The Influence of Eddy Effect of Coils on Flow and Temperature Fields of Molten Droplet in Electromagnetic Levitation Device

Abstract

In this work, the influence of eddy effect of coils on magnetic, flow, and temperature fields in an electromagnetically levitated molten droplet was investigated by a serial of axisymmetric numerical simulations. In an electromagnetic levitation device, both metal droplet and coils are conductive materials, therefore the distributions of current density in them should be nonuniform as a result of the eddy effect. However, in previous works, the eddy effect was considered alone in metal droplet but ignored in coils usually. As the distance of coils and metal droplet is several millimetres in general, the non-uniform distribution of current density in coils actually gives important influences on calculations of magnetic, flow, and temperature fields. Here, we consider the eddy effect both in metal droplet as well as that in coils simultaneously. Lifting force, absorbed power, fluid flow, and temperature field inside a 4-mm radius molten copper droplet as a typical example are then calculated and analyzed carefully under such condition. The results show that eddy effect leads to higher magnetic force, velocity, and temperature in both levitating and melting processes than those when the eddy effect is ignored. What is more, such influence increases as the distance of droplet and coils becomes closer, which corresponds to experimental measurement. Therefore, we suggest that eddy effect of coils should be considered in numerical simulation on this topic to obtain more reliable result.

Influence of Coil Angle Arrangement on Dynamic Deformation and Stability of Molten Droplet in Electromagnetic Levitation System

“…2. 26) Obviously, both the lifting force and absorbed power show well consistence with those in Ref. 10).…”

“…Through submitting Lorentz force and absorbed power into Navier-Stokes equations and energy equation respectively, the flow field and temperature field inside a fixed sphere can be obtained. 26) Figure 3 shows such a case and we compared our results with those in Ref. 10).…”

“…9) In other works, laminar flow regime was assumed but the effective viscosity was enhanced artificially on the order of 10-40 of molecular viscosity to compensate the differences. 10,26) Due to difficulties of strong coupling of turbulence and dynamic deformation, in this paper, the laminar regime is adopted and the artificially enhanced effective viscosity is predicted by k-ε model under fixed sphere. Since the temperature distribution over molten droplet is quite uniform, the buoyancy and Marangoni effects are neglected compared with Lorentz force and gravity.…”

“…The former way is more efficient while the latter is more accurate. 26) Here, to precisely predict the deformed shape of molten droplet, the latter way is adopted. The Lorentz force and absorbed power acted on molten droplet are given by: Where Re represents the real part of a complex quantity and the asterisk is the complex conjugate.…”

Containerless metal single-crystal growth via electromagnetic levitation

“…Feng and Shi developed a FEM model to investigate the effect of eddy currents inside the coil on the sample temperature. [42] They also modeled the internal fluid flow in the spherical sample and found that the temperature is not homogeneous but can vary up to 0.1 K within the sample. Later, they developed a model using the arbitrary Lagrangian-Eulerian (ALE) finite element technique, which has the main advantage that the computational mesh inside the domains can move arbitrarily to optimize the shapes of elements and follow the contours of moving materials.…”