Solidification Model Research Articles

Transient solidification and melting numerical simulation of lauric acid PCM filled stepped solar still basin used in water desalination process

It is crucial to produce potable water from salt water in arid places using a stepped solar still desalination process. This work presents the temperature distribution and phase transformation of lauric acid PCM in inclined stepped solar still desalination system. A second-order finite volume method is employed for discretizing the two-dimensional geometry, while energy, continuity, and momentum equations are solved and then coupled using the second-order PRESTO algorithm. The solidification and melting CFD models have been used to capture the melting stages of lauric acid PCM. Four steps with an inclination of 30° to ground and two different cases with saline water levels of 10 mm and 40 mm have been reported. The results reveal that the temperature and mass fraction of lauric acid PCM strongly depends on the saline water level at each step, the number of steps, the angle of inclination, and the location of the solar still step. The maximum percentage increase in PCM melting fraction is 50%, and a PCM temperature rise of 4 °C is observed in the case of SWL-max compared to SWL-min. The total enthalpy of lauric acid PCM is increased by 30% for the SWL-max water level compared to the SWL-min water level.

Development and validation of a one-dimensional solidification model — Part II: Model validation for molten lead-bismuth

The lead-bismuth eutectic (LBE) cooled fast reactor (LFR) has shown promising applications due to its excellent neutron economy and thermal-hydraulic characteristics. Nevertheless, the high-freezing point of LBE arises a risk of coolant solidification, which is identified as a design basis accident for LFRs. Accurate one-dimensional (1D) solidification models are critical for analyzing the coolant solidification behavior. However, the development and evaluation of solidification models are hindered by the lack of experimental data. In this study, a series of molten LBE horizontal penetration solidification experiments were designed and performed with different experimental conditions. The final penetration distances were measured, and the experimental conditions were used as boundary and initial conditions of 1D simulations based on the ASYST-SF code. The simulation results showed the relative error of the final penetration distance is within 12%. This study provides a series of LBE solidification experimental data and demonstrates the reliability of the ASYST-SF code.

Quantitative phase-field model for the isothermal solidification of a stoichiometric compound in a ternary liquid

The phase-field (PF) model is one of the most powerful mathematical models to simulate the solidification of multicomponent alloys. A major challenge faced by the PF model is the treatment of stoichiometric compounds (SCs). In the PF model, compositional derivatives of the free energies of phases need to be treated; however, those of SCs are thermodynamically defined only at a certain composition with respect to the stoichiometric components. Therefore, conventional studies used parabolic functions to provide a pseudo-compositional dependence to free energies. In this paper, we propose a methodology to treat SCs without using the parabolic free energy function. Time-evolution equations were rederived assuming that the free energy of the SC is independent of the composition of its stoichiometric component. We performed numerical calculations for a ternary system comprising two phases, olivine (stoichiometric solid phase) in a basaltic melt (liquid phase), whose free energies were gathered from a thermodynamic database, and we confirmed that the model represents the stoichiometry of the solid phase with high accuracy. This model provides a simple and straightforward methodology to handle SCs in the quantitative PF model.

Development and validation of a one-dimensional solidification model — Part I: Analytical model

The utilization of high-freezing point coolants in Gen IV reactors offers advantages in terms of high thermodynamic efficiency and inherent safety. However, it also introduces the risk of coolant solidification, which has been identified as a design basis accident for these reactor types. Accurate one-dimensional (1D) solidification models play a crucial role in reactor licensing and operation. Nevertheless, existing 1D models primarily focus on the growth of the solidified layer thickness, neglecting the important mushy zone effects that occur at the boundary layer overlap. This paper presents a novel general solidification model that incorporates the mushy zone effects and is applicable to high-freezing point coolants. The model has demonstrated favorable accuracy, with a maximum relative error of 10% when compared to experimental data. The findings highlight that the omission of mushy zone effects can lead to significant deviations from the actual scenario.

