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.

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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.