Freckles, a significant issue encountered during the directional solidification of superalloys, are recognised by a trail of equiaxed grains parallel to the direction of gravity accompanied by local eutectic enrichment. In the current study, a mixed-columnar-equiaxed multiphase volume-average solidification model was employed to study the formation of freckles in superalloy casting. Fragments produced via flow-driven and capillary-driven fragmentation mechanisms are considered as the source of spurious grains. The transport and the growth/remelting of the fragments are considered. According to the simulation results, some segregation channels develop at the corners of the casting. Flow-driven fragments are produced in/around the segregation channels, whereas capillary-driven fragments are produced at a certain depth of the mushy zone across the entire section of the casting. The fragmentation rate caused by the flow-driven mechanism is several orders of magnitude larger than that caused by the capillary-driven mechanism, i.e. the flow-driven fragmentation mechanism is dominant for the currently investigated sample. After the solidification process, four freckles formed at the casting corners on the shadowed side, whereas it was freckle-free on the bright side.

Previously, the authors have used a mixed columnar-equiaxed solidification model, successfully ‘reproduced’ the solidification benchmark experiments on the Sn-10wt.%Pb alloy under natural/forced convections (travelling magnetic stirring) as performed at SIMAP laboratory [Int. J. Heat Mass Transf. 85 (2015) 438-54]. The current contribution is to address the flow-effect on the remelting of settling/floating crystals during the mixed columnar-equiaxed solidification. The re-melting or growth is controlled by diffusion of solute in the liquid boundary layer. The diffusion length due to the flow-effect is modelled as a function of Schmidt and Reynolds numbers. The modelling results show that remelting rate of the floating/settling crystals, which originate from fragmentation and then brought to the superheated region by the forced flow, can be enhanced by the flow. In turn the released latent heat can reduce the temperature locally (even globally), hence to speed up the solidification of the columnar structure. Additionally, the solidification-migration-remelting of equiaxed grains present an important macrosegregation mechanism. By solidification of a crystal in the cold region it rejects solute, while by remelting of the crystal it dilutes the surrounding melt. These phenomena are found critical in many engineering castings with mixed columnar-equiaxed solidification.

Directional solidification experiment under forced convection condition was conducted. The AlSi7 alloy was solidified in an alumina cylindrical crucible (ø8 mm) in a Bridgeman furnace; and forced convection was induced by applying rotating magnetic field (RMF). The RMF induced flow in the sample during solidification leads to the formation of equiaxed crystals by the mechanism of crystal fragmentation (assumption). The current study is to use a mixed columnar-equiaxed solidification model to simulate this experiment by considering the crystal fragmentation as sole origin of equiaxed crystals. An inward flow (Ekman effect) forms in the front of the (columnar) mushy zone under the RMF. Solute-driven remelting, as enhanced by the interdendritic flow, leads to fragmentation near the columnar tip front. Some fragments are transported by the forced convection to the sample centre and remelted there, while many of them are captured by the columnar structure near the sample centre. The modelling result on the mixed columnar-equiaxed structure agrees with the post-mortem analysis of as-solidified sample. As conclusion following impacts of the crystal fragmentation on solidification are suggested: (1) it widens the central segregation channel and promotes the formation of side-arms; (2) it leads to the formation of relatively high volume fraction of equiaxed crystals near the sample centre.

A mixed columnar-equiaxed solidification model was used to investigate the solidification benchmark experiments, as performed at SIMAP Laboratory. The first experiment case of the benchmark made under natural convection condition was successfully simulated previously. The current work is to simulate the second experiment case, i.e. the casting under travelling magnetic stirring (TMS) which is applied in the direction of natural convection to enhance the natural convection. Crystal fragmentation of columnar dendrites is assumed as the sole origin of equiaxed crystals. Through the analysis of the simulation results, deep understanding to the experimentally reported phenomena was achieved. In comparison to the first experiment case of pure natural convection condition, the TMS-enhanced convection provides a favorable condition for columnar-to-equiaxed transition (CET) by homogenizing the temperature distribution in the bulk liquid region, enhancing the fragmentation of the columnar secondary arms and the transport of the fragments to bulk liquid region. Contradicting with the previous knowledge, the TMS-enhanced convection in this experiment case does not enhance the global macrosegregation significantly. However, it strengthens the channel segregates.