects of subgrid-scale mixture fraction variance in LES of a piloted diffusion flame

Abstract

A posteriori analysis of the statistics of two large-eddy simulation (LES) solutions describing a piloted methane–air (Sandia D) flame is performed on a series of grids with progressively increased resolution reaching about 10.5 million cells. Chemical compositions, density and temperature fields are modelled with a steady flamelet approach and parametrised by the mixture fraction. The difference between the LES solutions arises from a different numerical treatment of the subgrid scale (SGS) mixture fraction variance – an important quantity of interest in non-premixed combustion modelling. In the first case (model I), the variance transport equation is solved directly, while in the second (model II), an equation for the square of the mixture fraction is solved, and the variance is computed from its definition. The comparison of the LES solutions is based on the convergence properties of their statistics with respect to the turbulence resolution length scale. The dependence of the LES statistics is analysed for velocity and the mixture fraction fields, and tested for convergence. For the most part, the statistics converge for the finest grids, but the variance of the mixture fraction shows some residual grid dependence in the high-gradient regions of the jet near field. The SGS variance given by model I exhibits realisability everywhere, whereas in regions of the flame model II is non-realisable, predicting negative variances. Furthermore, the LES statistics of model I exhibit superior convergence behaviour.