A phenomenological model for predicting the early development of the flame kernel in spark-ignition engines

This work presents a simple and effective phenomenological model for the prediction of the early growth of the flame kernel in SI engines, including its initiation as a result of the electrical breakdown of the fuel/air mixture between the spark plug electrodes. The present model aims to provide an improved description of the ignition-affected early phases of flame kernel development compared to the majority of models currently available in literature. In particular, these models focus on electrical energy supply and turbulence, whereas the stretch-induced kernel growth slowdown is quantified with linear models that are inconsistent with the small kernel radius. For the flame kernel initiation, this model replaces the current methods that rely on 1D heat diffusion within a plasma column with a more consistent analysis of post-breakdown conditions. Concerning the kernel growth, the present model couples the mass and energy conservation equations of a spherical kernel with the species and temperature profiles outside of it. This combination leads to a non-linear description of the flame stretch, according to which the kernel development is controlled by the Lewis-number-dependent balance between the heat gained via combustion and the heat lost via thermal diffusion. As a result, the kernel temperature differs from the adiabatic flame temperature, causing the laminar flame speed to change from its adiabatic value and ultimately affecting the overall kernel development. Kernel growth predictions are conducted for laminar flames and compared to literature data, showing a satisfactory agreement and highlighting the ability to describe the stretch-induced kernel slowdown, up to its possible extinction. A good agreement with literature data is also obtained for kernel expansions under moderately turbulent conditions, typical of internal combustion engines. The simple formulation of the present model enables swift integration into phenomenological combustion models for spark-ignition engines, while simultaneously offering useful insight into the early kernel development even for CFD-based approaches.