Numerical Study of Flow Motion and Patterns Driven by a Rotating Permanent Helical Magnetic Field
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IN the past several decades, the application of magnetic fields to liquid metal to improve product quality has been widely used in the metallurgical industry. The electromagnetic body force generated by the interaction between liquid metal and magnetic fields can drive liquid metal and enhance the mixing of the melt, contributing significantly to homogenizing the ingredients and reducing segregations. Moreover, the forced convection strengthens the heat transfer between the liquid metal and the external environment, which increases the solidification cooling rate and stimulates nucleation. The two classic types of magnetic fields used in the metallurgical industry are traveling magnetic fields (TMFs) and rotating magnetic fields (RMFs). In recent years, many studies have investigated these two magnetic fields and their effects by means of experimental measurements, theoretical analyses, and numerical simulations.[1–4] The flow driven by an individual field has been well investigated, and the resulting theory is already relatively mature. For example, when the TMF is separately applied to the enclosed flow in a cylindrical container, the liquid metal flows along the sidewall in the same direction as the TMF. Because of the principle of continuity, the flow returns through the central part where the axial body force is weaker,[5] and WENZHI YANG, Graduate Student, XIAODONG WANG, Professor, and BO WANG, Ph.D. Student, are with the University of Chinese Academy of Sciences, 101408, Beijing, P.R. China. Contact e-mail: [email protected] FLORIN BALTARETU, Professor, is with the UTC Bucharest, 020396, Bucharest, Romania. JACQUELINE ETAY and YVES FAUTRELLE, Professors, are with the CNRS/SIMAP/EPM, ENSEEG, 38402, St Martin d’He´res Cedex, France. Manuscript submitted December 23, 2015. Article published online August 15, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS B
a converging global flow is subsequently formed, as shown schematically in Figure 1(a). The resulting flow of a separate RMF consists of a swirling flow in the horizontal cross section and a secondary recirculation in the meridional plane. The direction of the azimuthal velocity component follows the direction of the electromagnetic force driven by the RMF. Moreover, the Ekman boundary layer is generated near the wall because of the rotation. Thus, all streamlines of the meridional flow pass through these boundary layers, forming two symmetric tori (Figure 1(b)); i.e., a weak secondary meridional flow is formed in the closed cylinder.[6] Recently, the superposition of TMFs and RMFs has received significant interest.[7–9] The results demonstrate that the meridional flow patterns can exhibit either meridian secondary flow (two vortices) or global axial flow (one vortex), depending on the operating parameters.[9] Grants et al.[6] reported the transition between these two flow patterns by means of experiments based on current-carrying, coil-type-generating magnetic fields. Typically, the magnetic field is induced by an electric current field (DC or AC), and the corresponding Lorentz
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