Numerical Modeling of Energy Deposition Pathways in Sparking Events at Different Rates

The mechanisms driving energy deposition in a gas subjected to an extremely rapid, concentrated thermal source are investigated numerically. Such phenomena arise when considering ignition from spark discharges. Spark ignition is a critical risk for advanced aircraft subjected to lighting strikes. While spark ignition is well understood for conventional kerosene mixtures in the aviation context, novel fuels such as hydrogen remain poorly characterized in this environment. Hydrogen has a minimum ignition energy (MIE) one order of magnitude lower than that of kerosene. Accurately determining the MIE for such fuels is a challenge due to the highly nonlinear relationship between the inception of an ignition kernel, the total energy delivered, and the energy delivery rate. The conventional approach for deriving estimates of the MIE relies on phenomenological models of spark ignition. In this work, we take steps toward a rigorous, quantitative ignition risk assessment through the implementation of numerical models that study the localized input of thermal energy on various time scales and the ensuing gas dynamics. We implement a high-fidelity gas dynamics numerical model using the Exasim software. Exasim is a scalable DG/HDG finite element solver that supports high-order approximations on unstructured grids and allows for modular, multiphysics coupling. HDG methods possess advantageous properties such as reduced global degrees of freedom and optimal convergence that makes them well suited for this application. We construct a spatially resolved energy partition that categorizes energy delivery based on the transport terms in the energy equation. The modeling capability advanced in this work forms the basis of future studies that increase fidelity through the incorporation of multiphysics effects such as discharge and combustion chemistry.