Vincent Rat

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.

Understanding of suspension DC plasma spraying of finely structured coatings for SOFC

Suspension plasma spraying was used to achieve a dense and thin (/spl sim/30 /spl mu/m) yttria stabilized zirconia (YSZ) coating for the electrolyte of solid oxide fuel cells (SOFCs). A suspension of YSZ powder (d/sub 50//spl sim/1 /spl mu/m) was mechanically injected in direct current (dc) plasma jets. The plasma jet acted as an atomizer and the suspension drops (d/spl sim/200 /spl mu/m) were sheared, long before they started vaporizing, into many droplets (d/spl sim/2 /spl mu/m). The solvent of the latters was then very rapidly (a few microseconds) evaporated and decomposed by the plasma jet. The solid particles enclosed in each droplet were then accelerated and melted before impacting on the substrate where they formed splats. The thermal inertia of particles with sizes below 1 /spl mu/m being low, the standoff distance was much shorter than in conventional plasma spraying (40-60 against 100-120 mm). Thus, the heat flux from the plasma to the coating reached 20 MW/spl middot/m/sup -2/ when spraying YSZ suspensions with Ar-H/sub 2/ or Ar-H/sub 2/-He plasma jets. It allowed keeping the whole pass (about 0.8-/spl mu/m-thick) completely molten resulting after its solidification, for YSZ, in a fully dense coating (20-30-/spl mu/m-thick) with a granular microstructure.

Suspension and solution plasma spraying of finely structured layers: potential application to SOFCs

Suspension direct current plasma spraying allows achieving finely structured coatings whose thickness is between few tens and few hundreds of micrometres. Drops (200?300??m in diameter) or liquid jets are mechanically injected in the plasma jet. With radial injection they are rapidly (a few ?s) fragmented into droplets (a few ?m in diameter). The latter are vaporized (in a few ?s) and the solid particles contained in suspension droplets are accelerated and melted by the plasma jet. As in conventional plasma spraying (CPS), much smaller splats (with diameters between 0.2 and 3??m and thicknesses between 30 and 200?nm) are arranged in layers up to form the coating. The low inertia of particles requires spray distances between 40 and 60?mm which induces plasma heat fluxes up to 22?MW?m?2 participating in coating densification. Even more than in CPS, the plasma jet fluctuations, particularly for plasmas containing di-atomic gases, perturb drops penetration and fragmentation. It has been chosen to illustrate difficulties and possibilities of this new method, through the spraying of the three layers of an element of solid oxide fuel cells. Indeed, it requires a dense stabilized zirconia electrolyte, if possible thin (15?20??m) with two porous electrodes: cathode made of perovskite prone to decomposing upon spraying and anode made of two materials (nickel and zirconia) with very different melting points. These components were obtained by spraying ethanol suspensions, with, first, LaMnO3 perovskite particles doped with 10?mol% of MnO2 and 3??m in mean diameter sprayed with pure argon to limit their decomposition and achieve porous coatings, second, Yttria (13?wt%) stabilized zirconia (YSZ) with two different particle size distributions and morphologies for which plasma compositions were adapted, producing in both cases 15??m thick and fully dense coatings, third, porous Raneigh nickel by co-spraying the YSZ suspension and solution of nickel nitrate.

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.

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 30 000 K. 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.

Influence of configuration and operating conditions on the electric arc instabilities of a plasma spray torch: role of acoustic resonance

A theoretical approach is proposed to explain the particularities of the power spectrum of a plasma spray torch voltage. This is founded on an acoustic resonance of the rear part of the plasma torch which is occupied by the cold gas before it reaches the arc region. The spectrum is characterized by the presence of a sharp peak in the range 3–8 kHz, with an amplitude that represents up to ±30% of the voltage mean value. The peak frequency presents an evolution that is governed by the torch operating conditions, the thermal properties of the plasma forming gas and the geometrical configuration of the electrode assembly. The theory is compared with experimental values of the peak frequency recorded for different operating conditions and torch configurations. The injection ring through which the gas is injected also plays an important role. The torch behaviour is carefully characterized in order to collect all the experimental data required for the analysis on the involved phenomena.

Influence of Helmholtz oscillations on arc voltage fluctuations in a dc plasma spraying torch

Arc voltage fluctuations are studied for two different plasma torches. One of them is home-made, the other is a Sultzer Metco plasma torch. Both work under similar operating conditions, but they show very different voltage waveforms and spectra, depending on their electrode configurations. The first torch shows a rather intermittent behaviour and works under the restrike mode with a rather low fluctuation amplitude and with non-reproducible spectral components. The second torch also shows characteristic features related to the restrike mode, but they are superimposed on more regular oscillations which are due to pressure variations in the cold gas chamber, located upstream the arc region. This part of the torch together with the nozzle channel appears to be a Helmholtz resonator, whose resonance frequency is theoretically evaluated as a function of the torch geometry and of the operating conditions. The theoretical predictions are in very good agreement with the measured frequency of the main peak in the voltage spectrum of the second torch. A discussion about the coupling between the pressure and the voltage is proposed to explain how the torch design could influence the Helmholtz resonance.

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

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.