Three-Dimensional Lattice Boltzmann–Cellular Automata Model for Simulating the Solidification Microstructure Under Forced Convection

Melt convection strongly influences solidification microstructure, yet its three-dimensional interaction with evolving dendritic morphology remains insufficiently quantified. Here, a three-dimensional lattice Boltzmann–cellular automata (LBM–CA) model is developed to simulate the solidification microstructure of Fe–C alloys under forced convection. The LBM resolves melt flow, and the CA model employs a decentered-octahedron capture rule to track the solid–liquid interface. The capture rule is written for a general orientation; the present calculations use only (α,β,γ)=(0,0,0). The finite volume method solves heat and solute transport. Comparison with the Lipton–Glicksman–Kurz (LGK) solution shows that the simulated tip velocity in a quiescent melt approaches the analytical steady value. Under forced convection, the calculation is used to examine the directional difference in tip velocity, rather than as a validation against the same LGK value. The simulations reveal strong two-way coupling: forced convection thins the upstream solutal and thermal boundary layers while thickening them downstream, whereas the growing dendrite arms progressively obstruct and redistribute the surrounding flow. Increasing the inlet velocity makes this asymmetry more pronounced. At 0.0015 m/s, the upstream arm is longer than in the quiescent melt, the transverse arm is slightly longer, and the downstream arm is shorter. For the three inlet velocities examined, the downstream reduction is larger in magnitude than the upstream increase. These arm-length changes are numerical results for the present forced-convection calculations and are not compared with experimental measurements.