Dendritic equiaxed growth from the melt by continuous cooling-down is investigated by quantitative 2D phase-field simulations. The results are compared with detailed data from solidification experiments on Al-4 wt.% Cu alloy with in situ X-ray monitoring. In a first step, the simulation of an isolated equiaxed alloy dendrite growing freely in <100>-direction in the melt is performed. Then, the impingement between two grains is considered by simulating two dendritic crystals growing towards each other in <100>-direction. From the phase-field simulations, the time evolution of the equiaxed crystals is characterized by measuring the lengths and tip velocities of the primary dendrite arms in free growth and in the presence of neighbor interaction, which enables the analysis of growth dynamics. In a second part, the results of the phase-field simulations are compared to data extracted from an experiment on Al -4 wt.% Cu alloys carried out at the European Synchrotron Radiation Facility (ESRF), with in situ and real-time characterization by means of X-ray radiography, and to analytical relationship for dendrite tip growth. The limitations of 2D-phase-field simulations to fully describe the dynamic formation and interaction of dendritic equiaxed grains are briefly discussed.

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Motion of growing dendrites is a common phenomenon during solidification but often neglected in numerical simulations because of the complicate underlying multiphysics. Here a phase-field model incorporating dendrite-melt two-phase flow is proposed for simulating the dynamically interacted process. The proposed model circumvents complexity to resolve dendritic growth, natural convection and solid motion simultaneously. Simulations are performed for single and multiple dendritic growth of an Al-based alloy in a gravity environment. Computing results of an isolated dendrite settling down in the convective supersaturated melt shows that solid motion is able to overwhelm solutal convection and causes a rather different growth morphology from the stationary dendrite that considers natural convection alone. The simulated tip growth dynamics are correlated with a modified boundary layer model in the presence of melt flow, which well accounts for the variation of tip velocity with flow direction. Polycrystalline simulations reveal that the motion of dendrites accelerates the occurrence of growth impingement which causes the behaviors of multiple dendrites are distinct from that of single dendrite, including growth dynamics, morphology evolution and movement path. These polycrystalline simulations provide a primary understanding of the sedimentation of crystals and resulting chemical homogeneity in industrial ingots.