Solid-liquid Phase Change Phenomena Research Articles

Phase-field-based lattice Boltzmann method for containerless freezing.

In this paper we first propose a phase-field model for the containerless freezing problems, in which the volume expansion or shrinkage of the liquid caused by the density change during the phase change process is considered by adding a mass source term to the continuum equation. Then a phase-field-based lattice Boltzmann (LB) method is further developed to simulate solid-liquid phase change phenomena in multiphase systems. We test the developed LB method by the problem of conduction-induced freezing in a semi-infinite space, the three-phase Stefan problem, and the droplet solidification on a cold surface, and the numerical results are in agreement with the analytical and experimental solutions. In addition, the LB method is also used to study the rising bubbles with solidification. The results of the present method not only accurately capture the effect of bubbles on the solidification process, but also are in agreement with the previous work. Finally, a parametric study is carried out to examine the influences of some physical parameters on the sessile droplet solidification, and it is found that the time of droplet solidification increases with the increase of droplet volume and contact angle.

Experimental and numerical study of cylindrical encapsulated phase change material in packed bed thermal energy storage with expansion and shrinkage effects

Packed bed latent heat thermal energy storage (PBTES) is a promising technology for storing thermal energy with a relatively compact size and smaller temperature variation during phase change. In this study, a lab-scale low-cost PBTES with cylindrical shape encapsulation of phase change material (PCM) is designed and fabricated for evaluating the charging-alone and discharging-alone thermal performance for medium-temperature range (200–350 °C) latent heat storage applications. Air is used as a heat transfer fluid (HTF), and solar salt is employed as a PCM. A new numerical model incorporating shrinkage and expansion of PCM during phase change is developed by considering the packed bed as the porous medium and the melt fraction-based density variation of PCM to model the transport and solid-liquid phase change phenomena in the PBTES. The numerical model is validated with the in-house experimental results. The maximum thermal charging efficiency is found to be 67.1 % for the mass flow rate of 4.3 g/s and a maximum charging inlet air temperature of 360.9 °C. The maximum discharging efficiency of 86.1 % is obtained for the mass flow rate of 4.3 g/s and discharging inlet air temperature of 35 °C. It is found that the expansion and shrinkage effects are prominent during the phase change of PCM during the charging and discharging operations of the PBTES.

Analysis of the gallium melting problem with different heating configurations

A moving boundary problem is numerically investigated with gallium substance and FVM (finite volume method). Following the determination of the optimal grid size and time-step, a natural convection problem in a vertical slot is studied to validate the multi-cellular melting front. Different heating configurations are modelled to understand the solid-liquid phase change phenomenon under different scenarios for the gallium melting problem. These different scenarios include spatial differential heating (sinusoidal), temporal differential heating (pulsating), inclination angle, and MHD conditions. It is found that grid independence study should not be conducted with liquid fraction or similar average value. If the first time-step is larger than 0.1 s, early development of the Bénard cells will not be captured accurately, even when the outer iterations converge. It is also observed that if peak point of differential heating is close to the top of the domain, melting front will progress faster. When Lorentz force is active, at high Hartmann numbers, oscillation of the Nusselt number is dampened.

Investigation of heat source location on solid-liquid phase change using lattice Boltzmann method

The solid-liquid phase change phenomenon has wide applications in material manufacturing, thermal energy storage, green building, etc. In this paper, a novel solid-liquid phase change model with lattice Boltzmann method has been developed and the effects of heat source location on phase change heat transfer process are investigated. Heat transfer and fluid flow in a cavity with different heat source location along upper wall is explored including middle, left and right. The results show that the trend and direction of vortex for natural convection with heat source applied on the left region of upper wall is different from that of heat source used on the right region of upper wall. Fluid flow with heat transfer is more intense and uniform near the solid-liquid interface with heat source in the middle of upper wall. The melting rate in case of middle heat source in upper wall is faster than other two cases and shape of solid-liquid front changes from curve into horizontal line gradually. When Fourier number Fo equals 80, the melted area is 4800 lu2 larger than that of two other cases.

