Approximate analytical model for PCM solidification in a rectangular finned container with convective cooling boundaries

Thermal energy storage units that utilize latent heat storage materials have received increased attention in the recent years because of their relatively large heat storage capacities and isothermal behavior during charging and discharging. In this study, an analytical approach is presented for the prediction of temperature during the solidification in a two-dimensional rectangular latent heat storage using a phase change material (PCM) with internal plate fins. The basic energy equation is formulated accounting for the presence of a heat thermal fluid (HTF) on the walls. A two-dimensional numerical model is developed based on the enthalpy method to predict the distribution temperature of the fin and solid–liquid interface in storage. Results from the analytical solution and numerical model show a good agreement. The developed analytical model estimates satisfactorily the solidification time of PCM in storage, which is useful in the design of PCM-based thermal energy storages and cooling systems.     

Experimental and numerical investigation of thermal energy storage with a finned tube

A latent heat thermal energy storage system using a phase change material (PCM) is an efficient way of storing or releasing a large amount of heat during melting or solidification. It has been determined that the shell‐and‐tube type heat exchanger is the most promising device as a latent heat system that requires high efficiency for a minimum volume. In this type of heat exchanger, the PCM fills the annular shell space around the finned tube while the heat transfer fluid flows within the tube. One of the methods used for increasing the rate of energy storage is to increase the heat transfer surface area by employing finned surfaces. In this study, energy storage by phase change around a radially finned tube is investigated numerically and experimentally. The solution of the system consists of the solving governing equations for the heat transfer fluid (HTF), pipe wall and phase change material. Numerical simulations are performed to investigate the effect of several fin parameters (fin spacing and fin diameter) and flow parameter (Re number and inlet temperature of HTF) and compare with experimental results. The effect of each variable on energy storage and amount of solidification are presented graphically. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical and experimental investigation for heat transfer in triplex concentric tube with phase change material for thermal energy storage

This paper addresses a numerical and experimental investigation of a thermal energy storage unit involving phase change process dominated by heat conduction. The thermal energy storage unit involves a triplex concentric tube with phase change material (PCM) filling in the middle channel, with hot heat transfer fluid (HHTF) flowing outer channel during charging process and cold heat transfer fluid (CHTF) flowing inner channel during discharging process. A simple numerical method according to conversation of energy, called temperature & thermal resistance iteration method has been developed for the analysis of PCM solidification and melting in the triplex concentric tube. To test the physical validity of the numerical results, an experimental apparatus has been designed and built by which the effect of the inlet temperature and the flow rate of heat transfer fluid (HTF, including HHTF and CHTF) on the thermal energy storage has been studied. Comparison between the numerical predictions and the experimental data shows good agreement. Graphical results including fluid temperature and interface of solid and liquid phase of PCM versus time and axial position, time-wise variation of energy stored/released by the system were presented and discussed.     

Thermal Performance of a Phase Change Material‐Based Latent Heat Thermal Storage Unit

An experimental analysis is presented to establish the thermal performance of a latent heat thermal storage (LHTS) unit. Paraffin is used as the phase change material (PCM) on the shell side of the shell and tube‐type LHTS unit while water is used as the heat transfer fluid (HTF) flowing through the inner tube. The fluid inlet temperature and the mass flow rate of HTF are varied and the temperature distribution of paraffin in the shell side is measured along the radial and axial direction during melting and solidification process. The total melting time is established for different mass flow rates and fluid inlet temperature of HTF. The motion of the solid–liquid interface of the PCM with time along axial and radial direction of the test unit is critically evaluated. The experimental results indicate that the melting front moves from top to bottom along the axial direction while the solidification front moves only in the radial direction. The total melting time of PCM increases as the mass flow rate and inlet temperature of HTF decreases. A correlation is proposed for the dimensionless melting time in terms of Reynolds number and Stefan number of HTF. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21120     

Experimental and numerical study on charging processes of an ice‐on‐coil thermal energy storage system

