Phase-Field Simulation of Concentration and Temperature Distribution During Dendritic Growth in a Forced Liquid Metal Fl
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es of a material are strongly dependent upon its multi-scale microstructure that is formed during manufacturing processes. To improve materials performance, it is valuable to understand the key factors affecting the microstructure formation. As it is very difficult to observe the detailed evolution process of microstructure formation experimentally, computer simulations have drawn great attention in modeling of multi-scale structure formation and its effect on mechanical properties. For decades, phasefield method has been a popular technique to model various types of complicated microstructure formation and evolution during materials processing as well as mechanical loading, such as solidification, spinodal decomposition, Ostwald ripening, crystal growth and recrystallization, domain microstructure evolutions in ferroelectric materials, martensitic transformation, dislocation dynamics, and crack propagation.[1,2] In the past two decades, using phase-field method to simulate the solidification process has been widely reported, and this method has been used for the simulation of thermal-driven solidification from a pure melt as well as the solute-driven solidification of alloys.[3–18] Experimental results have already proved the influence of flow, geometry, and heat flow on directional solidification in three-dimensional samples, and the shape of the interface is essential in organizing LIFEI DU, Ph.D. Candidate, and RONG ZHANG, Professor, are with the Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education, Northwestern Polytechnical University, Xi’an, 710072, P. R. China. Contact e-mail: [email protected] Manuscript submitted April 14, 2014. Article published online August 26, 2014. 2504—VOLUME 45B, DECEMBER 2014
pattern formation.[19–21] A simulated solidification process was compared with these in situ and real-time observations by means of X-ray radiography as well as the related analytical theory.[22] Coupling convection field into phase-field model was first presented by Beckermann et al.[23] in 1999. They developed a novel diffusion interface model for the direct numerical simulation of microstructure evolution in solidification processes involving convection in the liquid phase. They treated the solidification front as a moving interface in the diffuse approximation, and used it to simulate the coarsening of a mush of a binary alloy and the dendritic growth in the presence of melt convection. In order to suppress the solute trapping due to the ‘‘thick’’ interface, Lan and co-authors[24–26] considered the anti-trapping current[7] in the diffusion equations, and carried out the efficient adaptive phase-field simulation for a nonisothermal free dendritic growth in a binary system with a forced liquid flow. Medvedev and co-authors[27,28] presented the first simulations coupling the thin-interface model with the lattice-Boltzmann method, which is a sophisticated approaches both for the solidification and the flow problem. And recently, much complex simulations have been carried out to study the directional solidifica
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