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Numerical Understanding of Electromagnetic Influence on Fluctuation Behavior at Slag/Steel Interface During LF Refining Process

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Abstract

The objective of this study was to create a novel 3D coupled numerical model that explores the impact of electromagnetism on the fluctuation of the slag/steel interface during the LF refining process. To evaluate the effects of alternating current power, an AC phasor was introduced to examine the Lorentz force and Joule heating phenomena. Turbulent motion was represented using the large eddy simulation technique, while the volume-of-fluid approach was utilized to illustrate the deformation of the air/slag/steel interface. The discrete phase model and the two-way coupled Euler–Lagrange technique were employed to track the motion of gas bubbles, accounting for bubble collision, coalescence, and breakup. By comparing the simulated results with experimental data, the model’s fundamental validity was confirmed. The findings emphasized the importance of concurrently considering both the electromagnetic field and the bubbly flow in the investigation of the LF refining process. It was observed that the Lorentz force played a crucial role in promoting the fluctuation of the slag/steel interface, potentially leading to the absorption of carbon by the molten steel.

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Abbreviations

\(A_{b}\) :

Bubble surface area (m2)

\(c_{p,a}\) :

Specific heat of air at constant pressure (J/(kg K))

\(c_{p,b}\) :

Specific heat of bubble at constant pressure (J/(kg K))

\(c_{p,m}\) :

Specific heat of molten steel at constant pressure (J/(kg K))

\(c_{p,s}\) :

Specific heat of molten slag at constant pressure (J/(kg K))

\(d_{b}\) :

Bubble diameter (m)

\(\overline{E}\) :

Internal energy of mixture liquid phase (J/m3)

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

Buoyancy force (N/m3)

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

Drag force (N/m3)

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

Gravitational force (N/m3)

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

Lorentz force (N/m3)

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

Lift force (N/m3)

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

Pressure gradient force (N/m3)

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

Interface tension (N/m3)

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

Virtual mass force (N/m3)

\(f\) :

Frequency of AC power (Hz)

\(\vec{J}\) :

Electric current (A/m2)

\(\vec{H}\) :

Magnetic field intensity (A/m)

\(\hat{H}\) :

Complex amplitude (A/m)

\(h_{m,b}\) :

Convective heat transfer coefficient between melt and bubble (W/(m2 K))

\(k_{T,eff}\) :

Effective thermal conductivity of liquid phase (W/(m K))

\(m_{b}\) :

Mass of bubble (kg)

\(p\) :

Pressure (Pa)

\(Q_{J}\) :

Joule heating density (W/m3)

\(\vec{S}_{mb}\) :

Source term used in Eq. [9] (N/m3)

\(T\) :

Temperature (K)

\(T_{b}\) :

Bubble temperature (K)

\(t\) :

Time (s)

\(\vec{v}\) :

Melt velocity (m/s)

\(\vec{v}_{b}\) :

Bubble velocity (m/s)

\(\alpha_{s}\) :

Molten slag volume fraction

\(\alpha_{m}\) :

Molten steel volume fraction

\(\overline{\eta }\) :

Magnetic diffusivity of mixture phase (m2/s)

\(\mu_{0}\) :

Vacuum permeability (H/m)

\(\overline{\mu }\) :

Mixture liquid phase dynamic viscosity (Pa s)

\(\overline{\mu }_{{{\text{sgs}}}}\) :

Mixture liquid phase eddy viscosity (Pa s)

\(\mu_{t}\) :

Turbulent viscosity (Pa s)

\(\rho_{a}\) :

Air density (kg/m3)

\(\rho_{b}\) :

Argon gas bubble density (kg/m3)

\(\rho_{m}\) :

Molten steel density (kg/m3)

\(\rho_{s}\) :

Molten slag density (kg/m3)

\(\overline{\sigma }\) :

Electrical conductivity of the mixture phase (Ω−1 m−1)

\(\omega\) :

Angular frequency (Hz)

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Acknowledgments

The authors acknowledge the financial support from the Young Elite Scientist Sponsorship Program by China Association for Science and Technology [Grant No. YESS20200210] and the National Natural Science Foundation of China [Grant No. U1860205]. They also extend their special thanks to the WISDRI Engineering Technology Co., Ltd. for providing the plant data.

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Authors and Affiliations

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

    Qiang Wang, Chang Liu, Changgui Cheng, Zhu He & Guangqiang Li

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

    Qiang Wang, Chang Liu, Changgui Cheng, Zhu He & Guangqiang Li

  3. WISDRI Engineering Technology Co., Ltd., Wuhan, 430223, Hubei, P.R. China

    Gong Cheng

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  1. Qiang Wang
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Wang, Q., Liu, C., Cheng, G. et al. Numerical Understanding of Electromagnetic Influence on Fluctuation Behavior at Slag/Steel Interface During LF Refining Process. Metall Mater Trans B 55, 626–636 (2024). https://doi.org/10.1007/s11663-023-02982-3

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