Lattice Boltzmann scheme for crystal growth in external flows.
A composite phase-field lattice-Boltzmann scheme is used to simulate dendritic growth from a supercooled melt, allowing for heat transport by both diffusion and convection. The phase-transition part of the problem is modelled by the phase-field approach of Karma and Rappel, whereas the flow of the liquid is computed by the lattice-Boltzmann-BGK (LBGK, referring to Bhatnagar, Gross, and Krook) method into which interactions with solid and thermal convection are incorporated. For simplicity, we have so far restricted ourselves to the symmetric model. Heat transport is simulated via the multicomponent LBGK method. Depending on the level of anisotropy and undercooling, dendrites or doublons are obtained in our simulations. Crystal growth in a shear flow is considered for different flow velocities and undercoolings. Doublons turn out to be robust against the perturbation imposed by a shear flow and display interesting dynamic behavior, quite different from that of dendrites. In addition, the influence of a parallel flow on the operating state of the tip of dendrites is studied. To complement information from selection theories such as the one presented by Bouissou and Pelcé, we measure selected growth characteristics of dendrites as a function of a flow imposed parallel to the growth direction, for intermediate undercoolings. The observed dependencies are compatible with power law behavior, if the undercooling is not too high. It is shown that for sufficiently large flow velocities, an oncoming flow can lead to tip oscillations of the dendrite and, consequently, to the generation of coherent side branches.
Medvedev
Dmitry
D
Otto-von-Guericke University, Postfach 4120 D-39016 Magdeburg, Germany. Dmitry.Medvedev@phsyik.uni-magdeburg.de
Kassner
Klaus
K