A Lattice‐Boltzmann model to simulate the growth of dendritic and eutectic microstructures under the influence of fluid flow

We present a new formulation of a composite phase‐field and Lattice‐Boltzmann model to analyze the effect of fluid flow on the formation of solidification microstructures. The phase‐field model is based on a description suitable to treat phase tansformation processes and moving boundary problems in multiphase and multicomponent systems as well as in polycrystalline structures. The flow of the liquid is simulated by a Lattice‐Boltzmann‐BGK (LBGK) method. Interactions of the flow field with thermal and solutal convection are incorporated by additional advection terms in the mass and heat diffusion equations. At the boundaries between solid and liquid phases, the flow is modelled by a diffuse bounce back approach. In two‐ and three‐dimensional numerical simulations, we apply the model to investigate flow driven changes of the dendritic morphology in the Ni–Cu system. In particular, we impose different flow velocities at the boundary of the computational domain and investigate the different growth rates of the dendritic tip towards the direction of flow and on the shielded side. Furthermore, the influence of a fluid field on lamellar and rod‐like eutectic growth structures is studied for Al–Cu alloys. Since new solute is supplied by the fluid, a more pronounced growth is observed in the direction of the flow for both cases, dendrites and eutectics. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)