In metals and alloys, complex solidification microstructures, such as dendrites, arise from a subtle interplay between phenomena occurring at much different scales: from atom attachment kinetics to macroscopic transport of heat and species in the different phases. As such, solidification modeling represents a challenge to bridge length and time scales, and the fundamental understanding of solidification still holds long-standing unknowns, such as the mechanisms of intra- and inter-grain dendritic microstructure selection, or the origin of morphological transitions in casting, in particular in the presence of unavoidable gravity-induced fluid flow in the liquid.
In order to address scale limitations of the reference phase-field (PF) models, we developed a multiscale approach to simulate the growth of dendritic crystals from the liquid. Our so-called dendritic needle network (DNN) approach, relies on a schematic representation of dendritic branches as paraboloids, thus superseding the need to explicitly track the morphologically complex solid-liquid interface. The resulting model was previously validated for solidification in a diffusive transport regime in two and three dimensions, as well as in isothermal conditions with fluid flow in 2D.
Here, we present an extension of the DNN model in three dimensions including convective transport in the melt, which we validate by comparison with classical benchmarks in fluid mechanics and for crystal growth. We present preliminary results of the 3D DNN model with fluid flow for a single equiaxed crystal under a forced convective flow. The resulting dendrite morphology differs strongly from the case of the purely diffusive regime and from similar two-dimensional simulations.
The current model will pave the way to computationally-efficient simulations of dendritic growth at the scale of entire grains. Further applications will bring new insight into the selection of microstructure in the presence of fluid flow, i.e. under conditions relevant to standard solidification processes.