Rotational electromagnetic stirring in continuous casting of round strands

On an Anomaly in the Modeling of Electromagnetic Stirring in Continuous Casting

“…Furthermore, in Eqs. [2] through [4], F r ; F h ; and F z denote the time-averaged components of the Lorentz force, which we write as F r ; F h ; and F z and which are given by…”

“…A cornerstone of the modeling literature in this area is a sequence of papers by Schwerdtfeger and co-workers [2][3][4][5][6][7] which explore, 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. The models in question 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.…”

“…To obtain adequate data for this, it may in practice mean using a Hall probe magnetometer to make measurements of the magnetic field at a point or points in the space between the outer surface of the steel strand and the periodic winding of the inductor on an iron comb, [2,3,7] or a Gauss meter [8,9] ; indeed, measurements acquired in the former way were used as the basis for prescribing the normal component of the magnetic flux density at the surface of the strand. However, some time later, and in a mathematically related problem, McKee et al [10] prescribed the tangential component in their model for particle tracking within a turbulent cylindrical electromagnetically driven steel melt.…”

“…Consequently, there appears to be some uncertainty as to what should be the correct boundary condition in this situation: indeed, McKee et al [10] followed Moffatt [11] in initially assuming that both the normal and tangential components of the magnetic flux density are required as boundary conditions, only to ultimately just use the latter. Moreover, the fact that the expressions for the components of the Lorentz force for round billets [2,7] and for rectangular strands [3] have been cited and used on numerous occasions since, even up to the present day, [9,[12][13][14][15][16][17][18][19] suggests that a resolution of the issue is timely.…”

Contribution to the Flow Calculation in Electromagnetic Stirrers for Continuous Casting.

“…using a rotational two-pole magnetic field, it is known, that the velocity measured with Pitot tube and hot-film anemometer 1) , mechanically 2) and with laser Doppler anemometer 3) increases in the middle vicinity, and cannot be calculated correctly with the k-e model of turbulence 4) . For example, the velocity depending only on the radius r in a long test stirrer described in Table 1 2) has a maximum near the middle, which cannot be obtained with the k-e model ( Fig.…”