Solidification Phenomena Research Articles

Experimental and model development of lead-bismuth eutectic solidification phenomenon flowing inside the tube

Lead-bismuth fast reactor may solidify under accident conditions due to overcooling in components such as steam generators, waste heat exhaust heat exchangers, etc. In order to investigate the impact of the solidified layer adhering to the wall surface on the transient flow heat transfer and pressure drop characteristics of lead-bismuth eutectic, an experimental study of lead-bismuth eutectic solidification phenomenon flowing in a vertical circular tube was conducted. Moreover, a rapid prediction model for lead-bismuth eutectic solidification phenomenon was developed and verified with experimental results. The experimental results demonstrate that the formation of solidification layer results in a reduction in time-averaged Nu by approximately 43%, while concurrently exhibiting a sustained increase in pressure drop of the fluid flow. Additionally, the maximum thickness of the solidification layer on one side is 6.4 mm (inner diameter of the round tube is 20 mm), while the average thickness is 1.97 mm. The findings demonstrate that the formation of the solidification layer not only markedly diminishes the heat transfer efficiency between the lead-bismuth eutectic fluid and the wall but also augments the flow resistance.

Temperature-induced structure evolution in monocrystalline and polycrystalline cobalt via molecular dynamics simulations

The structure transition of metallic melt strongly depends on temperature and significantly influences the comprehensive properties. However, observing the structure change in experiments is still challenging. Here, molecular dynamics is used to study the melting process and microstructural evolution in single crystal and polycrystal cobalt (Co). The results indicate that the melting process of single crystal structure starts from 1870 K and lasts for a very short period, while the polycrystal melts from about 1760 to 1870 K. In polycrystal Co, the melting initially occurs in grain boundaries, and the melting temperature shows a positive correlation with grain size. An interesting solidification phenomenon occurs on the surface of big grains in the beginning of melting process. The coordination number increasing from 12 to about 13.4 near melting point proves the local expansion of the first coordination shell, indicating the structural evolution from long-range order to short-range order in the continuous heating process. The common neighbor sub-cluster index and Voronoi polyhedron demonstrate the short-range icosahedron structures, while these polyhedrons become polydisperse and isolated in Co liquid. The findings ignite the investigation of the liquid structure origin of crystal materials and extend the understanding of the atomic structure evolution in melting.

Engineering Compounds for the Recovery of Critical Elements from Slags: Melt Characteristics of Li5AlO4, LiAlO2, and LiAl5O8.

Engineered artificial minerals (EnAMs) are the core of a new concept of designing scavenger compounds for the recovery of critical elements from slags. It requires a fundamental understanding of solidification from complex oxide melts. Ion diffusivity and viscosity play vital roles in this process. In the melt, phase separations and ion transport give rise to gradients/increments in composition and, with it, to ion diffusivity, temperature, and viscosity. Due to this complexity, solidification phenomena are yet not well understood. If the melt is understood as increments of simple composition on a microscopic level, then the properties of these are more easily accessible from models and experiments. Here, we obtain these data for three stoichiometric lithium aluminum oxides. LiAlO2 is a promising EnAM for the recovery of lithium from lithium-ion battery pyrometallurgical processing. It is obtained through the addition of aluminum to the recycling slag melt. The high temperature properties spanning from below to above the liquidus temperature of three stoichiometric Li-Al-Oxides: Li5AlO4, LiAlO2, and LiAl5O8 are determined using molecular dynamic simulations. The compounds are also synthesized via the sol-gel route. The Li+ ion exhibits the largest diffusivity. They are quite mobile already below the liquidus temperature, i.e., for LiAlO2 at T = 1700 K, the diffusion coefficient of the lithium ion equals D = 3.0 × 10-9 m2 s-1. The other ions Al3+ and O2- do not move considerably at that temperature. The diffusivity of Li+ is largest in the lithium-rich compound Li5AlO4 with D = 32 × 10-9 m2 s-1 at 2500 K. The lower the viscosity, the higher the lithium content. The Li5AlO4 exhibits a viscosity of η = 2.2 mPa s at 1328 K which matches well with the experimentally determined 2.5 mPa s at this temperature. The viscosity of LiAlO2 at 1800 K is more than two times higher. These data sets can help to describe the melts on a microscopic level and understand how the melt properties will change due to gradients in the Li/Al concentration.

