Numerical study of the ignition behavior of a post-discharge kernel in a turbulent stratified crossflow

Ensuring robust ignition is critical for the operability of aeronautical gas-turbine combustors. For ignition to be successful, an important aspect is the ability of the hot gas generated by the spark discharge to initiate combustion reactions, leading to the formation of a self-sustained ignition kernel. This study focuses on this phenomena by performing simulations of kernel ignition in a crossflow configuration that was characterized experimentally. First, inert simulations are performed to identify numerical parameters correctly reproducing the kernel ejection from the ignition cavity, which is here modeled as a pulsed jet. In particular, the kernel diameter and the transit time of the kernel to the reacting mixture are matched with measurements. Considering stochastic perturbations of the ejection velocity of the ignition kernel, the variability of the kernel transit time is also reproduced by the simulations. Subsequently, simulations of a series of ignition sequences are performed with varying equivalence ratio of the fuel-air mixture in the crossflow. The numerical results are shown to reproduce the ignition failure that occurs for the leanest equivalence ratio ($?=0.6$). For higher equivalence ratios, the simulations are shown to capture the sensitivity of the ignition to the equivalence ratio, and the kernel successfully transitions into a propagating flame. Significant stochastic dispersion of the ignition strength is observed, which relates to the variability of the transit time of the kernel to the reactive mixture. An analysis of the structure of the ignition kernel also highlights the transition towards a self-propagating flame for successful ignition conditions.