Computing the permeability of tilted columnar dendrites with phase-field and lattice Boltzmann methods

Permeability for interdendritic flow plays a crucial role in accurately simulating macrosegregation. The dimensionless permeability of normal flow for columnar structures growing along a temperature gradient is conventionally represented by using the Kozeny–Carman (KC) equation with a KC coefficient k_c= 9. In this study, we used high-performance computing to predict permeability for columnar dendrites tilted from the temperature gradient direction in both single crystals and polycrystals with phase-field and lattice Boltzmann methods. In single crystals, to cover all solid fractions, permeability was predicted for periodic hexagonal arrays as well as multiple dendrites. We found that the complexity of dendrite morphology and the directional dependency of interdendritic flow increased considerably with increasingly tilted angles for single crystals. The dimensionless permeability remained in good agreement with the KC equation for angles below 20° and deviated from the KC equation with k_c= 9 for tilted angles above 30°. For polycrystals, we predicted permeability for systems sufficiently large to be independent of the flow direction. The complexity of dendrite morphology decreased with growth owing to the overgrowth of grains with a large tilt angle by smaller grains. Consequently, the predicted dimensionless permeability deviated from the KC equation with k_c= 9.