Research on Optimization Model of Heat Exchange Fin Structure in Energy Storage System

Aiming at the thermodynamic problem of heat transfer fin in heat storage system, the solidification and melting model and thermodynamic conventional model are established by using simulation software, thermodynamic image processing and other methods. MATLABAB, COMSOL and other software are used to program the optimal rectangular fin spacing Angle and the optimal heat exchange fin structure. Firstly, based on the reason that the simulation software can simulate the heat transfer process of phase change material (PCM) in the actual process to the greatest extent, the plane modeling and thermodynamic equation method are used to analyze the distance Angle of the rectangular fin, and the melting solidification model is established, and the optimal solution is obtained. Finally, combined with the analytic hierarchy model and TOPSIS method, the triangular fin structure and rectangular fin structure were compared from three levels, namely, the heat sink area, temperature rise time and PCM maintenance time of different shapes. And create a heat transfer rate of return to more favorably analyze the data and visually present the comparative results.

Redefined interface error, 2D verification and validation for pure solid-gallium phase change modeling by enthalpy-porosity methodology

For simulating phase change process of pure solid gallium, previously published literature contains some key problems, including the inappropriate definition & computation for interface errors, and the unsatisfactory numerical verifications & validations. Herein, the 2D verifications and 2D validations for the enthalpy-porosity modeling of pure gallium melting starting from a vertical end wall have been reported comprehensively. The well-known and classic experimental data presented in literature are used to verify and validate the model. The groundbreaking contributions in this work are that: i) The definition and computational method of the interface-position errors between the numerical and experimental results are revisited and proven carefully; ii) The numerical schemes as well as major parameters of 2D modeling gallium melting are selected with overall interface error <9%. However, these schemes and parameters are not appropriate for the solidification modeling of gallium due to the irregular and non-reproducible interface shapes caused by highly anisotropic properties of solid crystal gallium as experimentally reported in literature; iii) The 2D validations of enthalpy-porosity modeling of gallium melting are investigated in detail, and the maximum interface error is within the limits of ±12%. Moreover, the simulated liquid volume fractions and dimensionless heat transfer coefficients are well correlated in terms of related criteria parameters, and they are compared with correlations available in literature. It is concluded that to solidly validate the modeling of pure metal melting, both the global parameters (e.g., volume-averaged liquid fraction) and the local parameters (e.g., interface position) need to be considered together.

Numerical solution to phase-field model of solidification: A review

Recent advances in improving the computational efficiency of the phase-field simulations of solidification microstructures are reviewed. The parallel progress of four typical approaches, namely, multigrid, adaptive mesh refinement method, semi-implicit Fourier spectral method, and graphical processing units (GPUs) architecture, is highlighted. Large-scale spatiotemporal simulations are successfully performed to cover essential aspects of multiphysics with the capability of these algorithms. Focus is put on the principles, applications, and comparison of the four algorithms, while solidification theories and discretization methods are outlined.

Effect of Feeding Strip Temperature on Macrosegregation in a Large Continuous Casting Round Bloom

Feeding a cold steel strip into continuous casting (CC) mold is an effective method to improve the quality of large round bloom. However, it is difficult to assess the correlation between the bloom quality and the initial temperature of the strip. Therefore, a three‐phase mixed columnar–equiaxed solidification model is developed to evaluate the effect of feeding strip temperature on macrosegregation and solidification structure in a large vertical CC round bloom. The results show that feeding the steel strip induces “crystal rain” in the liquid core of the bloom and increases the volume fraction of the equiaxed phase. After feeding a strip, the flow direction of molten steel is changed, and the flow velocity is increased in the liquid core of the bloom. Furthermore, with initial temperature of the strip decreases, the production efficiency is improved. Compared to the four conditions investigated, the carbon distribution in the bloom is the most uniform, the negative segregation at the centerline of the bloom is the weakest with the value of −35.50%, and the extreme value difference of the macrosegregation index at 20 m below the meniscus is the smallest with the value of 38.35% under the condition of Tinitial = 500 K.

