Modelling and simulation of macrosegregation has experienced explosive growth since the pioneering studies of Flemings and co-workers in the mid-1960s This paper presents a review of recent macrosegregation models, with particular emphasis on their application to selected industrially relevant casting processes The successes and shortfalls of the models in predicting measured macrosegregation patterns are noted Although it is still early in their development, advanced macrosegregation models that include a detailed consideration of the solidification microstructure are also reviewed Recent studies involving direct numerical simulation of macrosegregation related phenomena on a microscopic scale are highlighted Important issues deserving future research attention are identified

/pdf/modelling-of-macrosegregation-applications-and-future-needs-2n7b171i9v.pdf

Modelling of macrosegregation: applications and future needs

We describe a model for non-convecting diffusion-controlled solidification of a ternary
(three-component) alloy cooled from below at a planar boundary. The modelling
extends previous theory for binary alloy solidification by including a conservation
equation for the additional solute component and coupling the conservation equations
for heat and species to equilibrium relations from the ternary phase diagram. We
focus on growth conditions under which the solidification path (liquid line of descent)
through the ternary phase diagram gives rise to two distinct mushy layers. A primary
mushy layer, which corresponds to solidification along a liquidus surface in the ternary
phase diagram, forms above a secondary (or cotectic) mushy layer, which corresponds
to solidification along a cotectic line in the ternary phase diagram. These two mushy
layers are bounded above by a liquid layer and below by a eutectic solid layer. We
obtain a one-dimensional similarity solution and investigate numerically the role of
the control parameters in the growth characteristics. In the special case of zero solute
diffusion and zero latent heat an analytical solution can be obtained. We compare
our predictions with previous experimental results and with theoretical results from a
related model based on global conservation laws described in the Appendix. Finally,
we discuss the potentially rich convective behaviour anticipated for other growth
conditions.

/pdf/a-model-for-diffusion-controlled-solidification-of-ternary-b3m0sjm5xo.pdf

A model for diffusion-controlled solidification of ternary alloys in mushy layers

Macrosegregation development during solidification of a multicomponent alloy with free-floating solid particles

Foundations of modeling in cryobiology—II: Heat and mass transport in bulk and at cell membrane and ice-liquid interfaces

Since the Annual Review of Fluid Mechanics review of mushy layers by Worster (1997), there have been significant advances in the understanding of convective processes in mushy layers. These advance...

Convective Phenomena in Mushy Layers

Experiments were performed with a Pb-5 pct Sb-35 pct Sn system to experimentally validate simulations made with a continuum mixture model for ternary alloy solidification. Temperature histories were measured during casting, and composition profiles were found in the solidified ingot. Dendritic arm spacings were found from optical micrographs of the alloy microstructure and used to determine a constant in the Blake-Kozeny submodel for the mushy zone permeability in the liquid-solid interaction term of the momentum equations. Scaling analysis from a previous work and a large uncertainty in the permeability constant suggested that predictions of the composition are extremely sensitive to the choice of a permeability model. Three simulations were performed using the permeability constant as a parameter, and measured temperatures and compositions were compared with predictions based on different model constants. While the thermal histories had good agreement, the results near the liquidus interface, where all of the significant advection of solute occurs, suggest that the Blake-Kozeny model significantly underpredicts the resistance of the dendritic array to fluid flow.

Solidification of a ternary metal alloy: A comparison of experimental measurements and model predictions in a Pb-Sb-Sn system

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Solidification of a ternary metal alloy: A comparison of experimental measurements and model predictions in a Pb-Sb-Sn system