The effects of turbulence on molten pool transport during melting and solidification processes in continuous conduction mode laser welding of copper–nickel dissimilar couple

The melting and solidification stages of a continuous copper–nickel dissimilar metal conduction mode laser welding have been simulated numerically in this study. The heat, mass and momentum transports in molten metal pool have been analysed using both laminar and turbulent flow models separately for the same process parameters. The phase change aspects related to solidification and melting are accounted for by a modified enthalpy–porosity technique while the turbulent transport is modelled by a high Reynolds number k–ε model. It has been observed that temperature fields obtained from both laminar and turbulent transport simulations are qualitatively similar to each other. The molecular thermal diffusivity of the molten metal mixture is found to be in the same order of magnitude as eddy thermal diffusivity, as a result of which the thermal field gets marginally affected by fluid turbulence. By contrast, eddy viscosity remains much greater than molecular viscosity, which leads to greater amount of momentum diffusion in the case of a turbulent molten metal pool, in comparison to that obtained from the corresponding laminar simulation. This is reflected in the reduction in maximum velocity magnitude in the turbulent simulation in comparison to the maximum velocity obtained from laminar simulation. In the case of species transport, the turbulent mass diffusivity is found to be about 10⁷–10⁸ times greater than molecular mass diffusivity. As a result, the species field in turbulent simulation shows characteristics of better mixing between two dissimilar molten metals than the species field obtained using the laminar transport model. The species distribution obtained from turbulent transport is shown to be in better agreement with experimental data reported in literature than the corresponding mass fraction distribution obtained from laminar simulation. It is also found that species distribution in the molten pool is principally determined by advective and diffusive transport during the melting stage and species transport by advection and eddy diffusion in turbulent pool increasingly weakens with decreasing temperature during the cooling following the laser melting stage.     

A simplified numerical model for melting of ice with natural convection

Ice in a rectangular enclosure is melted by heating from the top, while maintained at its melting point at the bottom. The other surfaces are insulated. In the enclosure near the hot region, liquid phase starts forming as temperatures reach values higher than the melting point of ice. This phenomenon is first modeled by ignoring the effect of natural convection in the liquid phase. The resulting equations of conservation of energy are solved in each phase. The motion of melting front is governed by an energy balance at the interface. This conduction model is verified by applying it on a system for which an analytical solution is available. The model is then extended to include convective heat transfer in such a way that the liquid phase is assumed to be a mixed body subjected to natural convection from the top surface and the liquid-solid interface. The flux at the interface is obtained by finding a heat transfer coefficient for natural convection with a cold plate facing upward. Comparison of the results of the numerical work with experiments performed on water/ice system shows a strong effect of natural convection on melting of ice. The model involving natural convection in the liquid phase agrees well with the experimental work.     

Experimental and Scale Analysis of a Solid/Liquid Phase Change Thermal Energy Storage System

ABSTRACT

A detailed experimental study has been carried out to evaluate the heat transfer performance of a solid/liquid phase-change thermal energy storage system. The phase-change material, 99% pure eicosane with a melting temperature of 36.5°C, was contained in a vertically oriented test cylinder that was cooled or heated at its outside boundary, resulting in radially inward freezing or melting, respectively. Detailed quantitative time-dependent temperature distributions and melt-front motion and shape data were obtained. In the freezing case study, a mathematical model was developed based on a one-dimensional analysis, which considered heat conduction as the only mode of heat transfer. In the melting case study, a heat transfer scale analysis was used to help interpret the data and development of heat transfer correlations. In the melting scale analysis, conduction heat transfer in the solid and natural convection heat transfer in liquid were considered. Comparison of experimental data with scale analysis predictions of the solid-liquid interface position and temperature distribution was performed. The analytical results agreed, in the worst case, within 10% of the experimental results in both melting and freezing cases. In the case of melting, scale analysis results agreed within 5% (after initial superheat disappeared in 50 minutes) with experimental results, and experimental results confirm the existence of four melting regions.     