In this study, an external melt ice‐on‐coil thermal storage was studied and tested over various inlet conditions of secondary fluid—glycol solution—flow rate and temperature in charging process. Experiments were conducted to investigate the effect of inlet conditions of secondary fluid and validate the numerical model predictions on ice‐on‐coil thermal energy storage system. The total thermal storage energy and the heat transfer rate in the system were investigated in the range of 10 l min ^?1?V??60 l min ^?1. A new numerical model based on temperature transforming method for phase change material (PCM) described by Faghri was developed to solve the problem of the system consisting of governing equations for the heat transfer fluid, pipe wall and PCM. Numerical simulations were performed to investigate the effect of working conditions of secondary fluid and these were compared with the experimental results. The numerical results verified with experimental investigation show that the stored energy rises with increasing flow rate a decreasing tendency. It is also observed that the inlet temperature of the fluid has more influence on energy storage quantity than flow rate. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical simulation of high‐temperature phase change heat storage system

In this paper, numerical results pertaining to cyclic melting and freezing of an encapsulated phase‐change material (PCM) have been reported. The cyclic nature of the present problem is relevant to latent heat thermal energy storage system used to power solar Brayton engines in space. In particular, a physical and numerical model of the single‐tube phase change heat storage system was developed. A high‐temperature eutectic mixture of LiF‐CaF₂ was used as the PCM and dry air was used as the working fluid. Numerical results were compared with available experimental data. The trends were in close agreement. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 32–41, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10132     

An experimental and numerical investigation of heat transfer during technical grade paraffin melting and solidification in a shell-and-tube latent thermal energy storage unit

The latent thermal energy storage system of the shell-and-tube type during charging and discharging has been analysed in this paper. An experimental and numerical investigation of transient forced convective heat transfer between the heat transfer fluid (HTF) with moderate Prandtl numbers and the tube wall, heat conduction through the wall and solid–liquid phase change of the phase change material (PCM), based on the enthalpy formulation, has been presented. A fully implicit two-dimensional control volume Fortran computer code, with algorithm for non-isothermal phase transition, has been developed for the solution of the corresponding mathematical model. The comparison between numerical predictions and experimental data shows good agreement for both paraffin non-isothermal melting and isothermal solidification. In order to provide guidelines for system performance and design optimisation, unsteady temperature distributions of the HTF, tube wall and the PCM have been obtained by a series of numerical calculations for various HTF working conditions and various geometric parameters, and the thermal behaviour of the latent thermal energy storage unit during charging and discharging has been simulated.     

Thermal performance of myristic acid as a phase change material for energy storage application

Thermal performance and phase change stability of myristic acid as a latent heat energy storage material has been studied experimentally. In the experimental study, the thermal performance and heat transfer characteristics of the myristic acid were tested and compared with other studies given in the literature. In the present study is included some parameters such as transition times, temperature range, and propagation of the solid–liquid interface as well as heat flow rate effect on the phase change stability of myristic acid as a phase change material (PCM). The experimental results showed that the melting stability of the PCM is better in the radial direction than the axial direction. The variety of the melting and solidification parameters of the PCM with the change of inlet water temperature is also studied. The results show that the better stability of the myristic acid was accomplished at low inlet water temperature compared with the obtained results at high inlet water temperature. We also observed that while the heat exchanger tube is in the horizontal position, the PCM has more effective and steady phase change characteristics than in the vertical position. The heat storage capacity of the container (PCM tube) is not as good as we expected in this study and the average heat storage efficiency (or heat exchanger effectiveness) is 54%. It means that 46% of the heat acrually lost somewhere.     

