A mathematical model of slag and metal flow in the ESR Process

Dilawari, A. H.; Szekely, J.

doi:10.1007/bf02657651

Cited by 85 publications

(47 citation statements)

References 3 publications

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“…The use of AC implies that magnetic and electric fields are dependent on each other; hence, the phenomena are governed by the four Maxwell equations. The system formed by these equations can be reduced to a single one under the following assumptions: [9] (a) Magnetization is negligible. (b) Magnetic diffusion dominates and fluid flow does not influence the magnetic field, because the magnetic Reynolds number remains very low.…”

Section: A Electromagnetic Phenomenamentioning

confidence: 99%

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

Weber

Jardy

Dussoubs

et al. 2009

Metall Mater Trans B

174

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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.

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Section: A Electromagnetic Phenomenamentioning

confidence: 99%

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

Weber

Jardy

Dussoubs

et al. 2009

Metall Mater Trans B

174

View full text Add to dashboard Cite

show abstract

“…Dilwari and Szekely 1) developed the general framework for analyzing the electromagnetic fields in ESR. The electromagnetic field was formulated using the Maxwell equations, and a complete set of boundary conditions was also prescribed.…”

Section: Introductionmentioning

confidence: 99%

Current, Magnetic Field and Joule Heating in Electroslag Remelting Processes

Fang

Tsukihashi

2012

ISIJ Int.

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A three-dimensional (3D) finite element model was developed to simulate the current density, magnetic field, electromagnetic force and Joule heating for a system of electrode, slag and ingot in electroslag remelting processes. Especially, the skin effect is taken into account in electromagnetic field model by magnetic vector potential method. Simulated magnetic flux density is compared with experiment and obtained a good agreement. Numerical results show that the skin effect becomes strong and the maximum current occurs at the surface of electrode and ingot, the maximum of electromagnetic force is at the upper surface nearby the electrode in the slag and the maximum of Joule heating is at the interface of electrode and slag. The parametric study shows that the eddy current flow occurs in interior of electrode and ingot if the current frequency is more than 40 Hz. With the increasing of electrode immersion depth or decreasing of slag cap thickness, the maximum of the Joule heating in slag increases.

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“…According to the study made by Dilawari and Szekely, [16] the magnetic Reynolds number, which expresses the measure of the ratio of the magnetic convection to magnetic diffusion, remains very low in the ESR process. Thus, Eq.…”

Section: A Electromagnetic Phenomenamentioning

confidence: 99%

A General Coupled Mathematical Model of Electromagnetic Phenomena, Two-Phase Flow, and Heat Transfer in Electroslag Remelting Process Including Conducting in the Mold

Wang

et al. 2014

Metall Mater Trans B

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A transient three-dimensional finite-volume mathematical model has been developed to investigate the coupled physical fields in the electroslag remelting (ESR) process. Through equations solved by the electrical potential method, the electric current, electromagnetic force (EMF), and Joule heating fields are demonstrated. The mold is assumed to be conductive rather than insulated. The volume of fluid approach is implemented for the two-phase flow. Moreover, the EMF and Joule heating, which are the source terms of the momentum and energy sources, are recalculated at each iteration as a function of the phase distribution. The solidification is modeled by an enthalpy-porosity formulation, in which the mushy zone is treated as a porous medium with porosity equal to the liquid fraction. An innovative marking method of the metal pool profile is proposed in the experiment. The effect of the applied current on the ESR process is understood by the model. Good agreement is obtained between the experiment and calculation. The electric current flows to the mold lateral wall especially in the slag layer. A large amount of Joule heating around the metal droplet varies as it falls. The hottest region appears under the outer radius of the electrode tip, close to the slag/metal interface instead of the electrode tip. The metal pool becomes deeper with more power. The maximal temperature increases from 1951 K to 2015 K (1678°C to 1742°C), and the maximum metal pool depth increases from 34.0 to 59.5 mm with the applied current ranging from 1000 to 2000 A.

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A mathematical model of slag and metal flow in the ESR Process

Cited by 85 publications

References 3 publications

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

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

Current, Magnetic Field and Joule Heating in Electroslag Remelting Processes

A General Coupled Mathematical Model of Electromagnetic Phenomena, Two-Phase Flow, and Heat Transfer in Electroslag Remelting Process Including Conducting in the Mold

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