Macroscopic modeling of columnar dendritic solidification

Abstract

This paper deals with the derivation of a macroscopic model for columnar dendritic solidification of binary mixtures using the volume averaging method with closure. The main originalities of the model are first related to the explicit description of evolving heterogeneities of the dendritic structures and their consequences on the derivation of averaged conservation equations, where additional terms involving porosity gradients are present, and on the determination of effective transport properties. These average properties are defined by the associated closure problems taking into account the geometry of the dendrites and the local intensity of the flow. The macroscopic solute transport is obtained by considering macroscale non-equilibrium giving rise to macroscopic dispersion and interfacial exchange phenomena. Mass exchange coefficients are accurately explicited as a function of the local geometry.

SiC single fibre full-fragmentation during straining in a Ti–6Al–4V matrix studied by synchrotron X-rays

“…Three-dimensional data on semisolid structures obtained from quenched samples have been used to calculate the permeabilities (i.e., the ability of the solid material to transmit a fluid phase) of such structures. Classically, permeability calculations are made either on 2D real structures [65][66][67][68] or from 3D numerical data obtained from a 3D cellular automatonfinite difference model for the growth of a single equiaxed dendrite in a cubic domain. 69 The combination of 3D tomography data as an input in the 3D simulation of the permeability tensor has been investigated on dendritic or equiaxed Al-Cu alloys.…”