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Mathematical Model for Electroslag Remelting Process

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Abstract

A mathematical model, including electromagnetic field equation, fluid flow equation, and temperature field equation, was established for the simulation of the electroslag remelting process. The distribution of temperature field was obtained by solving this model. The relationship between the local solidification time and the interdendritic spacing during the ingot solidification process was established, which has been regarded as a criterion for the evaluation of the quality of crystallization. For a crucible of 950 mm in diameter, the local solidification time is more than 1 h at the center of the ingot with the longest interdendritic spacing, whereas it is the shortest at the edge of the ingot according to the calculated results. The model can be used to understand the ESR process and to predict the ingot quality.

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Abbreviations

C1, C2:

Constants in к-ε model

C d :

Dissipation rate constant

c P :

Specific heat

d:

Interdendritic spacing, m

G:

Generation term for turbulence kinetic energy

g:

Gravitational acceleration, (m · −2)

H:

Magnetic field intensity, (A · m−1)

H̑:

Complex amplitude of H

H̑r, H̑rθ, H̑rz:

Magnetic field intensity in r, θ, and z direction, respectively

h sw :

Overall heat transfer coefficient between slag and cooling water, (W · m−2 · K−1)

h/w,i:

Heat transfer coefficient of other position, (W · m−2 · K−1)

I 0 :

Reference value of current, A

J:

Current intensity, (A · m−1)

J̑:

Complex amplitude of J

J̑r:

Complex conjugation of J̑

k1, k2:

Coefficient, depending on steel grade

k eff :

Effective thermal conductivity, (W · m−1 · K−1)

Q s :

Rate of heat extraction from slag by metal droplets

q r :

Radiant heat loss, J

R:

Radius, m

r:

Radial coordinate, m

T:

Temperature

t:

Time, s

v c :

Solidification rate of ingot, (m · h−1)

vr, vz:

Velocity of r and z direction, (m · h−1)

z:

Axial coordinate, m

zs, zL:

Position of solidus and liquidus, m

β:

Coefficient of thermal expansion of slag

ξ:

Vorticity

ψ:

Stream function

к:

Kinetic energy of turbulence

ε:

Dissipation rate of turbulence energy

ρ:

Density, (kg · m−3)

σ:

Electrical conductivity, (Ω−1 · m−1)

ω:

Angular frequency of current, (rad · s−1)

μ:

Viscosity of slag, (Pa · s−1)

μ0:

Magnetic permeability, (H · m−1)

μeff:

Effective viscosity, (Pa · s−1)

μt:

Turbulent viscosity

e:

Electrode

i:

Ingot

L:

Metal pool

m:

Mushy zone

s:

Liquid slag

References

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Authors and Affiliations

  1. School of Materials and Metallurgy, Northeastern University, Shenyang, Liaoning, 110004, China

    Yan-wu Dong (Doctor Candidate) & Zhou-hua Jiang

  2. Institute for Metallurgical Technology, Central Iron and Steel Research Institute, Beijing, 100081, China

    Zheng-bang Li

Authors
  1. Yan-wu Dong
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  2. Zhou-hua Jiang
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  3. Zheng-bang Li
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Corresponding author

Correspondence to Yan-wu Dong.

Additional information

Foundation Item: Item Sponsored by Weaponry Pre-Research Fund (51412020304QT090l)

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Dong, Yw., Jiang, Zh. & Li, Zb. Mathematical Model for Electroslag Remelting Process. J. Iron Steel Res. Int. 14, 7–12 (2007). https://doi.org/10.1016/S1006-706X(08)60042-4

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  • DOI: https://doi.org/10.1016/S1006-706X(08)60042-4

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