A numerical study of unidirectional solidification of a binary metal alloy under influence of a rotating magnetic field

Abstract

In this paper we present a numerical study of the fluid flow during directional solidification of a binary alloy (Pb85wt%Sn) in presence of a forced convection. The latter is driven by a rotating magnetic field (RMF) the strength of which, expressed by the magnetic Taylor number, varies between 10 4 < Ta < 2 × 10 6. The focus of this paper is the problem when cooling starts simultaneously with the acceleration of the melt from a state of rest. Thus, we study the interference of the so-called spin-up problem with the solidification of the melt. The numerical simulations are based on a mixture model formulation. We show that three distinct fluid flow phases exist. During the first two phases ( initial adjustment and inertial phase) the acceleration of the liquid takes place which occurs in close similarity to the isothermal spin-up [P.A. Nikrityuk, M. Ungarish, K. Eckert, R. Grundmann, Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder. A numerical and analytical study, Phys. Fluids 17 (2005) 067101]. The third phase is characterized by a braking of the fluid flow due to the progressive solidification increasing the aspect ratio of the liquid (2 R 0/ H l) and decreasing the forcing. We show that as soon as the velocity of the secondary flow exceeds the velocity of the solidification front, a convex shape of the mushy zone can be observed. In parallel, Taylor–Görtler vortices advected by the secondary flow towards the mushy zone might impose a wavy substructure on the latter. At the end, predictions with respect to heat flux and macrosegregations are given.