The Role of Differential Diffusion during Early Flame Kernel Development under Engine Conditions -- Part II: Effect of Flame Structure and Geometry

From experimental spark ignition (SI) engine studies, it is known that the slow-down of early flame kernel development caused by the ($\mathrm{Le}>1$)-property of common transportation-fuel/air mixtures tends to increase cycle-to-cycle variations (CCV). To improve the fundamental understanding of the complex phenomena inside the flame structure of developing flame kernels, an engine-relevant DNS database is investigated in this work. Conclusive analyses are enabled by considering equivalent flame kernels and turbulent planar flames computed with $\mathrm{Le}>1$ and $\mathrm{Le}=1$. In Part I of the present study (Falkenstein et al., Combust. Flame, 2019), a reduced representation of the local mixture state based on the parameters local enthalpy, local equivalence ratio, and H-radical mass fraction was proposed for the purpose of this analysis. Here, a coupling relation for the diffusion-controlled mixture parameter local enthalpy with local flame geometry and structure is derived, characterized by the key parameters $\kappa$ and ${\ |\nabla c \ t|/\ |\nabla c \ |_{\mathrm{lam}}}$. The analysis shows that the large positive global mean curvature intrinsic to the flame kernel configuration may detrimentally affect the local mixture state inside the reaction zone, particularly during the initial kernel development phase. External energy supply by spark ignition may effectively bridge over this critical stage, which causes the impact of global mean flame kernel curvature to be small under the present conditions compared to the overall effect of $\mathrm{Le}\neq1$. Once ignition effects have decayed, the mixture state inside the reaction zone locally exhibits an identical dependence on $\ |\nabla c \ |$ as in a strained laminar flame. This implies that differential diffusion effects under engine-typical Karlovitz numbers are not weakened by small-scale turbulent mixing.