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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.

A transient magneto-hydrodynamic model based on @Ansys-Fluent software applied on a high-voltage circuit breaker (HVCB) geometry is presented. The model is turbulent (κ-ε realizable model), and radiation is taken into account by a hybrid model (Discrete Ordinates Method and P1). The insulating medium is SF 6 , and current I rms = 25 kA. An ablation model based on the literature was applied to represent the ablation of the Polytetrafluoroethylene (PTFE) walls. The theoretical and experimental results (pressure, ablation rate, and voltage drop variation) are presented and compared. Several cases were considered: no ablation (ceramic walls), ablation only from downstream parts, and ablation from upstream parts of HVCB walls. The corresponding pressure variations are presented. In order to explain the pressure increase, some additional quantities such as mass flow rate and energy integrated into one section of the heating channel are given. The results show that even if the mass of PTFE ablated is small, the pressure increase is due to the energy input from the vapor.Index Terms-Computational fluid dynamic (CFD) model, heating volume, high-voltage circuit breaker (HVCB), pressure increase, SF 6 and C 2 F 4 vapors.

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