Three-dimensional needle network model for dendritic growth with fluid flow

Abstract

We present a first implementation of the Dendritic Needle Network (DNN) model for dendritic crystal growth in three dimensions including convective transport in the melt. The numerical solving of the Navier-Stokes equations is performed with finite differences and is validated by comparison with a classical benchmark in fluid mechanics for unsteady flow. We compute the growth behavior of a single equiaxed crystal under a forced convective flow. As expected, the resulting dendrite morphology differs strongly from the case of the purely diffusive regime and from similar two-dimensional simulations. The resulting computationally efficient simulations open the way to studying mechanisms of microstructure selection in presence of fluid flow, using realistic alloy and process parameters.