J. Aubreton

Treatment of non-equilibrium phenomena in thermal plasma flows

Thermal plasma flows provide a uniquely high specific enthalpy source that is well suited to transformation of matter, often via phase changes. As a consequence, numerous thermal-plasma-based processes have been developed to, for example, destroy pollutants, modify surfaces (e.g. cutting and welding), synthesize nanostructures and deposit functionalized nanostructured coatings. In many cases, departures from equilibrium (both thermal and chemical) occur in regions of such plasmas; for example, in electrode erosion phenomena or in the injection of a liquid into a plasma jet. This paper reviews the treatment of non-equilibrium phenomena in thermal plasma flows, in particular the methods of calculation of the composition and transport coefficients of non-equilibrium plasmas, which are required for modelling the above processes. The focus is on two-temperature plasmas, in which electrons and heavy species are at different temperatures. Methods of calculation of the composition of plasmas both in local chemical equilibrium (LCE) and out of LCE are presented. A comparison of the different methods shows large discrepancies, even assuming LCE. Two-temperature transport coefficients obtained from simplified expressions, from the modified Chapman–Enskog method and from the Stefan–Maxwell relations are presented, as well as examples focusing on the influence of plasma composition. Different methods of calculation of the collision integrals required in determining the transport coefficients are also reviewed. Particular attention is paid to diffusion, in particular to the combined diffusion coefficient method, which simplifies treatment of plasmas in LCE. The method of calculation of the reactive thermal conductivity and the influence of excited states on transport coefficients are also addressed in some detail.

Transport coefficients including diffusion in a two-temperature argon plasma

This paper presents the first application to an argon atmospheric plasma of a very recent derivation of a two-temperature (2T) transport properties theory, based on the Chapman-Enskog method expanded up to the fourth approximation, where only elastic processes are considered. The kinetic electron temperature Te is assumed to be different from that of heavy species Th, chemical equilibrium being achieved. This new theory, where electrons and heavy species are coupled, allows one to determine 2T diffusion coefficients which was not the case of the previous ones. First, basic definitions of transport fluxes are recalled and a binary diffusion coefficient approximation is defined which involves an asymmetric relationship between these coefficients. Second, a particular care is taken in choosing the most recent data of potential interactions or elastic differential cross sections in order to determine the collision integrals. Third, a convergence study of transport coefficients is led to evaluate the influence of the non-equilibrium parameter θ = Te/Th on this convergence. It is shown that changing θ does not modify the convergence of transport coefficients. Moreover, ordinary and thermal diffusion coefficients, electrical and electron translational thermal conductivities as well as viscosity are displayed as functions of the electron temperature for different values of θ = Te/Th. It is pointed out that the non-equilibrium parameter θ has a non-negligible influence on transport coefficients. Besides, recently, it has been shown that the 2T simplified theory of transport properties, very often used in modelling, does not allow one to achieve mass conservation. Consequently, a comparison is presented between the 2T simplified theory and this new approach. Significant differences are found in the electrical conductivity and the electron translational thermal conductivity.

New Method to Calculate Thermodynamic and Transport Properties of a Multi-Temperature Plasma: Application to N2 Plasma

Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently André et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N2and N2+partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species Th, electrons Te, and vibrational Tvtemperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio θ=Te/Thwas varied between 1 and 2 as well as the ratio θv=Tv/Thfor a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N2are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N+. The effects of θvand θeon thermodynamic and transport properties of N2are then discussed.

Two-temperature transport coefficients in argon–helium thermal plasmas

The knowledge of two-temperature transport coefficients is of interest in the modelling of flow in plasma processes and heat transfer. The transport coefficients in argon–helium plasmas at atmospheric pressure are calculated assuming that the kinetic electron temperature, Te, is different from that of the heavy species, Th. The electrical conductivity, the viscosity, the total thermal conductivity and the combined diffusion coefficients are calculated up to 30u2009000u2009K. The influence of the molar percentage of argon as well as that of the non-equilibrium parameter θ = Te/Th are investigated. The plasma composition is calculated using the modified Saha equation of van den Sanden et al. The most recent data to obtain collision integrals are also presented. It is shown that the viscosity and the combined diffusion coefficients strongly depend on θ, through the plasma composition and the collision integrals. The ion-dominated regime occurs all the more quickly as θ is high, resulting in a regime of interactions between charged species which induces a decrease of the viscosity and the combined diffusion coefficients. The electrical conductivity, which is directly linked to the electron number density, and the thermal conductivity increase as θ increases.