管内流体流动管外PCM发生相变的贮能系统热性能研究

建立了分析空调贮能系统中管内流体流动管外PCM发生相变的相变的贮能器热性能的数学模型，并进行了数值计算。其中，把传热流体看作是沿轴向的—维无粘流动，对PCM相变过程的求解用显热容法。计算结果与文献中的计算结果吻合较好。所得结论对该类贮能系统的设计和性能优化有一定指导作用。     

Numerical simulation of a multi-layer latent heat thermal energy storage system

A computational model for the prediction of the thermal behaviour of a compact multi-layer latent heat storage unit is presented. The model is based on the conservation equations of energy for the phase change material (PCM) and the heat transfer fluid (HTF). Electrical heat sources embedded inside the PCM are used for heat storage (melting) while the flow of an HTF is employed for heat recovery (solidification). Parametric studies are performed to assess the effect of various design parameters and operating conditions on the thermal behaviour of the unit. Results indicate that the average output heat load during the recovery period is strongly dependent on the minimum operating temperature, on the thermal diffusivity of the liquid phase, on the thickness of the PCM layer and on the HTF inlet mass flowrate and temperature. It is, on the other hand, nearly independent of the wall thermal diffusivity and thickness and of the maximum operating temperature. Correlations are proposed for the total energy stored and the output heat load as a function of the design parameters and the operating conditions. © 1998 John Wiley & Sons, Ltd.     

Solidification process analysis of a heat storage device containing graphite foam and paraffin

石蜡相变材料的导热系数较小,严重影响了其传热速率和凝固速率。通过对填充石墨泡沫/石蜡的储能系统进行凝固过程的模拟,确定了石墨泡沫对相变储能系统性能的影响。研究结果表明石墨泡沫不仅大大缩短了相变凝固时间,也使储能系统的温度分布更加均匀;通过分析冷却水进口速度和温度对复合相变材料的凝固过程的影响,说明随着冷却水进口速度的增大和温度的降低,传热速率加快,凝固时间缩短。分析了复合材料相变区的自然对流对相变过程的影响,模拟结果证明自然对流能在一定程度上加快相变材料的凝固过程。     

Analytical solution of heat transfer in a shell-and-tube latent thermal energy storage system

An analytical solution of a latent heat storage unit (LHSU) consisting of a shell-and tube was obtained by using the Exponential Integral Function and the variables separation technique. The working fluid (water) circulating by forced convection inside the inner tube charges and discharges the storage unit. The comparison between analytical predictions and experimental data shows good agreement. Extensive parametric studies were conducted in order to examine the effect of the pertinent parameters (such as natural convection, mass flow rate of HTF, outer tube radius, pipe length etc.) on the melting and solidification processes of paraffin as a PCM. In order to provide guidelines for system performance and design optimisation, unsteady temperature distributions within PCM during melting/solidification, energy stored, position of moving interface and thermal efficiency have been obtained by a series of numerical calculations and represented graphically.     

Channel formation and visualization of melting and crystallization behaviors in direct-contact latent heat storage systems

Thermal storage systems are an essential component for increasing the share of renewable energies in residential heating and for the valorization of waste heat. A key challenge for the widespread application of thermal storage systems is their limited power-to-capacity ratio. One potential solution for this challenge is represented by direct-contact latent heat storage systems, in which a phase change material (PCM) is in direct contact with an immiscible heat transfer fluid (HTF). To demonstrate the applicability of the direct-contact concept for domestic hot water production, a PCM with a phase change temperature of 59°C is chosen. To enable cost-efficient implementation of the storage system, a eutectic mixture of two salt hydrates, magnesium chloride hexahydrate and magnesium nitrate hexahydrate, is chosen as the PCM. One key aspect for the direct-contact concept is that, during discharge, the HTF channels in the PCM do not become clogged during the solidification of the PCM. In this study, the formation and topology of the channels in direct-contact systems under an optimized flow condition are investigated via visual observation and X-ray computed tomography. The elucidation of the channel structure provides information on the melting and crystallization behaviors of the PCM, which are shown schematically.     

