Evolution Of Solid-liquid Interface Research Articles

A two-dimensional cellular automaton-finite difference (CA-FD) model for lithium dendrite simulation

The non-uniform lithium deposition behavior on the negative electrode during the charging process in lithium metal batteries leads to serious safety hazards in practical applications. The phase field (PF) method is the most commonly used to simulate the evolution of the microscopic morphology of lithium dendrite, which is computationally expensive due to the coupled partial differential equations (PDEs). Compared to PF, cellular automaton (CA) can efficiently process the evolution of solid-liquid interface with the neighbor configuration and interaction rules. In this paper, a two-dimensional cellular automaton-finite difference (CA-FD) model based on the decentered square algorithm (DSCA) is established. In this model, the growth of the moving solid-phase interface is described by CA, and the distribution of concentration and electric potential is solved by FD, therefore achieving a higher computation efficiency. During the modeling process, it has been verified that DSCA is more favorable to simulate the preferential growth of lithium dendrite tips than Neumann neighbors and Moore neighbors. Based on this model, the effect of different operating conditions of the lithium metal battery on the growth of lithium dendrites is investigated. The simulation results indicate that an increase in either the interfacial overpotential or the exchange current density accelerates the growth of lithium dendrites, in addition, more side branches are generated under higher overpotential. Therefore, low-rate charging mode is recommended in lithium metal battery to inhibit the growth of lithium dendrite.

Emergence of rapid solidification microstructure in additive manufacturing of a Magnesium alloy

Abstract Bioresorbable Mg-based alloys with low density, low elastic modulus, and excellent biocompatibility are outstanding candidates for temporary orthopedic implants. Coincidentally, metal additive manufacturing (AM) is disrupting the biomedical sector by providing fast access to patient-customized implants. Due to the high cooling rates associated with fusion-based AM techniques, they are often described as rapid solidification processes. However, conclusive observations or rapid solidification in metal AM — attested by drastic microstructural changes induced by solute trapping, kinetic undercooling, or morphological transitions of the solid-liquid interface — are scarce. Here we study the formation of banded microstructures during laser powder-bed fusion (LPBF) of a biomedical-grade Magnesium-rare earth alloy, combining advanced characterization and state-of-the-art thermal and phase-field modeling. Our experiments unambiguously identify microstructures as the result of an oscillatory banding instability known from other rapid solidification processes. Our simulations confirm that LPBF-relevant solidification conditions strongly promote the development of banded microstructures in a Mg-Nd alloy. Simulations also allow us to peer into the sub-micrometer nanosecond-scale details of the solid-liquid interface evolution giving rise to the distinctive banded patterns. Since rapidly solidified Mg alloys may exhibit significantly different mechanical and corrosion response compared to their cast counterparts, the ability to predict the emergence of rapid solidification microstructures (and to correlate them with local solidification conditions) may open new pathways for the design of bioresorbable orthopedic implants, not only fitted geometrically to each patient, but also optimized with locally-tuned mechanical and corrosion properties.

Effect of aspect ratio on PCM melting behavior in a square cavity

For latent heat thermal energy storage applications with phase change material (PCM) in restricted space, the factors such as container shape and heating surface must be considered. In this paper, a 2D square cavity PCM is taken as the research object, and the melting process of PCM with different square cavity aspect ratio (AR) was simulated under the condition of constant heat flux (60 W) at the left wall/bottom wall. An innovative and effective indicator, i.e., differential liquid fraction curve along with solid-liquid interface evolution is proposed to reveal the melting rate and typical phase change characteristics. The results show that the complete melting time increases with the increase of AR for both left wall and bottom wall heating conditions. For general applications, the bottom wall heating has a higher melting rate compared with left wall, especially for the cavity with AR >1. During the phase change process, the melting rate can reach its maximum value at the peak of differential liquid fraction curve with an observation of the longest solid-liquid interface. In addition, the melting pattern of high AR cavity during the latter part of the left wall heating process would become similar to the low AR case under the “scouring effect” of natural convection on the solid-liquid interface. For bottom wall cases, the natural convection waveform presents Rayleigh-Benard convection cells, and with the increase of AR, the irregularity of the vortex structure becomes more obvious. The results can provide useful guidance for accurately evaluating phase change characteristics and designing thermal energy storage system.

