A Comprehensive Model of the Electroslag Remelting Process: Description and Validation

Electroslag remelting (ESR) is widely used for the production of high-value-added alloys such as special steels or nickel-based superalloys. Because of high trial costs and the complexity of the mechanisms involved, trial-and-error-based approaches are not well suited for fundamental studies or for optimization of the process. Consequently, a transient-state numerical model has been developed that accounts for electromagnetic phenomena and coupled heat and momentum transfers in an axisymmetrical geometry. The model simulates the continuous growth of the electroslag-remelted ingot through a mesh-splitting method. In addition, solidification of the metal is modeled by an enthalpy-based technique. A turbulence model is implemented to compute the motion of liquid phases (slag and metal), while the mushy zone is described as a porous medium the permeability of which varies with the liquid fraction, thus enabling accurate calculation of solid/liquid interaction. The coupled partial differential equations (PDEs) are solved using a finite-volume technique. The computed results are compared to the experimental observation of an industrial remelted ingot; the melt pool depth and shape, in particular, are investigated, in order to validate the model. These results provide valuable information about the process performance and the influence of the operating parameters. In this way, we present an example of a model used as a support in analyzing the influence of the electrode fill ratio.

C _P :

specific heat ( \( {\text{J}}{\cdot} {\text{kg}}^{{ - 1}} {\cdot} {\text{K}}^{{ - 1}} \))

F :

electromagnetic (Lorenz) body force (\( {\text{N}}{\cdot} {\text{m}}^{{ - 3}} \))

g _l :

liquid fraction

g _z :

gravity (\( {\text{m}} {\cdot} {\text{s}}^{{ - 2}} \))

H :

magnetic field (\( {\text{A}}{\cdot} {\text{m}}^{{ - 1}} \))

\( \hat{H} \) :

complex representation of H (\( {\text{A}}{\cdot} {\text{m}}^{{ - 1}} \))

H :

enthalpy (J·kg⁻¹)

h _slag :

height of the slag cap (m)

J :

current density (\( {\text{A}}{\cdot} {\text{m}}^{{ - 2}} \))

K :

permeability of the mushy zone (m²)

N _x :

equivalent alumina molar fraction

P :

pressure (Pa)

Q _Joule :

volumetric Joule power (\( {\text{W}} {\cdot} {\text{m}}^{{ - 3}} \))

q _l :

latent heat of solidification (J·kg⁻¹)

R _electrode :

electrode radius (m)

R _ingot :

ingot radius (m)

R _slag :

slag equivalent resistance (Ω)

S _electrode :

cross-sectional area of the electrode (m²)

S _ingot :

cross-sectional area of the ingot (m²)

T :

temperature (°C)

u _r :

radial component of velocity (\( {\text{m}} {\cdot} {\text{s}}^{{ - 1}} \))

v _z :

axial component of velocity (\( {\text{m}} {\cdot} {\text{s}}^{{ - 1}} \))

∇ :

vector operator nabla (m⁻¹)

φ :

electrode fill ratio (m⁻¹)

ω :

pulsation (\( {\text{rad}} {\cdot} {\text{s}}^{{ - 1}} \))

σ :

electrical conductivity (\( \Omega ^{{ - 1}} {\cdot} {\text{m}}^{{ - 1}} \))

μ ₀ :

magnetic permeability (\( {\text{H}} {\cdot} {\text{m}}^{{ - 1}} \))

ρ :

density (\( {\text{kg}} {\cdot} {\text{m}}^{{ - 3}} \))

μ :

dynamic viscosity (\( {\text{kg}} {\cdot} {\text{m}}^{{ - 1}} {\cdot} {\text{s}}^{{ - 1}} \))

μ _t :

turbulent viscosity (\( {\text{kg}} {\cdot} {\text{m}}^{{ - 1}} {\cdot} {\text{s}}^{{ - 1}} \))

λ :

thermal conductivity (\( {\text{W}} {\cdot} {\text{m}}^{{ - 1}} {\cdot} {\text{K}}^{{ - 1}} \))

λ _t :

turbulent thermal conductivity (\( {\text{W}} {\cdot} {\text{m}}^{{ - 1}} {\cdot} {\text{K}}^{{ - 1}} \))

1. V. Weber (Postdoctoral Student, Research Engineer)

   Present address: ArcelorMittal, Maizières-lès-Metz, 57283, France

Authors and Affiliations

1. LSG2M, Ecole des Mines de Nancy, Nancy Cedex, 54042, France

   V. Weber (Postdoctoral Student, Research Engineer), A. Jardy (CNRS Research Scientist), B. Dussoubs (Research Engineer) & D. Ablitzer (Professor)

2. Aubert & Duval, Les Ancizes, 63770, France

   S. Rybéron (Development Technician), V. Schmitt (Development Engineer), S. Hans (Development Engineer) & H. Poisson (Development Engineer)

Corresponding author

Correspondence to A. Jardy.

This article is based on a presentation given at the International Symposium on Liquid Metal Processing and Casting (LMPC 2007), which occurred in September 2007 in Nancy, France.

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