Melt Convection Research Articles

GPU parallel computation of dendrite growth competition in forced convection using the multi-phase-field-lattice Boltzmann model

A graphics-processing-unit (GPU)-parallel-based computational scheme is developed to realize the competitive growth process of converging bi-crystal in two-dimensional states in the presence of forced convection conditions by coupling a multi-phase field model and a lattice Boltzmann model. The elimination mechanism in the evolution process is analyzed for the three conformational schemes constituting converging bi-crystals under pure diffusion and forced convection conditions, respectively, expanding the research of the competitive growth of columnar dendrites under melt convection conditions. The results show that the elimination mechanism for the competitive growth of converging bi-crystals of all three configurations under pure diffusion conditions follows the conventional Walton–Chalmers model. When there is forced convection with lateral flow in the liquid phase, the anomalous elimination phenomenon of unfavorable dendrites eliminating favorable dendrites occurs in the grain boundaries. In particular, the anomalous elimination phenomenon is relatively strong in conformation 1 and conformation 2 when the orientation angle of unfavorable dendrites is small, and relatively weak in conformation 3. Moreover, the presence of convection increases the tip growth rate of both favorable and unfavorable dendrites in the grain boundary. In addition, the parallelization of the multi-phase-field-lattice Boltzmann model is achieved by designing the parallel computation of the model on the GPU platform concerning the computer-unified-device-architecture parallel technique, and the results show that the parallel computation of this model based on the GPU has absolute advantages, and the parallel acceleration is more obvious as the computation area increases.

Data assimilation for dendritic solidification with melt convection: phase-field lattice Boltzmann study

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.

Thermal heat storage and convective melting dynamics of phase change materials in inclined square enclosures: Effect of the Prandtl number

We study numerically the effect of the Prandtl number on the thermal heat storage, heat flux, and melting dynamics in phase change materials enclosed in square geometries inclined from 0° (bottom horizontal heating) to 180° (top horizontal heating) at increments of at least 5°. Chosen phase change materials are representative of very low, moderate, and high Prandtl numbers: gallium ( P r = 0 . 021 ), water ( P r = 13 . 5 ), and erythritol ( P r = 201 ). The Stefan number is fixed to 0.5, and the Rayleigh number to R a ∼ 1 0 8 . Water and erythritol exhibit a global bifurcation angle at θ c = 3 0 ∘ , separating the liquid phase dynamics from turbulent to laminar. Gallium exhibits stages of turbulent behavior up to 165°. The optimum tilt for harvested thermal energy corresponds to 95° for water and erythritol, and 100° for gallium. The maximum energy efficiency in harvesting thermal energy corresponds to small inclinations within the turbulent region, and 50° for water and erythritol, and the region about 45° for gallium. The maxima at 50° and 95° are very close to those values of the most frequent inclinations 45° and 90° investigated in the experimental literature. There is a power-law dependence between the Nusselt and Rayleigh number N u ∼ R a α for all the Prandtl numbers. Power-law exponents for water and erythritol exhibit a global upward trend with the inclination and undefined for gallium. • Simulations on erythritol (Pr=201), water (Pr=13.5), gallium (Pr=0.021) for Rã10̂8. • Power-law with inclination between Nusselt and Rayleigh numbers for all the Prandtl. • Similar melting time, energy storage and efficiency curves for all Prandtl. • Exists a critical inclination splitting laminar from turbulent flow for all Prandtl. • Optimal inclination for energy storage: 95° water and erythritol, 100° for gallium.

Numerical Study on Heat-Transfer Characteristics of Convection Melting in Metal Foam under Sinusoidal Temperature Boundary Conditions.

Convection melting in metal foam under sinusoidal temperature boundary conditions is numerically studied in the present study. A multiple-relaxation-time lattice Boltzmann method, in conjunction with the enthalpy approach, is constructed to model the melting process without iteration steps. The effects of the porosity, phase deviation, and periodicity parameter on the heat-transfer characteristics are investigated. For the cases considered in this work, it is found that the effects of the phase deviation and periodicity parameter on the melting rate are weak, but the melting front can be significantly affected by the sinusoidal temperature boundary conditions.

