Electrical arcs and, more generally thermal plasmas, are widely used in many applications and the understanding or the improvement of the corresponding processes or systems, often requires precise modelling of the plasma. We present, here, a double approach to thermal plasma modelling, which combines the scientific procedure with an engineering point of view. First, we present the fundamental properties of thermal plasmas that are required in the models, followed by the basic equations and structures of the models. The third part is devoted to test cases, and its objectives are the study of some basic phenomena to show their influence on arc behaviour in simple configurations, and the validation of the models: we point out the roles of radiation, thermal conductivity and electrical conductivity for a stationary or transient wall-stabilized arc and we validate a three-dimensional model for a free-burning arc.Sections 4–6 deal with several industrial configurations and the model is useful in each case for studying important phenomena or processes in greater detail. For transferred arcs, such as those used in metallurgy, the energy transfer from the arc to the anode, and the presence of metallic vapour and pumping gas are essential. For a non-transferred plasma torch used for plasma spraying, we illustrate the relevance of a three-dimensional model and we present the interaction of the plasma with powders. Problems related to high- and low-voltage circuit-breakers are then presented, and various typical mechanisms are modelled. Finally, several non-equilibrium models useful for quasi-thermal conditions are presented in detail, showing how they take into account the chemical kinetics and two-temperature plasmas occurring under particular conditions, such as decaying arcs or inductively coupled plasmas.

https://iopscience.iop.org/article/10.1088/0022-3727/38/9/R01/pdf

Thermal plasma modelling

Plasma-aided nanofabrication is a rapidly expanding area of research spanning disciplines ranging from physics and chemistry of plasmas and gas discharges to solid state physics, materials science, surface science, nanoscience and nanotechnology and related engineering subjects. The current status of the research field is discussed and examples of superior performance and competitive advantage of plasma processes and techniques are given. These examples are selected to represent a range of applications of two major types of plasmas suitable for nanoscale synthesis and processing, namely thermally non-equilibrium and thermal plasmas. Major concepts and terminology used in the field are introduced. The paper also pinpoints the major challenges facing plasma-aided nanofabrication and identifies some emerging topics for future research.

http://iopscience.iop.org/article/10.1088/0022-3727/40/8/S01/pdf

Plasma-aided nanofabrication: where is the cutting edge?

Metal vapour is formed in arc welding processes by the evaporation of molten metal in the weld pool, and in the case of gas–metal arc welding, in the wire electrode and droplets. The presence of metal vapour can have a major influence on the properties of the arc and the size and shape of the weld pool. Previous experimental and computational works on the production and transport of metal vapour in welding arcs, in particular those relevant to gas–metal arc welding and gas–tungsten arc welding, are reviewed. The influence of metal vapour on the thermodynamic, transport and radiative properties of plasmas is discussed. The effect of metal vapour on the distributions of temperature, current density and heat flux in arcs is examined in terms of these thermophysical properties. Different approaches to treating diffusion of metal vapour in plasmas, and the production of vapour from molten metal, are compared. The production of welding fume by the nucleation and subsequent condensation of metal vapour is considered. Recommendations are presented about subjects requiring further investigation, and the requirements for accurate computational modelling of welding arcs.

https://iopscience.iop.org/article/10.1088/0022-3727/43/43/434001/pdf

The effects of metal vapour in arc welding

A two-dimensional numerical model of the interaction between an electric arc and a solid anode of different types is presented in this study. The CFD commercial code FLUENT is used to model the plasma flow and the solid anode domain. Quantities such as the velocities or the temperature are presented, and the energy transfer components between the plasma and the anode are quantified. Comparisons of the calculated results with the available experimental data in the literature show that the model predictions are in good agreement. In the case of argon gas and a copper anode, with the distance between the two electrodes 10 mm, the maximum temperature near the cathode tip is 21 000 K for a current of I = 200 A. For the same configuration, the maximum of the current density in the copper electrode is found to be −2.5 × 106 A m−2. The electrical flux is the main component of the transferred flux on the anode. Once validated, our model is applied to other theoretical and experimental configurations and allows us to study several parameters when attention is focused on the influence of metal vapour from the vaporization of the anode or the current-carrying path in the electrode on the arc behaviour. According to the current-carrying path in the anode, the current density distribution is affected in the material and its surface.