Thermodynamic and transport properties of a ternary Ar–H2–He mixture out of equilibrium up to 30 000 K at atmospheric pressure

This paper is devoted to a study of the effect of the non-equilibrium parameter θ = Te/Th on the plasma composition and thermodynamic and transport properties of ternary mixtures Ar–H2–He, which are commonly used in dc plasma spraying. Calculations are performed in the temperature range 300–30 000 K and at atmospheric pressure. First, to calculate the non-equilibrium composition, two techniques are used: the equilibrium constant (van de Sanden) and pseudo-kinetic methods. Second, the specific heat at constant pressure is obtained by a five-point numerical differentiation of the specific mass enthalpy. Third, the most recent data of potential interactions or elastic differential cross sections are carefully examined in order to choose the most appropriate ones to determine the collision integrals. Finally a convergence study of transport coefficients (thermal conductivity, viscosity and electrical conductivity) is conducted to evaluate the influence of the non-equilibrium parameter θ on this convergence. It has to be pointed out that the latter has a non-negligible influence on transport coefficients

High temperature transport coefficients in e/C/H/N/O mixtures

The knowledge of transport coefficients is of interest in the modelling of flow in plasma processes and heat transfer. Calculations are performed in the temperature range of 9000–20 000 K and for different pressures (1, 3, 6 and 10 bar). The composition of e/C/H/N/O mixture plasmas is determined at equilibrium and four examples are studied: H2O, CO2, CO–H2O and CH4–air plasmas. First, the most recent data of potential interactions or elastic differential cross sections are carefully examined in order to choose the most appropriate ones to determine the collision integrals. Second, in this study devoted to high temperature calculations, we have restricted the species number to 12 (only atoms and atomic ions). Then we have tested the validity of our calculated composition and deduced that our transport properties are available for the temperature range of 9000–20 000 K at p = 1 bar and 11 000–20 000 K at p = 10 bar. Finally, the electrical conductivity, the viscosity and the total thermal conductivity are calculated for the four compositions and different pressures.

A modified pseudo-equilibrium model competing with kinetic models to determine the composition of a two-temperature SF6 atmosphere plasma

This paper is devoted to calculation of the non-equilibrium composition in a SF6 thermal plasma at atmospheric pressure. Non-equilibrium thermal plasmas are characterized by heavy species temperatures Th below 9000 K with electron temperatures at the maximum three times higher than Th when the latter is below 4000 K. Different theories have been used based on either multi-temperature plasmas, Saha-Potapov modified by Andre et al, van de Sanden et al, Cliteur et al, or kinetic calculations or the pseudo-equilibrium model, recently developed. This model gives results similar to those of kinetic calculations for N2 and H2 plasmas but with calculation times two orders magnitude faster. Pseudo-equilibrium calculation takes into account the reactions with low activation energies instead of ionization reactions, while keeping all the species present in the kinetic calculation. First, the theories are compared in a case already studied in the literature by Cliteur: a heavy species temperature Th at 6000 K, with the electron temperature Te varying between 6000 and 15 000 K. Comparison of the results shows that the multi-temperature calculations, except those of Cliteur, are far from kinetic especially for ne and nF-. In addition, the pseudo-equilibrium model fits rather well with the kinetic calculations as long as molecular species are present in the plasma. Second, to calculate the composition of non-equilibrium thermal plasmas the ratio Te/Th is assumed to vary as the logarithm of the electron densities ratio ne/ncmax, nemax being the electron density over which equilibrium prevails, i.e. 1023 m-3. For kinetic reactions where electrons are involved (in the direct reaction while heavy species intervene in the reverse reaction), a temperature T* between Te and Th is defined. T* is calculated as a function of the electron flux to that of heavy species. The variation of T* with Th is smoother than that of Te. In such conditions again, there is an excellent agreement between kinetic and pseudo-equilibrium calculations performed at T*, which is not the case for multi-temperature calculations. These results demonstrate that the pseudo-equilibrium calculation developed for thermal plasma simple forming gases such as N2 and H2 can also be applied to more complex gases such as SF6.