Benchmark Al-Cu Solidification Experiments in Microgravity and on Earth

Predicting macrosegregation and grain structure, including the columnar to equiaxed transition (CET), in alloy solidification is an ongoing challenge. Gravity-driven melt convection and transport of unattached solid grains complicate such efforts. Cylindrical samples of aluminum alloys containing 4, 10, and 18 wt pct copper are solidified from the bottom upwards on Earth and in microgravity conditions aboard the International Space Station. The chosen alloys possess primary solid densities that are greater than, equal to, and less than their melt densities promoting different gravity-driven solid transport phenomena. Significant differences in grain structure are observed between microgravity and terrestrial samples. All microgravity samples are entirely equiaxed, while the terrestrial samples exhibit a CET. The columnar grains near the cooled surface in the terrestrial samples can only be attributed to melt convection. The Al-4 wt pct Cu terrestrial sample shows evidence of grain sedimentation, while the Al-18 wt pct Cu terrestrial sample exhibits the effects of grain floatation. Measurements of eutectic fraction and solute concentration in the samples show inverse segregation due to shrinkage-driven flow in all samples. Terrestrially solidified samples have areas of high solute concentration that are not uniformly distributed over the diameter, indicating the presence of melt convection. The eutectic and macrosegregation measurements generally have good correspondence. Temperature, grain structure, eutectic fraction, and macrosegregation data are presented as benchmark data to validate future modeling efforts. Heat flux boundary conditions on the sample are determined using thermal modeling. Thermal process parameters are calculated for all samples.

Improving Performance of Cast Silicon Ingot by Forcing Silicon Melt Convection with Mechanical Stirring

Improving Performance of Cast Silicon Ingot by Forcing Silicon Melt Convection with Mechanical Stirring

Simulation of flow field in silicon single-crystal growth using physics-informed neural network with spatial information

Melt convection plays a crucial role in the growth of silicon single crystals. In particular, melt flow transfers mass and heat, and it may strongly affect the crystal growth conditions. Understanding and controlling convection remains a significant challenge in industrial crystal production. Currently, numerical methods such as the finite element method and the finite volume method are mainly used to simulate melt convection in the crystal growth process. However, these methods are not suitable for most applications with real-time requirements. Physics-informed neural networks (PINNs) have the advantages of fast calculation and wide application. They provide a new concept for the numerical solutions of nonlinear partial differential equations (PDEs). This paper proposes a PINN with spatial information to solve the silicon melt flow model, which does not depend on any simulation data. As the network depth (number of layers) increases, the derivative information in the PDE loss becomes weak, which reduces the expression of the original features in the loss function. Therefore, this study introduces spatial information into the hidden layer of the network, thereby enhancing the correlation between the network and the original input and improving the expression ability of the network. Specifically, silicon melt flow models under three rotating conditions are considered. Compared with other methods, the proposed algorithm can accurately capture regions with complex local morphology. The experimental results reveal the flow characteristics of the silicon melt and confirm the effectiveness of the proposed algorithm. All codes and data attached to this manuscript are publicly available on the following websites: https://github.com/callmedrcom/SIPINN.

Interface-resolved simulation of solid-liquid phase change with thermal convection using discrete unified gas kinetic scheme

This work presents an interface-resolved model for simulating the solid-liquid phase transition problems. In the method, the natural convection flow is handled by the recently proposed discrete unified gas kinetic scheme (DUGKS). Compared with the conventional lattice Boltzmann equation, DUGKS has more advantages on numerical stability and multiscale computation. On the other hand, the ghost-cell (GC) immersed boundary scheme is applied to capturing the solid-liquid interface of pure material. In contrast to the phase-field or enthalpy-based method, the interface here with zero thickness is resolved and explicitly tracked on the fixed Cartesian grid. It is worth noting that due to the adsorption or release of latent heat, the phase front should be evolved according to the Stefan condition. Since compatible with the GC method, the position of the melting front is directly identified by the intersection point, and the complicated treatment of marker inserting and/or deleting in the previous studies is removed. Three numerical examples, including the one-dimension conduction melting, convection melting in a square cavity and melting in a circular cavity with natural convection are conducted to test the present model. The result demonstrates the accuracy of the method for solid-liquid phase change problems.