Lattice Boltzmann solidification modeling of forced convection internal flows applied to Gen-IV nuclear reactor coolants

Generation-IV nuclear reactors involve novel coolants such as molten salts and lead. One of the issues that must be assessed with these coolants is the risk of solidification during reactor operation owing to their high melting temperature. However, the numerical simulation of solidification problems is computationally demanding. In this work, we assess the applicability of Lattice Boltzmann Method (LBM) to nuclear coolants solidification problems under laminar internal forced flow conditions. The double distribution Total Enthalpy-Partially Saturated Method is implemented in the open-source code OpenLB and compared against more standard Finite-Volume Computational Fluid Dynamics (FV-CFD) results, which uses the enthalpy-porosity Eulerian Multiphase method, in commercial code Star-CCM+. The test cases comprise the solidification of two fluids with significantly different Prandtl numbers, molten salt and lead, in a 3D pipe geometry in laminar flow conditions with an initial Reynolds number of 100. The solid interface advances from the cooled wall towards the bulk of the pipe reducing the area of flow passage as the transient evolves. Results of LBM velocity fields, solid fraction profiles, temperature fields, and pressure fields are in good agreement with FV-CFD results for both coolants. Furthermore, LBM stability and accuracy limits are independently explored for molten salts and lead using Two-Relaxation Time (TRT) and Bhatnagar-Gross-Krook (BGK) collision operators. Simulation time between FV-CFD and LBM is also contrasted for both coolants. In this work, LBM solvers use explicit time schemes with a regular grid, whereas FV-CFD solutions are able to include implicit time schemes and near-wall mesh refinement. For molten salt flows (high Prandtl number) FV-CFD allows for considerably larger timesteps than LBM, which is limited by the maximum lattice Mach number limitation and stability considerations. For lead flows (low Prandtl number), the implicit scheme in FV-CFD is limited in terms of accuracy for large timesteps due to the limiting Fourier-number. On the other hand, LBM does not present notable stability issues for lead and the lattice Mach number limit is not as relevant as for the molten salt case for this Reynolds number, allowing for faster simulation times than FV-CFD.

Evaluation of solidification cracking susceptibility factors in carbon steel and availability of Ti addition based on theoretical analysis

This study conducted a basic investigation to improve the solidification cracking susceptibility of carbon steel. BTR is one of the susceptibilities to solidification cracking, and it is said that solidification cracking susceptibility is reduced when BTR is smaller. BTR of three commercial filler metals was evaluated by using Trans-Varestraint test. EPMA and EDS analysis of the weld metal microstructure revealed two compounds. The white structure was composed of silicon, manganese, and sulphur, and the black structure was Ti-based compound. Theoretical analysis of BTR was conducted by applying a two-phase peritectic solidification model in FA mode and considering MnS crystallization during solidification segregation. The analysis results indicated that BTR of carbon steel is attributed to the difference in solidification completion temperatures, and carbon is the most deleterious element. Also, MX compound (Ti, C, N) crystallized in addition to MnS at the end of solidification. Theoretical analysis was conducted for Ti virtual addition materials because MX compound (Ti, C, N) crystallization by Ti addition may lead to BTR reduction by trapping C in the liquid phase. The results showed that Ti addition reduced BTR. The amount of C in the residual liquid phase was reduced by an increase in MX compound (Ti, C, N) crystallization due to Ti addition. Based on theoretical considerations, it can be concluded that Ti addition to carbon steel is effective in reducing BTR.

A comparative study of Kim-Kim-Suzuki (KKS), Partition Coefficient Relaxation (PCR), and Finite Interface Dissipation (FID) phase field models for rapid solidification

A comparative study of Kim-Kim-Suzuki (KKS), Partition Coefficient Relaxation (PCR), and Finite Interface Dissipation (FID) phase field models for rapid solidification

Supporting Imaging of Austenitic Welds with Finite Element Welding Simulation—Which Parameters Matter?

