Publisher Summary This chapter reviews that internal convection strongly influences alloy-solidification processes. Local cooling and solidification rates are affected by convection conditions, which, in turn, have a strong influence on the microstructural features of a casting. Moreover, advective transport of interdendritic liquid is responsible for macrosegregation. To improve solid/liquid-phase-change processes involving multicomponent materials, it is vital that engineers understand the convection conditions associated with the processes. However, obtaining a reliable knowledge base for guiding process improvements is made difficult by several complicating features associated with alloy solidification. The chapter highlights that single-domain models for binary solid/liquid-phase- change systems have contributed to enhancing the knowledge base, and the results of several computational studies were reviewed to demonstrate the potential of the models to predict convective transport phenomena for a wide variety of process conditions. Possible means of intelligently controlling alloy-solidification processes were discussed and the role of numerical simulation in developing control strategies was reviewed.

Convection heat and mass transfer in alloy solidification

Numerical modelling of electromagnetic casting processes

A mathematical representation for the electromagnetic force field and the fluid flow field in a coreless induction furnace is presented. The fluid flow field was represented by writing the axisymmetric turbulent Navier-Stokes equation, containing the electromagnetic body force term. The electromagnetic body force field was calculated by using a technique of mutual inductances. The kappa-epsilon model was employed for evaluating the turbulent viscosity and the resultant differential equations were solved numerically. Theoretically predicted velocity fields are in reasonably good agreement with the experimental measurements reported by Hunt and Moore; furthermore, the agreement regarding the turbulent intensities are essentially quantitative. These results indicate that the kappa-epsilon model provides a good engineering representation of the turbulent recirculating flows occurring in induction furnaces. At this stage it is not clear whether the discrepancies between measurements and the predictions, which were not very great in any case, are attributable either to the model or to the measurement techniques employed.

The turbulent recirculating flow field in a coreless induction furnace. A comparison of theoretical predictions with measurements

For pt.I see ibid., vol.25, no.6, p.4443-8 (1989). An algorithm is developed for the calculation of surface currents and melt geometry for electromagnetic casters in three dimensions. The algorithm is shown to yield computed surface currents matching an analytical equation for the surface currents in a somewhat simpler geometry. The nonequilibrium meniscus shapes yielded computed surface currents that were fully three-dimensional. The induced surface currents produced by a horizontal inductor appear to have negligible vertical components provided the meniscus is at equilibrium. Computed meniscus shapes are presented for two inductor geometries, and the results appear reasonable in terms of the height and curvature of the molten metal pool. >

Computation of shapes of electromagnetically supported menisci in electromagnetic casters. II. Calculations in three dimensions

We consider the family of approximate deconvolution models (ADM) for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows. We prove the existence and uniqueness of solutions to the ADM-MHD equations, their weak converge to the solution of the MHD equations as the averaging radii tend to zero, and derive a bound on the modeling error. We demonstrate that the energy and helicity of the models are conserved, and the models preserve the Alfven waves. We provide the results of the computational tests, that verify the accuracy and physical fidelity of the models.

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Approximate Deconvolution Models for Magnetohydrodynamics

The paper describes a mathematical model which predicts the meniscus shape and melt flow in an electromagnetic caster. Computations were carried out for the two types of caster (with and without a screen to shape the magnetic field) in commercial use. The dependence of meniscus shape on parameters such as inductor geometry, placement, current, and frequency, as well as screen properties and placement, was determined. Calculated velocities showed agreement with measurements of other investigators on a physical model and an actual caster. The effect of an auxiliary low frequency inductor on melt flow was also computed.

J. Sakane

Papers

Mathematical modeling of meniscus profile and melt flow in electromagnetic casters