Influence of Lewis number on the surface density function transport in the thin reaction zone regime for turbulent premixed flames

Abstract

The effects of tangential strain rate and curvature on the surface density function (SDF) and on different terms within the SDF transport equation in the thin reaction zone regime are studied for statistically planar turbulent premixed flames with global Lewis numbers Le=0.8, 1.0, and 1.2 by using three-dimensional direct numerical simulations with simplified chemistry. A positive correlation is observed between the SDF and tangential strain rate, and this is explained in terms of the local statistical behaviors of tangential strain rate and dilatation rate. Curvature is shown to affect the SDF through the curvature response of both tangential strain rate and dilatation rate on a given flame isosurface. The correlation between the curvature and SDF is positive in the Le=0.8 flame and negative in the Le=1.2 flame. The curvature dependence of the SDF is weak in the case of unity Lewis number. Strain rate and curvature are found to have an appreciable effect on different terms of the SDF transport equation. The SDF strain rate term arising from tangential strain rate contribution in all the flames is positively correlated with tangential strain rate as expected and is also negatively correlated with curvature. For the Le=1.0 and 1.2 flames, the SDF propagation term is found to negatively correlate with flame curvature toward the reactant side of the flame and positively toward the product side. By contrast, for the Le=0.8 flame, the SDF propagation term is negatively correlated with curvature throughout the flame brush. The variation of the SDF curvature term with local flame curvature for all the flames is found to be nonlinear due to the additional stretch induced by the tangential diffusion component of the displacement speed. Physical explanations are provided for all of these effects, and the modeling implications are discussed in detail.