The basic principle of ultrasound is to relate the time of flight of a received echo to the location of a reflector, assuming a known and constant velocity of sound. This assumption breaks down in austenitic welds, in which a microstructure with large oriented austenitic grains induces local velocity differences resulting in deviations of the ultrasonic beam. The inspection problem is further complicated by scattering at grain boundaries, which introduces structural noise and attenuation. Embedding material information into imaging algorithms usually improves image quality and aids interpretation. Imaging algorithms can take the weld structure into account if it is known. The usual way to obtain such information is by metallurgical analysis of slices of a representative mock-up fabricated using the same materials and welding procedures as in the actual component. A non-destructive alternative to predict the weld structure is based on the record of the welding procedure, using either phenomenological models or the finite element method. The latter requires detailed modelling of the welding process to capture the weld pool and the microstructure formation. Several parameters are at play, and uncertainties intrinsically affect the process owing to the limited information available. This paper reports a case study aiming to determine the most critical parameters and levels of complexity of the weld formation models from the perspective of ultrasonic imaging. By combining state-of-the-art welding simulation with time-domain finite element prediction of ultrasound in complex welds, we assess the impact of the modelling choices on the offset and spatial spreading of defect signatures. The novelty of this work is in linking welding simulation with ultrasonic imaging and quantifying the effect of the common assumptions in solidification modelling from the non-destructive examination perspective. Both aspects have not been explored in the literature to date since solidification modelling has not been used to support ultrasonic inspection extensively. The results suggest that capturing electrode tilt, welding power, and weld path correctly is less significant. Bead shape was identified as having the greatest influence on delay laws used to compute ultrasonic images. Most importantly, we show that neglecting mechanical deformation in FE, allowing for simpler thermal simulation supplemented with a phenomenological grain growth loop, does not reduce the quality of the images considerably. Our results offer a pragmatic balance between the complexity of the model and the quality of ultrasonic images and suggest a perspective on how weld formation modelling may serve inspections and guide pragmatic implementation.

The efficiency of multithreaded computing in casting simulation software

The utilization of computer simulation software for casting process simulation is becoming essential in the advancement of casting technology in aviation and other high-tech engineering fields. With the increase in the number of computational cores in modern CPUs, the use of multi-threaded computations is becoming increasingly relevant. In this study, the efficiency of multi-threaded computations in modeling casting processes was evaluated using finite element method casting simulation software ProCast and PoligonSoft, which utilize parallel computing architectures with distributed (DMP) and shared (SMP) memory, respectively. Computations were performed on Intel and AMD-based computers, varying the number of computational threads from 4 to 32. The calculation efficiency was evaluated by measuring the calculation speed increase in the filling and solidification of GP25 castings made of ML10 alloy, as well as the complex task of filling and solidification modeling nickel superalloy casing castings with radiation heat transfer simulation. The results indicate that the minimum computation time in ProCast software is observed when using 16 computational threads. This pattern holds true for both computing systems (Intel and AMD processors), and increasing the number of threads beyond this point does not make a practical difference. The performance decrease in this scenario can be attributed to the low-performance energy-efficient cores in systems based on Intel processors or the decrease in core frequency and full loading of physical cores in systems based on AMD processors. Multi-threading the modeling task in PoligonSoft software is less efficient than in ProCast, which is a result of the shared-memory architecture used in PoligonSoft. Despite the significant difference in parallel efficiency, the task of GP25 casting solidification in both PoligonSoft and ProCast is solved in a time close enough to be considered sufficient.

A coupled domain–boundary type meshless method for phase-field modelling of dendritic solidification with the fluid flow

PurposeThis study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method.Design/methodology/approachA preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case.FindingsThe solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented.Originality/valueA combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.

Solidification Behavior of Fe-6.5Si Alloy Powder for AM-SLM Processing, as Assessed by Differential Scanning Calorimetry.