Experimental investigation of the effect of external forces on convection-driven melting of phase change material in a rectangular enclosure

This paper studied the convection-driven melting characteristics of the pure phase change material (PCM) under different external force conditions. A centrifugal rotation experimental system was designed and built. The melting behavior of the PCM was investigated at the centrifugal accelerations of -5, -3, -1, 0, 1, 3 and 5 g with the heat flux direction as the reference direction. The melting photographs and recorded temperatures of PCM were used to calculate the melt fraction, time-averaged Nusselt number and latent heat storage. The results show that external forces have a significant effect on the natural convection of PCM during the melting process, which further affect the solid-liquid interface evolution rate, heat transfer rate and latent heat storage. To be specific, the external force in the opposite direction of the heat flux can promote the melting process of PCM. Compared with the case at 0 g, the full melting time is reduced by 30.56%, 44.44% and 51.39%, and the time-averaged Nusselt number is improved by 46%, 90% and 98% at -1 g, -3 g and -5 g, respectively. Under the reverse external forces, the melting rate and heat transfer coefficient of the PCM are significantly reduced. In addition, the external force has a significant effect on the latent heat storage of the PCM during melting. In short, it is better to use the external force in opposite direction of the heat flux to enhance the latent heat storage rate of the PCM.

Thermal performance investigation of concentric and eccentric shell and tube heat exchangers with different fin configurations containing phase change material

The aim of this study is to evaluate the combined effect of fin configuration and eccentricity of heat transfer tube on melting behavior of phase change material (PCM) inside the shell and tube heat exchanger (HX). Two unfinned HXs with concentric and eccentric heat transfer tubes and six other HXs with different arrangements of straight and bifurcated fins were fabricated while the total fin mass was kept constant. The shells of heat exchangers were made of transparent Plexiglas and the melting process was photographed to enable the analysis of the solid-liquid interface evolution. Experimental findings of the unfinned HXs showed that applying the eccentric tube HX leads to a 54% reduction in melting time compared to the concentric tube HX. Among all the cases considered, bifurcated fin configuration outperforms the straight fin configuration. The maximum melting time reduction compared to the HX with concentric unfinned tube was 85% obtained by eccentric tube HX with a long upper bifurcated fin and a short lower straight fin. Transient numerical simulations using a control volume approach were carried out for three tube wall temperatures of 75, 85 and 95 °C. Numerical results showed that the bifurcations increase the total heat transfer rate while the convective heat transfer coefficient decreases.

Numerical Study on the Solid–Liquid Interface Evolution of Large-Scale Titanium Alloy Ingots During High Energy Consumption Electron Beam Cold Hearth Melting

In the present paper, a three-dimensional thermal-fluid multi-physical model has been established to investigate the effect of energy consumption operations on the evolutionary tendency of the solid–liquid interface for large-scale Ti-6 wt.%Al-4 wt.%V (TC4) round (Φ260 mm and Φ620 mm)/slab (1050 mm × 220 mm) ingots produced by electron beam cold hearth melting. The results qualitatively revealed the evolutionary tendency of the solid–liquid interface in different casting conditions, indicating that the solid–liquid interface with a gentle casting speed at a low pouring temperature will generate symmetric solid–liquid interfaces which were slightly affected by the modification of the pouring temperature. With an increasing energy input resulting from the rising casting speed, the deformation of the solid–liquid interface near the inlet was increased. As a result, the risk of breaking out and the formation of a non-uniform microstructure in the Φ620-mm round ingots and slab ingots was greatly increased.

Improving the energy discharging performance of a latent heat storage (LHS) unit using fractal-tree-shaped fins

The fractal tree-shaped structure has been demonstrated as a promising optimization method to maximize the point-area heat flow access. Aiming to enhance the energy discharging rate of the latent heat storage (LHS) unit, an innovative fractal-tree-shaped structure is introduced to construct the metal fin of a shell-tube LHS unit. An unsteady model of solidification heat transfer in a LHS unit with tree-shaped fins is developed and numerically analyzed using commercial CFD software, in an effort to demonstrate the improvement of the energy discharging performance for a latent heat storage unit using fractal tree-shaped fins. The transient temperature distribution, solid-liquid interface evolution, and dynamic changes of the liquid fraction and the sensible and latent heat in a tree-fin LHS unit are compared with those of a radial-fin LHS unit. The effects of length ratio and width index on energy discharge performance are examined and analyzed. The results indicate that the tree-shaped fin significantly improves the energy discharge performance of a shell-tube LHS unit. The tree-fin LHS unit possesses a faster solidification rate, higher energy discharge rate, and stronger temperature uniformity. The complete solidification time of the tree-fin LHS unit is decreased by 66.2% and its complete melting time is reduced by 4.4% when compared with the radial-fin LHS unit. For superior thermal energy discharge performance, the length of tree-shaped fins in a shell-tube LHS unit should be shorter inward and longer outward; the optimum length ratio is about 1.3 and an appropriate width index is 1.

