Low artificial anisotropy cellular automaton model and its applications to the cell-to-dendrite transition in directional solidification

A low artificial anisotropy cellular automaton (CA) model is developed for the simulation of microstructure evolution in directional solidification. The CA model's capture rule was modified by a limited neighbor solid fraction (LNSF) method. Various interface curvature calculation methods have been compared. A modified curvature calculation method based on the variation of the unit vector normal (VUVN) to the solid-liquid interface using volume of fluid (VOF) interpolation technique gets better results. The equilibrium shapes were simulated to quantify the artificial anisotropy, when the interface energy anisotropy coefficient is varied from ε = 0.0 to ε = 0.05. The low artificial anisotropy CA model is used in the numerical simulation of the cell-to-dendrite transition (CDT) in directional solidification. The influence of physical parameters (Г, D_l, k₀, m_l) on CDT has been investigated. The main finding in this paper is the discovery of the changing behavior of the V_cd when the solute partition coefficient k₀ is larger than a critical value. When k₀ is less than 0.125, the V_cd follows the Kurz and Fisher criterion V_c/k₀; while when k₀ > 0.125, the V_cd equals to 8 V_c. The experimental data of succinonitrile-acetone (SCN-ace, k₀ = 0.1) and SCN-camphor (k₀ = 0.33) support the conclusions from CA simulations.