Abstract
Recent work highlighting an anomaly in the modelling of rotary electromagnetic stirring (EMS) in the continuous casting of round steel billets is extended to the case of longitudinal stirring for rectangular blooms. An earlier, still often-cited, model forms the basis of the current analysis, which uses asymptotic methods on the three-dimensional (3D) Maxwell equations and demonstrates how the earlier result for the components of the Lorentz force is but a particular case of a more general form. Time-dependent 3D computations using finite-element methods are also performed to verify the validity of the asymptotic analysis, and the relevance of the results to modulated EMS is noted.
Highlights
Electromagnetic stirring (EMS) has been used in the continuous casting of steel [1] since as early as the 1970s as a way to control solidification structures, thereby increasing yield and productivity
These models consist of the Navier–Stokes equations for the velocity field of the molten metal and Maxwell’s equations for the induced magnetic flux density; in principle, these are two-way coupled, since the alternating magnetic field gives rise to a Lorentz force which drives the velocity field, which can in turn affect the magnetic field
The frequency of the magnetic field is typically great enough to allow the use of the time average of the Lorentz force as input to the Navier–Stokes equations
Summary
Electromagnetic stirring (EMS) has been used in the continuous casting of steel [1] since as early as the 1970s as a way to control solidification structures, thereby increasing yield and productivity. A series of papers by Schwerdtfeger et al [2,3,4,5,6,7] which explored, both experimentally and theoretically, the effect of stirring in the round-billet, rectangular-bloom and slab geometries that are characteristic for the continuous casting of steel, have formed the cornerstone of the modelling literature in this area These models consist of the Navier–Stokes equations for the velocity field of the molten metal and Maxwell’s equations for the induced magnetic flux density; in principle, these are two-way coupled, since the alternating magnetic field gives rise to a Lorentz force which drives the velocity field, which can in turn affect the magnetic field.
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