GPU phase-field lattice Boltzmann simulations of growth and motion of a binary alloy dendrite

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

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.

Numerical Model Study of Multiple Dendrite Motion Behavior in Melt Based on LBM-CA Method

In this paper, a new method is proposed to solve the solute field of moving grains, and a Cellular automaton (CA)-Lattice Boltzmann method (LBM)-Semi rebound format(Ladd) coupling model which can accurately simulate the motion behavior of multiple dendrites is established. The growth process of microstructure in the solidification process of Al-4.7% Cu alloy ingot was calculated by Cellular automaton (CA) method, the momentum, heat, and mass transfer processes were calculated by Lattice Boltzmann method (LBM), and the melt-dendrite sharp interface interaction was treated by Ladd method. The reliability of the model is verified, and then the growth and movement of single dendrite and multiple dendrites under the action of gravity field are simulated. The simulation results show that the growth and movement mode of multiple dendrites are quite different from that of single dendrite, which is shown in two aspects: (1) the original motion state of dendrites is changed by the combination of flow field, which slows down the falling speed of dendrites to a certain extent; (2) the fusion of solute field between dendrites changed the original growth mode of boundary dendrites and increased their rotation speed.

Modeling of coupled motion and growth interaction of equiaxed dendritic crystals in a binary alloy during solidification

Motion of growing dendrites is a common phenomenon during solidification but often neglected in numerical simulations because of the complicate underlying multiphysics. Here a phase-field model incorporating dendrite-melt two-phase flow is proposed for simulating the dynamically interacted process. The proposed model circumvents complexity to resolve dendritic growth, natural convection and solid motion simultaneously. Simulations are performed for single and multiple dendritic growth of an Al-based alloy in a gravity environment. Computing results of an isolated dendrite settling down in the convective supersaturated melt shows that solid motion is able to overwhelm solutal convection and causes a rather different growth morphology from the stationary dendrite that considers natural convection alone. The simulated tip growth dynamics are correlated with a modified boundary layer model in the presence of melt flow, which well accounts for the variation of tip velocity with flow direction. Polycrystalline simulations reveal that the motion of dendrites accelerates the occurrence of growth impingement which causes the behaviors of multiple dendrites are distinct from that of single dendrite, including growth dynamics, morphology evolution and movement path. These polycrystalline simulations provide a primary understanding of the sedimentation of crystals and resulting chemical homogeneity in industrial ingots.