On the Modeling of Thermal Radiation at the Top Surface of a Vacuum Arc Remelting Ingot
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DUCTION
VACUUM arc remelting (VAR) is a metallurgical process used for the production of high-quality ingots of special steel or nickel-based superalloy. It is also the final stage in the melting cycle of reactive metals such as titanium and zirconium alloys. A detailed understanding of the VAR process is of prime importance because of the strategic role and high market value of those alloys.[1] The VAR process, as illustrated in Figure 1, involves melting a consumable metallic electrode under a high vacuum to form a secondary ingot with a good structural quality. Melting of the electrode is assured by an electric arc maintained between the electrode tip (acting as the cathode) and the top of the ingot (acting as the anode). The liquid metal drops formed at the electrode tip fall through the arc plasma and progressively build up the ingot, which solidifies in contact with
P.-O. DELZANT is with the Institut Jean Lamour, UMR 7198, Universite´ de Lorraine/CNRS - LabEx DAMAS, 2 alle´e Andre´ Guinier, BP 50840, 54011 Nancy Cedex, France and also with the TIMET Savoie, Avenue Paul Girod, 73400 Ugine, France. B. BAQUE´, P. CHAPELLE, and A. JARDY are with the Institut Jean Lamour, UMR 7198, Universite´ de Lorraine/CNRS - LabEx DAMAS. Contact e-mail: [email protected] Manuscript submitted September 19, 2017.
METALLURGICAL AND MATERIALS TRANSACTIONS B
the walls of a water-cooled copper crucible. This ingot is composed of three parts: the liquid pool, the fully solidified metal, and the intermediate mushy zone. The electric arc can be confined by an axial magnetic field created by an external induction coil in order to stabilize the arc. This magnetic field is also used to stir the liquid metal, in order to enhance the chemical homogeneity of the ingot. The energy flux at the ingot top plays a key role in the process, as it has direct effects on the temperature and velocity fields in the molten metal, which both determine the local solidification conditions. The total energy flux at the ingot top may be divided to include three main contributions: the heat stored in the incoming drops, the energy input from the arc plasma, and the net radiative energy flux at the ingot top surface. In the current paper, we will concentrate on this latter contribution. Note that the radiative energy flux is expected to be much smaller than the two other input energy fluxes during most of the melt, yet its contribution may become more important during the hot-topping stage at the end of the melt, which is performed with a reduced arc power. One of the classical approaches adopted to study the VAR process is based on the development of a mathematical CFD model that describes the ingot growth and solidification during a VAR operation. Several such models have been described in the literature. They involve solving the conservation equations of mass, momentum, and energy, while accounting for turbulence and electromagnetic effects in the molten pool as well as the solidification of the metal. The majority of
II.
MODELS
In the radiative heat-tra
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