A Triangulated Lagrangian Ignition Kernel Model with Detailed Kinetics for Modeling Spark Ignition with the G-Equation-Part I: Geometric Aspects 2018-01-0195

Modeling ignition kernel development in spark ignition engines is crucial to capturing the sources of cyclic variability, both with RANS and LES simulations. Appropriate kernel modeling must ensure that energy transfer from the electrodes to the gas phase has the correct timing, rate and locations, until the flame surface is large enough to be represented on the mesh by the G-Equation level-set method. However, in most kernel models, geometric details driving kernel growth are missing: either because it is described as Lagrangian particles, or because its development is simplified, i.e., down to multiple spherical flames.

This paper covers the geometric aspects of kernel development, which makes up the core of a Triangulated Lagrangian Ignition Kernel model. One (or multiple, if it restrikes) spark channel is initialized as a one-dimensional Lagrangian particle thread. Each channel particle is advected as a Lagrangian tracker plus a turbulent dispersion term, with least-squares field reconstruction to compensate for the lesser mesh resolution. The 1D thread discretization is dynamically updated to stick to the user’s resolution request; plus, particles falling into the wall boundary layer are flagged and deactivated, such that actual spark channel can effectively translate along the electrode’s surface. Energy transfer to the gas phase is accounted for via direct chemical kinetics integration at each channel particle, added with a time-varying energy source term. Flame kernels can develop at any particle locations: they are initialized as a triangulated icosahedron, and evolved (and merged) as a unique particle-based triangulation, with dynamically enforced resolution, employing the G-Equation formulation directly at the kernel level. Preliminary kernel development tests show that the triangulated geometry implementation allows to capture sub-grid-scale features of the early flame kernel development, which cannot be achieved with the former DPIK model.