Thermal response of annuli filled with metal foam for thermal energy storage: An experimental study

Latent heat thermal energy storage is a practical way to solve the intermittent of solar energy. However, the inherent low thermal conductivity of phase change materials (PCMs) hampers their widely-used applications. In this study, a visual experiment test rig was designed to investigate the effect of open-cell metal foam embedded into paraffin (PCM) on the thermal response of a shell-and-tube unit during charging process. High temperature water, selected as heat transfer fluid (HTF), was injected from top of copper tube. The evolution of solid-liquid interface in inside and outside views was captured and recorded by a high-definition camera. 3D interface model was reconstructed based on these interface images and melting fraction was thus calculated. T type thermocouples were arranged separately on the radial and axial positions inside the PCM. Heat transfer annuli filled with PCM and composite PCM were tested under different HTF injection velocities. Experimental results demonstrated that the involvement of open-cell metal foam can dramatically enhance the efficiency of thermal energy storage. Compared with pure PCM, the full melting time of composite PCM was reduced by 64%, and the temperature distribution was more uniformity. Increasing the injection velocities of HTF made little contribution to promoting charging process of two samples.

A visualization study on the unconstrained melting of paraffin in spherical container

A visualization experiment is carried out to investigate the void-affected unconstrained melting process in a spherical container. Factors including the diameter of spherical container (20.05–70.30 mm), filling ratio of PCM (0.8–0.98), heating temperature (32–47 °C) and initial temperature (7–22 °C) are studied. Melting behaviors concerning the evolution of solid-liquid interface and the motion of solid PCM are revealed, from which a new unconstrained melting mode (i.e., floating melting which occurs before the close-contact melting) is observed due to the existence of void in solid PCM. In addition, the quantitative results of floating melting time, total melting time and liquid fraction are obtained. The results show that as the melting mode changes from floating melting to close-contact melting, the melting rate is slightly enhanced. With the increase of spherical container diameter, the floating melting time increases first and then decreases, while the total melting time has a continually increasing trend. The higher heating temperature and higher initial temperature will decrease the floating melting time and total melting time. As the filling ratio of PCM increases, the floating melting time and the total melting time increase at first and then decrease. Finally, the correlations of dimensionless total melting time and liquid fraction are proposed.

Comparison of direct numerical simulation with volume-averaged method on composite phase change materials for thermal energy storage

Melting heat transfer in open-cell metal foams embedded in phase-change materials (PCMS) predicted by the volume-averaged method (VAM) was systematically compared with that calculated using direct numerical simulation (DNS), with particular attention placed upon the contribution of natural convection in the melt region to overall phase change heat transfer. The two-temperature model based on the assumption of local thermal non-equilibrium was employed to account for the large difference of thermal conductivity between metallic ligaments and PCM (paraffin). The Forchheimer extended Darcy model was employed to describe the additional flow resistance induced by metal foam. For the DNS, a geometric model of metal foam based on tetrakaidehedron cells was reconstructed. The DNS results demonstrated significant temperature difference between ligament surface and PCM, thus confirming the feasibility of local thermal non-equilibrium employed in VAM simulations. Relative to the DNS results, the VAM combined with the two-temperature model could satisfactorily predict transient solid-liquid interface evolution and local temperature distribution, although pore-scale features of phase change were lost. The presence of natural convection affected significantly the melting front shape, temperature distribution and full melting. The contribution of natural convection to overall phase change heat transfer should be qualitatively and quantitatively given sufficient consideration from both macroscopic (VAM) and microscopic (DNS) point of views. Besides, practical significance and economic prospective using metal foam in TES unit for WHR system to provide residential heating or hot water is discussed and analyzed.

Heat transfer enhancement of phase change materials by fins under simultaneous charging and discharging

Due to the inherent intermittency of renewable energy sources such as solar, latent heat thermal energy storage in phase change materials (PCMs) has received considerable attention. Among several techniques to enhance PCMs’ thermal conductivity, the majority of studies have focused on fin integration due to its simplicity, ease of manufacturing, and low cost. In this study, utilization of extended surfaces (by longitudinal fins) was investigated by development of a numerical model to study the performance of a triplex tube heat exchanger (TTHX) equipped with a PCM under simultaneous charging and discharging (SCD). Governing equations were developed and numerically solved using ANSYS Fluent v16.2. Three conventional fin geometries and six developed fin configurations were compared based on the temperature, liquid fraction, and natural convection behavior under both SCD and non-SCD conditions. The intensity of natural convection was investigated for different fins for the inside heating/outside cooling scenario based on the solid–liquid interface evolution over time. The results indicated that since the buoyancy forces induce upward melted PCM motion, the inner hot tube requires fins on its lower half, while the outer cold one should be extended from its upper half. It was concluded that the case with 3 hot tube fins and 1 cold tube fin is most compatible with natural convection and provides the best performance under SCD conditions.

