Modeling fluid flow in three-dimensional single crystal dendritic structures

Abstract 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 ( f S ). Anisotropy of permeability varies significantly from 0.4 f S f S = 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.