The Recovery of Sulfuric Acid in the Presence of Zr(IV) and Hf(IV) by Solvent Extraction with TEHA and Its Mixtures

The recovery of sulfuric acid in the presence of Zr(IV) and Hf(IV) was studied via solvent extraction using TEHA (tri-2-ethylhexyl amine) and its mixtures. A solidification phenomenon occurred in the loaded organic phase when a single TEHA was employed in the extraction of 1 to 5 M H2SO4. Octanol, decanol and TBP (tri butyl phosphate) were mixed with TEHA, separately, to prevent the solidification of sulfuric-acid-loaded organic. Due to the relatively high aqueous solubility of octanol and decanol, the mixture of TEHA + TBP was selected as the optimal system for the extraction of H2SO4. Simulated counter-current extraction and stripping experiments were performed on the basis of the McCabe–Thiele diagrams, indicating that sulfuric acid could be reduced by TEHA + TBP from 4.2 to around 0.5 M without Zr(IV) and Hf(IV) extraction and recovered by its complete stripping with water. The proposed sulfuric acid recovery step would contribute to the completion of the closed-circuit of the Zr(IV) and Hf(IV) separation process in our previous work and help to re-separate the remaining Zr(IV) and Hf(IV) in the sulfuric acid stripping solution.

The influence of SEN structure on the flow and solidification phenomena in ultra-large-section beam blank mould

Due to the complex cross-section and scale effects, surface and internal defects are prone to occur in the ultra-large-section beam blank. In this study, a coupled model of steel liquid flow and heat transfer within a 1300 × 510 × 140 mm cross-section beam blank mould was established. The results indicate that single-port SEN reduced the flow activity on the meniscus, and the three-ports SEN led to significant high temperature zones and re-melting of the solidified shell in the flange tip and web. The four-ports nozzle not only optimizes the internal flow behavior of the mould but also enhances the uniformity of temperature and solidification. The maximum circumferential difference in shell thickness under the four-ports SEN was only 8.1 mm, compared to 13.2 mm and 13.8 mm under the single-port and three-ports SEN, respectively.

Heat transfer simulation of reline flowing in an elliptic shaped duct: A deep eutectic solvent

Deep Eutectic solvents have emerged as promising alternatives to conventional solvents due to their unique properties and applications. The flow of deep eutectic solvents in various industrial processes has garnered significant attention due to their versatile applications in fields ranging from chemical engineering to energy storage. This study presents a comprehensive mathematical model aimed at elucidating the intricate behavior of eutectic solvent flow within an elliptic duct, a geometric configuration relevant to many real-world systems. In this article, the deep eutectic solvent is composed of choline chloride–urea and is also called Reline. The proposed mathematical model accounts for the complex interplay of fluid dynamics, thermodynamics, and elliptic duct geometry. Key components of the model include the Navier-Stokes equations, which describe the fluid flow, coupled with heat transfer equations to account for temperature variations within the system. The model also considers the phase change behavior of the eutectic solvent, which may exhibit solidification or crystallization phenomena under certain conditions. Numerical simulations and analytical solutions are employed to investigate various aspects of eutectic solvent flow within elliptic ducts, such as velocity profiles, pressure distributions, temperature gradients, and phase transition phenomena. The study explores the influence of key parameters, including the Reynolds number, the aspect ratio of the duct, and the thermophysical properties of the eutectic solvent, on the system’s behavior. From the results, it was clearly observed that the velocity at the narrow region decreased as the pressure raised and the Reynold’s number profile indicated the presence of turbulent flow behavior.