An experimental optimization study on a tube-in-shell latent heat storage

Thermal energy storage (TES) using phase change materials (PCMs) has recently received considerable attention in the literature, due to its high storage capacity and isothermal behaviour during the storage (melting or charging) and removal (discharging or solidification). In this study, a novel modification on a tube-in-shell-type storage geometry is suggested. In the proposed geometry, the outer surface of the shell is inclined and it is the objective of this study to determine the optimum range for the inclination angle of the shell surface. Paraffin with a melting temperature of 58.06°C, which is supplied by the Merck Company, is used as the PCM. The PCM is stored in the vertical annular space between an inner tube through which the heat transfer fluid (HTF), hot water, is flowing and a concentrically placed outer shell. At first, the thermophysical properties of this paraffin are determined through the differential scanning calorimeter (DSC) analysis. Temporal behaviour of the PCM undergoing a non-isothermal solid–liquid phase change during its melting or charging by the HTF are determined for different values of the inlet temperature and the mass flow rate of the HTF. The new geometry is shown to respond well with the melting characteristics of the PCM and to enhance heat transfer inside the PCM for a specific range of the shell inclination angle. Copyright © 2006 John Wiley & Sons, Ltd.     

Phase change and heat transfer characteristics of a eutectic mixture of palmitic and stearic acids as PCM in a latent heat storage system

The phase change and heat transfer characteristics of a eutectic mixture of palmitic and stearic acids as phase change material (PCM) during the melting and solidification processes were determined experimentally in a vertical two concentric pipes energy storage system. This study deals with three important subjects. First is determination of the eutectic composition ratio of the palmitic acid (PA) and stearic acid (SA) binary system and measurement of its thermophysical properties by differential scanning calorimetry (DSC). Second is establishment of the phase transition characteristics of the mixture, such as the total melting and solidification temperatures and times, the heat transfer modes in the melted and solidified PCM and the effect of Reynolds and Stefan numbers as initial heat transfer fluid (HTF) conditions on the phase transition behaviors. Third is calculation of the heat transfer coefficients between the outside wall of the HTF pipe and the PCM, the heat recovery rates and heat fractions during the phase change processes of the mixture and also discussion of the effect of the inlet HTF parameters on these characteristics. The DSC results showed that the PA–SA binary system in the mixture ratio of 64.2:35.8 wt% forms a eutectic, which melts at 52.3 °C and has a latent heat of 181.7 J g⁻¹, and thus, these properties make it a suitable PCM for passive solar space heating and domestic water heating applications with respect to climate conditions. The experimental results also indicated that the eutectic mixture of PA–SA encapsulated in the annulus of concentric double pipes has good phase change and heat transfer characteristics during the melting and solidification processes, and it is an attractive candidate as a potential PCM for heat storage in latent heat thermal energy storage systems.     

Medium‐ and high‐temperature latent heat thermal energy storage: Material database,system review,and corrosivity assessment

Latent heat thermal energy storage refers to the storage and recovery of the latent heat during the melting/solidification process of a phase change material (PCM). Among various PCMs, medium‐ and high‐temperature candidates are attractive due to their high energy storage densities and the potentials in achieving high round trip efficiency. Although a few review studies on high‐temperature PCMs have emerged in the past few years, the quantity, completeness, and accuracy of the presented data are relatively poor. Also, an efficient indexing methodology for retrieving useful PCM data is missing in the open literature. In this article, we created an up‐to‐date PCM database following a holistic review of the PCMs in medium‐ and high‐temperature applications over a temperature range of 100°C to 1680°C. Such effort then allows us to develop an accurate indexing tool for the fast selection of suitable PCM candidates and extraction of the related property data. More specifically, the created PCM database covers 496 entries of PCM materials, which are extracted from the scattered research works published during the year 1956 to 2017. The collected information includes both the basic thermo‐physical properties of PCMs (eg, melting temperature, heat of fusion, and thermal conductivity) and crucial design factors during construction and engineering phases (eg, energy storage density, volume expansion, liquid/solid densities, and cost). The reviewed PCMs comprise a wide variety of materials, including fluorides, chlorides, hydrates, nitrates, carbonates, metals and alloys, and other uncommon compounds and salts. In addition, the current work presents a brief review on high‐temperature latent heat thermal energy storage systems categorized into metallic and non‐metallic systems. The corrosivity and stability of PCMs, which are commonly ignored in previous studies, are also examined.     