Two-Temperature Transport Coefficients in Argon-Hydrogen Plasmas—II: Inelastic Processes and Influence of Composition

Recently, a two-temperature transport properties theory has been proposed that retains the coupling between electrons and heavy species in thermal plasmas where the kinetic temperature of electrons Te can be different from that of heavy species Th. This paper is devoted to the application of this approach to an argon–hydrogen mixture at atmospheric pressure, taking into account inelastic processes and considering chemical equilibrium. In this second part are studied:• the development of a new method to calculate the reaction thermal conductivity (inelastic collisions) in a non-equilibrium (two-temperature) plasma taking into account the coupling between electrons and heavy species;• the influence of the composition calculation methods comparing the modified equilibrium constant method used in part 1 to the stationary kinetic calculation one;• the influence on the transport properties (σ, μ, κ) of the composition calculation method and non-equilibrium parameter θ=Te/Th.The different plasma compositions obtained either through an equilibrium constant or a stationary kinetic method are first compared and, for example, for θ=1.6, a discontinuity at Te=11,000 K and an ionization delay are observed in stationary kinetic calculation, relative to the equilibrium constant method. Electrical conductivity, viscosity as well as thermal conductivity, including the translational, internal and reactional contributions, are calculated up to 25,000 K. It is shown that the plasma composition has a strong influence on transport coefficients, inducing shifts or discontinuities in the curves of transport coefficients, depending on the chosen method of calculation.

Two-Temperature Transport Coefficients in Argon–Hydrogen Plasmas—I: Elastic Processes and Collision Integrals

The calculation of two-temperature transport coefficients in an argon–hydrogen plasma at atmospheric pressure is performed using a new theory of two-temperature transport properties recently presented. The latter takes into account the coupling between electrons and heavy species, coupling neglected in the already existing theories of Devoto and Bonnefoi. Transport coefficients are calculated at two-temperatures, the kinetic temperature of electrons Te being different from that of heavy species Th. This paper is divided into two parts. The first one is related to elastic processes and its aim is to compare the results obtained with this new theory for viscosity μ, translational thermal conductivities κtre and κtrh and electrical conductivity σ with the previous results of Bonnefoi. The composition is calculated with the modified equilibrium constant of van de Sanden et al. and the most recent interaction potential are discussed. As it could be expected the electron translational thermal conductivity and the electrical conductivity calculated when taking into account or not the coupling between electrons and heavy species show non-negligible discrepancies. Besides this comparison, the results also show the drastic influence of the non-equilibrium parameter θ=Te/Th on the values of σ, μ, κtre, and κtrh.

Transport coefficients of typical biomass equimolar CO?H2 plasma

Knowledge of the transport properties of biomass gases is important for modelling plasma flow processes and heat transfer. In this study, calculations were performed for typical biomass equimolar CO–H2 plasma in a temperature range from 500 to 30u2009000u2009K at pressures of 1.0, 2.0, 5.0 and 10.0u2009bar. Herein, the plasma composition was determined at equilibrium using the Gibbs free energy equation. First, we restricted the species number to 18 for CO–H2 plasma. Second, the most recent data on potential interactions and elastic differential cross sections were carefully investigated in order to choose those most appropriate to define the collision integrals. Due to a lack of data we used an improvement of the Lennard-Jones function. Third, we tested our collision integrals by comparing (1) the viscosity to experimental data of CO2, CH4 and CO (low temperature) and (2) the thermal conductivity and vicosity to theoretical results for CO2 plasma (up to 17u2009000u2009K). Finally, the viscosity, thermal conductivity and electrical conductivity were calculated for different pressures.