Residential differentiation characteristics based on “socio-spatial” coupling: A case study of Zhengzhou

Residential differentiation transcends its physical aspect, necessitating attention to deeper issues such as group-based disparities underlying spatial configurations. This paper based on multiple data sources, utilizes indicator dimensionality reduction, spatial clustering, and indices of dissimilarity to conducts clustering and matching analysis of social groups and residential spaces. It summarizes and distills the social-spatial coupling types of residential differentiation in Zhengzhou city under a layered model, focusing on social spatial polarization and solidification phenomena in China, and proposing optimization and control recommendations. Findings include: (1) Residential space differences primarily manifest in pricing, while social group distinctions focus on consumption capacity and age. Residential differentiation is a process of continuous differentiation and interaction between two dimensions; (2) Urban housing types do not strictly align with socio-economic attributes, with six typical coupling types observed within the “inner city - new city - outskirts” framework; (3) The “filtering” effect of high housing prices in Zhengzhou leads to wealthy clustering in new city outskirts, while low-income groups aggregate in peripheral and declining inner-city areas, resulting in pronounced spatial segregation; (4) Urban residential differentiation reflects the interaction between macro-controls in the housing market and individual residential choices, serving as a spatial representation of social stratification outcomes.

Influence of the Hot-Top Thermal Regime on the Severity and Extent of Macrosegregation in Large-Size Steel Ingots

The influence of hot-top designs with different heat capacities on the distribution of positive and negative macrosegregation was investigated on a 12 metric tonne (MT) cast ingot made using Cr-Mo low-alloy steel. The three-dimensional finite element modeling code THERCAST® was used to simulate the thermo-mechanical phenomena associated with the solidification process, running from filling the mold until complete solidification. The model was validated on an industrial-scale ingot and then utilized to evaluate the influence of the thermal history of the hot-top, a crucial component in the cast ingot setup. This assessment aimed to comprehend changes in solidification time, temperature, and heat flux—all of which contribute to the determination of macrosegregation severity. The results showed that preheating the hot-top had a minor effect on solidification time, while modifications of thermal conductivity in the hot-top region increased the solidification time by 31%, thereby significantly affecting the macrosegregation patterns. The results are discussed and interpreted in terms of the fundamental mechanisms governing the kinetics of solidification and macrosegregation phenomena.

Development of numerical code for mathematical simulating of unsteady solidification phenomena in existence of nanomaterial

This research zeroes in on improving the freezing process by synergistically employing a wavy wall and fins. To enhance cold penetration, the phase change material (PCM) is enriched with nanoparticles, and a single-phase model is adopted due to the low nanoparticle concentration. The numerical simulations leverage the Galerkin method and the validation procedure affirms the precision of the code, extensively evaluating the impacts of φ (concentration of additives) and dp (particle diameter). With an increase in particle diameter (dp), there is an initial 19.76% decrease in the required time, succeeded by a subsequent 50.56% increase when φ = 0.04. Furthermore, an escalation in φ results in an 11.04%, 40.91%, and 26.36% reduction in completion time for dp values of 50, 40, and 30 nm, respectively. Without the inclusion of powders, the solidification process lasts for 84.8 s. However, with the introduction of the optimal powder size, this duration significantly reduces to 50.1 s. This emphasizes the efficiency improvements attained through the strategic integration of a wavy wall, fins, and PCM infused with nanoparticles.

The Impact of Marangoni and Buoyancy Convections on Flow and Segregation Patterns during the Solidification of Fe-0.82wt%C Steel.

Due to the high computational costs of the Eulerian multiphase model, which solves the conservation equations for each considered phase, a two-phase mixture model is proposed to reduce these costs in the current study. Only one single equation for each the momentum and enthalpy equations has to be solved for the mixture phase. The Navier-Stokes and energy equations were solved using the 3D finite volume method. The model was used to simulate the liquid-solid phase transformation of a Fe-0.82wt%C steel alloy under the effect of both thermocapillary and buoyancy convections. The alloy was cooled in a rectangular ingot (100 × 100 × 10 mm3) from the bottom cold surface to the top hot free surface by applying a heat transfer coefficient of h = 600 W/m2/K, which allows for heat exchange with the outer medium. The purpose of this work is to study the effect of the surface tension on the flow and segregation patterns. The results before solidification show that Marangoni flow was formed at the free surface of the molten alloy, extending into the liquid depth and creating polygonized hexagonal patterns. The size and the number of these hexagons were found to be dependent on the Marangoni number, where the number of convective cells increases with the increase in the Marangoni number. During solidification, the solid front grew in a concave morphology, as the centers of the cells were hotter; a macro-segregation pattern with hexagonal cells was formed, which was analogous to the hexagonal flow cells generated by the Marangoni effect. After full solidification, the segregation was found to be in perfect hexagonal shapes with a strong compositional variation at the free surface. This study illuminates the crucial role of surface-tension-driven Marangoni flow in producing hexagonal patterns before and during the solidification process and provides valuable insights into the complex interplay between the Marangoni flow, buoyancy convection, and solidification phenomena.

