Modeling fluid flow in three-dimensional single crystal dendritic structures

Convection during directional solidification can cause defects such as freckles and misoriented grains. To gain a better understanding of conditions associated with the onset of convective instabilities, flow was investigated using three-dimensional (3D) computational fluid dynamics simulations in an experimentally obtained dendritic network. A serial-sectioned, 3D data set of directionally solidified nickel-base superalloy measuring 2.3 × 2.3 × 1.5 mm was used to determine the permeability for flow parallel and normal to the solidification direction as a function of solid fraction (fS). Anisotropy of permeability varies significantly from 0.4 < fS < 0.6. High flow velocity channels exhibit spacings commensurate with primary dendrite arms at the base of the mushy zone but rapidly increase by a factor of three to four towards dendrite tips. Permeability is strongly dependent on interfacial surface area, which reaches a maximum at fS = 0.65. Results from the 3D simulation are also compared with empirical permeability models, and the microstructural origins of departures from these models are discussed.