Open AccessModelling of solutal dendritic growth in three dimensions
Author(s) -
Pan Shi-Yan,
Zhu Ming-Fang
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.278
Subject(s) - dendrite (mathematics) , curvature , materials science , supercooling , anisotropy , directional solidification , thermodynamics , isotropy , radius , orientation (vector space) , steady state (chemistry) , mechanics , physics , geometry , optics , alloy , chemistry , computer science , mathematics , computer security , composite material
A three-dimensional 3D model for the simulation of solutal dendritic growth in the low Pclet number region is presented. In the model is adopted a solutal equilibrium approach previously proposed by Zhu and Stefanescu to calculate the evolution of the solid/liquidSL interface which allows the accurate simulation of dendritic growth from the initial unstable stage to the steady-state stage with a good computational efficiency. In this approach the kinetics of dendritic growth is driven by the difference between the local equilibrium composition calculated from the local temperature and curvature and the local actual liquid compositionobtained by solving the solutal transport equation. To describe the specific crystallographic orientation of 3D dendritic growth a weighted mean curvature WMC algorithm which is incorporated with the anisotropy of surface tension is proposed to calculate the local SL interface curvature. This approach is convenient to be implemented and to make the transformation for WMC calculation from two to three dimensions. The model is verified by the comparison of our numerical resuets with the analytical ones. The simulated steady-state tip velocity and radius varying with the degree of undercooling of an Al-2wt%Cu alloy are found to be close to the ones predicted by the Lipton-Glicksman-Kurz analytical model. The steady-state morphology of the needle dendrite tip is analyzed. It is found that the tip is nonaxisymmetric and deviates from a paraboloid in the manner of the fourfold symmetry. Finally the simulated 3D multi-equiaxed dendrites with various crystallographic orientations are presented.