The Formation of the Solidification Microstructure from Liquid Metal in Industrial Processes

This paper focuses on the role played by the liquid metal management on the solidification microstructure in industrial solidification processes. In particular attention is paid to the elimination of solidification defects by governing the microstructure evolution through fluid-dynamics and heat and mass transport in the liquid. The formation of hot tearing and gas porosities as well as columnar and equiaxed microstructures and micro and macro segregation are analyzed to explain how the liquid management is used to avoid defects. Examples on continuous casting and welding are also included.A very powerful tool for dealing with the complex phenomena associated with the solidification process is numerical modeling. Its increasingly growing use contemplates fluid-dynamics of the liquid phase, mass transport of solutes and solid-liquid interface evolution. Models using phase field and volume-averaging techniques, as well as models integrating multi-physics and multi-scale phenomena, are described as their use is taking on increasing importance in the design of solidification processes.

Numerical investigation of a triplex tube heat exchanger with phase change material: Simultaneous charging and discharging

Thermal energy storage by phase change materials (PCMs) has received considerable attention in recent years. Its potential application is due to the issue of energy supply and demand time mismatch management. Thus, at the time of energy availability at supply side, it is stored in PCMs so as to be extracted later on when it is needed. However, in order to provide continuous operation, there might be some times that a system needs to be simultaneously charged and discharged. Most studies focused either on charging, discharging, or consecutive charging and discharging process, while limited work has been conducted for the case of simultaneous processes namely: simultaneous charging and discharging (SCD). This study presents the development of a numerical model to study the performance of a triplex tube heat exchanger equipped with a PCM under SCD. Governing equations were developed and numerically solved using ANSYS Fluent v16.2. Based on the solid-liquid interface evolution over time, the effect of natural convection on the heat transfer was investigated, and internal heating/external cooling mode was compared with the internal cooling/external heating for a triplex tube heat exchanger. According to the mode of heating and initial condition of the storage (fully melted or fully solidified), four different cases were compared based on the steady solid-liquid interface. The results indicated that the upward melted PCM motion had a great impact on the process. Interestingly, depending upon the initial PCM condition, different final solid-liquid interfaces were found. Finally, the pure conduction model was compared with combined conduction and natural convection to identify the dominant heat transfer mechanism. It was found that the former could be applied to the initially fully melted PCMs under SCD with small error, but for the initially solidified PCMs neglecting the natural convection would result in unacceptably large error.

Experimental study on enhancement of thermal energy storage with phase-change material

Latent heat thermal energy storage is a promising option for efficient utilization of intermitted and instable energy. However, the intrinsically low thermal conductivity of phase-change materials (PCMs) is the major shortage, leading to low energy charging and discharging rate. An experimental setup was designed to investigate the dynamic thermal behavior of a shell-and-tube latent heat thermal storage unit. Paraffin wax was employed as the PCM, of which the thermal properties, including that of melting temperature and latent heat, were detected by Differential Scanning Calorimetry. In order to improve the heat transfer performance, copper foam and a bottom fin were compounded to the PCM. High temperature water flowed through the copper tube as the heat transfer fluid (HTF). The temperature variations of the selected detected points inside PCM and the solid–liquid interface evolution in axial plane of symmetry for three samples, including that of pure paraffin, paraffin–copper foam composites without and with the bottom fin, were recorded under the different heating temperatures and flow rates of HTF. The experimental results indicate that completely melting the PCM in composite takes over 1/3 less time than that of pure paraffin under the same operating conditions. The total charging time consumption of the composite with a bottom fin is the least, as well as the heat transfer rate is the largest among the three samples. The influence of HTF temperature on the charging process is more significant than that of the HTF flow rate.

A comparison study on melting inside the rectangular and curved unit with a vertical heating wall

Efficient and rational use of thermal energy requires the design and development of suitable and cost-effective latent heat storage systems. In this study, a novel curved thermal storage unit is put forward and its thermal behavior has been numerically compared with the traditional rectangular PCM-based thermal storage unit. The solid–liquid interface evolution, liquid flow pattern and temperature distribution are presented. Transient Nu at the heating wall and full melting time are also calculated. The numerical results show the high impact of the enclosure geometry on melting and nature convection. A reduction of 30.6 % in thermal storage time has been achieved by changing the unit from rectangular to curve. Moreover, parametric studies are conducted to assess how thermal performance of the units is affected by the heating wall temperature and PCM thermal conductivity. Correlations encompassing a wide range of parameters are developed in terms of full melting time. Results indicate that proportion of full melting time reduced for the curved unit is almost a constant value and does not vary significantly with these factors. All these may be very helpful for the design of more efficient thermal storage units.

