Variational multiscale method for nonequilibrium plasma flows

Abstract

Plasmas at atmospheric or higher pressures, typically denoted as thermal plasmas, are partially ionized gases in which the high collision frequency among its constituents (molecules, atoms, ions, and electrons) causes intense transfer of electromagnetic to thermal energy. Thermal plasma flows, often generated by electric arcs, are at the core of diverse technologies, such as plasma cutting, spraying, circuit breakers, lighting, fuel reforming, and gasification. A computational nonequilibrium thermal plasma flow model based on the Variational Multiscale (VMS) paradigm is presented. The plasma is described as a compressible reactive electromagnetic fluid in chemical equilibrium and thermodynamic nonequilibrium. Two energy conservation equations, one for electrons and the other for the heavy-species, are used to describe deviations from Local Thermodynamic Equilibrium. Material properties (e.g., mass density, enthalpy, viscosity, and electrical conductivity) vary by several orders of magnitude in a strongly nonlinear manner within these flows, which severely increases the stiffness of the model. The equations describing the plasma flow are treated in a monolithic approach as a transient–advective–diffusive–reactive (TADR) transport system. An algebraic VMS Finite Element Method appropriate for the treatment of general TADR problems is presented. The method is complemented with an intrinsic time-scales matrix definition to model the fluid–electromagnetic sub-grid scales inexpensively and a discontinuity-capturing operator to increase its robustness in the handling of large gradients. The resulting discrete system is solved by a generalized-alpha time-stepper together with a globalized inexact Newton–Krylov nonlinear solver. The VMS method is verified with incompressible, compressible, and magnetohydrodynamic (MHD) benchmark flow problems, and the VMS plasma model is validated with three canonical and industrially-relevant flows: the free-burning arc, and the transferred and non-transferred arc flows in a plasma torch.