J J Gonzalez

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

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.

Numerical and experimental study of a plasma cutting torch

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.

Comparison between a two- and a three-dimensional arc plasma configuration

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.

Calculation of a two-temperature plasma composition : bases and application to SF6

In this paper we discuss the use of generalized Saha and Guldberg-Waage equations for calculating the composition of a two-temperature SF6 plasma in a pressure range 0.1-1.6 MPa, for an electron temperature in the range 300-20 000 K. We compare two sets of two-temperature laws and we recommend the expressions proposed by the team from Eindhoven. Furthermore, knowing the great influence of the choice of the excitation temperature on the plasma composition, we propose, on the basis of a chemical kinetics approach, a simple general relation allowing the calculation of this temperature versus the electron temperature, the heavy particle temperature and the electron number density. The application of these relations to a real case of a two-temperature SF6 arc plasma gives a realistic radial profile of the electron number density.

Complementary experimental and theoretical approaches to the determination of the plasma characteristics in a cutting plasma torch

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.

Comparisons between two- and three-dimensional models: gas injection and arc attachment

Numerous papers report numerical models in one or two dimensions, but the three-dimensional models remain scarce due to the limited computing possibilities in the nineties. But currently, the new computer power makes it possible to develop and characterize, when necessary, the plasma medium in three dimensions, using geometries closer to reality. Indeed, some specific points like for example describing the lateral powder or the vortex gas injections or some complex geometries requires a three-dimensional co-ordinate system. The aim of this paper is to present configurations developed in three dimensions, to compare the results with the classically used two-dimensional approach which necessitates several assumptions and to determine the limitation of the two-dimensional model. For this study, two configurations are presented: a transferred arc and a plasma torch and two main points are studied: vortex injection and lateral arc attachment. The results show the validity of the two-dimensional model on temperatures prediction on the axis, and also the limitation of the two-dimensional approach for the velocities and the temperature determinations at the plasma edges.

Arc/Cathode Interaction Model

A 1-D model of the interaction between an electric arc and a solid refractory cathode has been developed. This model is based on the equilibrium of the charged particle fluxes in the cathode layer by considering current density conservation, and balance of energy at the sheath/presheath and at the sheath/cathode surface interfaces forming a closed system of equations. It allows the sheath and presheath to be described and the main physical quantities to be obtained by only using current density as input parameter. The calculations were performed for atmospheric argon discharge and a tungsten refractory cathode. The results obtained, such as the cathode sheath voltage drop and the power flux transmitted to the cathode, are compared with those of the literature, and good agreement is observed. Moreover, our model can be used for a range of current densities (1 times 104-5 times 108 A ldr m-2) accurately describing attachment at low current. The heat flux deduced reaches a maximum of 6 times 107 W ldr m-2 at equilibrium between ionic heating and thermionic cooling. The thermionic electron emission current density is dominant for current densities higher than 5 times 106 A ldr m-2.

Decay and post-arc phases of a SF6 arc plasma: a thermal and chemical non-equilibrium model

After current zero in a high-voltage SF6 circuit breaker, the recovery voltage heats the remaining electrons, producing departures from thermal equilibrium that may modify the electrical conductivity of the medium and thus the interruption capability of the apparatus. In this study we present a two-temperature hydrodynamic model coupled with a kinetic model, applied to the extinction of a blown SF6 arc in a two-dimensional simplified geometry. The free decay and the post-arc phase with the recovery voltage have been studied. The kinetic part of the modelling allows us to calculate the evolution of the electron number density. A simplified turbulence model has been added to study its influence on the post-arc phase. The main results of this study reinforce the conclusions obtained taking into account only the chemical non-equilibrium: the departures from equilibrium tend to decrease the interruption capability predicted by the model. This effect is due to the weak energy exchange by elastic collisions between the electrons and the heavy particles, leading to an electron temperature higher than the gas temperature which favours the ionization of the medium submitted to a recovery voltage.

Simulation of a decaying arc plasma: hydrodynamic and kinetic coupling study

During the decay of a circuit-breaker arc, the plasma is subjected to strong blowing which can lead to deviations from chemical equilibrium. The intense convection may therefore be responsible for the presence of cold gas in the hot parts of the plasma. The cold particles then rapidly recombine with electrons, modifying the resistivity of the plasma. In order to study this phenomenon as it appears in circuit-breakers, we made a modelling of the extinction of an arc for a simplified geometry. The two-dimensional model that was set up was followed by a study of the kinetics of which enabled us to identify the various reaction processes governing the disappearance of electrons. The results show that convection acts on molecules which, at the edge of the discharge and for temperatures of between 4000 and 6000 K, are overpopulated with respect to equilibrium. Through charge exchange processes between and particles, the overpopulation of leads to an overpopulation of the ions. These ions mainly recombine with electrons, lowering the electron population and modifying the electrical conductivity of the plasma.

Calculation of the interruption capability of SF/sub 6/-CF/sub 4/ and SF/sub 6/-C/sub 2/F/sub 6/ mixtures. II. Arc decay modeling

We evaluate, in this paper, the interruption capability of gas mixtures by simulating the decay of a nonblown wall-stabilized arc at atmospheric pressure. We have calculated, by a one-dimensional (1-D) transient model assuming local thermodynamic equilibrium and solving the mass and energy conservation equations, the variations of temperature and conductance. From our calculations, we can bring out that the most efficient gas for the interruption capability is the SF/sub 6/, and that the mixtures SF/sub 6/-CF/sub 4/ and SF/sub 6/-C/sub 2/F/sub 6/ are more efficient than SF/sub 6/-N/sub 2/ mixtures.