Lab-scale investigations on the processing of small powder volumes are of special importance for applications in additive manufacturing (AM) techniques. Due to the technological importance of high-silicon electrical steel, and the increasing need for optimal near-net-shape AM processing, the aim of this study was to investigate the thermal behavior of a high-alloy Fe-Si powder for AM. An Fe-6.5wt%Si spherical powder was characterized using chemical, metallographic, and thermal analyses. Before thermal processing, the surface oxidation of the as-received powder particles was observed by metallography and confirmed by microanalysis (FE-SEM/EDS). The melting, as well as the solidification behavior of the powder, was evaluated using differential scanning calorimetry (DSC). Due to the remelting of the powder, a significant loss of silicon occurred. The morphology and microstructure analyses of the solidified Fe-6.5wt%Si revealed the formation of needle-shaped eutectics in a ferrite matrix. The presence of a high-temperature phase of silica was confirmed by the Scheil-Gulliver solidification model for the ternary model Fe-6.5wt%Si-1.0wt%O alloy. In contrast, for the binary model Fe-6.5wt%Si alloy, thermodynamic calculations predict the solidification exclusively with the precipitation of b.c.c. ferrite. The presence of high-temperature eutectics of silica in the microstructure is a significant weakness for the efficiency of the magnetization processes of soft magnetic materials from the Fe-Si alloy system.

Surrogate-based Shape Optimization of Immersion Nozzle in Continuous Casting

In continuous casting, molten steel is fed from the tundish into the mold through the immersion nozzle. In the immersion nozzle, inclusions mainly composed of alumina present in the molten steel adhere and accumulate, it causes limitation of continuous castings. To prevent the nozzle clogging, Ar gas is blown into the immersion nozzle. However, Ar bubbles flow into the mold along with the molten steel and become trapped in the solidifying shell, causing bubbling defects of the slab. To suppress bubbling defects, it is effective to keep Ar bubbles away from the solidification interface or to use molten steel to wash away Ar bubbles that have adhered to the solidification interface. The molten steel flow in the mold is greatly affected by the shape of the immersion nozzle. In this paper, we consider the optimization of the shape of the immersion nozzle to reduce Ar bubbles trapped in the solidifying shell. A numerical model of molten steel flow and heat transfer solidification in the mold is combined with an optimization method. In the optimization process, Ar bubbles trapped in the solidifying shell are evaluated by a neural network to improve the calculation speed. The application of this method to the search for immersion nozzle shape is also reported, and the effectiveness of the obtained nozzle shape in reducing Ar bubbles is discussed.

Modeling Alumina Feeding With the µ(I)-Rheology

Efficient feeding and dissolution of alumina are necessary in order to maintain a stable Hall–Héroult process. One dose of alumina contains several thousand grains, and simulating the motion of individual particles is in practice impossible. The current work proposes to model the alumina dose through a continuous formulation, using the µ(I)-rheology. The rheology is implemented as a viscosity model in OpenFOAM and initial verification cases showed an average deviation below 0.1 pct, and a benchmark case had an average deviation of 7.4 pct. A parametric study, where grains were simulated to collapse on a flat surface identified the two rheology parameters mu _2 and I_{text{0}} to be of particular importance, accounting for more than 70 pct of the variation seen. Finally, three-phase cases simulating the feeding of a dose in cryolite were conducted, and the µ(I)-rheology was able to let the parts of the dose disperse into the melt and detach, which is in accordance with what has been seen in experiments. The current work was also able to couple the model with an earlier developed solidification model, hence, creating a framework for developing a full model for alumina feeding.