Interactions between hybrid nanosized particles and convection melting inside an enclosure with partially active walls: 2D lattice Boltzmann-based numerical investigation

The ice melting is investigated inside a square cavity with two isothermally partially active walls. The concept of dispersing hybrid alumina–Cu nanoparticles and hybrid silica–multiwalled carbon nanotubes (MWCNTs) nanoparticles is recommended for thermal performance enhancement in this thermal energy storage (TES) system. The two-dimensional explicit lattice Boltzmann convection melting scheme in the single-phase model is applied to account for the natural convection flow induced in the melt region and evolution of the solid–liquid interface. The complete melting time for the pure phase change material (PCM) using case (II) is 33.3% lower compared with other cases. If the price of hybrid Al₂O₃–Cu nanoparticles and heat storage capacity is important, the full melt time diminishes by 16.6% with a volume fraction of 0.01 in case (II). Once hybrid silica–MWCNT nanoparticles with a volume fraction of 0.01 are utilized inside case (II), the lowest charging time is achieved. The complete melting time abates by 23.66% in contrast to the pure PCM melting. The use of single/hybrid nanoparticles to enhance the PCM melting is not necessarily economical as efficient positions of active parts could further lessen the charging time. The efficiency of hybrid nanoparticles is linked to the type and weight proportions of nanoparticles, and positions of thermally active parts.     

Investigation on the thermal performance of phase change material/porous medium‐based battery thermal management in pore scale

With the latent heat, the phase change material (PCM) is widely used in battery thermal management (BTM) to control the temperature. In this paper, the porous medium is employed to enhance the heat transfer of PCM. The lattice Boltzmann model for PCM/porous medium in pore scale is considered, where the mesh system with porous medium (fixed point) is generated by quartet structure generation set (QSGS) method. The effects of the Rayleigh number and porosity on the heat transfer process in BTM are investigated. The results show that decreasing the porosity will accelerate the melting rate. When the porosities are 0.9, 0.8, 0.7, and 0.6, the total melting times are decreased by 23.7%, 43.3%, 58.0%, and 75.4%, compared with pure PCM. The heat is transferred through the high‐conductivity framework. The natural convection in the porous medium is weak, and the conduction is the dominated heat transfer. As a result, the area of solid–liquid interface will be increased, and the heat‐transferred rate is accelerated. However, when the Rayleigh number is raised to 10⁵, applying the porous medium with porosity of 0.9 will increase the total melting time, resulted from the stronger natural convection of PCM. The present study is helpful for design of PCM/porous medium‐based BTM.     

Lattice Boltzmann simulation of tree-shaped fins enhanced melting heat transfer

Abstract

A thermal lattice Boltzmann model is developed to simulate the melting process with natural convection in a cavity filled with tree-shaped solid fins, in which the velocity field and temperature field distribution functions are considered. The present model incorporates the total enthalpy and a free parameter in the equilibrium distribution function to handle conjugate heat transfer. The results indicate that natural convection of liquid phase change material (PCM) plays a significant role in the melting heat transfer of PCM. Increasing the number of branching levels leads to a more rapid melting process, and selecting appropriate bifurcation angle has more efficient heat transfer performance.     

Numerical investigation of the thermal mechanism of the solid-liquid phase changing process

由于相变换热储能技术可以协调能量在时间和空间尺度的分配,成为了目前研究的热点问题。本工作用焓值法分别对充填低温无机盐相变材料的二维和三维管壳式相变储能换热器模型的储/放热特性进行了模拟研究,采用Boussinesq近似研究了液相区密度变化引起的自然对流的影响。研究表明换热器的入口温度对相变换热效率影响显著;在储热过程中自然对流发挥了重要作用,换热效率与液相区的运动状态直接相关,而放热过程中的热交换主要依靠热传导完成;三维模拟的结果表明换热管出口温度与管壁的平均努赛尔数高度相关,且换热管水平放置的换热效率略低于竖直放置。     

Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs)

