J. J. Gonzalez

Thermal plasma modelling

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.

Advances in low-voltage circuit breaker modelling

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.

Numerical modelling of an electric arc and its interaction with the anode: part II. The three-dimensional model—influence of external forces on the arc column

This paper reports the second part of the study of an electric arc and its interaction with the anode material. First, a three-dimensional model is presented and validated in a natural symmetric configuration for which many experimental results exist. In the three-dimensional model, two situations are considered for the anode surface: the classical zero heat flux condition and the use of the anode model. In the second case, the specific properties of the anode material are taken into account and play a role in the current conservation between the plasma and the anode, and therefore, affect the arc behaviour near the electrode. The results for the two approaches are similar in two dimensions, but differences exist in real three-dimensional cases when external forces such as cross flow or magnetic field tend to bend the arc. Second, we present a comparison between the two methods in the case where the arc is deviated by an external magnetic field. For this comparison, we adopt a configuration used at Odeillo during the 1970s and compare the results obtained by our code with the experimental ones. We find that it is essential to consider the complete anode model if the arc deflection is to be predicted correctly. Once our developments are validated, the computational code is applied in a free-burning arc configuration, where the plasma column is deflected by an external cross flow.

Experimental and theoretical study of the expansion of a metallic vapour plasma produced by laser

The interaction between a metallic plasma produced by laser ablation and an ambient gas (argon, air and nitrogen) at atmospheric pressure is studied. The experimental results are compared with theoretical ones given by numerical simulation. Aluminium and copper targets are used. The uniform repartition of iron impurities included in the target (1.6% for Al and 2% for Cu) is warranted by the manufacturer. The Nd : YAG laser delivers pulses of 8 ns FWHM duration with an energy ranging from 70 to 100 mJ at a rate of 10 Hz. The temperature measurements have been performed by the Boltzmann diagram method using iron lines. The influence of ambient gas and target material is studied. After an Abel transform, we observe a maximum of the line intensities off the plasma axis. This shows the formation of gas plasma around the metallic one before complete diffusion of the ambient gas in the metallic plasma. The hydrodynamic model built in one dimension uses the continuity equations. This code is based on the control volume method of Patankar. A temperature and mass fraction profiles are needed as initial conditions. This model is able to describe the temporal evolution of the temperature and of the diffusion in the plasma. It allows us to study the mixture of the metallic plasma and the ambient gas as soon as the plasma is thermalized and local thermodynamic equilibrium is established. There is good agreement between the results of the simulation and the experimental results.

A numerical modelling of an electric arc and its interaction with the anode: part III. Application to the interaction of a lightning strike and an aircraft in flight

A numerical model is proposed to describe the arc and its interaction with a composite material in an anodic configuration. After a validation step with experimental results in two dimensions (2D) from the literature, the model is used to quantify the degradation level of the material versus the pulse duration and the current intensity value. The flux components show the importance of the Joule effect in the composite. Then, in order to simulate the aircraft displacement, an external convective force is applied. A three-dimensional (3D) model is thus developed and used to evaluate the degradation of the composite material. This model shows the behaviour of the plasma column representing the lightning strike and quantifies the power transferred to the anode.

Magnetic field approaches in dc thermal plasma modelling

The self-induced magnetic field has an important role in thermal plasma configurations generated by electric arcs as it generates velocity through Lorentz forces. In the models a good representation of the magnetic field is thus necessary. Several approaches exist to calculate the self-induced magnetic field such as the Maxwell–Ampere formulation, the vector potential approach combined with different kinds of boundary conditions or the Biot & Savart (B&S) formulation. The calculation of the self-induced magnetic field is alone a difficult problem and only few papers of the thermal plasma community speak on this subject. In this study different approaches with different boundary conditions are applied on two geometries to compare the methods and their limitations. The calculation time is also one of the criteria for the choice of the method and a compromise must be found between method precision and computation time. The study shows the importance of the current carrying path representation in the electrode on the deduced magnetic field. The best compromise consists of using the B&S formulation on the walls and/or edges of the calculation domain to determine the boundary conditions and to solve the vector potential in a 2D system. This approach provides results identical to those obtained using the B&S formulation over the entire domain but with a considerable decrease in calculation time.

Tomographic reconstruction of 3D thermal plasma systems: a feasibility study

A preliminary investigation of tomographic reconstruction of arc plasma in three dimensions has been carried out. The main goal of this work was to define both the optimal experimental scheme for tomographic measurements and the most appropriate tomographic method with minimum constraints to obtain images of good quality in real situations. Numerical calculations were developed and performed to define a test case corresponding to an experimental device. The multiplicative algebraic reconstruction technique (MART) was applied for reconstruction of the emission profile from the acquired projections. Numerical reconstruction from two, three, four and seven projections are presented and discussed in a theoretical three-dimensional (3D) transferred arc configuration. The dependence of the reconstructed image quality on both the projection directions and the noise level was studied. Numerical simulation demonstrated that MART was perfectly suitable for reconstructing satisfactory 3D emission and temperature profiles of the arc plasma with a four-view configuration, proving the feasibility and the utility of tomography to characterize a 3D plasma medium.

Experimental quantification in thermal plasma medium of the heat flux transferred to an anode material

This paper is devoted to a plasma characterization with an experimental quantification of the energy transferred to the anode material in a transferred arc configuration. After spectroscopic measurements in an argon plasma medium, measurements in the anode material were performed using thermocouples. The flux applied by the plasma medium to the anode material was deduced from experimental measurements and the use of an iterative inverse method, the conjugate gradient method. The optimal temperature sensor positions were deduced from a previous theoretical study showing the suitability of the method for flux quantification using recommendations exposed in the paper. The measurements were made for various values of the current intensity around 100 A leading to fluxes close to 107 W m−2.

Theoretical study in two dimensions of the energy transfer between an electric arc and an anode material

In many thermal plasma applications, the knowledge and control of energy transfer is essential. Numerical models taking the interaction between plasma and material into account are being developed but the results need to be validated by experiment. Before considering experimental measurements to deduce the heat transferred to a material, we develop a theoretical approach studying the ability of inverse methods to reconstruct the temperature field and the heat flux profile applied at the surface, starting from temperature values in the material. After a study of the literature, the conjugate gradient method and the least squares methods were chosen for our configuration. Numerous parametric tests were performed (position, number of temperature points and the introduction of noise on data) to compare the two methods and to study their suitability. In the case of heat fluxes of around 107–108W m−2 and iron materials, the Tikhonov method showed its limitations but the conjugate gradient method demonstrated its suitability for implementation in our experimental setup to reconstruct the heat flux and the temperature field that could be obtained by the interaction of an electric arc with a material in an axisymmetrical configuration.

INFLUENCE OF METAL VAPOR AND COMPOSITE MATERIAL ON THE DECAYING CONDUCTANCE OF A LOW -VOLTAGE CIRCUIT BREAKER

In a low-voltage circuit-breaker (LVCB), the contact opening leads to the formation of an arc in air, that is moved to an extinction chamber. During its displacement, largely due to external electromagnetic forces, the arc interacts with rails and with the walls made of composite material. The material ablation creates an increase of the local pressure that favors the arc movement. But the presence of metal and carbon vapors that have rather low ionization potentials, may increase the electron number density and, in certain cases, it has been observed an arc restriking near the contacts. In order to study this phenomenon we have been developing a numerical study for calculating the arc movement, the interaction with the walls and all the problems related to the extinction.