Phase-field lattice Boltzmann simulations of multiple dendrite growth with motion, collision, and coalescence and subsequent grain growth

Abstract

In the formation of a typical equiaxed structure during the solidification of metals and alloys, multiple equiaxed dendrites typically grow with motion, collision, and coalescence and subsequently grain growth occurs after the formation of grain boundaries. In this study, we develop a phase-field lattice Boltzmann model that can simulate these complex formation processes involving equiaxed structures. In this model, multiple dendrites are represented by employing multiple phase-field variables, and the formation of grain boundaries is modeled by simply introducing an interaction term between the phase-field variables. Liquid flow is computed using the lattice Boltzmann method, and the motion of a solid is described by solving the equations of motion. Collision-coalescence representation in the present model was validated by performing simulations of collisions between two circular objects. Furthermore, grain growth was validated through static and dynamic conditions in a simple three-grain system. Good agreements with theoretical solutions were obtained for both cases. Finally, using the developed model, a series of formation processes of multiple-dendrite growth with motion, collision, and coalescence and the subsequent grain growth are successfully performed for the first time.