In this paper the experimental investigation on the solid/liquid phase change (melting and solidification) processes have been carried out. Paraffin wax RT58 is used as phase change material (PCM), in which metal foams are embedded to enhance the heat transfer. During the melting process, the test samples are electrically heated on the bottom surface with a constant heat flux. The PCM with metal foams has been heated from the solid state to the pure liquid phase. The temperature differences between the heated wall and PCM have been analysed to examine the effects of heat flux and metal foam structure (pore size and relative density). Compared to the results of the pure PCM sample, the effect of metal foam on solid/liquid phase change heat transfer is very significant, particularly at the solid zone of PCMs. When the PCM starts melting, natural convection can improve the heat transfer performance, thereby reducing the temperature difference between the wall and PCM. The addition of metal foam can increase the overall heat transfer rate by 3-10 times (depending on the metal foam structures and materials) during the melting process (two-phase zone) and the pure liquid zone. The tests for investigating the solidification process under different cooling conditions (e.g. natural convection and forced convection) have been carried out. The results show that the use of metal foams can make the sample solidified much faster than pure PCM samples, evidenced by the solidification time being reduced by more than half. In addition, a two-dimensional numerical analysis has been carried out for heat transfer enhancement in PCMs by using metal foams, and the prediction results agree reasonably well with the experimental data.     

A numerical investigation into the charge behaviour of a spherical phase change material particle for high temperature thermal energy storage in packed beds

基于高温相变材料,对填充床储热系统中储热单元球体的储热性能进行了模拟研究.研究了不同传热流体温度和球体直径对球体储热性能的影响规律,对导热为主的相变储热过程与导热和自然对流共同作用的相变储热过程进行了比较分析,同时还探讨了高温辐射换热的影响.结果表明,相变时间随球体直径的增大而增大,随传热流体温度的增大而减小.当考虑相变区域自然对流时,总的相变时间显著减少,和单纯导热相比,完全相变时间缩短了近16%.在导热和自然对流的基础上加上辐射传热后可以看出,辐射换热强化了球体内的传热过程,加快了相变材料的熔化速度,强化了自然对流的作用.     

Numerical investigation of the shell configuration effect on the melting of various phase change materials in the presence of porous medium and non-Newtonian fluid

By considering the ability of phase change materials (PCMs) in the storage of energy, the melting of four types PCMs including RT22, RT26, RT35, and RT41 in a heat exchanger is examined in this research. The impact of various shell cross-sectional configurations on the complete melting time of materials, temperature changes, and liquid fraction throughout the melting process are presented. It is assumed that the main heat transfer fluid in the tube is non-Newtonian and the tube is filled with a porous medium. The enthalpy porosity manner is applied for simulating the process of phase change and the heat natural convection and conduction cases are discussed. On the basis of the obtained results, the decrease in complete melting time is about 20% compared with the absence of a porous medium in the circular cross-section configuration. The shell configuration has a noticeable impact on the reduction of the required time for melting. In the square cross-section configuration, RT22 has the lowest melting time, as well as RT41 has the longest melting time in the inverted triangular cross-section configuration in which the maximum time difference for RT22 is about 77% less. So, the best cross-section for the shortest complete melting time is square.     

A new general model for phase-change heat transfer of waxy crude oil during the ambient-induced cooling process

The thermal process during shutdown (a stoppage state of the pipeline), of which the essence is an irregular phase-change process accompanied by natural convection, non-Newtonian behavior, and sometimes turbulence, is a critical problem in crude oil transportation engineering. An accurate calculation of the thermal process during shutdown is more than necessary for the safety of crude oil pipeline; however, it faces some challenges due to the complexity of the phase change. In this study, the phase change of waxy crude oil during the cooling process is divided into four stages, which includes a pure liquid natural convection, solid/liquid dispersion natural convection, coexistence of dispersion system natural convection and porous media natural convection, and pure porous media convection, according to different heat transfer mechanisms on different stages. Based on this division, a general phase-change heat transfer model is proposed for the thermal calculation of waxy crude oil during shutdown. Compared with the previous research, this model appropriately includes the influences of non-Newtonian behavior, phase evolution as well as turbulence. With the proposed model, the temperature drop characteristic of a sample pipeline is analyzed and the influencing factors are investigated.     