Enhancement of nanoparticle-phase change material melting performance using a sinusoidal heat pipe

Thermal energy storage with an assisted-heat pipe has several useful applications in engineering fields. Due to the large latent heat and nearly constant melting temperature, phase change materials become attractive for thermal energy storage applications. Unfortunately, the low thermal conductivities of phase change materials become a significant issue which should be overcome to achieve high energy storage efficiency. In the current work, a novel sinusoidal heat pipe is designed instead of a circular heat pipe in order to accelerate the melting rate of nanoparticle-enhanced phase change material without affecting the thermal energy storage capacity of system. By developing an enthalpy-based immersed boundary-lattice Boltzmann method for the solid-liquid phase change phenomenon, the melting process of nanoparticle-enhanced phase change material with a sinusoidal heat pipe is investigated with respect to different heat pipe temperature, heat pipe undulation number and sinusoidal amplitude, nanoparticle volume fraction, and eccentric location of heat pipe. The results indicate that the energy storage rate of nanoparticle-enhanced phase change material is highly improved by applying a sinusoidal heat pipe because of its enlarged heat transfer area between heat transfer fluid and nanoparticle-enhanced phase change material. Furthermore, through an optimization study, it is found that applying a sinusoidal heat pipe with larger radius is more effective than adding high thermal conductivity nanoparticles into phase change material to enhance the thermal energy storage rate. Besides, the sinusoidal heat pipe with an eccentric location near the bottom of thermal energy storage cavity is highly recommended to realize a faster phase change material melting rate due to the enhanced effect of natural convective heat transfer.

Inconel 718 laser welding simulation tool based on a moving heat source and phase change

Modern aerospace industry demands the union of different Inconel 718 parts ensuring the quality of the joint. Therefore, in the present work a novel fiber laser welding model that considers wobbling strategy is developed. The heat source model definition and solid-liquid phase change phenomena are taken into account as bead is considered liquid zone during the melting, getting a robust-but-simple tool for prediction of bead and heat affected zone geometries depending on process parameters. One of the main drawbacks is the maximum welded bead width, which is limited by the beam spot. In order to overcome this handicap, wobbling strategy allows covering a wider area by combining elliptical and linear motions. Optimal relation between these orbital and translation speeds is defined for minimum overlap among consecutive wobble rings. Likewise, temperature rise at welded joint is estimated by existing and modified heat source models after relying on experimental validation.

The melting process of a freezing molten salt pipe of concentracted solar power plant

Concentrated solar power plants are potential to provide based load power of the future electrical power system. Commercial concentrated solar power plants using molten salt as the heat transfer fluid and the energy storage medium have been built and show great promising. However, due to high freezing point, the molten salt has a freezing possibility and may block the pipe. In practical, an electrical heat tracing is installed along the flow path of the molten salt to protect against freezing. Once the molten salt is freezing inside the pipe, the electrical heat tracing can be used to melt the molten salt. This paper studied the melting process of a molten salt (60% NaNO3 and 40% KNO3, referred to as Solar Salt) inside a horizontal pipe by an electrical heat tracing. The molten salt is a binary mixture, its freezing point (511 K) is higher than melting point (494 K). A solid-liquid mixture mushy zone exists between the melting point and the freezing point during the melting process. The enthalpy method was used to simulate the solid-liquid phase change phenomenon of the molten salt. The effect of the natural convection inside the pipe was also considerate. The effect of the installation position and the heating power of the electrical heat tracing on the melting process and the melting time were studied. During the heating process, the molten salt close to the electrical heat tracing melts first and forms a mushy zone. With the assistance of the natural convection, the molten salt in the mushy zone flows upward and gathers in the upper zone of the pipe. Thus, the upper zone of the pipe has a higher liquid fraction than the lower zone, which results in a liquid fraction gradient inside the pipe. The results show than the installation position of the electrical heat tracing effects the gradient of the liquid fraction during the melting process. The increase in the angle between the gravity and the installation position, γ , increases the liquid fraction gradient. It takes a same time to completely melt the molten salt when γ equals to 30° and 60°. When γ is 90°, due to a larger liquid fraction gradient, it needs more 5 min than γ is 60°. Therefore, large γ should be avoided for the practically installation of the electrical heat tracing. The results also show that the melting time is 165 min for a 35 W/m heating power, 85 min for 70 W/m, and 51 min for 140 W/m. Increasing the heating power from 35 W/m to 70 W/m can shorten 48.5% of the melting time, while increasing the heating power from 70 W/m to 140 W/m can only shorten 40% of the melting time. This is because a higher electrical heating power increases the liquid fraction gradient of the mushy zone during the melting process. Thus, the percentages of the shorten melting time decreases with the increases of the heating power. This study gives practical reference to the choose and the installation of the electrical heating tracing of the molten salt pipe.

