Numerical Investigation of the Position and Asymmetric Deformation of a Molten Droplet in the Electromagnetic Levitation System

Abstract

In this study, a numerical model was developed of the electromagnetic levitation system based on the actual structure and size of the levitation coil. The model was then used to investigate the effects of the induced magnetic field, the electric field, and the magnetic force on the lateral drift and irregular deformation of different sized copper droplets. In addition, several tests were conducted in order to verify the conclusions obtained from the numerical simulation analysis.

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Abbreviations

H :

Magnetic field intensity vector, A/m

\( \varvec{\theta} \) :

Deflection angle of the spiral coil, pct

I :

Excitation current, A

\( \nabla \) :

Nabla operators

\( \nabla \cdot \) :

Divergence operators

\( \nabla \times \) :

Curl operators

B :

Mgnetic flux density vector, T; (\( \varvec{B} =\varvec{\mu}_{\varvec{o}}\varvec{\mu}_{\varvec{r}} \varvec{H} \))

\( \varvec{\mu}_{\varvec{o}} \) :

Permeability of free space, \( 4 \times 10^{ - 7} \varvec{ }{\text{H}}/{\text{m}} \)

\( \varvec{\mu}_{\varvec{r}} \) :

Relative permeability

E :

Electric field intensity vector, N/C

\( \varvec{\varepsilon}_{\varvec{o}} \) :

Permittivity of free space, \( 8.54187817 \times 10^{ - 12} \;\varvec{ }{\text{F}}/{\text{m}} \)

\( \varvec{\varepsilon}_{\varvec{r}} \) :

Relative permeability

D :

Electric flux density vector, C/m2; \( (\varvec{D} =\varvec{\varepsilon}_{0}\varvec{\varepsilon}_{\varvec{r}} \varvec{E}) \)

J :

Current density vector, A/m2; (\( \varvec{J} = \varvec{\sigma E} \))

\( \varvec{\sigma} \) :

Electric conductivity, S/m

\( \varvec{\rho} \) :

Electric density, C/m3

\( \varvec{A} \) :

Magnetic vector Potentia

\( \varvec{\varphi } \) :

Scalar voltage potential

\( \varvec{F}_{\varvec{y}} \) :

Lorentz force (Lifting force) along Y axis, N/m3

\( \varvec{F}_{{\varvec{Y},\varvec{T}}} \) :

Total force acted on the droplet along Y axis, N/m3

x, y, z :

Coordinates of a point in the droplet, m

\( \varvec{\rho}_{\varvec{d}} \) :

Density of the molten droplet, kg/m3

g :

Gravitational acceleration, 9.8 m/s2

δ :

Skin depth, m

f :

Current frequency of the excitation power, Hz

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Acknowledgments

Financial support for this study was provided by the National Natural Science Foundation of China (Project No. 51664036), China Scholarship Council (Project No. 2018[3058]), and the Analysis and Testing Foundation of Kunming University of Science and Technology.

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Correspondence to Guifang Zhang.

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Manuscript submitted June 4, 2019.

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Yan, P., Zhang, G., Yang, Y. et al. Numerical Investigation of the Position and Asymmetric Deformation of a Molten Droplet in the Electromagnetic Levitation System. Metall Mater Trans B 51, 247–257 (2020). https://doi.org/10.1007/s11663-019-01723-9

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