A consistent set of thermodynamic properties and transport coefficients for high temperature plasmas

This paper describes a consistent set of thermodynamic properties and transport coefficients for different gases and gas mixtures depending on temperature and pressure. The species thermochemical properties have been computed directly from their partition functions. Atomic and molecular energy levels have been incorporated up to 50.000 K avoiding extrapolation of the JANAF data. Equlibrium particle densities are shown for pure PTFE (C2F4) and selected gas mixtures of PTFE, SF6 and N2. From the equilibrium calculations, the system thermodynamic properties (Gibbs and Helmholtz energies, specific enthalpy and internal energy) are obtained directly. The derivatives of these quantities (cp, cv, velocity of sound and adiabatic coefficient) have been calculated using an essentially exact numerical calculation of both the frozen and reaction parts, avoiding numerical differentiation. The calculation of the transport properties like viscosity, electrical and thermal conductivity is based on the Chapman-Enskog approximation. The set of input data consists of collision integrals, particle densities, thermodynamic properties and their derivatives. The influence of the above described modifications to the thermodynamic properties and transport coefficients calculations will be presented. Introduction For the modelling of high temperature gases and plasmas in circuit breakers, calculation of material functions for the specific gas or gas mixture under consideration is necessary. In circuit breakers the gas differs over a wide temperature and pressure range. In some situations, there is an arc with temperatures up to several 10000 K and pressures up to some 10Mpa; in other cases, there are colder gas regions with temperatures in the range of 300 to several 1000K. Due to ablated material formed by a wall surrounding the arc, the composition of the gas mixture is changing during switching operation. Therefore the material properties of the gas mixture must be known over a wide temperature and pressure range, and also as a function of gas composition. The objective of this paper is to show the dependencies on the temperature and mixture ratios; the pressure is fixed at 1.0MPa. Equilibrium composition To calculate the thermodynamic properties of a plasma or gas mixture in local thermodynamic equilibrium (LTE) at a specified temperature T and pressure p, the principle of minimization of the Gibbs energy is used [1]. A key first step is calculation of the particle densities of the involved species as a function of T, p, and overall gas composition. The ideal-system standard chemical potentials for each species, ) , ( 0 P T id io μ (where 0 P is the standard state pressure of 1 bar) are used as input data for the equilibrium calculation. In several papers concerning the calculation of thermodynamic properties the JANAF tables [2] are used for this purpose, which extend only to 6000K. As we consider much higher temperatures, we calculated the chemical potentials of atoms and ions by means of summation over the atomic energy levels, as follows. In general, we calculated the ideal-system chemical potentials using ) , ( ) , ( ) , ( 0 0 0 0 0 P T Ts P T h P T i i id io − = μ (1) where the species enthalpy, ) , ( 0 0 P T hi , and entropy, ) , ( 0 0 P T si , are given by dT P T C P T H P T h T