Modeling Time-Resolved Compressible Effects in Low-Mach Solvers: Numerical Simulations of a Nanosecond Discharge

A detailed description of the sub-microsecond thermal, chemical, and flow-dynamic effects induced by nanosecond electrical discharges requires comprehensive thermo-chemical models and fully compressible flow solvers. In addition, accurately simulating the non-thermal kinetics requires solving two energy equations, one for trans-rotational energy and one for vibrational energy. This approach is computationally expensive, and thus simplified models are needed. Phenomenological models have been proposed to simplify plasma kinetics, and low-Mach CFD solvers including a single energy equation have been employed to accelerate fluid-dynamic simulations of these discharges. However, such solvers are unable to reproduce the fluid dynamics phenomena that follow a nanosecond pulse (such as the blast wave, and the post-discharge expansion, which are driven by gas compressibility). These effects significantly influence the temperature and pressure within the interelectrode gap as well as the discharge radius and the densities of species. Thus, the blast wave plays a critical role in thermal and species diffusion, as well as in the cumulative impact of multi-pulse discharges on ambient gases. In this article, we propose methods to account for the highly compressible effects of a nanosecond discharge in low-Mach solvers. To capture these fast temporal dynamics, we introduce a sub-timestep model that resolves the temporal scales below the primary integration timestep of the low-Mach solvers. The model extends the phenomenological pulse models developed in the literature during the past decade by incorporating the subsequent expansion phase. We also propose adjustments to better account for fast trans-rotational heating and slow vibrational-translational energy transfer, in both compressible and incompressible flow solvers. We implemented the model in a low-Mach solver and validated it through comparisons with fully compressible flow computations.