Rotational electromagnetic stirring in continuous casting of round strands
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I.
INTRODUCTION
IN continuous casting
the solidification structure of steel strands can be improved by electromagnetic stirring. 1,2 The stirring is brought about by an inductor which produces a traveling magnetic field. The field induces eddy currents in the strand which, together with the field, give rise to the electromagnetic force (Lorentz Force) moving the liquid metal in the core of the strand. The optimum stirring conditions are explored in the steel works essentially by trial and error. It is believed that the progress could be accelerated if the physics of stirring are understood quantitatively. The present work deals with the flow velocities in rotational stirring of round strands. The stirrer, which is similar to the stator of an electrical motor, is placed around the strand (Figure 1). The magnetic field rotates around the cylindrical axis of the strand. Therefore, the main component of the flow velocity is that in azimuthal direction. However, due to the centrifugal force the liquid metal moves outward in the stirrer region. It then flows upward (and downward) in a region adjacent to the solidification front, and returns to the stirrer in a region at the center of the strand. Hence, a secondary flow pattern with radial and axial velocity components develops. This secondary flow is interesting in itself; it is also of practical importance because it has a large effect on how far the stirring action reaches downward and upward beyond the region of the stirrer. The flow field is computed in the present work by solving the Navier-Stokes equations together with the Maxwell equations. The turbulent viscosity was computed for the interior region with the k-e-model, and for the region close to the wall with the mixing length model. The set of differential equations was solved numerically by a method of finite differences using an iteration scheme similar to the Gauss-Seidel procedure. The computations were checked with experiments using mercury as liquid. The stirring of a cylindrical liquid body by a rotating electromagnetic field has been investigated by several authors. 3-13 A recent review has been given by Moffatt. 3 In most of the studies laminar flow is treated which is, of course, of limited practical importance. The velocity distribution in an infinitely long system has been investigated by Smith, 4 Kapusta, 5 Dahlberg, 6 and Alemany and Moreau 7 mostly under the assumption of a small magnetic Reynolds K A R L - H E I N Z S P I T Z E R , M A T H I A S D U B K E , and K L A U S SCHWERDTFEGER are with Institut f'tir Allgemeine Metallurgie, RobertKoch-Str. 42, D-3392 Clausthal-Zellerfeld, Germany. Manuscript submitted February 12, 1985. METALLURGICAL TRANSACTIONS B
strand d
stirrer
Fig. 1 - - Rotational stirring of round strands (schematical).
number Rm. For small values of Rm the effects of the induced current on the field is weak so that the magnetic field penetrates the liquid in a similar way as an insulator. For two-polar fields the profile of angular velocity becomes parabolic. The velocity
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