Two-dimensional direct numerical simulation evaluation of the flame-surface density model for flames developing from an ignition kernel in lean methane/air mixtures under engine conditions

Flame surface density (FSD) models are often used in premixed turbulent combustion modeling to provide closure in large eddy simulations (LES) and Reynolds-averaged simulations. In the present study, data obtained from direct numerical simulation, with reduced chemistry, of flames developing from ignition kernels in lean methane-air mixtures is used to study the accuracy of the FSD modeling terms for LES applications. This study is conducted at elevated temperature and pressure conditions relevant to lean-burn natural gas engines. The closure models for four terms in the FSD transport equation are studied. It is observed that the propagation term as resolved by the LES grid adequately models the actual propagation term without additional sub-grid scale modeling. On the other hand, the closure of the curvature term requires a sub-grid scale model. Two sub-grid scale curvature models are studied and it is seen that there are differences between the actual and the modeled curvature terms during the early evolution of the ignition kernel. The agreement improves as the developing flame approaches a statistically steady-state. The modeling of the sub-grid convection term is analyzed and differences between the actual and the modeled terms are observed to grow during the transient evolution of the ignition kernel. A sub-grid scale model for the closure of the strain rate term shows disagreement at both early and late stages of kernel growth. In general, the sensitivity of the strain rate and curvature models to the filter width is found to be greater than for convection and propagation.