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Comprehensive model for a slag bath in electroslag remelting process with a current-conductive mould

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Abstract

A mathematical model was developed to describe the interaction of multiple physical fields in a slag bath during electroslag remelting (ESR) process with a current-conductive mould. The distributions of current density, magnetic induction intensity, electromagnetic force, Joule heating, fluid flow and temperature were simulated. The model was verified by temperature measurements during remelting 12CrMoVG steel with a slag of 50wt%–70wt% CaF2, 20wt%-30wt% CaO, 10wt%–20wt% Al2O3, and ≤10wt% SiO2 in a 600 mm diameter current-conductive mould. There is a good agreement between the calculated temperature results and the measured data in the slag bath. The calculated results show that the maximum values of current density, electromagnetic force and Joule heating are in the region between the corner electrodes and the conductivity element. The characteristics of current density distribution, magnetic induction intensity, electromagnetic force, Joule heating, velocity patterns and temperature profiles in the slag bath during ESR process with current-conductive mould were analyzed.

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Abbreviations

G :

Gravitational acceleration, m·s−2

H :

Magnetic field intensity, A·m−1

\(\hat H\) :

Complex amplitude of H

\(\hat H_r\), \(\hat H_\theta\), \(\hat H_z\) :

Magnetic field intensities in r, θ and z directions, respectively

\(\hat I\) :

Complex amplitude of the total current entering the slag bath

\(\hat I_{Ingot}\) :

Complex amplitude of the total current entering the ingot

\(\hat I_{CE}\) :

Complex amplitude of the total current entering the conductivity element

J :

Current intensity, A·m−2

\(\hat J\) :

Complex amplitude of J

R m :

Inside radius of the mould, m

R e :

Radius of the electrode, m

R :

Radial coordinate, m

Z :

Axial coordinate, m

α :

Angle of cone on the electrode tip, (°)

δ :

Electrical conductivity, Ω−1·m−1

ω :

Angular frequency of current, rad·s−1

μ :

Viscosity of slag, Pa·s−1

μ 0 :

Magnetic permeability, H·m−1

μ eff :

Effective viscosity, Pa·s−1

μ t :

Turbulent viscosity, Pa·s−1

ρ :

Density, kg·m−3

β :

Thermal expansivity of slag, K−1

S k :

Source item of kinetic energy of turbulence

S ɛ :

Source item of dissipation rate of turbulence energy

κ :

Kinetic energy of turbulence

ɛ :

Dissipation rate of turbulence energy

ξ :

Vorticity

ψ :

Stream function

t :

Time, s

C p :

Specific heat of slag, J·kg−1·K−1

ν :

Velocity, m/s

T :

Temperature, K

λ :

Thermal conductivity of slag bath, W·m−1·K−1

λ t :

Turbulent thermal conductivity of slag bath, W·m−1·K−1

Q Joule :

Joule heat generation, W·m−3

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Authors and Affiliations

  1. School of Materials and Metallurgy, Northeastern University, Shenyang, 110819, China

    Fu-bin Liu, Zhou-hua Jiang & Xin Geng

  2. School of Materials and Metallurgy, University of Science and Technology Liaoning, Anshang, 114051, China

    Xi-min Zang

  3. School of Materials Science and Engineering, Dalian University of Technology, Dalian, 116024, China

    Man Yao

Authors
  1. Fu-bin Liu
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  2. Xi-min Zang
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  3. Zhou-hua Jiang
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  4. Xin Geng
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  5. Man Yao
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Correspondence to Fu-bin Liu.

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This work was financially supported by China Postdoctoral Science Foundation (No.20100471452).

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Liu, Fb., Zang, Xm., Jiang, Zh. et al. Comprehensive model for a slag bath in electroslag remelting process with a current-conductive mould. Int J Miner Metall Mater 19, 303–311 (2012). https://doi.org/10.1007/s12613-012-0555-9

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  • DOI: https://doi.org/10.1007/s12613-012-0555-9

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