Three-dimensional mesoscopic modeling of equiaxed dendritic solidification of a binary alloy

Abstract

The mesoscopic envelope model is a recent multiscale model that is intended to bridge the gap between purely microscopic and macroscopic approaches for the study of dendritic solidification. It consists of the description of a dendritic grain by an envelope that links the active dendrite branches. The envelope growth is deduced from an analytical microscopic model of the dendrite tip growth kinetics matched to the numerical solution of the mesoscopic solute concentration field in the vicinity of the envelope. The branched dendritic structure inside the envelope is described in a volume-averaged sense by phase fractions and averaged solute concentrations. We present a careful quantitative analysis of the influence of numerical and model parameters on the accuracy of the model predictions. We further perform a validation study through comparisons of 3D simulations to experimental scaling laws giving the shape and the internal solid fraction of freely growing binary alloy dendrites and to analytical solutions for the primary dendrite tip speed. We provide generally valid guidelines for the calibration of the mesoscopic model, enabling reliable control of the accuracy of model predictions over a wide range of undercoolings. The model is applied to simulate strong solutal interactions in large ensembles of equiaxed grains. The potential for mesoscopic simulations to provide refined modeling of microstructures in volume-averaged macroscopic models via scale bridging is demonstrated.