Contactless Mixing of Liquid Metals

Abstract

This work is devoted to the numerical study of mixing two miscible liquid metals, e.g., Sn and Pb, that are driven either separately by a rotating magnetic field (RMF), by a traveling magnetic field (TMF), or by a combination of both fields from the state of rest. The geometry studied is an enclosed cylindrical cavity with an aspect ratio equal to unity (the diameter of the cylinder is equal to its height, 2R 0 = H 0 ). The initial condition is a cylinder with the lower half filled with a melt that has two times the molecular viscosity of the liquid in the upper part of the cavity. Based on the mixture model of the two-fluid flow and the axisymmetric Navier-Stokes equations, the transient transport of momentum as well as the species for rotary and axial stirring is modeled. The numerical simulations were performed under microgravity conditions for Ekman numbers between 10 À3 and 10 À4 for the RMF-driven flow and for Reynolds numbers between 100 and 400 for TMF-driven flow that corresponded to both laminar and weak turbulent flows. The simulations analysis showed that for RMF, the rapid increase in the mixing rate occurs because of randomly appearing Taylor-Go¨rtler vortices that move up and down along the side wall of the cylinder and that dissipate in the Bo¨dewadt layers. The TMF stirring with forcing parameters that produced laminar flow offers a better mixing performance than the RMF stirring at the same magnetic field intensity. However, with an increase in magnetic forcing, the RMF and TMF lead to comparable mixing times for the same value of magnetic field induction. Additionally, we discuss different mixing scenarios that include the use of time-modulated RMF and TMF. Numerical simulations showed that the discontinuous superposition of RMF and TMF-defined as the sequential switching on and off of both fields with a well-defined period-enhances the mixing in comparison with the non-superimposed case.

Lorentz forces caused by rotating magnetic field

“…This equation corresponds to the published results of other authors as well, see [4,5]. Forces in the radial and axial direction are zero in this simplification.…”

Intermittent Behavior Caused by Surface Oxidation in a Liquid Metal Flow Driven by a Rotating Magnetic Field

“…Equations [5][6][7] were solved using a pseudospectral method. [29] The solutions were obtained in the collocation Gauss-Lobatto mesh points r(i), z(k):…”

“…[1][2][3][4][5][6][7][8] Predictions with respect to the resulting heat and mass transfer in such electromagnetically stirred liquid metals are of key interest for an optimization of the respective industrial technologies. RMF-driven liquid metal flows inside infinitely long as well as finite cylindrical containers have been investigated frequently by numerical simulations.…”

A fixed-grid method for transient simulations of dopant segregation in VGF-RMF growth

“…Due to the finite length of the melt cavity, this rotation causes an axisymmetric meridional flow driven by the well-known Ekman pumping effect (see [12,13] for a detailed explanation). This secondary flow leads to an enhancement of the melt mixing, as pointed out for instance, in experimental [14] and numerical [15] studies.From this point of view the use of RMF in crystal growth applications is similar to the accelerated crucible rotation technique utilized for vertical Bridgman growth e.g., see [16].…”

“…The melting temperature does not depend on the composition. The thermoelectrical effects (Peltier, Thomson) and Joule effect are neglected [15]. The radiative heat transfer is not taken into account.…”