On the choice of electromagnetic model for short high-intensity arcs, applied to welding

We have considered four different approaches for modelling the electromagnetic fields of high-intensity electric arcs: (i) three-dimensional, (ii) two-dimensional axi-symmetric, (iii) the electric potential formulation and (iv) the magnetic field formulation. The underlying assumptions and the differences between these models are described in detail. Models (i) to (iii) reduce to the same limit for an axi-symmetric configuration with negligible radial current density, contrary to model (iv). Models (i) to (iii) were retained and implemented in the open source CFD software OpenFOAM. The simulation results were first validated against the analytic solution of an infinite electric rod. Perfect agreement was obtained for all the models tested. The electromagnetic models (i) to (iii) were then coupled with thermal fluid mechanics, and applied to axi-symmetric gas tungsten arc welding test cases with short arc (2, 3 and 5 mm) and truncated conical electrode tip. Models (i) and (ii) lead to the same simulation results, but not model (iii). Model (iii) is suited in the specific limit of long axi-symmetric arc with negligible electrode tip effect, i.e. negligible radial current density. For short axi-symmetric arc with significant electrode tip effect, the more general axi-symmetric formulation of model (ii) should instead be used.