Meso-scale simulation of liquid feeding in an equiaxed dendritic mushy zone

A 3D meso-scale model is developed to predict the flow of liquid within a semi-solid binary Fe-C alloy with various equiaxed microstructure, ranging from dendritic to globular. The model domain consists of a set of 8000 grains given by a Voronoi tessellation. Solidification of each grain is simulated independently via a volume average approach, providing the semi-solid microstructure for the fluid flow simulation. A single domain Darcy-Brinkman model is then used to calculate the resulting pressure field. The model results are found to be in good agreement with the Carman-Kozeny equation for two limiting cases of interfacial area concentration S-v, demonstrating the model's utility in quantifying permeability of semisolid structures where the fluid flow occurs either in the intra-dendritic (within the envelope enclosed by the dendrite) or extra-dendritic (between dendritic grains) regions. Deviation from Carman-Kozeny behaviour is observed with a transition in microstructure, i.e. when the domain contains a mixture of both dendritic and globular structures or when fluid flow occurs simultaneously in the intra-dendritic and extra-dendritic regions. A permeability-microstructure map is created as a function of grain size, secondary dendrite arm spacing, and cooling rate to show the range where the limiting values of S-v are valid and, importantly, where they are not. A comparison of the net volumetric inflow caused by shrinkage and deformation is performed, demonstrating that the shrinkage induced by the peritectic transformation is the dominant factor requiring liquid feeding. The present dendritic fluid flow model is useful in the context of multi-physics modelling of defects in peritectic steel grades and other commercially relevant alloys.