Selected aspects of the solididfication process in a moist granular bed

This work presents issues related to the solidification process taking place in moist granular porous media in which water undergoes a phase change as a result of low temperatures. The characteristics of porous materials are also presented, as well as the description and method of determining the basic parameters related to solidification in porous granular deposits. Moreover, as part of the theoretical analysis of the solidification process in a granular bed, a simplified theoretical model of a wet porous material was presented, enabling the development of appropriate theoretical formulas describing the solidification phenomenon. In order to verify the theoretical solutions to the problem, a description and construction of a research stand for conducting experimental research were presented. Using defined dimensionless quantities and formulas, presented in detail in the works of other researchers, charts were developed and illustrated in the work. The entire study is summarized with conclusions that concern the great practical importance of the presented issues, especially for the technical condition of road surfaces

Modeling and numerical studies of high-precision laser powder bed fusion

In order to comprehensively reveal the evolutionary dynamics of the molten pool and the state of motion of the fluid during the high-precision laser powder bed fusion (HP-LPBF) process, this study aims to deeply investigate the specific manifestations of the multiphase flow, solidification phenomena, and heat transfer during the process by means of numerical simulation methods. Numerical simulation models of SS316L single-layer HP-LPBF formation with single and double tracks were constructed using the discrete element method and the computational fluid dynamics method. The effects of various factors such as Marangoni convection, surface tension, vapor recoil, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool have been paid attention to during the model construction process. The results show that the molten pool exhibits a “comet” shape, in which the temperature gradient at the front end of the pool is significantly larger than that at the tail end, with the highest temperature gradient up to 1.69 × 108 K/s. It is also found that the depth of the second track is larger than that of the first one, and the process parameter window has been determined preliminarily. In addition, the application of HP-LPBF technology helps to reduce the surface roughness and minimize the forming size.

Climate related phase transitions with moving boundaries by virtue of mushy zone investigation in Al–Cu: Experiment and phase‐field modeling

Studying Arctic ice formation stays in the focus of research groups over the past decades in the context of ice cover changes, thermal budget and climate agenda in general. Nevertheless, the phenomenon's underlying mechanisms are still not completely understood and described. The main reason for the lack in understanding is the limited experimental access to the field data when it comes to the processes that occur below the ice floe. Thus, there is a need to build competent analogies between the natural (ocean water–ice) and laboratory (here: binary alloy) conditions of the experiment as a step of data preparation for the verification of the mathematical model. In the current paper, the existing qualitative models describing the process of melting and crystallization were expanded and the experimental method was developed copying the layering of the natural ocean water–ice mixture. The experimental set‐up for studying the solidification within the intermediate zone was designed for Al–Cu alloys being the system with appropriate solidus line for creating a sufficient concentration gradient and by that temperature dependent phase fraction under isothermal conditions. The gained experimental data were used for validating a binary phase‐field model for solidification considering moving boundaries. The model includes the description of the free energy of both phases and their respective diffusion coefficients. It allows modeling a binary system at a mesoscopic spatial level by including the concentration‐driven phase transition and resolidification in the two‐phase region. The novel results will help the quantitative understanding of solidification phenomena and are highly‐evaluated from interdisciplinary point of view, including glaciology and geosciences, being ultimately significant for the understanding the global climate change landscape.

