On the calculation of the electromagnetic force field in the circular stirring of metallic melts

Abstract

A mathematical representation has been developed to represent the electromagnetic force field used to impart rotary motion to a cylindrically shaped molten metal pool. Problems of this type arise in the electromagnetic stirring of continuous casting systems. The formulation given here introduces two new facets which have been neglected by previous investigations, namely, an allowance for the nonlinear dependence of the magnetic flux intensity on the radial distance, and the coupling between the melt velocity and the induced field. It is shown that neglecting these factors may involve errors in the 20%–50% range.

Multiphysics modeling of an induction‐stirred ladle in two and three dimensions

“…This model solved Navier-Stokes equation and included turbulent equations as well as simplified form of Maxwell's equations. Saluja et al [4] presented a mathematical model to represent the electromagnetic force field used to impart a rotary motion to This paper is organized as follows: Section 2 presents a theoretical model for calculation of Lorentz forces and flow field in an induction-stirred ladle. El-Kaddah et al [2] presented a theoretical model to study flow conditions and mass transfer in a 4-ton inductively stirred ladle.…”

“…In 1987, Ilegbusi and Szekely [3] improved the theoretical model for induction stirring of a ladle by including a solution for the evolution of temperature and velocity profiles in ladles holding molten steel. Saluja et al [4] presented a mathematical model to represent the electromagnetic force field used to impart a rotary motion to MODEL OF AN INDUCTION-STIRRED LADLE 1379 a cylindrically shaped molten metal pool. Their formulation introduced two new facets: allowance for the nonlinear dependence of the magnetic flux intensity on the radial distance, and the coupling between melt velocity and the induced current.…”

A tribute to D.B. Spalding and his contributions in science and engineering

“…During the 1980s and early 1990s, PHOENICS was also used extensively at Massachusetts Institute of Technology by Szekely and co-workers for the development of CFD models of materialsprocessing operations, A large number of papers were published during this period, for example: Ilegbusi and Szekely [222,223] (tundishes and continuous casting), Cartwright et al [223] (Czochralski systems) Choo and Szkeley [224] (arc welding). and Saluja et al [225] (stirred melts). PHOENICS has also been in use at Metallurgical Research Institute AB (Sweden) and the Center for Advanced Study and Research of the National Polytechnic Institute (Mexico) for many years to this day, to conduct research into metals processing, see, for example, Solhed and Jonsson [226] and Rodriguez et al [227].…”

Surface-coupled modeling of magnetically confined liquid metal in three-dimensional geometry

“…In addition, free surface effects coupled to bulk fluid flow have been described in applications in which the magnetic field drives significant fluid motion. [13,14] However, this bulk-coupled approach requires solving the distribution of fluid velocity and pressure within the molten metal. In many applications involving magnetic levitation or confinement, the fluid region of interest is small enough that the liquid momentum and associated pressure variation along the surface have a negligible effect upon the liquid metal shape.…”