Dendritic Growth Under Natural and Forced Convection in Al-Cu Alloys: From Equiaxed to Columnar Dendrites and from 2D to
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LT flow during solidification is unavoidable under terrestrial condition, which can be induced by either natural forces (e.g., buoyancy force due to thermal and/or solutal gradient) or external forces (e.g., electromagnetic force or stirring).[1] Experimental investigation demonstrates that the convection can drastically change microstructure evolution or even the formation of defects such as freckles.[2,3] It is recognized that the melt flow has a profound effect on the interface dynamics and hence the properties of solidified materials.[4] Extensive numerical studies have been performed to simulate the dendritic evolution during solidification. The classical Ivantsov solution can predict the growing operation state but not the details of the dendritic evolution.[5] Recently, more advanced techniques, such
ANG ZHANG, SHAOXING MENG, ZHIPENG GUO, and JINGLIAN DU are with the School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China. Contact e-mail: [email protected] QIGUI WANG is with Materials Technology, GM Global Propulsion Systems, Pontiac, MI 48340-2920. SHOUMEI XIONG is with the School of Materials Science and Engineering, Tsinghua University and also with the Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Tsinghua University, Beijing 100084, China. Contact e-mail: [email protected] Manuscript submitted December 5, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS B
as phase-field,[6–9] cellular automaton,[10,11] and ab-initio calculation,[12–15] have been developed to further reveal the solidification mechanism. As a more promising approach, the phase-field method (PFM) is consistent with the thermodynamic theory, and can recover the Gibbs-Thomson effect with high accuracy.[16–19] By diffusing the near-tip zone spatially, the PFM can avoid tracking the evolution of sharp interface inherent in the traditional cohesive zone methods,[20] which makes it capable to describe the complex dendritic contour. By incorporating the convection effect, extensive work has been done by Beckermann et al.,[21,22] Dantzig et al.,[23] Lan et al.,[24] and Lee et al.[5] The convective flux is coupled into the solute field equation in the PFM, and the flow velocity is determined by solving the Navier– Stokes equations using sophisticated numerical tools, such as multigrid method,[21,22] adaptive grid technique,[23,25] and parallel computing.[26] However, stemming from the implicit or semi-implicit iteration on solving the Poisson term in the Navier– Stokes equations, the convergence and stability of the solution deteriorate with increasing solid fraction, especially for the complex interface.[27,28] As an alternative, the lattice-Boltzmann method (LBM) can characterize the macroscopic flow by introducing a collection of pseudoparticles,[29] which has attractive advantages in handling the problems with high solid fraction and complex interface evolution. Since Miller et al.[30] first adopted the phase-field lattice-Boltzmann (PFLB) scheme to simulate solid–liqu