Numerical Analysis of Cold Storage System with Array of Solid-Liquid Phase Change Module

This paper is the fundamental study for the application of cold storage system to the transportation equipment by sea and land. This numerical study presents the solid-liquid phase change phenomenon of calcium chloride solution of 30wt %. The governing equations are 1-dimensional unsteady state heat transfer equations of order partial differential equations. This type of latent heat storage material is often usable in fishery vessel for controlling the temperature of container with constant condition. The governing equation was discretized with finite difference method and the program was composed with Mathcad program. The main parameters of this solution were the initial temperature of heat storage material, ambient temperature of cold air and the velocity of cold air. The data of boundary layer thickness becomes thin with the increasing of cold air flowing velocity and also the heat storage completion time become shorten.

Lattice Boltzmann simulation for solid–liquid phase change phenomenon of phase change material under constant heat flux

Phase change material (PCM) is receiving significant attention for the ability of storing thermal energy in recent years. In order to better understand the heat and mass transfer of PCM during solid–liquid phase change process and then improve the application of PCM, in this paper, the solution of solid–liquid phase change problem of PCM is investigated by using lattice Boltzmann method (LBM). A thermal LB model for describing the solid–liquid phase change phenomenon has been established and verified by the solution of conduction phase change under constant heat flux. Three kinds of heat flux distribution on left wall have been investigated: uniform distribution, linear distribution and parabolic symmetry distribution. The simulation results showed that concentrating more energy on upper region of left wall can reinforce the clockwise convective circulation. More input energy concentrating on the middle of left wall is the effective way to accelerate the rate of solid–liquid phase change and maintain the temperature of PCM.

Numerical modeling for solid–liquid phase change phenomena in porous media: Shell-and-tube type latent heat thermal energy storage

In this paper, a numerical model is established to predict the phase change material (PCM) melting process in porous media. The heat transfer enhancement technique using metal foam in a shell-and-tube type latent heat thermal energy storage (LHTES) unit is investigated. The solid–liquid phase change phenomenon is solved with the enthalpy porosity theory. The computational fluid dynamic technology is adopted to predict the flow and heat transfer for the liquid PCM and heat transfer fluid (HTF). The appropriate source terms accounting for the pressure drop caused by the presence of solid PCM and porous media are added to the momentum equations. The solid–liquid interface position and the temperature distribution are predicted to describe the melting process. The effects of the structural parameters of porous media and the inlet conditions of HTF on the thermal characteristics of LHTES unit are analyzed. The numerical model can be further extended to investigate the thermal performance of different types of storage units in LHTES system.

A fast strategy for simulation of phase change phenomena at multiple length scales

