An eddy current constraint formulation for 3D electromagnetic field calculations

et al. 2020

Field structures including electromagnetic, concentration of ions, and flow fields in an ESR-like process composed of a graphite crucible containing a molten slag, air, and an iron electrode are computed. Both CaF 2-(mass pct 2) CaO and CaF 2-(mass pct 2) Al 2 O 3 slags are examined. Tertiary current distribution is calculated. Therefore, polarization overpotential and Faradic reactions at metal-slag interface are considered using Tafel law, whereas transport of ions in the bulk of slag is determined through Nernst-Planck equations. The main goal is to shed light on the invisible phenomena such as magnetohydrodynamics caused by transport of ions, electrical conductivity of CaF 2-based slag using additives (e.g., CaO or Al 2 O 3), and the role of complexation of ions (e.g., AlO 3À 3) in the molten slag applied to the ESR. An explanation is given for the observation of higher oxygen content in the metal using Al 2 O 3 than that using equivalent amount of CaO in the CaF 2-based slag of a DC-operated ESR.

Section: A Governing Equationsmentioning

confidence: 99%

A Numerical Investigation on the Electrochemical Behavior of CaO and Al2O3 in the ESR Slags

et al. 2020

“…[3], the Coulomb gauge (r ÁÃ ¼ 0) is used. [26] Additionally, the displacement currents are ignored and the magnetic permeability (l 0 ) is assumed to be constant (4p 9 10 À7 J m À1 A À2 ). Finally, the Joule heating (Q) and Lorentz force (F L ) are computed and added as source terms to the energy and momentum conservation equations, respectively.…”

Section: Table I Thermal and Electrical Boundary Conditionsmentioning

confidence: 99%

A Dynamic Mesh-Based Approach to Model Melting and Shape of an ESR Electrode

Boháček

et al. 2015

This paper presents a numerical method to investigate the shape of tip and melt rate of an electrode during electroslag remelting process. The interactions between flow, temperature, and electromagnetic fields are taken into account. A dynamic mesh-based approach is employed to model the dynamic formation of the shape of electrode tip. The effect of slag properties such as thermal and electrical conductivities on the melt rate and electrode immersion depth is discussed. The thermal conductivity of slag has a dominant influence on the heat transfer in the system, hence on melt rate of electrode. The melt rate decreases with increasing thermal conductivity of slag. The electrical conductivity of slag governs the electric current path that in turn influences flow and temperature fields. The melting of electrode is a quite unstable process due to the complex interaction between the melt rate, immersion depth, and shape of electrode tip. Therefore, a numerical adaptation of electrode position in the slag has been implemented in order to achieve steady state melting. In fact, the melt rate, immersion depth, and shape of electrode tip are interdependent parameters of process. The generated power in the system is found to be dependent on both immersion depth and shape of electrode tip. In other words, the same amount of power was generated for the systems where the shapes of tip and immersion depth were different. Furthermore, it was observed that the shape of electrode tip is very similar for the systems running with the same ratio of power generation to melt rate. Comparison between simulations and experimental results was made to verify the numerical model.

“…The A-/ formulation is utilized to determine the electromagnetic field, [75,76] where / denotes the electric scalar potential and A is the magnetic vector potential. The method is very robust and accurate to model the current path including side-arcing.…”

Section: Electromagnetic Fieldmentioning

confidence: 99%

A Parametric Study of the Vacuum Arc Remelting (VAR) Process: Effects of Arc Radius, Side-Arcing, and Gas Cooling

et al. 2019

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.