Numerical modelling of free surface dynamics of melt in an alternate electromagnetic field

Abstract

INTRODUCTION. Induction furnaces that ensure contact less control of electromagnetic (EM) alloy stirring, temperature and free surface shape are widely applied in metallurgical industry. In great induction crucible furnaces (ICF) the melt is usually covered with slag layer that acts both as a thermal and chemical insulator. Free surface deformations might cause slag displacement and lead to undesirable contact between the melt and atmosphere accompanied with chemical reactions and thermal losses. In case of higher power densities, e.g. induction furnace with cold crucible (IFCC), the EM pressure squeezes the melt and semi-levitation is achieved. In this instance the melt is fully abutted upon the skull. Moreover, for reactive alloys of high purity the furnace design leads to complete alloy levitation in a non-reactive atmosphere. In the same time the behaviour of free surface might be notably unsteady due to operational parameter change, mean flow instabilities and high values of turbulence kinetic energy. Mass transfer processes in induction furnaces considering free surface [1], as well as, phenomenon of EM levitation [2], are actively studied numerically. Since the problem of free surface shape control appears to be significant for processing of metallic materials, the development of models for free surface dynamics calculation remains relevant. In the recent work the model for free surface dynamics calculation in simplified twodimensional (2D) axisymmetric [3], as well as, in three-dimensional (3D) [4] consideration was developed. The calculation was arranged by means of ANSYS Classic for EM problem, ANSYS/CFX for hydrodynamic (HD) problem and their external coupler (V. Geza, UL). Volume of Fluid (VOF) numerical technique and k-ω SST turbulence model were applied for high Reynolds number two phase flow calculation. Due to the low magnetic Reynolds number the EM and HD parts of the complicated magnetohydrodynamic (MHD) problem were solved sequently, considering only the change of free surface shape reciprocal interaction with the change of EM field distribution. Moreover, because of much greater inertia times of melt in comparison to the alternate EM field timescale, only the steady part of the Lorentz force was taken into account. The verification of free surface oscillation period T in case of small amplitude deviation according to analytical formula from [5] approved 2D and 3D model accuracy. In this paper the further model verification and calculation results are discussed.