Solid–liquid phase change phenomena are commonly encountered in many material processing operations, such as, crystal growth, casting, welding, laser processing, metal joining and so on. The physics of solid–liquid phase transition is highly complex involving many phenomena at many spatial and temporal scales, such as, fluid flow, heat transfer, undercooling, nucleation, atomic attachment and so on. Modeling of phenomena at a particular scale needs an appropriate computational strategy to capture the physics. In this paper, we present a brief overview on the various strategies for mathematical modeling of transport phenomena during solidification at macroscopic, mesoscopic and microscopic levels. This is followed by an algorithmic representation of an appropriate multiscale simulation strategy for solid–liquid phase change. At the macroscopic level, a modified mixture continuum model has been adopted where the turbulence fields have been appropriately modeled for evolution of solidification and coupled with the mass, momentum, energy and species conservation fields. At mesocopic level, transport phenomena within a grain envelope has been modeled following Rappaz and Thevoz. At microscopic level, the grain density, nucleation rate and the solidification path has been modeled with the help of a Gaussian distribution function, following Rappaz and Thevoz. A novel concept of fractal measure of the dendritic microstructure has been introduced and improved correlations for dendritic arm spacing and the permeability of the porous dendritic network have been derived and successfully validated with data from published literature for directional solidification of various alloy systems. The algorithm is arguably easier and faster to implement than other algorithms for macro–micro coupling published in the literature. The implementation of various aspects of this algorithm to problems of alloy solidification will be discussed elsewhere.

Mathematical model for turbulent flow, heat transfer, and solidification

AbstractA steady‐state, two‐dimensional numerical model has been used to describe coupled liquid steel's turbulent flow and heat transfer with solidification for Fe‐C binary alloy in a crystallizer of inverse casting. The solid‐liquid phase change phenomena have been modeled by using continuum formulations and considering the mushy zone as porous media. The turbulence flow in the crystallizer has been accounted for using a modified version of the low‐Reynolds‐number κ−ε turbulence model. The flow pattern in the liquid zone and the temperature distribution in the solid, mushy, and liquid regions have been predicted. The numerical analysis indicates that the residence time of the mother sheet in the crystallizer is one of the key parameters. The effects of some other main parameters on the solidification behavior have also been studied, such as the thickness and the initial temperature of the mother sheet, and the superheat degree of liquid steel. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 582–592, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10112

Numerical prediction of turbulent flow and heat transfer with phase change in crystallizer of inverse casting

A two-dimensional mathematical model has been undertaken to describe coupled liquid steel’s turbulent flow and heat transfer with solidification in the crystallizer of inverse casting. The solid-liquid phase change phenomena have been modeled by using the continuum formulations and considering the mush zone as porous media. The turbulence flow has been accounted for, using a modified version of the low-Reynolds-number k - ɛ turbulence model. A well-known numerical procedure, SIMPLE, has been used to solve the control equations. The effects of some main parameters on the solidification behavior have been studied, such as the casting speed, the thickness and the initial temperature of mother sheet, the superheat degree of liquid steel.

Modélisation par éléments finis d'écoulements à surface libre avec changement de phase solide-liquide

Industrial processes such as welding and mould casting generally involve flows with free surfaces and solid-liquid phase change phenomena. Computation of such processes requires front tracking Techniques. For that purpose we have develop an Eulerian finite element model which can deal with both kinds of interfaces (fluid-fluid, liquid-solid) on unstructured meshes. Then, In order to accurately take into account the material discontinuity through the fluid-fluid interface the mesh is locally adapted for the flow computation steps. Moreover, this interface mesh fitting allows us to easily include interfacial phenomena such as surface tension or radiative fluxes. On the other hand, the evolution of the phase change front is undertaken through an enthalpy formulation of the heat transfer problem. For most industrial applications, the phase change occurs over a finite temperature range, thus leading to a mushy region. So no mesh adaptation is required for this second type of interfaces. However, the governing flow equations must be modified in order to consider the porous nature of the material in the mushy region. The 2D numerical analysis of an electron beam welding process with our model is presented.

Numerical simulation of solid-liquid phase change phenomena

Abstract A two-dimensional numerical simulation of the thermal behaviour of a solid-liquid phase change material (PCM), confined in a rectangular domain, has been carried out. A numerical coupling between the PCM enclosure and two heat exchangers forming a thermal storage device has been made. The natural convection in the fluid and the conduction in the solid are both considered. The enthalpy-porosity approach proposed by Voller et al. has been applied to formulate the governing equations. A fixed grid and the semi-implicit method for pressure-linked equations consistent (SIMPLEC) are used to obtain the numerical solution of the governing equations. Numerical results corresponding to three different PCMs under different work conditions are presented. The numerical predictions have been compared with experimental data found in the literature.