Atomistic simulation assisted error-inclusive Bayesian machine learning for probabilistically unraveling the mechanical properties of solidified metals

Solidification phenomenon has been an integral part of the manufacturing processes of metals, where the quantification of stochastic variations and manufacturing uncertainties is critically important. Accurate molecular dynamics (MD) simulations of metal solidification and the resulting properties require excessive computational expenses for probabilistic stochastic analyses where thousands of random realizations are necessary. The adoption of inadequate model sizes and time scales in MD simulations leads to inaccuracies in each random realization, causing a large cumulative statistical error in the probabilistic results obtained through Monte Carlo (MC) simulations. In this work, we present a machine learning (ML) approach, as a data-driven surrogate to MD simulations, which only needs a few MD simulations. This efficient yet high-fidelity ML approach enables MC simulations for full-scale probabilistic characterization of solidified metal properties considering stochasticity in influencing factors like temperature and strain rate. Unlike conventional ML models, the proposed hybrid polynomial correlated function expansion here, being a Bayesian ML approach, is data efficient. Further, it can account for the effect of uncertainty in training data by exploiting mean and standard deviation of the MD simulations, which in principle addresses the issue of repeatability in stochastic simulations with low variance. Stochastic numerical results for solidified aluminum are presented here based on complete probabilistic uncertainty quantification of mechanical properties like Young’s modulus, yield strength and ultimate strength, illustrating that the proposed error-inclusive data-driven framework can reasonably predict the properties with a significant level of computational efficiency.

Simulation on liquid phase sintering of CeO2-CoO ceramic by diffusional Monte Carlo Potts model

Difficulty in control of in-situ crystal growth of CeO2-CoO ceramics limits its catalyst application of solid oxide fuel cells. It is necessary to explore a method to simulate the microstructure growth process of this ceramics under high temperature. In this work, the diffusional Monte Carlo Potts model for the simulation on liquid phase sintering of CeO2-CoO ceramics is established. With geometric and concentration-dependent probability calculated, the phenomena of solidification and melting in liquid phase sintering process are simulated. Moreover, effects of diffusion and grain consolidation are also taken into consideration. The simulation on both isothermal sintering and cooling process is run. The properties of grain growth, grain size distribution and sintering neck evolution are studied. It is found that the grain growth exponent, temporal revolution of grain number and sintering neck obtained from simulation basically agree with relevant theories. In addition, grain size distribution basically remains constant and follows lognormal distribution during the sintering process. This work provides a method to study the in-situ crystal growth process of liquid phase sintered ceramics.

Numerical modelling of high-power laser spot melting of thin stainless steel

Numerical modelling is an important scientific tool in laser materials processing to study different melting, evaporation, and solidification phenomena. It can assist in understanding why certain defects are formed, and thus may provide solution paths for how to decrease certain defects and to increase the quality of a product. Laser spot melting in heat conduction mode represents a simple case and is an excellent first step to build and test solvers prior to moving on to more complicated cases such as laser keyhole welding of thick plates. Modelling of laser spot melting requires only a limited computational domain and allows more complex physics to be added gradually. In this work, a thin 3.0 mm thick stainless steel plate was melted with high-power fiber laser and numerically simulated using a native and custom-build solver based on the VOF method within OpenFOAM. The process was captured with a high-speed imaging camera and simulation results are compared with the experimental results. It was found that temperature-dependent surface tension plays a vital role in controlling melt flow directions within melt pool.

Experimental analyses of solidification phenomena in an ice-based thermal energy storage system

Latent thermal energy storage devices can efficiently store surplus thermal energy during off-peak hours. The system's phase change material (PCM) improves energy storage capacity and isothermal properties. Most PCMs have weak thermal conductivity, which hampers heat transfer. Thus, the present analysis involves an insight into the heat transfer characteristics and thermal performance of a vertical tube-in-tank cold storage system. The objective of this investigation is to gain a better understanding of the significance of buoyancy-driven convection within the side bulk region during the discharging of water as PCM in the heat exchanger. A series of experiments are conducted to investigate the effect of varying the initial bulk temperature on the rate of PCM solidification. The effects of three distinct initial bulk temperatures which are 20 °C, 15 °C, and 5 °C on the solidified mass fraction, thermal performance, and heat transfer rate at various radial and axial locations in PCM are examined. It is seen that PCM experienced a varying cooling rate with varying axial height and is found to be the highest in the bottom region. PCM temperature decreases from top to bottom under the cases of 20 °C and 15 °C, respectively. In contrast, a narrow-ranged thermocline layer is observed under 5 °C bulk temperature, making uniform temperature distribution within the bulk. The influence of bulk natural convection prevails in the later stages of the discharging process under 5 °C bulk, whereas it predominantly exists during the initial stages of solidification under bulk temperatures of 20 °C and 15 °C.

