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

  • Peng Yan
  • Guifang ZhangEmail author
  • Yindong Yang
  • Alexander Mclean
Article
  • 66 Downloads

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.

List of Symbols

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

Notes

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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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  • Peng Yan
    • 1
  • Guifang Zhang
    • 1
    Email author
  • Yindong Yang
    • 2
  • Alexander Mclean
    • 2
  1. 1.Faculty of Metallurgical and Energy EngineeringKunming University of Science and TechnologyKunmingChina
  2. 2.Department of Materials Science and EngineeringUniversity of TorontoTorontoCanada

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