Simulation of Natural Convection Effects on Dendritic Growth

Abstract

We have recently used the phase field method to study the growth of individual dendritic crystals in the presence of convection in the melt. Forced convection past a crystal growing from a nucleus on a solid wall has been studied in Tönhardt & Amberg (1998), Tönhardt & Amberg (2000a).

In the present contribution (see Tönhardt & Amberg (2000b) for a full account), a numerical study of the effect of natural convection on the growth of SCN crystals from a single stationary nucleus has been performed. All simulations are 2D phase-field computations using an adaptive Finite Element Method. The undercooling has been varied between 1.92 K to 0.12 K, which is within the range used in experiments. Due to the use of an adaptive mesh, it has been possible to use a very large computational domain, resembling that in comparable experiments. The thermal natural convection has minor effects at 1.92 K, but the influence increases with decreasing undercooling, due to the fact that the size of the crystal increases. A representative case with strong gravitational influence on the isotherms is shown in figure 1. The simulation results show an increase of the growth Péclet number with decreasing undercooling that is very similar to that observed in terrestrial experiments. Also, the simulated results for the orientation effect of the gravity vector agree qualitatively with experiments.