Numerical Simulation of Three-Dimensional Dendrite Movement Based on the CA–LBM Method

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.

Phase-field lattice Boltzmann simulation of three-dimensional settling dendrite with natural convection during nonisothermal solidification of binary alloy

“…The cellular automata (CA) [20][21][22] and phase-field (PF) models [23][24][25] are representative computational methods for studying dendrite growth. CA [26][27][28][29] and PF [30][31][32][33][34][35][36][37][38][39][40] models have also been applied to dendrite growth with solid motion and liquid flow. The CA model is capable of dendrite growth simulations for a larger domain than the PF model.…”

Development and Numerical Testing of a Model of Equiaxed Alloy Solidification Using a Phase Field Formulation

“…In recent decades, many numerical models have been developed to simulate the evolution of dendritic morphologies during solidification. These include techniques such as level set [4], Monte Carlo [5], cellular automata [6][7][8][9][10][11], and the phase-field method (PFM) [12][13][14]. Amongst the various computational methods, phase-field methods have gained tremendous attention among researchers.…”