Convective instabilities in the Czochralski model with different radii ratios

In this work, we explore the instability of the complex convection in the Czochralski model concerning the effects of the radii ratio, melt materials, and crystal rotation. Particularly, linear stability analysis is conducted based on the spectral element method for three groups of cases with the same interval for the variation of the radii ratio (Λ) but different material Prandtl number (Pr) and dimensionless crystal rotation velocity ωs. We observe that, for both ωs = 0 and ωs = 300, the mixed convection of silicon melt (Pr = 0.011) becomes less stable with the increase in radii ratio and the instability is of purely inertial mechanism. In contrast, as for the LiCaAlF6 melt (Pr = 1.4), a larger radii ratio would improve the stability and the instability is dominated by buoyancy mechanism for ωs = 300. Moreover, two times of critical wavenumber transitions occur in the critical stability curve for silicon melt (Pr = 0.011). Each transition associates with a convex turning point of the critical stability curve for ωs = 0, while only one turning point remains when ωs shifts to 300.

Atomic diffusion in liquid Al–Cu melt under static magnetic fields

Atomic diffusion is a natural phenomenon in liquid melt. Avoiding the melt convection is the most challenging when accuracy in measuring the diffusion coefficient of atoms is desired. The diffusion in liquid Al–Cu melts is studied under various static magnetic fields (SMFs). Thermoelectric magnetic convection is induced during the diffusion in the conductive crucible. It is suppressed by increasing the magnetic flux density or eliminated by using an insulated crucible. The interdiffusion coefficient can be accurately measured in the SMF greater than 3 T. The present work provides a new view to study the solidification of alloys under the SMF.

Melting processes of phase change materials in a horizontally placed rectangular cavity

This paper revisits the melting process of phase change materials (PCMs) enclosed in a horizontally placed rectangular cavity, with isothermal and adiabatic conditions subjected to the vertical and horizontal walls, respectively. First, numerical simulations based on an improved lattice Boltzmann method are conducted to illustrate and to inform the theoretical modelling. It is shown that, compared with the traditional two-stage conduction–convection melting description, it is more reasonable to include a third stage in terms of the heat transfer behaviour. During the third stage, the remnant solid PCM is located in the corner formed by the cold and bottom walls of the cavity, and an increasing part of the input energy will be transferred directly out of the cavity without compensating for the melting latent heat, thus inducing a continuously decreasing melting rate until the end of the melting process. Then theoretical predictions are derived piecewise for the melted liquid fraction during the entire melting process, and the corresponding transitions between two successive stages are also discussed. The results are validated successfully via the available experimental and numerical data in the literature, and could guide the design and operation of latent heat storage systems.

Melt convection and macrosegregation in the vacuum arc remelted Ti2AlNb ingot: Numerical methods and experimental verification

Vacuum arc remelting (VAR) is an ultra-high temperature and opaque process. It is difficult to conduct experimental research on the melt flow behavior and the formation of macrosegregation in this process. This work develops a two-dimensional Eulerian three-phase model to predict the solidification structure and macrosegregation of industrial Ti 2 AlNb ingots under complex multi-physics mechanism. The model is also used to study the influence of stirring magnetic field on the melt flow behaviors and macrosegregation of VAR ingots. The results show that Al content of the columnar zone increases gradually from the outside to the inside due to the flow behavior of the melt and the sedimentation of equiaxed grains. External magnetic field applied to stabilize the arc also makes significant effects on the melt convection and macrosegregation. Stirring Lorentz force induced by the external magnetic field drives the melt flow to rotate as a centrifugal force in the top, while drives the melt to flow downward along the metal pool and reduces the influence of the self-induced Lorentz force in the bottom. Superimposing the proper stirring magnetic field on the self-induced magnetic field can strengthen the solute mixing in the molten pool and improve the overall macrosegregation degree of the ingot. Increasing the stirring magnetic field can improve negative segregation in the center of the ingot but intensify the positive segregation in the periphery of the ingot.

