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

Abstract

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.

Statistical Analysis of Turbulent Flame-Droplet Interaction: A Direct Numerical Simulation Study

“…The simulation time used in the current analysis remains comparable to a number of recent DNS analyses [19,21,[24][25][26][40][41][42][43], which significantly contributed to the fundamental understanding of turbulent combustion.…”

“…This ensures that enough number of integral eddies are retained when the statistics are extracted. The number of integral eddies within the domain for this analysis is either comparable to or greater than that used in several previous DNS based analyses [24][25][26][27][40][41][42][43]. It would indeed be desirable to have a larger number of eddies within the domain than that used here, but that would require a larger domain size which would greatly increase the computational cost for the parametric analysis carried out in this paper.…”

“…The statistics of displacement speed play key roles in level-set [44] and Flame Surface Density (FSD) [33,41,42,53] based closures in the context of premixed turbulent combustion. Finally, the flame displacement speed is affected by the heat release and, thus, it is more appropriate to consider the density-weighted displacement speed and its components [21, 33, The effects of subdividing this range of c reveals that the probability of finding positive (negative) values of S * r (S * n ) increases from c = 0.5 to c = 0.9, which is consistent with the variations of the mean values ofω c and N ·∇ ρD N · ∇c shown in Fig.…”

Flow topologies in different regimes of premixed turbulent combustion: A direct numerical simulation analysis

“…Case C has the highest value of turbulent Reynolds number and thus this case requires the smallest grid spacing to resolve the Kolmogorov length and flame thickness among all the cases considered here. For the purpose of computational economy a smaller computational domain than cases A and B has been chosen here for case C. Simulations have been carried out for 1.0t e , 6.8t e , and 6.7t e (i.e., t e = l T /u ) for cases A-C, respectively, and this simulation time remains comparable to several previous analyses [15,16,[27][28][29]. 2 , and third invariant R * = R × (δ th /S L ) 3 fields when the statistics were extracted are shown in Fig.…”

Flame Structure and Propagation in Turbulent Flame-Droplet Interaction: A Direct Numerical Simulation Analysis

“…All simulations have been carried out until t final = max(3t turb , 4t chem ), where t turb =L 11 /u is the initial turbulent eddy turnover time and t chem =D 0 /S 2 b( g =1) the chemical timescale. This simulation time is either comparable to or greater than the simulation duration used in a number of recent DNS analyses [22,24,25,27,[29][30][31][44][45][46][47], which significantly contributed to the fundamental understanding of turbulent combustion. It was shown in Ref.…”