Effects of differential diffusion and stratification characteristic length-scale on the propagation of a spherical methane-air flame kernel

Early flame kernel development and propagation in globally lean stratified fuel--air mixtures is of importance in various practical devices such as internal combustion engines. In this work, three-dimensional direct numerical simulation (DNS) is used to study the influence of the differential diffusion effects in a globally lean methane--air mixtures in presence of mixture heterogeneities with the goal of understanding the flame kernel behavior in such conditions. The DNS typical configuration corresponds to a homogeneous isotropic flow with an expanding spherical flame kernel. The local forced ignition of the kernel is performed by appending as source term in the sensible enthalpy transport equation that emulates spark ignition by energy deposit for a prescribed duration. The combustion chemistry is described with a skeletal methane-air mechanism, which i) features 14 species and 38 reactions, and ii) uses a multicomponent approach to evaluate transport coefficients. To assess the joint effects of differential diffusion and the stratification characteristic length-scale $L_{\Phi}$ on the flame kernel development, we considered cases with constant (unitary) and variable fuel Lewis number, both with different values for $L_{\Phi}$.