三套管式相变蓄热器强化传热研究

基于三套管式相变蓄热器的特点,提出应用T字形翅片来强化相变蓄热器的传热性能。研究结果表明:添加翅片可有效地降低蓄热器中相变材料的凝固和融化时间,直翅片和T字形翅片的混合强化结构能使凝固过程比未强化结构节省74%的时间,使融化过程节省60%的时间。因此直翅片和T字形翅片的混合使用可以达到进一步强化传热的目的。     

Thermal Energy Storage Performance of Fatty Acids as a Phase Change Material

Thermal energy storage performance of fatty acids and a eutectic mixture as phase change materials (PCMs) has been investigated experimentally. The selected PCMs for this study were palmitic acid, myristic acid, stearic acid, and a mixture of stearic and myristic acids in eutectic combination ratio of 65.7 wt% myristic acid and 34.3 wt% stearic acid. The PCMs have a melting temperature range of 50.0°C to 61.20°C and a latent heat range of 162.0 J/g to 204.5 J/g. The inlet temperature and the mass flow rate of heat transfer fluid (HTF) were selected as experimental parameters to test the thermal energy storage performance of the PCMs. The transition times, temperature range, propagation of the solid-liquid interface, as well as heat flow rate characteristics of the employed cylindrical tube storage system were studied at varied experimental parameters. The experimental results show that the melting front moves to inward in the radial directions as well as in the axial directions from the top toward to the bottom of the PCM tube. It was observed that the convection heat transfer in the liquid phase plays an important role in the melting process. The changes in the studied HTF parameters have more effect on the melting processes than the solidification processes of the PCMs. The average heat storage efficiency calculated from data for all the PCMs is 51.5%, meaning that 48.5% of the heat actually was lost somewhere.     

Experimental analysis and numerical modelling of inward solidification on a finned vertical tube for a latent heat storage unit

The enhancement of heat transfer in a thermal storage system consisting of a cylindrical vertical tube with internal longitudinal fin arrangement is discussed in this paper. This configuration that forms a V-shaped enclosure for the phase change material (PCM) gives maximum benefit to the fin arrangement. A theoretical model that also accounts for the circumferential heat flow through the tube wall is developed using enthalpy formulation and is employed in conjunction with the fully implicit finite difference method to solve the solidification in the convectively cooled vertical tube. A generalised enthalpy-temperature (H-T) relationship, developed by Date, is suitable for constant phase change temperature and this is modified in the present work to accommodate materials having either constant or a range of phase change temperatures. The numerical model is validated with experimental data. The instantaneous surface heat flux and the solidified fraction for different number of fins and tube radii, that are of interest for the design of latent heat thermal storage system consisting of an array of vertical cylindrical tubes containing PCM inside it, are also discussed in this article.     

Fluid flow and heat transfer in PCM panels arranged vertically and horizontally for application in heating systems

The rectangular panel is within the most common geometries in phase change materials (PCM). Nevertheless, there is a lack of knowledge regarding how the arrangement (vertical or horizontal) and thickness affect heat flux and phase change duration. Such knowledge would be very helpful both in the design of PCM heat exchangers. This paper studies the behavior of the RT60 paraffin, Pr ≈ 330, phase change temperature between 53 and 61 °C; and the fatty acid Palmitic Acid, Pr ≈ 110, phase change temperature of 65 °C. Parametric studies analyzing the influence of: temperature of the walls (5 × 10⁵ < Ra ≤ 2 × 10⁶), phase change processes (melting and solidification), panel position and PCM thickness (aspect ratio1/20 and 3/20) are performed. The flow behavior is analyzed over time using velocity plots and volumetric liquid fraction contours. The formation of Bénard cells and their evolution is described. Free convection dependence of dimensionless string function and Rayleigh number is discussed. Free convection during melting for horizontal panels becomes very important and the mean heat fluxes increase up to twofold compared to vertical panels. For solidification, however, conduction becomes more relevant. The importance of both mechanisms is highlighted by calculating heat transfer rates.