A numerical modelling of an electric arc and its interaction with the anode: Part I. The two-dimensional model

Electric arc anodes frequently determine functional performance and lifetime of a number of arcing devices, ranging from discharge lamps to plasma spray torches. While there have been numerous studies of the anode region of electric arcs, our understanding of the detailed physical processes is still limited. The reason for this lack of detailed knowledge is that numerous factors influence the arc–anode interaction, and that the plasma–solid interface in high intensity arcs is in general not accessible to diagnostics and one has to rely on indirect measurements. Throughout this survey, the emphasis will be on high intensity arc anodes, i.e. on plasmas with temperatures of more than 10 000 K and electron densities exceeding 1022 m−3 outside the boundary layer, and heat fluxes exceeding 107 W m−2. The plasma parameters in the boundary layer as obtained with different techniques by a number of investigators for a variety of conditions are presented, and the effect of macroscopic flow conditions is discussed. Experimental and modelling results are presented. A brief comparison with low current arcs is also given, and the areas that need further research are highlighted.

https://iopscience.iop.org/article/10.1088/0022-3727/43/2/023001/pdf

The anode region of electric arcs: a survey

Spectroscopic measurements have been made on a transferred arc burning in pure argon at atmospheric pressure seeded with iron vapours arising from the anode erosion. The transferred arc was operated with a current intensity of 90 A, an arc length of 18 mm, and a gas flow rate of . Temperature and relative iron concentration profiles determined experimentally were compared to theoretical values obtained from a two-dimensional model based on mass, momentum, and energy conservation equations and taking into account anode erosion. This comparison partially validated the model and showed that the presence of iron vapours, with a relative concentration of about 0.1%, led to a temperature decrease of about 1000 K. Differences between experimental and calculated temperature fields may be due to departures from equilibrium and to uncertainties about the iron vapour concentration and the radiative losses.

The influence of iron vapour on an argon transferred arc

The interaction between the arc and the anode was experimentally studied by means of a transferred arc burning in argon with copper, iron, or steel anodes. Depending on the rate of anode cooling, a stable plasma was obtained just above the anode, established either in pure argon (strong cooling) or in a mixture of argon with metal vapor. Temperature and metal concentration fields were deduced from spectroscopic measurements. Two important results were reached: the arc radius near the anode depends on the nature of the electrode, even without anode erosion; and the presence of metal vapor leads to a cooling of the plasma. The same arc configurations were theoretically simulated by a two-dimensional model. The comparison between experimental and numerical results allows a large proportion of the observed phenomena to be interpreted, in spite of partial discrepancies between predicted and measured values. The dimension of the arc root at the anode depends on the thermal conductivity of the solid metal, whereas the cooling effect due to metal vapor in the plasma is explained by the increases of electrical conductivity and of radiative losses in the presence of the vapor.

Influence of the anode material on an argon arc

Spectroscopic measurements on an argon transferred arc have been performed in the plasma region just above the copper anode, by means of the arc interruption technique. This technique, based on the recording of the transient evolution of total spectral line intensities, allows one to determine the difference Te−Th between the electron temperature and the heavy particle temperature, existing in steady state. During the extinction of the low arc current, the evolution of some argon lines presents first a sudden increase before a slow general decrease, whereas the evolution of copper lines shows first a very fast decrease followed by a slow extinction. These phenomena have been interpreted considering that argon excited-state populations are strongly correlated with ions and electrons (Saha equilibrium) whereas the copper excited-state populations are correlated with the ground-state density (Boltzmann equilibrium). The difference Te−Th deduced from both kinds of measurements varies between 500 and 800 K.

Departures from equilibrium near the copper anode of an argon transferred arc

This study into radiative transfer in a arc plasma is devoted first to measure the relative absorption of the arc radiation by cold gas; second, to calculate this absorption; and third, to obtain a simplified expression for this absorption useful in arc modelling. In general, more than 50% of the radiation emitted by a arc is absorbed in the surrounding gas.

An experimental and theoretical study of the absorption of ? arc plasma radiation by cold ? gas

This paper deals with an experimental and theoretical study of the influence of copper vapours on the properties of a arc plasma. Spectroscopic measurements in pure plasma and in a -copper mixture in which copper was provided from the erosion of the anode have been realized. Temperature and relative copper concentration profiles determined experimentally were compared with theoretical values obtained from a two-dimensional physical model. This comparison validated partially the model and the transport coefficients calculated by our team and used in the model. The results showed that the effect of the presence of metallic vapours with a relative concentration of about 1% is too weak to induce noticeable modifications of the properties of plasma. However, a significant cooling of the plasma is calculated for a copper concentration of about 10%.

https://iopscience.iop.org/article/10.1088/0022-3727/31/13/011/pdf

M. Bouaziz

Papers

The influence of iron vapour on an argon transferred arc

Influence of the anode material on an argon arc

Departures from equilibrium near the copper anode of an argon transferred arc

An experimental and theoretical study of the absorption of ? arc plasma radiation by cold ? gas

An experimental and theoretical study of the influence of copper vapour on a arc plasma at atmospheric pressure