Modelling of dendritic growth during alloy solidification under natural convection

A two-dimensional (2D) lattice Boltzmann method (LBM)-cellular automaton model is presented to investigate the dendritic growth of binary alloys in the presence of natural convection. The kinetic-based LBM is adopted to calculate the transport phenomena by the evolution of distribution functions of moving pseudo-particles. To numerically solve natural convection thermal and solute transport simultaneously, three sets of distribution functions are employed in conjunction with the lattice Bhatnagar–Gross–Krook scheme. Based on the LBM calculated local temperature and concentration at the solid/liquid interface, the kinetics of dendritic growth is determined according to a local solute equilibrium approach. Thus, the physics of a complete time-dependent interaction of natural convection, thermal and solutal transport, and dendritic growth during alloy solidification is embedded in themodel. Model validation is performed by comparing the simulated results with literature data and analytical predictions. The model is applied to simulate dendritic growth in binary alloys under the influence of natural convection. The effects of Rayleigh numbers and initial undercooling on dendrite growth are investigated. The results show that natural buoyancy flow, induced by thermal and solutal gradients under gravity, transports the heat and solute from the lower region to the upper region. The dendritic growth is thus accelerated in the downward direction, whereas it is inhibited in the upward direction, yielding asymmetrical dendrite patterns. Increasing the Rayleigh number and undercooling will enhance and reduce, respectively, the influence of natural flow on the dendritic growth.