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Modeling and Characterization of Surface Deformation and Current Distribution of Molten Droplets Under Electromagnetic Levitation

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Abstract

Electromagnetic levitation technology is used in the preparation of new materials and the study of metallurgical reactions. However, the surface deformation of droplets in the levitation process can introduce errors in the experimental measurements. The modeling and characterization of molten droplet surface deformation and current distribution under electromagnetic levitation are studied in this paper. The results show that under the influence of surface tension or other factors such as electromagnetic force, molten droplets will oscillate and deform, before finally attaining a relatively stable configuration. Under the conditions of the present work, the relationship between surface current density and applied current is y = 142.65 x2 + 35,998.53 x + 1.14 × 108 and the deformation ratio of the droplet (longitudinal diameter/transverse diameter) is least when the applied current is 470 A. When the current is less than 470 A, the longitudinal diameter of the droplet is greater than the transverse diameter. However, when the current is greater than 470 A, the transverse diameter is greater than the longitudinal diameter.

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Abbreviations

B:

Magnetic flux intensity [T]

Bz :

Axial magnetic field intensity [T]

D:

Electric flux density vector [C/m2]

ρ:

Density [Kg/m3]

E:

Electric field vector [V/m]

J:

Electric density vector [A/m2]

H:

Magnetic intensity [A/m]

T:

Temperature [K]

\({C}_{p}\) :

Specific heat [J/kg K]

σ:

Electric conductivity [S/m]

Fac :

Electromagnetic force [N/m3]

Fz :

Component of electromagnetic force in Z direction [N]

Qv :

Power absorption [W/m3]

g:

Gravity acceleration [m/s2]

μ:

Dynamic viscosity [Pa s]

γ:

Surface tension coefficient [N/K]

Z:

Position in Z direction [mm]

P:

Pressure [Pa]

ρ1 :

Charge density [C/m3]

I:

Current [A]

χ:

Thermal conductivity [W/m K]

t:

Time [s]

r:

Droplet radius [m]

v:

Motion velocity in Z direction [m/s]

n:

Unit normal vector [-]

\( \xi \) :

Average curvature [1/m]

P:

Pressure [Pa]

τ:

Temperature coefficient of surface tension [N/m K]

f:

Frequency [Hz]

ε :

The dissipation rate of the turbulent kinetic energy [–]

K :

The turbulence kinetic energy per unit mass [J]

∀:

Surface gradient of surface tension [–]

p:

Positioning

* :

Conjugate complex

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Acknowledgments

This work was supported by National Natural Science Foundation of China [grant number 52074140] and the Analysis and Testing Foundation of Kunming University of Science and Technology [grant number 2020P20193102006].

Competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Authors and Affiliations

  1. Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, 650093, P.R. China

    Qi Jiang, Guifang Zhang & Xin Qi

  2. Department of Materials Science and Engineering, University of Toronto, Toronto, ON, M5S 3E4, Canada

    Alexander McLean

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  1. Qi Jiang
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  2. Guifang Zhang
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Correspondence to Guifang Zhang.

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Jiang, Q., Zhang, G., Qi, X. et al. Modeling and Characterization of Surface Deformation and Current Distribution of Molten Droplets Under Electromagnetic Levitation. Metall Mater Trans B 54, 1798–1806 (2023). https://doi.org/10.1007/s11663-023-02794-5

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