Main modeling challenges for vacuum arc remelting (VAR) are briefly highlighted concerning various involving phenomena during the process such as formation and movement of cathode spots on the surface of electrode, the vacuum plasma, side-arcing, the thermal radiation in the vacuum region, magnetohydrodynamics (MHD) in the molten pool, melting of the electrode, and solidification of the ingot. A numerical model is proposed to investigate the influence of several decisive parameters such as arc mode (diffusive or constricted), amount of side-arcing, and gas cooling of shrinkage gap at mold–ingot interface on the solidification behavior of a Titanium-based (Ti-6Al-4V) VAR ingot. The electromagnetic and thermal fields are solved in the entire system including the electrode, vacuum plasma, ingot, and mold. The flow field in the molten pool and the solidification pool profile are computed. The depth of molten pool decreases as the radius of arc increases. With the decreasing amount of side-arcing, the depth of the molten pool increases. Furthermore, gas cooling fairly improves the internal quality of ingot (shallow pool depth) without affecting hydrodynamics in the molten pool. Modeling results are validated against an experiment.

A comprehensive numerical model is proposed to study the influence of an axial magnetic field (AMF) on the solidification behavior of a Titanium-based (Ti–6Al–4V) vacuum arc remelting (VAR) ingot. Both static and time-varying AMF are examined. The proposed 2D axisymmetric swirl model includes calculating electromagnetic and thermal fields in the entire system composed of the electrode, vacuum plasma, ingot, and mold. A combination of vector potential formulation and induction equation is proposed to model the electromagnetic field accurately. Calculations of the flow in the melt pool and solidification of the ingot are also carried out. All governing equations are presented in cylindrical coordinate. The presence of a weak AMF, such as the earth magnetic field, can dramatically influence the flow pattern in the melt pool. The “Electro-vortex flow” is predicted ignoring AMF or in the presence of a time-varying AMF. However, the flow pattern is “Ekman pumping” in the presence of a static AMF. The amount of side-arcing has no influence on the pool depth in the presence of an AMF. Modeling results are validated against experiments.