Adaptive phase field simulation of dendritic crystal growth in a forced flow: 2D vs 3D morphologies

Two- and three-dimensional (3D) adaptive phase field simulations of dendritic crystal growth in a forced flow are presented. The simulations are based on an adaptive finite volume mesh for a better resolution on the dendrite morphology. It also allows the simulation in a large domain without much additional computing cost, so that the boundary effect can be neglected for the comparison with classic solutions. With the efficient simulations, the effect of forced convection on the growth behavior at high undercooling is discussed, and the results agree well with Oseen–Ivantsov solution and the reported results. For the case of low undercooling, the simulated tip radius and speed are also consistent with the experimental ones. As compared with 2D morphologies, side branches are easily induced in 3D dendrites, and the dramatic difference can be explained through the simulated flow structures and temperature fields. The effect of the flow on the side branching for different undercoolings is also illustrated.