Search

Abstract In the engineering field, it is necessary to construct a numerical model that can reproduce multiphase flows containing three or more phases with high accuracy. In our previous study, by extending the conservative Allen–Cahn (CAC) model, which is computationally considerably more efficient than the conventional Cahn–Hilliard (CH) model, to the multiphase flow problem with three or more phases, we developed the conservative Allen–Cahn type multi-phase-field (CAC–MPF) model. In this study, we newly construct the improved CAC–MPF model by modifying the Lagrange multiplier term of the previous CAC–MPF model to a conservative form. The accuracy of the improved CAC–MPF model is evaluated through a comparison of five models: three CAC–MPF models and two CH–MPF models. The results indicate that the improved CAC–MPF model can accurately and efficiently perform simulations of multiphase flows with three or more phases while maintaining the same level of volume conservation as the CH model. We expect that the improved CAC–MPF model will be applied to various engineering problems with multiphase flows with high accuracy. Graphic abstract

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.

Permeability is a very important multiscale parameter providing information of dendritic structures in macroscale simulations of solidification with liquid flow during casting. In our previous study, it was demonstrated that the permeability of liquid flow normal to a columnar dendritic structure can be well approximated by the Kozeny–Carman (KC) equation with a coefficient kc = 9. In this study, the permeability of liquid flow parallel to a columnar dendritic structure is investigated using a method that combines both phase–field and lattice Boltzmann simulations. It is shown that the permeability of parallel flow can also be approximated by the KC equation with kc = 3. A permeability tensor is then proposed for a columnar dendritic structure. Validity of the permeability tensor is confirmed by simulations of liquid flow in arbitrary directions of a columnar dendritic structure.

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.

Temperature dependence of solid–liquid interfacial properties during crystal growth in nickel was investigated by ensemble Kalman filter (EnKF)-based data assimilation, in which the phase-field simulation was combined with atomic configurations of molecular dynamics (MD) simulation. Negative temperature dependence was found in the solid–liquid interfacial energy, the kinetic coefficient, and their anisotropy parameters from simultaneous estimation of four parameters. On the other hand, it is difficult to obtain a concrete value for the anisotropy parameter of solid–liquid interfacial energy since this factor is less influential for the MD simulation of crystal growth at high undercooling temperatures. The present study is significant in shedding light on the high potential of Bayesian data assimilation as a novel methodology of parameter estimation of practical materials an out of equilibrium condition.

In solidification of metals and alloys under earth’s gravity, the growing free equiaxed dendrites either settle or float because of the difference between the solid and liquid densities. In this study, we developed a two-dimensional computational method that can efficiently simulate the growth of free dendrite settling over a long distance. In the developed method, the growth of the dendrite is expressed by a phase-field method, the liquid flow is computed by a lattice Boltzmann method, and the settling of dendrite is expressed by equations of motion. A moving-frame algorithm is employed to track the dendrite settling over a long distance. The computation is accelerated using a multi-level mesh method and GPU computing. The validity of the developed method was evaluated through simulation of the settling of a single circular particle. Specifically, using the developed method, we simulated the growth of a single dendrite in an isothermal undercooled melt of a binary alloy under gravity, and evaluated the time evolutions of the growth velocity of the primary arms, settling velocity, and crystal orientation of the dendrite. The results confirmed that the developed computational method can efficiently express the dendrite growth and settling over a long distance at a reasonable computational cost.

Morphological change of equiaxed dendritic structure in fcc-based alloys associated with transition in preferred growth direction was investigated by means of three-dimensional quantitative phase-field simulations. The anisotropy parameters of interfacial energy e1 and e2 were systematically changed to investigate the growth direction and growth morphology. The growth morphologies can be classified into four types; 〈1 0 0〉 growth, 〈1 0 0〉-like hyperbranched growth, 〈1 1 0〉-like hyperbranched growth and 〈1 1 0〉 growth morphologies. An orientation selection map for these morphologies was constructed in a space spanned by e1 and e2. Furthermore, dependence of the orientation selection map on solidification condition and alloy system was investigated. When initial supersaturation is large and/or partition coefficient of alloy is small, the region of 〈1 0 0〉 growth, typical growth direction of fcc alloy, diminishes in the orientation selection map.

Computer simulation is the most promising approach for the systematical permeability prediction of liquid flow in the mushy zone for various solidification conditions. In this study, we propose a permeability prediction method by using large–scale simulation of phase–field and lattice Boltzmann methods. Using the proposed method, permeability predictions are performed for the flow normal to the columnar solidification structures with multiple dendrites/cells. In addition, the prediction is also performed for columnar solidification structures with periodically arranged dendrites/cells to evaluate the permeability in the full range of solidification fraction and investigate the effect of primary arm array on the permeability. As a result, it is concluded that the dimensionless permeability using a specific interface area of columnar solidification structures can be well approximated by that of a regular hexagonal array of cylinders. Moreover, it is confirmed that the columnar dendrite/cell structure with a periodic regular hexagonal array provides realistic permeability predictions for columnar solidification structures.

Radiation necrosis with massive hemorrhage is a rare complication of radiotherapy. We report the case of a male patient who had undergone radiotherapy therapy 18 years earlier and presently underwent gamma knife radiosurgery for a metastatic brain tumor in his right occipital lobe. The patient showed aberrant behavior with left homonymous hemianopsia and a gradual deterioration of cognitive function after radiotherapy. A CT scan showed the presence of an intracerebral hematoma over the right occipital lobe with mass effect, and small spotty enhancements on the lesion when enhanced on gadolinium contrast-enhanced MRI. Intraoperative findings revealed necrosis of the occipital surface and a hematoma in the occipital lobe. Pathological findings showed damage to the walls of the sinusoidal capillaries and vitreous degeneration of the inner membrane with a spongiform hemangioma. After surgery, the cerebral edema resolved, and the patient's clinical symptoms improved. The cause of the radiation necrosis and bleeding in this patient was assumed to be due to the breakdown of the congested walls of the sinusoidal capillary vessels.

The phase-field (PF) method is a method for interface tracking that can treat complex topological changes relatively easily because of its diffuse interface model. Therefore, as computational resources become increasingly powerful, it is a promising interface tracking method for multiphase flow problems. In this study, we developed a novel multi-PF (MPF) model for expressing flows that consist of an arbitrary number of phases. Here, we adopt the conservative Allen–Cahn (CAC) model instead of the Cahn–Hilliard model, which is often employed in multiphase flow problems, to reduce computational cost and increase the flexibility of the model for various problems. Six sets of two-dimensional simulations were performed to confirm the validity of the developed model for simulating the static and dynamic phenomena of the multiphase flow problem while conserving the volume of each phase. The results confirm that the developed CAC-type MPF model can accurately express the contact angle of a droplet placed on a solid substrate and the motion of bubbles interacting with liquid–liquid interfaces.

An array of columnar dendrites is important to the microsegregation and permeability of interdendritic liquid flow. In this study, an array of tilted columnar dendrites growing during the directional solidification of a binary alloy was investigated via large-scale phase-field simulation. The main conclusion is that the hexagonal array is the dominant array for reasonably tilted dendrites as well as dendrites that grow along the temperature gradient. It is also concluded that the array ordering gradually improves with growth for all tilt angles, and the ordering rate is faster for a small tilt angle.