Prediction of permeability in mushy zone of Al-4.5 %Mg alloy based on CA-LBM model

Permeability is a key parameter in hot tearing prediction, and the solidification microstructure of alloys has an important influence on permeability prediction. The present paper builds a cellular automata–lattice Boltzmann method (CA-LBM) model to simulate the grain growth and liquid flow of semi-solid binary aluminum alloys. The CA model was used to simulate the microstructure of the mushy region, including the growth of dendrites and the overlap between the dendrite arms, and the LBM model was used to observe the liquid phase flow in the mushy zone. The model takes into account the complex inter-dendritic flow, including the liquid flow between the dendrite arms. The paper compared the permeability results of the current model with the Carman–Kozeny equation for two limiting cases of interfacial area concentration Sv (the dendrite structure with Sv and the globular structure with Sv) and investigated the effect of different cooling rates on permeability. Deviation from the Carman–Kozeny behavior was observed with a transition in microstructure, i.e., when the domain contained a mixture of dendritic and globular structures or when fluid flow occurred simultaneously in the intra-dendritic and extra-dendritic regions. From the analysis of the permeability results of the mushy zone under different cooling rates, the higher the cooling rate, the lower the permeability. The permeability is not only related to the solid volume fraction but also to the morphology and size of grains.