Phase-field simulations of dendritic crystal growth in a forced flow - art. no. 061601

Convective effects on free dendritic crystal growth into a supercooled melt in two dimensions are investigated using the phase-field method. The phase -field model incorporates both melt convection and thermal noise. A multigr id method is used to solve the conservation equations for flow. To fully re solve the diffuse interface region and the interactions of dendritic growth with flow, both the phase-field and flow equations are solved on a highly refined grid where up to 2.1 million control volumes are employed. A multip le time-step algorithm is developed that uses a large time step for the flo w-field calculations while reserving a fine time step for the phase-field e volution. The operating state (velocity and shape) of a dendrite tip in a u niform axial flow is found to be in quantitative agreement with the predict ion of the Oseen-Ivantsov transport theory if a tip radius based on a parab olic fit is used. Furthermore, using this parabolic tip radius, the ratio o f the selection parameters without and with flow is shown to be close to un ity, which is in agreement with linearized solvability theory for the range s of the parameters considered. Dendritic sidebranching in a forced flow is also quantitalively studied. Compared to a dendrite growing at the same su percooling in a diffusive environment, convection is found to increase the amplitude and frequency of the sidebranches. The phase-field results for th e scaled sidebranch amplitude and wavelength variations with distance from the tip are compared to linear Wentzel-Kramers-Brillouin theory. It is also shown that the asymmetric sidebranch growth on the upstream and downstream sides of a dendrite arm growing at an angle with respect to the flow can b e explained by the differences in the mean shapes of the two sides of the a rm.