Fluid flow and defect formation in the three-dimensional dendritic structure of nickel-based single crystals

Fluid flow within the dendritic structure at the solid-liquid interface in nickel-based superalloys has been studied in two directionally solidified alloy systems. Millimeter-scale, three-dimensional (3D) datasets of dendritic structure have been collected by serial sectioning, and the reconstructed mushy zones have been used as domains for fluid-flow modeling. Flow permeability and the influence of dendritic structure on flow patterns have been investigated. Permeability analyses indicate that the cross flow normal to the withdrawal direction limits the development of flow instabilities. Local Rayleigh numbers calculated using the permeabilities extracted from the 3D dataset are higher than predicted by conventional empirical calculations in the regions of the mushy zone that are prone to the onset of convective instabilities. The ability to measure dendrite surface area in 3D volumes permit improved prediction of permeability as well.