相变材料在含翅片球形容器内的约束熔化传热过程

Spherical capsules are widely used as housing for phase change materials (PCMs) in heat exchangers for thermal energy storage applications. In view of the low thermal conductivity of common PCM candidates, extended surfaces, such as fins, are routinely added to PCM capsules to improve the thermal performance. In this paper, to quantitatively evaluate the influence of fins on the thermal performance of PCM-filled spherical capsules, constrained melting heat transfer of a PCM in a circumferentially finned spherical capsule with various fin heights was investigated both numerically and experimentally under constant-temperature boundary conditions. The enthalpy-based model was used in the numerical simulations to deal with phase change, while the control volume method was used to solve the governing equations for the melting problem with natural convection in the liquid phase. A spherical melting facility that allows for direct observation of the solid-liquid phase interface during melting was designed and constructed. The spherical capsule and fins were made of glass and aluminum, respectively. Octadecane with a nominal melting point at 28.2°C was used as the PCM. Qualitative agreement was obtained between the experimentally observed and numerically predicted results of solid-liquid interface evolution. The sources of the differences were identified to be the departure of the physical model from the real system, as well as simplifications of the numerical model. The evolution of the natural convective flow and temperature fields during melting are presented in the form of a series of snapshots of streamline and isotherm contours. The heat transfer mechanisms during melting were interpreted by these contour snapshots. The presence of circumferential fins not only enhances heat conduction, but also augments natural convection heat transfer in localized areas in the vicinity of the fins. The localized interactions between these two effects are significantly affected by the fin height. Under the specific conditions considered, fins with height-to-radius ratios of 0.25, 0.50, and 0.75 decrease the total melting time by 10.6%, 20.2%, and 28.7%, respectively, leading to a significant increase of the thermal energy storage rates in the spherical capsule. Although the presence of fins benefits heat transfer enhancement, a more comprehensive understanding of the effects of other important factors, such as the inclination angle of the spherical capsule, is required.

Computational modelling of transport phenomena in high energy materials processing application: large eddy simulation and parallelisation

A comprehensive three-dimensional numerical model is presented in order to address the coupled turbulent momentum, heat and species transport during molten metal-pool convection in association with continuous evolution of solid-liquid interface typically encountered in high energy materials processing applications. The turbulent aspect is handled by a large eddy simulation (LES) model and the phase changing phenomena is taken care of by a modified enthalpy-porosity technique. The proposed finite volume based LES model is subsequently parallelised for effective computational economy. To demonstrate the effectiveness of the present model, a systematic analysis is subsequently carried out to simulate a typical high power laser surface alloying process, where the effects of turbulent transport can actually be realised.

Reactive wetting in metal/metal systems: Dissolutive versus compound-forming systems

Reactive wetting in metal–metal systems involves complex interactions between the molten phase and the solid substrate. The simplest interaction involves only the dissolution of the substrate into the molten phase. The more complex interaction involves both dissolution of the substrate and compound formation at the solid–liquid boundary. The fundamental differences between these two types of reactive wetting are identified by studying the purely dissolutive system Bi–Sn and the compound-forming system Au–Sn. Experiments employ the traditional sessile drop technique as well as a novel two-dimensional drop transfer technique that enables real-time visualization of the solid–liquid interface evolution. Recent results from wetting of pure Sn on Au-coated Cu substrates are also presented and reveal a much richer wetting behavior than either Sn on Au or Sn on Cu binary systems.

Morphologies of solid-liquid interface and surface steps during rapid growth of BaB2O4 single crystals

The evolution of solid-liquid interface during BBO single crystal growth was studied by the differential interference microscopy. And the step morphology on (0001) surface of the as-grown crystal was observed by the atomic force microscopy as well. It was found that the transition from a flat solid-liquid interface to a skeletal shape will occur in case of rapid growth. However, AFM images of surface steps revealed morphology differences correlated with crystallographic directions. The steps advancing along 〈10 $$\overline 1 $$ 0〉 direction form the step flow, whereas those steps propagating along 〈01 $$\overline 1 $$ 0〉 direction shape into step segments. Measurements of step heights by AFM indicated that it is the high anisotropy of the dimension of growth unit and step bunching due to the enlargement of concentration difference along the surface that results in the anisotropy of step morphologies.