MeltFlow: MeltFlow-ESR

The ESR process uses AC power to heat an electrically resistive slag contained in a water-cooled mold. The heated slag melts the electrode and the droplets of molten metal descend through the slag to form a pool of molten metal under the slag-metal interface. The electrode is continuously advanced into the slag as it melts to build up an ingot of improved structure and composition.

MeltFlow-ESR performs a rigorous analysis of the process by considering all the physical phenomena as listed below:

• Electromagnetic phenomena with AC power (sinusoidal- or square-wave current patterns) to determine Joule heating in the slag, current flow in the slag and the ingot including the Skin effect in the ingot, and the distribution of Lorentz forces in the slag and the ingot
• Use of the two-equation k-e model for an accurate treatment of the turbulent flow in the molten pool and the slag
• Convective heat transfer in the slag and the molten pool, and phase change in the mushy region of the ingot, and conduction heat transfer in the solidified ingot
• Formation of the slag skin on the mold and the growth of the ingot within the solidified slag skin
• Heat loss from the ingot surface to the mold due to the combined effect of radiation and contact heat transfer in presence of the slag skin
• Effect of ingot shrinkage on the loss of contact heat transfer between the ingot and the mold
• Macrosegregation of the alloying elements caused by the selective rejection or absorption of the alloying elements by the solid and the redistribution of the elements within the molten metal pool
• Determination of the distributions of the Local Solidification Time (LST), dendrite arm spacings (DAS and SDAS), and interdendritic Rayleigh number that quantifies the probability of freckle formation in superalloys
• Motion and dissolution of inclusions
• Treatment of temperature-dependent material properties of the alloy

The control-volume method is used for performing the solution of the governing equations in an axisymmetric domain. The computational method incorporates many algorithms that address specific aspects of the ESR process as described below:

• A single computational domain for an implicit treatment of the electromagnetic, flow, and thermal interactions across the slag-metal interface
• Use of complex-variables and Fourier analysis in the solution of the magnetic diffusion equation for the analysis of the periodic steady state of electromagnetics with AC power
• Automatic determination of the time step
• Robust treatment of nonlinear heat loss from the top, bottom, and side surfaces of the ingot

Thus, MeltFlow-ESR provides a robust and efficient computational solution of the equations governing the physical processes in the slag and the ingot.

MeltFlow-ESR allows easy creation of a process model by specifying process geometry, temperature-dependent slag and alloy properties, and melt schedule through a user-friendly graphical interface. Results of analysis are conveniently examined using Tecplot - a powerful visualization software.

MeltFlow-ESR has been shown to accurately predict the observed pool profiles in practical ESR processes for superalloys and steels. It is being actively used in the following manner by leading specialty metals companies to obtain substantial cost-savings in process design:

• Refinement of Melt Schedules
• Investigation of Process Anomalies
• Exploration of Process Variants
• Processing of Superalloys and Steels

The computational method and its application for the analysis of practical ESR processes are discussed in the following technical papers:

Computational Modeling of the Electroslag Remelting (ESR) Process Used for the Production of Ingots of High-Performance Alloys

New Insights into the Electroslag Remelting Process Using Mathematical Modeling

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