Comparing Low-Mach and Fully-Compressible CFD Solvers for Phenomenological Modeling of Nanosecond Pulsed Plasma Discharges with and without Turbulence

This work aims at comparing the accuracy and overall performance of a low-Mach CFD solver and a fully-compressible CFD solver for direct numerical simulation (DNS) of nonequilibrium plasma assisted ignition (PAI) using a phenomenological model described in Castela et al. [1]. The phenomenological model describes the impact of nanosecond pulsed plasma discharges by introducing source terms in the reacting flow equations, instead of solving the detailed plasma kinetics at every time step of the discharge. Ultra-fast gas heating and dissociation of O₂ are attributed to the electronic excitation of N₂ and the subsequent quenching to ground state. This process is highly exothermic, and is responsible for dissociation of O₂ to form O radicals; both of which promote faster ignition. Another relatively slower process of gas heating associated with vibrational-to-translational relaxation is also accounted for, by solving an additional vibrational energy transport equation. A fully-compressible CFD solver for high Mach (M>0.2) reacting flows, developed by extending the default rhoCentralFoam solver in OpenFOAM, is used to perform DNS of PAI in a 2D domain representing a cross section of a pin-to-pin plasma discharge configuration. The same case is also simulated using a low-Mach, pressure-based CFD solver, built by extending the default reactingFoam solver. The lack of flow or wave dominated transport after the plasma-induced weak shock wave leaves the domain causes inaccurate computation of all the transport variables, with a rather small time step dictated by the CFL condition, with the fully-compressible solver. These issues are not encountered in the low-Mach solver. Finally, the low-Mach solver is used to perform DNS of PAI in lean, premixed, isotropic turbulent mixtures of CH₄-air at two different Reynolds numbers of 44 and 395. Local convection of the radicals and vibrational energy from the discharge domain, and straining of the high temperature reaction zones resulted in slower ignition of the case with the higher Re. A cascade effect of temperature reduction in the more turbulent case also resulted in a five-six times smaller value of the vibrational to translational gas heating source term, which further inhibited ignition. Two pulses were sufficient for ignition of the Re = 44 case, whereas three pulses were required for the Re = 395 case; consistent with the results of Ref. [1].