Design and optimization of large-scale single-crystal furnaces asymmetric hooked magnetic fields

The solar photovoltaic power generation industry and large-scale integrated circuit industry put forward higher requirements for the size and quality of monocrystalline silicon. However, there are some problems in the production of large-diameter and high-quality monocrystalline silicon, such as uneven crucible thermal field and strong melt convection, which affect the quality of monocrystalline silicon. Therefore, by adopting the finite element 2D modeling method, this paper established the asymmetric hook magnetic field model of the 40-inch crucible. Hence the key magnetic field parameters affecting the growth of a single crystal were determined by controlling the melt convection in the crucible. Meanwhile, through finite element static magnetic field simulations, the effect of the magnetic field at the crucible wall was analyzed by adding the upper and lower guide rings of the magnetic shield structure, the magnetic shield structure with intermediate permeability ring, and the coil parameters. In addition, the parameters of the asymmetric hooked magnetic field structure were also optimized based on the simulation data. On the above basis, a numerical simulation analysis of the key parameters of the magnetic field was carried out. The simulation results show that the optimized asymmetric hook magnetic field structure can effectively control the melt convection in the crucible. In addition, the magnetic field strength at the crucible wall can meet the target of restraining convection by a magnetic field. Hence, it provides a certain reference value for the design of a large-scale single crystal furnace magnetic field.

Solidification shrinkage and shrinkage-induced melt convection and their relation with solute segregation in binary alloys

Shrinkage flow of melt in the mushy zone are closely related to solidification cracking. Here, the phase field (PF) and Lattice Boltzmann Method (LBM) used to predict the dendrite morphology, solute precipitation and diffusion with different solid and liquid densities. A novel species conservation equation considering density changes was constructed to model convective and diffusive of solutes. We demonstrated that solidification shrinkage and shrinkage-flow can strongly affect the dendritic morphology and solute segregation. When solid density is considered, the predicted outline of dendritic decrease significantly, while the solute diffusion layer and the solute concentration at the front of dendrite increase with solid density. For multi-order solidification, solidification shrinkage cause larger solute segregation in the liquid. Then studied direction solidification with shrinkage flow in crystal growth and observed the effect of continuous feeding of melt to the liquid channel. The solute concentration in the channel increases with the orientation angle and solid density. The results from this work have application prospects in the simulation of solidification cracking.

Numerical simulation of natural convection and heat transfer in a molten pool with embedded cooling tubes

This study described the natural circulation and heat transfer of a molten pool in a specifically designed core catcher conceived for a pressurized water reactor. In addition to external cooling, the core catcher features internal cooling tubes embedded in the molten pool. To investigate the coolability in such a configuration, first, a full-scale core catcher simulation is conducted to give a preliminary study under a real SA situation. Results illustrated that cooling efficiency can be remarkably enhanced due to the inner tubes. Then a test facility of the 2D slice with the geometrical scaled factor of 1:4 has been developed, and molten salt (NaNO3–KNO3) experiments will be implemented in the near future. This study also performed a pre-test simulation using molten NaNO3–KNO3 as a stimulant to study the heat transfer and flow characteristics of the salt pool. The melt convection in the test section was represented by a two-dimensional mesh with a WMLES turbulence model using the FLUENT code. The simulation captured the heat transfer enhancement by the cooling tubes as expected, and the results would help decide the proper test matrix and improvement of instrumentation required to obtain the necessary data for code validation.

