Growth direction selection of tilted dendritic arrays in directional solidification over a wide range of pulling velocity: A phase-field study

In this paper, the growth direction selection of tilted dendritic arrays in directional solidification over a wide range of pulling velocity was investigated by using a thin-interface phase-field model. A systematic convergence study with respect to the interface width for various pulling velocities was first carried out to keep simulated results that are independent of interface width. In our simulations, all data points effectively collapse to the DGP (Deschamps, Georgelin, and Pocheau) law (Phys Rev E 78 (2008) 011605-1-13) for lower pulling velocities while numerical results departure from the DGP law for higher pulling velocity. Based on the data from phase-field simulations, we discussed the dependence of the coefficients f and g in DGP law on μ (μ = V_p/V_c) for a fixed misorientation angle. The dendritic tip shapes of tilted and non-tilted dendrites were compared, and the evolution of tip radius with the variation of V_p was studied. Then, we discuss the reason why our numerical results departure from the DGP law for larger pulling velocities based on the variation of dendritic tip radius with the increase of the pulling velocity for a given Péclet number.