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A coupled mathematical model and experimental validation of oxygen transport behavior in the electro-slag refining process

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Abstract

Electro-slag refining process is widely employed in steel industry for the production of special alloys used in ocean, aeronautics, and nuclear industries. Because of the adverse effect on the ductility of metal, it is critical to remove oxygen in the process. This study established a transient three-dimensional (3D) coupled mathematical model for understanding oxygen transport behavior in the electro-slag refining process. The finite volume method was invoked to simultaneously solve mass, momentum, energy, and species conservation equations. Using the magnetic potential vector, Maxwell’s equations were solved, during which the obtained Joule heating and Lorentz force were coupled with the energy and momentum equations, respectively. The movement of metal–slag interface was described through the application of the volume of fluid (VOF) technique. Additionally, an auxiliary metallurgical kinetic module was introduced to determine the electrochemical reaction rate. An experiment was then conducted to validate the model, where the predicted oxygen contents agreed with the measured data within an acceptable accuracy range. Oxygen redistribution in both fluids is clarified: its transport rate at the metal droplet–slag interface is approximately one order of magnitude larger than that at the metal pool–slag interface. Further, the oxygen content in the metal pool is shown to increase with time, while the content in the slag layer is decreased. In order to effectively remove the oxygen in the metal, one more positive electrode, which is more likely to react with the oxygen, is proposed to be added in the unit.

Graphical abstract

Distributions of the electric streamlines and the phase distribution at 151.25 s with a current of 1800 A

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Abbreviations

\(\vec{A}\) :

Magnetic potential vector/V s m-1

\(\vec{B}\) :

Magnetic flux density/T

\(c\) :

Mass percent of oxygen

\({{c}_{0}}\) :

Coefficient in Eqs. (10) and (12)

\(D\) :

Diffusion coefficient of oxygen/m2 s

\(E\) :

Internal energy of mixture phase/J m3

\(F\) :

Faraday law constant/C mol

\({{\vec{F}}_{e}}\) :

Lorentz force/N m3

\({{\vec{F}}_{s}}\) :

Solute buoyancy force/N m3

\({{\vec{F}}_{t}}\) :

Thermal buoyancy force/N m3

\(I\) :

Current/A

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {J}\) :

Current density/A m2

\(k\) :

Mass transfer rate/kg m3 s

\({{k}_{T}}\) :

Effective thermal conductivity/W m−1 K−1

\(L\) :

Latent heat of fusion/J kg

\(\dot{m}\) :

Melt rate/kg s

\(n\) :

Number of electrons entering in the reaction

\(\vec{n}\) :

Unit normal vector

\(p\) :

Pressure/Pa

\({{Q}_{J}}\) :

Joule heating/W m3

\(R\) :

Gas constant/J mol−1 K−1

\(S\) :

Source term in Eq. (8)

\(T\) :

Temperature/K

\(t\) :

Time/s

\(\vec{v}\) :

Velocity/m s-1

\(x,y,z\) :

Cartesian coordinates

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Acknowledgements

The authors’ gratitude goes to the National Natural Science Foundation of China (Grant No. 51210007) and the Key Program of Joint Funds of the National Natural Science Foundation of China and the Government of Liaoning Province (Grant No. U1508214).

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Authors and Affiliations

  1. The State Key Laboratory of Refractories and Metallurgy, Wuhan University of Science and Technology, Wuhan, Hubei, 430081, China

    Qiang Wang, Guangqiang Li, Yunming Gao & Zhu He

  2. Key Laboratory for Ferrous Metallurgy and Resources Utilization of Ministry of Education, Wuhan University of Science and Technology, Wuhan, Hubei, 430081, China

    Qiang Wang, Guangqiang Li, Yunming Gao & Zhu He

  3. School of Metallurgy, Northeastern University, Shenyang, Liaoning, 110819, China

    Baokuan Li

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  1. Qiang Wang
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Correspondence to Guangqiang Li.

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Wang, Q., Li, G., Gao, Y. et al. A coupled mathematical model and experimental validation of oxygen transport behavior in the electro-slag refining process. J Appl Electrochem 47, 445–456 (2017). https://doi.org/10.1007/s10800-017-1048-3

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  • DOI: https://doi.org/10.1007/s10800-017-1048-3

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