An Improved Cellular Automata Solidification Model Considering Kinetic Undercooling

Abstract

A cellular automata (CA) model has been developed for solidification simulation considering the kinetic undercooling at the interface. The state-of-the-art model incorporates a decentered growth algorithm to suppress the grid anisotropy and a generalized height function method to calculate the curvature accurately. To develop a CA model which is independent of the mesh size, a new diffusion term is proposed to handle the diffusion between the interface cells and liquid cells. The developed CA model is employed to simulate the single-dendritic solidification of an Al–3Cu (wt pct) alloy. The simulated tip velocities agree with the prediction of the Kurz–Giovanola–Trivedi (KGT) model. Further studies show that the developed CA model converges to an equilibrium model with increasing kinetic mobility values. Moreover, it is found that the virtual liquid cell assumption which is commonly used in existing CA models may lead to a deviation in the mass balance. The mass balance error has been resolved by redistributing solutes from neighboring liquid cells in each time step. The developed CA model could be potentially used in solidification simulations with a high undercooling, which is common in welding and additive manufacturing.