Natural convection melting of phase change material in corrugated porous cavities

In this paper, a numerical study is carried out to examine the melting inside a wavy cavity under partial heating. A wide range of numerical computations have been performed to understand the effect of porosity, pore density, wall waviness, and heater location and intensity on the melting process. The results revealed that lower metal foam porosity resulted in higher melting rate and lower thermal storage capacity. However, pore density indicated no effect on melting performance for porosity in the range 80–96 %. When considering heater location at various porosities, its impact on melting performance is small at low porosity but becomes significant at higher porosity. Top–bottom partial heating can save almost 10 % of the melting time at ɛ = 0.96. Moreover, the PCM can store more energy, i. e. 11.36 %, when the heater location was changed from center or top–bottom position to top or bottom position at ɛ = 0.96. The results further showed that increasing the number of undulations can save 27.4 % of the melting time at ε = 0.96. Therefore, it can be concluded that higher energy storage and melting rate can be achieved by increasing the number of undulations.

Improved Polymer Crystal Phase Field Model and Numerical Simulation

The existing phase field model of polymer crystallization contains many parameters that lack actual physical meaning. Although the value of these parameters can be adjusted to obtain results consistent with the experiment, it cannot correspond to the experimental conditions. In this paper, a new phase field model is established. By adjusting the latent heat, various forms of isotactic polystyrene crystals, such as dendrites, spherulites, lamellas, etc., can be simulated. Latent heat refers to the heat absorbed or released by a substance from one phase to another and has important physical meaning during the solidification process. The finite difference method was used to solve the model, and then the data were used to visualize. The simulation results were consistent with the experiment. Numerical simulation results under pure diffusion conditions show that the newly established phase field model can qualitatively predict the polymer growth process and provide a theoretical basis for the preparation and optimization of high-performance polymers. In order to make the simulation result closer to the actual growth of the crystal, the flow velocity is added in the simulation to make the melt convection. Under forced convection, the simulated polymer crystal image is no longer symmetrical.

In situ radiographic study of the grain refining behavior of Al3Sc during the solidification of Al-10Cu alloy

Grain refinement of Al alloys inoculated by rare earth elements, such as Sc, has been extensively acknowledged, while the practical behavior of how inoculant Al3Sc particles affect the refinement in solidification has not been clarified due to the non-transparency of the solidification process. Here, the microstructural evolution of primary Al3Sc particles and α-Al grains in Al-10 wt.% Cu alloy solidifications with 0.2 wt.%, 0.6 wt.%, and 1.0 wt.% Sc additions was investigated by in situ synchrotron X-ray radiography. The detailed mechanisms of curve motion of grains (CMG) and melt convection were revealed. The efficient grains nucleation, uniformly scattered small initial grains, and long duration of melt convection contributed to the best refinement in the 0.6 wt.% Sc addition sample. This work provides a deep insight into grain refinement in solidification with Sc addition, which will enlighten the composition design and casting process of Al alloys inoculated by rare earth elements.

Comparative evaluation of RANS eddy-viscosity turbulence models for calculating the silicon melt convection in crystal growth systems

Comparative evaluation of RANS eddy-viscosity turbulence models for calculating the silicon melt convection in crystal growth systems

Synthesis of single metallic crystal in microgravity simulated by static magnetic field

Static magnetic field is useful in processing materials with various microstructures. A self-designed gravity-assisted automatic docking device was used to study diffusion in liquid Al-Cu melts under various SMFs up to 22 T. SMF reduces the coefficient of interdiffusion (DAlCu) by damping the melt convection, which is more efficient with a horizontal SMF than a vertical SMF. A simulated microgravity is achieved when the SMF is greater than the critical 3 T. The simulated microgravity is in favor of growing a single α-Al dendrite in Al-Cu melt. The physical mechanism, which is called the diffusion-limited favored single crystal growth, is established. The present work provides a potential method in processing the single metallic crystal rapidly in the future.