Permeability prediction for flow normal to columnar solidification structures by large–scale simulations of phase–field and lattice Boltzmann methods

Abstract Computer simulation is the most promising approach for the systematical permeability prediction of liquid flow in the mushy zone for various solidification conditions. In this study, we propose a permeability prediction method by using large–scale simulation of phase–field and lattice Boltzmann methods. Using the proposed method, permeability predictions are performed for the flow normal to the columnar solidification structures with multiple dendrites/cells. In addition, the prediction is also performed for columnar solidification structures with periodically arranged dendrites/cells to evaluate the permeability in the full range of solidification fraction and investigate the effect of primary arm array on the permeability. As a result, it is concluded that the dimensionless permeability using a specific interface area of columnar solidification structures can be well approximated by that of a regular hexagonal array of cylinders. Moreover, it is confirmed that the columnar dendrite/cell structure with a periodic regular hexagonal array provides realistic permeability predictions for columnar solidification structures.