Equilibrium discharges (thermal plasmas) have nowadays a large range of industrial applications including cutting, welding, spraying, waste destruction, and surface treatment (Ref. 1).The current methods used for producing thermal plasmas generally employ high-intensity arcs, inductively coupled high-frequency discharges, or microwave discharges. The purpose of the Equilibrium Discharge interface is to help users model thermal plasmas generated by the first two methods (that is, arcs or inductively coupled discharges). Accordingly, the targeted applications are primarily DC and inductively coupled plasma torches as well as arc welding devices and circuit breakers.

Thermal plasmas are assumed to be under partial to complete local thermodynamic equilibrium (LTE) conditions (Ref. 1). At a macroscopic level, these kind of plasma can be considered as conductive fluid mixtures, which leads to the magnetohydrodynamics (MHD) equations. The latter combine the Navier–Stokes, heat, and Maxwell’s equations to describe the motion of the conducting fluid in an electromagnetic field.

The source Q (W/m3) defined in the Equilibrium Discharge Heat Source multiphysics coupling feature includes three source/sink components:

Note that the enthalpy transport term prevails, for example, in the boundary layers close to electrodes in a fully ionized electric discharge, Ref. 1.

Where μ is the dynamic viscosity of the fluid, I is the identity matrix and

The above equations require specification of material properties, which are functions of temperature. The Equilibrium Discharge folder in the Material Browser contains properties for density, specific heat, viscosity, thermal conductivity and electric conductivity as a function of temperature up to 24,000 K. Available gases include air, argon, helium, hydrogen, nitrogen, and oxygen. The data is taken from the tables in the Appendix of Ref. 1.

The Equilibrium Discharge interfaces include by default cooling/heating of electrodes in contact with the equilibrium discharge Ref. 2.

Where k is the thermal conductivity (W/(m·K)), ϕs is the surface work function of the electrode (V), and Vion is the ionization potential of the plasma (V). The ion current density norm is defined by

Where AR is the Richardson’s constant (A/(m2·K2)), q is the electronic charge (C), kB is the Boltzmann’s constant (J/K), and ϕeff is the effective work function of the surface (V). Note that the ion current density norm Jion = 0 if the Richardson-Dushman current density is larger than the total normal current at the interface.

Electron entering the anode generates heat. Following the approach presented in Ref. 2, you can assume that there is no ion current and hence no ion heating at the anode. Accordingly the anode heat flux is defined as:

is the normal current density at the interface, k is the thermal conductivity, and ϕs is the surface work function of the anode. Note that all the physics features available in the individual interfaces are also available to the multiphysics interface in use. This include, for instance, radiation heat losses, and wall boundary conditions.