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.

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 low current intensity study of a cutting plasma torch is presented. The operating gas is oxygen discharging in an air environment. A two-dimensional turbulent plasma model is developed with the commercial code Fluent 4.5. An experimental and a theoretical study are presented. Two configurations were used: one where the arc is transferred to a rotating anode 19 mm away and the other in a real cutting configuration (distance nozzle exit-workpiece around a few millimetres). In the first configuration, spectroscopic measurements are made and compared with the model. The supersonic plasma behaviour is shown with a Mach number of 1.5 at the nozzle exit. The turbulent effect on the mass fraction field is presented. It concerns the effects of turbulence on the presence of oxygen near the plate, and by a comparison of theoretical and experimental temperatures we conclude that the arc presents turbulent behaviour. In the second configuration, a power balance of the cutting process is presented above and in the thickness of the plate. The model shows that the most important contribution to the fusion process is due to convection, conduction and radiation terms.

The net emission coefficient of Ar-Cu, N2-Cu, SF6-Cu and Ar-Fe mixtures was calculated for homogeneous and isothermal plasmas at atmospheric pressure in the temperature range between 3000 and 25000 K. The increase in power radiated due to the presence of metal vapours depends on the vapour itself (the net emission is higher with iron than with copper) and on the type of gas. The influence of pressure was calculated for the SF6-Cu mixture. In the last part of the paper the values of the net emission coefficient were used to calculate the temperature profile in stationary arc in Ar-Cu and N2-Cu mixtures. The influence of copper on radiation is preponderant on the temperature field at higher currents whereas the effect on electrical conductivity is important at lower currents.

A three-dimensional (3D) argon arc plasma at atmospheric pressure is presented. The model is developed using the commercial code Fluent. Two arc plasma configurations are studied: a free burning arc and a transferred arc. In the free burning arc configuration, the 3D results are compared with a two-dimensional (2D) configuration. The natural axis of symmetry of the system, given by the physical operating conditions and by the cathode tip geometry, leads to a good agreement between the 2D and 3D results. The model is validated by comparisons with experimental and theoretical temperature fields. The results show a small difference between the 2D and 3D models, as does the other literature. In the transferred arc configuration model the injection is given by three injectors. A rigorous modelling of the injection cannot be treated using a symmetric plane or a symmetric axis, so the results are presented in a real 3D configuration and compared with results obtained in a 2D configuration. Indeed, in a 2D configuration, due to the symmetrical condition on the axis, the main assumption consists of representation of the real injection geometry by an equivalent surface injection. The imposed mass flow rate is then distributed along a ring and differences can appear in the results.

This paper is devoted to the study of electric arc behaviour under the influence of an external magnetic field. This situation is close to that occurring in a low-voltage circuit breaker where an arc, after ignition, is submitted to the magnetic field of the circuit. After a discussion of the literature, we present our contribution. Two different methods are compared to take the magnetic effects into account. Arc displacement in the geometry studied is dealt within a specific development presented in this paper. We show the influence of the nature of the gas on the arc velocity and on possible re-strike using air and an air–PA6 mixture as the plasma gas.

In this paper, a cutting plasma torch is studied. We show how experimental and theoretical approaches are complementary for a full characterization of the plasma due to its specific parameters: high temperature, shock wave, pumping of surrounding gas, high velocity. Classical measurement methods cannot be used and two original methods are proposed: the first in the shock wave, where the pressure is unknown, and the second 11.2 mm from the nozzle exit, where the plasma composition depends on the pumping of ambient air.By using a back and forth approach between the theory and experiment, all the plasma characteristics can be estimated. The shock wave location is well predicted and temperatures around 18 kK are obtained in the shock wave and around 14 kK near the anode.

The transfer of energy between the plasma and the iron anode and the evaporation of metal were taken into account in modeling a short free-burning arc in argon at atmospheric pressure. The presence of metal vapor in the plasma modifies the electrical conductivity and the radiated power and leads to arc cooling in the anode region. In return, the arc cooling modifies the rate of vaporization of the anode and thus the calculated concentration of iron vapor in the arc.