Lateral Boundary Conditions for Heat Transfer and Electrical Current Flow during Vacuum Arc Remelting of a Zirconium All
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TRODUCTION
OVER the past two decades, considerable progress in understanding of the vacuum arc remelting (VAR) process has been made by using numerical modeling. Among the various models published, the code BAR developed at Sandia National Laboratories and the code SOLAR developed at the School of Mines in Nancy should be mentioned. As a general rule, the reliability of the results of a model is largely dependent among others on the formulation of ‘‘realistic’’ and coherent boundary conditions. The boundary conditions used in the mentioned models, especially at the ingot-crucible interface and at the crucible-cooling water interface but also at the ingot top, are however still sketchy in many ways as they remain only partially understood.
P. CHAPELLE and A. JARDY, CNRS Research Scientists, and J.P. BELLOT, Professor, are with Laboratoire de Science et Ge´nie des Mate´riaux et de Me´tallurgie (UMR CNRS-INPL 7584), Ecole des Mines, Parc de Saurupt, 54042 Nancy Cedex, France. V. WEBER, formerly Postdoctoral Student, Laboratoire de Science et Ge´nie des Mate´riaux et de Me´tallurgie (UMR CNRS-INPL 7584), Ecole des Mines, is Research Engineer, ArcelorMittal Company. R.M. WARD, Research Fellow, is with the IRC in Materials Processing, University of Birmingham, Birmingham B15 2TT, United Kingdom. M. MINVIELLE, Research Engineer, is with the Centre de Recherches de la Compagnie Europe´enne du Zirconium CEZUS, AREVA, 73403 Ugine Cedex, France. Contact e-mail: [email protected] This article is based on a presentation given at the International Symposium on Liquid Metal Processing and Casting (LMPC 2007), which occurred in September 2007 in Nancy, France. Article published online October 7, 2008. 254—VOLUME 40B, JUNE 2009
The present work focuses on some of the aspects of the lateral boundary conditions for heat transfer and electrical current at the inner and outer walls of a VAR crucible. One of the difficulties of formulating those conditions is the large variety of transfer phenomena involved (including conduction, radiation, forced convection, etc.), which are affected by a number of factors (crucible surface conditions, cooling water flow rate, etc.). Another critical issue is the representation of the gradual shrinkage of the ingot away from the crucible during the cooling process. The latter imposes varying boundary conditions along the axial position. Experimentally, the only parameters accessible to gain some physical insights into those conditions are the temperature and voltage of the outer wall of the crucible. These parameters may then be used to infer the axial current flowing through the crucible via Ohm’s law, with the knowledge of the temperature needed to account for its influence on the resistivity. Although simple in their principle, these measurements remain technically delicate to perform in the context of the VAR process. In the literature, such measurements have been performed during the remelting of various metallic alloys (alloy 718[1–3] and Ti-6Al-4V[4]). In this article, we first present simi
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