We analyzed the columnar solidification of a binary alloy under the influence of an electromagnetic forced convection of various types and investigated the influence of a rotating magnetic field on segregation during directional solidification of Al-Si alloy as well as the influence of a travelling magnetic field on segregation during solidification of Al-Ni alloy through directional solidification experiments and numerical modeling of macrosegregation. The numerical model is capable of predicting fluid flow, heat transfer, solute concentration field, and columnar solidification and takes into account the existence of a mushy zone. Fluid flows are created by both natural convection as well as electromagnetic body forces. Both the experiments and the numerical modeling, which were achieved in axisymmetric geometry, show that the forced-flow configuration changes the segregation pattern. The change is a result of the coupling between the liquid flow and the top of the mushy zone via the pressure distribution along the solidification front. In a forced flow, the pressure difference along the front drives a mush flow that transports the solute within the mushy region. The channel forms at the junction of two meridional vortices in the liquid zone where the fluid leaves the front. The latter phenomenon is observed for both the rotating magnetic field (RMF) and traveling magnetic field (TMF) cases. The liquid enrichment in the segregated channel is strong enough that the local solute concentration may reach the eutectic composition.

A new multiphase Eulerian model for columnar and equiaxed dendritic solidification has been developed. The mean conservation equations are derived by means of a statistical phase averaging technique, and the mathematical formulation of the model can be used for both columnar and equiaxed solidification. The model uses three different phases, respectively, the columnar, the equiaxed solid and the liquid. The new set of equations enables us to simulate the columnar-to-equiaxed transition (CET) during the directional solidification of a binary alloy. Owing to the statistical nature of the model, we are able to treat rigorously the coexistence of equiaxed and columnar structures and consequently the CET phenomena. The averaged equations are closed by means of the cell model approximation. This technique can be successfully used to model the various interactions between the liquid and the solid. It may also incorporate the effects of the inhomogeneities of the various scalar fields, e.g. the solute and temperature gradients. An envelope model is used to parametrize the small scales, i.e. the dendrite scale. This leads us to distinguish two types of liquid, namely, the extra-dendritic and the inter-dendritic liquids. In part I the equations are rigorously derived in the purely diffusive case, whilst in part II we will present one-dimensional simulations of Sn–Pb and Al–Cu directional solidification experiments involving CET phenomena. Quasi-steady state CET maps are also computed.

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A new multi-phase Eulerian model for the columnar and equiaxed dendritic solidification has been developed. In this paper we first focus on the numerical simulation of quasi-steady solidification experiments in order to obtain corresponding CET maps. We have identified three main zones on the CET map: the pure columnar, the pure equiaxed zone and finally the mixed columnar+equiaxed zone. The mixed c/e zone was further quantified by means of a columnar fraction εc which quantifies in a rigorous way the two coexisting structures. Since it intrinsically includes the solutal and the mechanical blocking effects, the new ensemble model unifies the semi-empirical Hunt's approach (pure mechanical blocking mechanism) and the Martorano et al approach (pure solutal blocking mechanism). Secondly the present model was used to simulate unidirectional solidification experiments. It was found that the columnar front evolved in a quasi-steady state until a time very close to the critical CET moment. It is also found that the equiaxed nucleation undercooling is close to the maximum columnar dendrite tip undercooling and that the CET is virtually independent of the equiaxed zone ahead of the columnar front. If the equiaxed zone is not taken into account it is observed that the columnar front velocity exhibits a sudden increase at the beginning of the solidification followed by a quasi-plateau corresponding to a quasi-state at the columnar tips and finally, above a critical time, an oscillatory evolution. The beginning of the oscillatory evolution of the columnar front was well correlated with the CET position measured in the experiments. We also find that this oscillatory evolution of the columnar front is very favourable for the fragmentation of the columnar dendrites and thus for the CET. In this respect, it seems that the unsteady regime of the columnar front with respect to the local cooling conditions represents the main cause for the CET phenomena, at least for the non-refined alloys.