A comparative study on the performances of different shell-and-tube type latent heat thermal energy storage units including the effects of natural convection

Numerical modeling was performed to simulate the melting process of a fixed volume/mass phase-change material (PCM) in different shell-and-tube type latent thermal energy storage units with identical heat transfer area. The effect of liquid PCM natural convection (NC) on the latent heat storage performance of the pipe and cylinder models was investigated using a 3D numerical model with FLUENT software. Result shows that NC can cause a non-uniform distribution of the solid–liquid interface, which accelerates PCM melting rate. The PCM melting rate and heat storage rate in the horizontal cylinder model are higher than those in the horizontal pipe model because of the combined effects of heat conduction and NC. A comparative study was conducted to determine the effects of horizontal and vertical shell-and-tube models with different heat transfer fluid (HTF) inlets including the effects of NC. The results indicate that the vertical model with an HTF inlet at the bottom exhibits the highest PCM melting rate and heat storage rate for the pipe models. For the cylinder models, the horizontal model and the vertical model with an HTF inlet at the bottom can achieve nearly the same completed melting time. In addition, NC has minimal effect on any model with an HTF inlet at the top.     

Passive thermal management using metal foam saturated with phase change material in a heat sink

An electronic passive thermal management system was designed. The system featured a hybrid heat sink with parallel fins sintered onto its top and copper metal foam–paraffin composite saturated in its hollow basement. The other two types of basement patterns for thermal dissipation were also employed: (1) a hollow basement saturated with pure paraffin; (2) a solid copper basement. The experimental results showed that the use of the copper metal foam reduced the surface temperature and the time required to reach the melting point of the paraffin. Lower surface temperature can be achieved by either reducing foam porosity or foam pore density. During the melting process, temperature increased more linearly for the foam–PCM composite than for the case of pure paraffin since the enhancement in thermal conduction caused by the metal foam exceeded the level of its suppression to natural convection of melted paraffin.     

An Interfacial Tracking Model for Convection-Controlled Melting Problems

An interfacial tracking model is used to simulate melting in an enclosure in the presence of natural convection. It obtains the melting-front location by calculating the energy balance at the solid–liquid interface and is a simple and convenient method to solve the solid–liquid phase-change problem. It combines the advantages of the both deforming and fixed grids method and can handle natural convection–controlled melting and solidification problems. It is demonstrated through comparisons with various experiments and numerical results that the interfacial tracking model can be used to solve melting problems controlled by natural convection at different Rayleigh numbers ranging from 10⁵ to 10⁸.     

The Effect of a Magnetic Field on the Melting of Gallium in a Rectangular Cavity

The role of magnetic field and natural convection on the solid–liquid interface motion, flow, and heat transfer during melting of gallium on a vertical wall is reported in this paper. The classical geometry consisting of a rectangular cavity with uniform but different temperatures imposed at two opposite side walls, insulated top, and bottom walls is considered. The magnetic field is imposed in the horizontal direction. A numerical code is developed to solve for natural convection coupled to solid–liquid phase transition and magnetic effects. The corresponding streamlines and isotherms predicted by the numerical model serve to visualize the complicated flow and temperature field. The interplay between the conduction and convection modes of heat transfer stimulated by the combination of the buoyancy-driven flow and the Lorentz force on the fluid due to the magnetic field are studied. The results show that the increase of Rayleigh number promotes heat transfer by convection, while the increase of Hartmann number dampens the strength of circulating convective currents and the heat transfer is then mainly due to heat conduction. These results are applicable in general to electrically conducting fluids and we show that magnetic field is a vital external control parameter in solid–liquid interface motion.     

Thermal analysis of a phase change material based heat sink for cooling protruding electronic chips

This work aims to numerically study the melting natural convection in a rectangular enclosure heated by three discreet protruding electronic chips. The heat sources generate heat at a constant and uniform volumetric rate. A part of the power generated in the heat sources is dissipated to a phase change material (PCM, n-eicosane with melting temperature, Tm = 36°C). Numerical investigations were carried out in order to examine the effects of the plate thickness on the maximum temperature of electronic components, the percentage contribution of plate heat conduction on the total removed heat and temperature profiles in the plate. Correlations for the dimensionless secured working time (time to reach the threshold temperature, Tcr = 75°C) and the corresponding liquid fraction were derived.     

