The Study Of The Transport Properties For Non-equilibrium Thermal Plasmas

Numerical simulation, the accuracy of which depends on the exact transport coefficients and the governing equation, plays an important role in studying the physical and chemical processes in thermal plasmas. This paper focuses on the theoretical study of the transport coefficients for non-equilibrium thermal plasmas, and presenting the exact expressions of these transport coefficients and the self-consistent governing equations. Furthermore, we develop the corresponding program code to conduct the calculations.Two main methods have been used to calculate the transport coefficients of two-temperature plasmas in local chemical equilibrium:the decoupled method of Devoto, in which coupling between electrons and heavy species is neglected and electrons and heavy species are treated as two isolated subsystems; and the completely coupled method of Rat, in which coupling is included without any simplifications. The calculation of the former method is really simple, however, a complete set of species diffusion coefficient cannot be obtained using the decoupled method (since the diffusion between electrons and heavy species is ignored). The coupled method is able to get the complete diffusion coefficients at the cost of a considerable increase in complexity. In this paper, motivated by the disadvantages of the two methods, a method is presented, based on the modified Chapman-Enskog solution of the species Boltzmann equations, to obtain the expressions of transport coefficients. In the derivation, the physical fact that the mass of electrons is much smaller than that of heavy species are used to simplify the species Boltzmann equations. While the electron-heavy-species collision term in the heavy-species Boltzmann equation is included to retain the coupling between electrons and heavy species. Thus, accurate transport coefficients are bale to be obtained by using the new simplified method, especially for the diffusion coefficients. Furthermore, the complexity of calculations using the new method is not increased compared with the decoupled method; that is to say, the calculation procedure is much simpler than with the coupled method. The calculations of the transport coefficients for two-temperature argon plasmas are used to verify the new method.The self-consistency between the definitions of transport properties and the transport fluxes existing in the governing equations plays a very important role in the simulation of plasmas. However, due to the separate studies of the two topics, people have to define the two-temperature reactive thermal conductivity and the specific heat at constant pressure, in which considerable controversies still exist, since there is no definite physical meaning for the reactive thermal conductivity and the specific heat in two-temperature plasmas. Furthermore, this separation usually makes the governing equations used by the researchers cannot match with the transport properties chosen by them. In this paper, the same modified Chapman-Enskog method has been used to solve the Boltzmann equation, especially the same definitions of the transport fluxes have been adopted to derive the governing equations. A complete and self-consistent physics-mathematics model is established to describe the thermal plasma. Based the new model, it is not necessary to define the two-temperature reactive thermal conductivity and specific heat.The combined diffusion coefficient method has been demonstrated to greatly simplify the treatment of diffusion in the modelling of thermal plasmas in gas mixtures without loss of accuracy. However, in the previous studies, the combined diffusion coefficients were employed for the diffusion of only two gases. In this paper, an extension of this method to allow treatment of diffusion of a three-gas mixture has been achieved, and combined diffusion coefficients for different mixtures of helium, argon and carbon are calculated as an example. Finally, based on our new transport theory, the expressions of combined diffusion coefficients for two-temperature plasmas are presented.Based on our study, a complete and self-consistent physical-mathematical model, including the transport properties and the governing equations, is established to describe the complicated processes in non-equilibrium plasmas.