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The effect of natural convection on dendrite morphology is investigated through three-dimensional large-scale phase-field lattice Boltzmann simulations using a block-structured adaptive mesh refinement scheme with the mother-leaf method in a parallel-GPU environment. The simulations confirmed that downward buoyancy enhances the growth of the primary and secondary arms, and upward buoyancy delays the growth of those arms. In addition, the effect of natural convection on the solidification morphologies gradually decreased as the primary arm tip reached the top of the computational domain and finally stopped. Furthermore, in the longer simulation under purely isothermal diffusive conditions, detachment of the secondary arms owing to curvature-driven fragmentation was observed. A large-scale non-isothermal dendrite growth simulation was also conducted, wherein it was observed that the tip growth rate of the primary arm was delayed, and the secondary arm spacing was larger than that in the isothermal condition.

An understanding of the morphology of growing dendrites in alloys is needed for an analysis of microsegregation, as well as an estimation of the permeability for macroscopic fluid dynamics. Quantitative phase-field simulations were used to study the growth process of three-dimensional (3D) equiaxed dendrites in an Al-1.0 mass%Cu alloy during continuous cooling. The dendrites were analysed using an interface shape distribution (ISD) map, which provides the probability of the local interface having a morphology with a given curvedness (C) and shape factor (S). Morphological changes in the microstructure can be measured sensitively from the change in the average value of the curvedness 〈C〉 relative to the solid volume fraction. The ISD map continued to change over time during continuous cooling, implying that it was not time-invariant. Furthermore, when microstructural changes occurred, similarities between the ISD maps were observed, independent of the cooling rates and system sizes.

Time-resolved in-situ X-ray tomography and high-performance phase-field simulations are state-of-the-art approaches to clarifying dendrite solidification. However, major issues persist, such as the insufficiency of spatiotemporal resolution in experiments and lack of material properties in simulations. To overcome these issues, in this study, we developed a data assimilation system using an ensemble Kalman filter based on the phase-field lattice Boltzmann method as a simulation model for the dendrite solidification of binary alloys with liquid flow. The validity of the developed system was confirmed through twin experiments to infer the kinematic viscosity in a two-dimensional dendrite growth problem with forced convection.

Mechanisms of semi-solid deformation are crucial for reducing solidification defects. In this study, a multi-phase-field lattice Boltzmann (MPF-LB) model, which can simulate growth of multiple dendrites with liquid flow, solid motion and collision, is applied to semi-solid deformation. An elastic contact is introduced to the MPF-LB model to consider collision of two grains. The semi-solid deformation with globular morphology is simulated in the two-dimension by the MPF-LB method. Through the simulations, high potential of the MPF-LB model as the evaluation method of semi-solid deformation is confirmed.

Permeability is a very important parameter determining fluid dynamics in macroscale casting simulations. For a columnar solidification structure, the permeability has anisotropy and becomes a tensor quantity. In our previous study, we proposed a permeability tensor and confirmed its validity. In this study, the applicability of the permeability tensor is shown through a series of permeability computations that are conducted for some columnar dendritic structures with different morphologies.

A GPU code has been developed for a phase-field lattice Boltzmann (PFLB) method, which can simulate the dendritic growth with motion of solids in a dilute binary alloy melt. The GPU accelerated PFLB method has been implemented using CUDA C. The equiaxed dendritic growth in a shear flow and settling condition have been simulated by the developed GPU code. It has been confirmed that the PFLB simulations were efficiently accelerated by introducing the GPU computation. The characteristic dendrite morphologies which depend on the melt flow and the motion of the dendrite could also be confirmed by the simulations.

Microsegregation behaviour in a ternary alloy system has been analysed by means of quantitative phase-field (Q-PF) simulations with a particular attention directed at an influence of tie-line shift stemming from different liquid diffusivities of the solute elements. The Q-PF model developed for non-isothermal solidification in multicomponent alloys with non-zero solid diffusivities was applied to analysis of microsegregation in a ternary alloy consisting of fast and slow diffusing solute elements. The accuracy of the Q-PF simulation was first verified by performing the convergence test of segregation ratio with respect to the interface thickness. From one-dimensional analysis, it was found that the microsegregation of slow diffusing element is reduced due to the tie-line shift. In two-dimensional simulations, the refinement of microstructure, viz., the decrease of secondary arms spacing occurs at low cooling rates due to the formation of diffusion layer of slow diffusing element. It yields the reductions of degrees of microsegregation for both the fast and slow diffusing elements. Importantly, in a wide range of cooling rates, the degree of microsegregation of the slow diffusing element is always lower than that of the fast diffusing element, which is entirely ascribable to the influence of tie-line shift.