Microstructure engineering of fusion zone in resistance spot welding of martensitic stainless steels: The role of Ni interlayer thickness

Martensitic stainless steel (MSS) spot welds show low fracture toughness due to the formation of a brittle microstructure at the joint area. To realize the full advantage of this class of steels in industrial applications, the strategy of altering the microstructure of the weld nugget through introduction of a Ni interlayer was investigated. For this purpose, Ni interlayers with variable thicknesses of 50 to 400 μm were utilized. The microstructural evolutions were thoroughly scrutinized using Scheil-Gulliver solidification modeling and electron backscatter diffraction (EBSD) analysis. Conventional quasi-static mechanical tests, namely, tensile-shear (TS) and cross-tension (CT) were used to correlate microstructure-mechanical properties relationships. In the absence of Ni interlayer, the weld nugget was predominantly composed martensite-M and presumably residual delta ferrite-δ (M+ δ-95%) phases with minor amounts of austenite-γ (5%), failing to meet the minimum peak load requirements under TS and CT loading conditions. By applying Ni interlayers of 50 and 75 μm, a noticeable increase in the fraction of austenite phase (up to 31%) in the weld nugget was detected; nevertheless, a slight to moderate improvement in the mechanical properties was observed since the solidification mode was still primary δ, and M+δ were still the predominant phases in the microstructure. A significant improvement in mechanical properties was achieved in 100 μm Ni interlayer owing to change in the solidification mode from primary δ to γ along with the formation of a mainly austenitic microstructure. However, due to the incomplete mixing of melted base metals and Ni interlayer, a different microstructure consisting of M, δ and γ was also occasionally perceptible in the weld nugget of this sample. The best mechanical properties in terms of strength and ductility occurred with increasing thickness to 200 μm and above, which coincided with the formation of a fully austenitic microstructure in the entire weld nugget.

Solidification Principle in Large Vertical Steel Casting Under the EMS Effect

The surging demand for large high-quality rotor shafts or similar steel components in heavy industries (energy sector) poses new challenges to steelmakers. Based on the experience of conventional ingot and continuous casting, several new process concepts have been proposed, e.g., vertical continuous casting (VCC), semi-continuous casting (SCC), and segment casting (SC), but none of them are optimally put in operation. The main problems include the control of the as-cast structure and macrosegregation. Electromagnetic stirring (EMS) is necessary to obtain the center equiaxed zone, but EMS-induced multiphase flow can cause severe macrosegregation and uneven distribution of the as-cast structure between equiaxed and columnar. In this study, an advanced mixed columnar-equiaxed solidification model was used to investigate the formation of the as-cast structure and macrosegregation in an example of SCC with a large format (diameter 1 m). The main role of EMS is to create crystal fragments by fragmentation, which is regarded in this work as the only origin of equiaxed grains. The created equiaxed grains are brought by the EMS-induced (primary and secondary) flow and gravity-induced sedimentation to the central/lower part of the casting. The main goal of this study was to understand the solidification principle of SCC. In addition, a numerical parameter study by varying the EMS parameters was also performed to demonstrate the model capability towards the process optimization of SCC.

Cesaro fins parametric optimization for enhancement in the solidification performance of a latent heat storage system with combined fins, foam, and nanoparticle

The use of Phase Change Materials (PCMs) for latent thermal energy storage enhances the availability of solar energy. PCMs can store a large amount of energy in a small volume using almost entirely isothermal processes. Despite this, the poor thermal conductivity of PCMs is a significant disadvantage of current PCMs, severely limiting their energy storage capabilities. As a result, the solidification/melting rates are reduced to an unacceptable level, and the system reaction time is increased unreasonably. By combining the novel fin arrangement, nanoparticles, and metal foam, the current study improved the solidification rate of the PCM in the Latent Heat Thermal Energy Storage System (LHTESS). LHTESS was numerically evaluated in ANSYS Fluent 18.1 using a solidification and melting model. The addition of cesaro fins, nanoparticles, and metal foam significantly improved PCM solidification in the LHTESS. PCM solidification time was reduced by 42.42% and 39.39% in Type-3 and Type-5 fin configurations, respectively, when compared to Type-4 fin configuration. Furthermore, a temperature difference of 27 K between the Heat Thermal Fluid (HTF) and the PCM ensures the best solidification performance. By incorporating nanoparticles into PCM and metal foam, the solidification time is reduced by 73.68%. Depending on the foam structure and volume fraction of the nanoparticles, dispersing nanoparticles in PCM with metal foam saves up to 75% of the time.