The influence on grain refinement of electromagnetic vibrations imposed during solidification of various aluminum alloys has been examined. The vibrations were produced, without any material contact with the solidifying alloys, by the simultaneous application of a stationary magnetic fieldB
 0 and a periodic magnetic fieldb(t) of 50 Hz frequency. Extensive grain refinement has been observed in both continuous casting and batch-type mold casting. This investigation shows that the mean grain size obtained by this electromagnetic vibrational method is smaller than that produced by the variable magnetic field acting alone (electromagnetic stirring), particularly when the alloys are characterized by a narrow freezing range.

Effects of forced electromagnetic vibrations during the solidification of aluminum alloys : Part II. Solidification in the presence of colinear variable and stationary magnetic fields

For the Monte Carlo simulation of Knudsen diffusion, the porous solid was modeled as one of four types of assemblages of spheres: simple cubic array, face-centered cubic array, randomly packed with a size distribution, and randomly arranged overlapping with a size distribution. The porous solid in each case consisted of several hundred spheres bounded by six large ''boundary spheres''. The gas molecule travels in a randomly chosen x-direction until it impacts a sphere and undergoes a random reflection. A comparison with available data showed that the simulation predicts reasonable tortuosities. The model will be extended to other diffusion regimes and is expected to have applications in catalysis and solid fuel conversion.

A Monte Carlo simulation of the diffusion of gases in porous solids

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

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.

Mathematical modeling of meniscus profile and melt flow in electromagnetic casters

The paper describes a physical model aimed at studying two important phenomena in electromagnetic (EM) casting of aluminum: the support of the molten metal pool and stirring caused by EM forces. The physical model is used both to test an improved mathematical model for EM casting and to provide insight into the effect of design changes on the two EM phenomena. Examples of design changes are changes in inductor current and position and screen position. The improved mathematical model, a two-dimensional (2-D) (axisymmetric) one, constrains the melt surface at the solidification line and neglects (with justification) buoyancy, surface tension, and the impact of flow on meniscus shape. The physical model was a cylindrical one where the solidified metal was simulated by a 248-mm-diameter aluminum bronze cylinder and the molten metal by Wood’s alloy. Measurements were made of electric field, magnetic field, meniscus deformation, and velocities for the two types of caster in commercial use. Generally, good agreement was obtained between the mathematical model and the experimental measurements.

An improved mathematical model for electromagnetic casters and testing by a physical model

A diffusion bridge apparatus has been used to measure diffusivities for the gas pairs CO2−N2, CO2−Ar, and CH4−N2 at temperatures ranging from 300 to 1000 K. The apparatus measured effective diffusivities which were transformed into ordinary diffusivities after calibration with a gas pair (CO2−N2) of known diffusivity. The apparatus was also used to measure the viscosities of the four gases over the same temperature range. The results were compared with the predictions of the Chapman-Enskog correlation (ordinary diffusivities and viscosities) and predictions for diffusion rates in porous solids developed in Monte Carlo simulations. Additional experiments examined the effect of changing pore structure on the diffusivities of gases.

B. Q. Li

Papers

Mathematical modeling of meniscus profile and melt flow in electromagnetic casters

An improved mathematical model for electromagnetic casters and testing by a physical model

Diffusivities and viscosities of some gases at elevated temperatures: Gas diffusivities in porous solids