Developing a new 2D model for heat transfer and foam degradation in EPS lost foam casting (LFC) process

In this study, a 2D model is developed for heat transfer, foam degradation and gas diffusion at the interfaces of the liquid metal, foam pattern and gaseous gap in between, for EPS lost foam casting process. In this model based on mass and energy balance between gas and molten metal, radiation and conduction between foam and molten metal and convection between gas and molten metal are considered, both metal and foam surfaces are tracked and gap volume and pressure are calculated. A combination of energy balance and geometric correlations is used to define receding foam surface during mold filling. Gas flow in the gap is considered as wedge flow and Nusselt number for a laminar incompressible wedge flow is used for it. To apply our model to an example case, SOLA-VOF algorithm was used to simulate the flow of molten metal with free boundaries. Model results are compared with some data reported in the literature which show acceptable agreement. It is found that besides radiation in the gaseous area between foam and molten metal, conduction also plays an important role in foam degradation and control of molten metal velocity. This model can acceptably predict the effect of some parameters like foam density, coating permeability and foam degradation temperature.     

An analysis of isothermal phase change of phase change material within rectangular and cylindrical containers

In this paper, a simple computational model for isothermal phase change of phase change material (PCM) encapsulated in a single container is presented. The mathematical model was based on an enthalpy formulation with equations cast in such a form that the only unknown variable is the PCM’s temperature. The theoretical model was verified with a test problem and an experiment performed in order to assess the validity of the assumptions of the mathematical model. With very good agreement between experimental and computational data, it can be concluded that conduction within the PCM in the direction of heat transfer fluid flow, thermal resistance of the container’s wall, and the effects of natural convection within the melt can be ignored for the conditions investigated in this study. The numerical analysis of the melting time for rectangular and cylindrical containers was then performed using the computational model presented in this paper. Results show that the rectangular container requires nearly half of the melting time as for the cylindrical container of the same volume and heat transfer area.     

Thermal and heat transfer characteristics in a latent heat storage system using lauric acid

The thermal and heat transfer characteristics of lauric acid during the melting and solidification processes were determined experimentally in a vertical double pipe energy storage system. In this study, three important subjects were addressed. The first one is temperature distributions and temporal temperature variations in the radial and axial distances in the phase change material (PCM) during phase change processes. The second one is the thermal characteristics of the lauric acid, which include total melting and total solidification times, the nature of heat transfer in melted and solidified PCM and the effect of Reynolds and Stefan numbers as inlet heat transfer fluid (HTF) conditions on the phase transition parameters. The final one is to calculate the heat transfer coefficient and the heat flow rate and also discuss the role of Reynolds and Stefan numbers on the heat transfer parameters. The experimental results proved that the PCM melts and solidifies congruently, and the melting and solidification front moved from the outer wall of the HTF pipe (HTFP) to the inner wall of the PCM container in radial distances as the melting front moved from the top to the bottom of the PCM container in axial distances. However, it was difficult to establish the solidification proceeding at the axial distances in the PCM. Though natural convection in the liquid phase played a dominant role during the melting process due to buoyancy effects, the solidification process was controlled by conduction heat transfer, and it was slowed by the conduction thermal resistance through the solidified layer. The results also indicated that the average heat transfer coefficient and the heat flow rate were affected by varying the Reynolds and Stefan numbers more during the melting process than during the solidification process due to the natural convection effect during the melting process.     

Phase change characteristic study of spherical PCMs in solar energy storage

This paper investigates the phase change behavior of 65 mol% capric acid and 35 mol% lauric acid, calcium chloride hexahydrate, n-octadecane, n-hexadecane, and n-eicosane inside spherical enclosures to identify a suitable heat storage material. Analytical models are developed for solidification and melting of sphere with conduction, natural convection, and heat generation. Both the models are validated with previous experimental studies. Good agreement was found between the analytical predictions and experimental study and the deviations were lesser than 20%. Heat flux release at the wall, cumulative energy release to the external fluid, are revealed for the best PCM. The influence of the size of encapsulation, initial temperature of the PCM, the external fluid temperature on solidified and molten mass fraction, and the total phase change time are also investigated.