Electromagnetic and thermal-flow modeling of a cold-wall crucible induction melter
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I. INTRODUCTION
ONE approach to inductive heating and melting of metals is to contain the molten metal in a water-cooled copper container. The container is typically cylindrical with a helical induction coil surrounding it. The crucible walls are segmented with thin layers of dielectric material separating the segments to minimize induced currents and, therefore, Joule heating losses in the crucible. One variation of this type of melter has no bottom and relies on a solidified ingot below to support the molten metal. This so-called bottomless melter can be used to add feedstock continuously to the melt while withdrawing a solidified ingot from the bottom.[3–6] Other segmented cylindrical crucibles have water-cooled copper bottoms and are typically used for batch processing of various alloys. The cold container results in a solidified layer known as the skull on the inner surface of the container. The skull effectively isolates the molten metal from the container, which is advantageous for alloy purity and melter durability with reactive metals such as titanium. This type of melter is referred to in industry as an induction skull melter (ISM). At high coil frequencies (on the order of kilohertz), the induced current is limited to a “skin” layer in highly conductive materials. The “standard” skin depth is approximated as d
2 A mosv
[1]
where o is the magnetic permeability of free space, is the electrical conductivity of the material and is the freJIM FORT, Staff Engineer, and NICK KLYMYSHYN, Senior Research Engineer, are with the Pacific Northwest National Laboratory, Richland, WA 99352. Contact e-mail: [email protected] MARK GARNICH, formerly Senior Research Scientist, with Pacific Northwest National Laboratory, is Associate Professor, University of Wyoming, Laramie, WY 82071. Manuscript submitted February 24, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS B
quency of the magnetic field in rad/s. Through Joule heating, the temperature of material in the skin layer is elevated. By increasing the drive current in the coil, this process can readily melt most metals. A variable capacitance in the electric circuit is used to tune the phase angle of the input current to maximize the inductive coupling and efficiency of the system. In addition to resistive heating, knowledge of the electromagnetic fields is important because of the effects of Lorentz force on the molten charge. The Lorentz force is defined at a point by the cross product of the electric current and the magnetic field vectors. Given that the eddy current and associated magnetic field are tangential to the material surface, the Lorentz force is always normal and into the surface. It plays an important role in the ISM as the driving force for mixing and changing the shape of the molten pool. The magnitude of the Lorentz force dominates the buoyancy force and is in fact sufficient to circulate the melt at turbulent flow velocities. The Lorentz force is a maximum in the high-current region at the outer diameter of the melt and deforms the surface of
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