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Electric arcs used in welding manufacturing often involve 3-dimensional configurations. However, a large fraction of the numerical simulations done to deeper understand high intensity arc in the frame of welding is based on axi-symmetric models.
The electric potential formulation introduced by Hsu and Pfender is the most commonly used electromagnetic model for computing axi-symmetric high intensity arcs. This model was initially developed for long arc. But the high intensity arcs applied to welding manufacturing use to be short. And it turns out that when considering an axi-symmetric configuration, when accounting for the electrode geometry, or when studying a short arc, the 3-dimensional model used in the literature for calculating the electromagnetic fields and the electric potential formulation do not provide the same simulation results: they do not represent the same physics. Some care is thus needed for selecting the relevant electromagnetic model for axi-symmetric short arc, or when accounting for the electrode geometry.
In the present study, four different approaches were considered for modeling the electromagnetic fields of an high intensity electric arc: i) the three-dimensional model, ii) its two-dimensional axi-symmetric formulation, iii) the electric potential formulation, and iv) the magnetic field formulation. The differences between these models are described in detail. Model iv) is not closed compared to models i) to iii). Models i) to iii) are applied to the calculation of an axi-symmetric Gas Tungsten Arc Welding (GTAW) test case with short arc (2mm) 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. For short arc, or to account for electrode tip geometry, the more general axi-symmetric formulation, model ii), should instead be used.