Numerical Modeling and Simulation of Melting Phenomena for Freeze Valve Analysis in Molten Salt Reactors

In recent years, molten salt reactors (MSRs) have gained new momentum thanks to their potential for innovation in the nuclear industry, and several studies on their compliance with all the expected safety features are currently underway. In terms of passive safety, a strategy currently envisaged in accidental scenarios is to drain by gravity the molten salt, which acts both as fuel and coolant, in an emergency draining tank, ensuring both a subcritical geometry and proper cooling. To activate the draining system, a freeze plug, made of the same salt used in the core, is expected to open when the temperature in the core reaches high values. Up to this point, the freeze valve is still a key concept in the molten salt fast reactor (MSFR), and special attention must be paid to its analysis, given the requirement for passive safety, especially focusing on melting and solidification phenomena related to the molten salt mixture. This work aims to contribute to the macroscale modeling of melting and solidification phenomena relevant to the analysis of the freeze valve behavior. In particular, the focus is on the identification of the numerical models that can be adopted to achieve the quantitative insights needed for the design of the freeze valve. Among the ones available in the literature, the most appropriate models were selected based on a compromise between accuracy and computational efficiency. A critical look at the models allows for a synthetic and consistent formulation of the numerical models and their implementation in the open-source software OpenFOAM. The code was subsequently verified using analytical and numerical solutions already well established in the literature. A good agreement between the results produced by the developed solver and the reference solutions was obtained. In the end, the code was applied to simple case studies related to the freeze valve system, focusing on recognizing whether the developed code can model physical phenomena that can occur in a freeze valve. The results of the simulations are encouraging and show that the code can be used to model single-region melting or solidification problems. As such, this work constitutes a starting point for further development of the code, intending to achieve better quantitative predictions for the design of a freeze valve.

Atomistic characterization of multi nano-crystal formation process in Fe–Cr–Ni alloy during directional solidification: Perspective to the additive manufacturing

The directional solidification phenomenon has been observed in conventional castings and state-of-the-art manufacturing processes like additive manufacturing of steel. Precise control of temperature gradient during directional solidification in the additive manufactured components is essential to get growth and evolution of various crystalline structures, which enhance the properties. In this study, we have used molecular dynamics simulation to investigate the directional solidification of Fe–Cr–Ni steel under a wide range of temperature gradients. It is observed that multiple crystal morphology such as single crystal, nano-grains, multiple stacking faults, twins etc. Form during directional solidification depending on the temperature gradient. Evolution of various crystalline structures characterized by adaptive common neighbour analysis, surface area, volume and corresponding dimensionless aspect ratio. The current investigation adds to the pedagogical understanding of the effects of thermal gradients on the evolution characteristics of crystal morphology evolved during modern additive manufacturing processes.

Electrophoresis of a dielectric droplet with constant surface charge density.

Electrophoresis of a dielectric fluid droplet with constant surface charge density is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the governing electrokinetic equations. It is found, among other things, that the larger the electrolyte strength in the ambient solution is, the slower the droplet moves in general. This is due to the strong screening effect of the large amount of indifferent counterions in the neighborhood of the droplet, with no reinforcement of potential-determining ions adsorbing to the droplet surface. The droplet comes to a complete halt eventually. Critical points are discovered for highly charged droplets, at which the droplet surface becomes immobile and the interior fluid stops recirculating. The droplet moves like a rigid particle with constant mobility regardless of its viscosity, a situation referred to as the "solidification phenomenon." The deadlock between the spinning motions on the charged droplet surface induced by the electric driving force and the hydrodynamic driving force respectively is responsible for this peculiar phenomenon. This is also observed for a dielectric droplet with constant surface electric potential. We demonstrate here that it occurs in the constant surface charge density situation as well.