Electromagnetic Stirring of Steel: Effect of Stirrer Design on Mixing in Horizontal Electromagnetic Stirring of Steel Slabs

Electromagnetic stirring is widely used in continuous casting of steel as a means to improve homogeneity of cast slabs. Industrial experience has shown that stirrer design and operating conditions have a strong influence on the metallurgical quality of the cast slab. This paper examines the effect of the stirrer current and field frequency on the flow in horizontal EMS of steel slabs. A threedimensional model for computing the electromagnetic and velocity fields in continuous casting systems is presented. The stirrer current and frequency were found to affect the primary horizontal flow in the vertical section covered by the stirrer and to have a significant effect on the upward flow in the force-free region above the edges of the stirrer. It was also found that flow is quite turbulent in the region facing the stirrer, and turbulent mixing diminishes rapidly beyond the edges of the stirrer. It has also been demonstrated that through changes in the stirrer current and/or field frequency, it is possible to modify the magnitude and distribution of turbulent characteristics of the induced flow. NOMENCLATURE D deformation tensor Fem Lorentz force H magnetic field intensity I stirrer current J current flux density k turbulent kinetic energy P pressure T current vector potential U velocity ε turbulent energy dissipation μo magnetic permeability μl laminar viscosity μt turbulent viscosity ρ density σ electrical conductivity φ phase shift Ψ reduced magnetic scalar potential ω frequency INTRODUCTION In recent years most steel producers have recognized that control of fluid flow and mixing phenomena in continuous casters is necessary to improve the overall quality of cast billets and slabs. More specifically, it has been appreciated that in addition to reducing solute segregation during solidification, the flow may play a key role in eliminating inclusions, blowholes and center porosity. As a result, electromagnetic stirring (EMS) has become an integral component of the continuous casting process (Birat and Chone, 1982; Kollberg, 1980). In EMS of billets and slabs, induction stirrers are placed in the mold, below the mold, and/or in the final solidification zone depending on metallurgical objectives. For slab casting, melt stirring is accomplished using linear stirrers of finite height. These stirrers can be regarded as induction motor stators producing traveling a magnetic field, which generates a force field in the strand, resulting in a recirculating flow field in the molten pool. It is generally accepted that the maximum velocities have to be in excess of about 0.2 ~ 0.5 m/s for the stirring to be effective, although these limits are not firmly established. During the past decade a considerable effort has been made to develop a quantitative description of the electromagnetic and flow phenomena in sub-mold stirring of slabs. The early work by Dubke et al. (1988) and Saluja et al. (1990) employed an approximate twodimensional analytical expression for the force field. The most recent efforts have made use of numerical techniques for the solution of Maxwell's equations to describe the field in terms of the stirrer geometry and the stirrer current and frequency (Meyer et al., 1987; Natarajan and El-Kaddah, 1998). As a result of this latter work, one may now, with some confidence, quantitatively predict the electromagnetic and velocity fields for any given stirrer configuration and operating conditions. The purpose of this paper is to investigate the effect of stirrer current and frequency on the induced flow in sub-mold horizontal EMS of slabs. FORMULATION The mathematical description of the EMS system involves the solution of Maxwell's equations to determine the induced force field in the slab, and the turbulent Navier-Stokes equations together with turbulent-model equations to calculate the velocity field in the molten pool. It is assumed that the thickness of the solidified shell in the solution domain is infinitesimally small. It is also assumed that the flow in the molten pool due to pouring does not affect the electromagnetically induced flow. This assumption is