Boundary conditions at the ablative walls in two-temperature modelling of thermal plasmas with reactive working gas

Abstract

In this paper, we propose a new set of boundary conditions at ablative hot walls with thermionic electron emission for two-temperature thermal arc models in which the temperature of electrons can deviate from the temperature of heavy particles,. The boundary conditions are for the electric potential, the two energy equations for electrons and heavy particles (ions and neutrals), and the two mass conservation equations for the working gas and the vapour of the wall material. In these boundary conditions, the plasma sheath formed at the wall is viewed as the interface between the plasma and the wall, the plasma composition is assumed to be determined by a generalized Saha equation adapted to the case , and the reactive gas is assumed to form a stoichiometric film at the wall. The derived boundary conditions allow the calculation of the heat flux from the plasma to the wall, the thermionic electron current density, and the erosion rate of the wall that makes the model of wall–plasma interaction self-consistent. The derived boundary conditions are reduced to the case of non-reactive working gas and to the case of walls with materials with a low melting point, such as copper, where the thermionic electron emission of the wall is small and can be neglected. The case of the boundary conditions for high-pressure arcs burning in the vapour of the wall material (no working gas) is also considered. The boundary conditions obtained are applied to the cathode spot at an ablative tungsten cathode and to the anode attachment at a copper anode in argon.