Abstract
At present, the calculation of three-dimensional (3D) dendrite motion using the cellular automata (CA) method is still in its infancy. In this paper, a 3D dendrite motion model is constructed. The heat, mass, and momentum transfer process in the solidification process of the alloy melt are calculated using a 3D Lattice–Boltzmann method (LBM). The growth process for the alloy microstructure is calculated using the CA method. The interactions between dendrites and the melt are assessed using the Ladd method. The solid–liquid boundary of the solute field in the movement process is assessed using the solute extrapolation method. The translational velocity of the equiaxed crystals in motion is calculated using the classical mechanical law. The rationality of the model is verified and the movement of single and multiple 3D equiaxed crystals is simulated. Additionally, the difference between 3D dendrite movement and two-dimensional (2D) dendrite movement is analyzed. The results demonstrate that the growth of moving dendrites is asymmetric. The growth velocity and falling velocity of the dendrite in the 3D model are faster than that in 2D model, while the simulation result is more realistic than that of the 2D model. When multiple dendrites move, the movement direction of the dendrites will change due to the merging of flow fields and other factors.
Highlights
In recent years, with the increase in research on microstructure simulation and the rapid development of computer technology, scholars have realized that the movement of dendrites will change their growth mode, and have begun to study the influence of dendrite movement more deeply
The Ladd method [17] is used to calculate the solid–liquid boundary and the solute extrapolation distribution method is used to distribute the solute at the solid–liquid boundary, while Newton’s law of mechanics is used to calculate the settling velocity in the process of dendrite movement, so as to calculate the 3D dendrite movement
The rationality test used for calculation of the cellular automata (CA) model was confirmed in relevant studies [21,22], while the calculation of dendrite growth using the Lattice–Boltzmann method (LBM)–CA model was verified by Pian [23], which will not be described in this paper
Summary
With the increase in research on microstructure simulation and the rapid development of computer technology, scholars have realized that the movement of dendrites will change their growth mode, and have begun to study the influence of dendrite movement more deeply. In 2007, Amerg et al [2] used the phase field method (PF) model to simulate the melt flow and convective heat transfer process, as well as the growth and fall of dendrites under the action of gravity, revealing the complex coupling relationship between the settlement and evolution of grains. Rojas et al [8] used phase-field LBM to simulate the growth and movement of single equiaxed crystals in alloy melt under shear flow. Takaki and Rojas et al [9] improved the calculation efficiency by introducing GPU calculation technology and used this model to simulate the growth and movement of equiaxed grains in a binary alloy single-phase solid solution. The Ladd method [17] is used to calculate the solid–liquid boundary and the solute extrapolation distribution method is used to distribute the solute at the solid–liquid boundary, while Newton’s law of mechanics is used to calculate the settling velocity in the process of dendrite movement, so as to calculate the 3D dendrite movement
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