Energy equation formulations for two-temperature modelling of 'thermal' plasmas

Based on an equilibrium fluid model, built from the commercial Fluent software previously validated for thermal plasma characterizations on several geometries, a non-equilibrium two-temperature model was developed. This kind of model needs the use of two energy equations: one for the electrons, and the other for heavy particles. Nevertheless, depending on the authors, divergences exist in the expressions of equations. The main differences are related to the attribution of the ionization term and to the components of thermal conductivity in the energy equations. The two-temperature model developed is applied in a transferred arc configuration where the medium is described using the different formulations for the energy equations. The right formulation, based on the Boltzmann equation, is then applied in a transferred arc configuration for two values of current intensity of 100 and 600 A. We show that in order to obtain coherent and physical results in all the cases, special attention needs to be given: the ionization term, the reactive thermal conductivity and the radiation line contribution need to be considered in electron energy equations, whereas the reactive thermal conductivity due to dissociations and the continuum radiation contributions need to be associated with the heavy energy equations.