Numerical study of the role of mush permeability in the solidifying mushy zone under forced convection

Permeability of the mushy zone during alloy solidification is an important modeling parameter for many phenomena which accompany solidification, such as the formation of macrosegregation, shrinkage porosity, hot tearing, etc. The current study incorporates a two-phase, volume-average based columnar solidification model to study the role of mush permeability in the solidifying mushy zone under forced convection conditions. A unidirectional solidification of Al-7.0 wt %Si alloy sample (cylindrical with a diameter of 8 mm), referring to the experiments of MICAST project [Ratke, et al., MICAST research report - Phase IV, ESA-MAP AO-99-031, 2013], is considered. The forced convection is applied with a rotating magnetic field (20mT). The basic permeability law for the numerical model is derived from Carman-Kozeny, but it has been modified by an artificial factor for the parameter study. The modeling results show that (1) the thickness of the mushy zone decreases and (2) the global macrosegregation intensity increases monotonically with growing permeability. A special macrosegregation profile resembling a "Christmas tree", as typically observed experimentally, could also be numerically predicted. However, the formation of the "Christmas tree" segregation profile depends strongly on the permeability of the material. The formation mechanism of "Christmas tree" segregation can be analyzed according to the flow-solidification interaction in the mushy zone. A quantitative determination of the permeability, depending on the dendritic structure of the mushy zone, is beyond the scope of the current study, nevertheless it also includes a brief discussion (literature review) on this topic.