Thermal response of a packed bed of spheres containing a phase-change material

A computational model of the transient thermal response of a packed bed of spheres containing a phase-change material (PCM) is presented. A one-dimensional separate phases formulation is used to develop a numerical analysis of the dynamic response of the bed which is subject to the flow of a heat transfer fluid, for arbitrary initial conditions and inlet fluid temperature temporal variations. Phase-change models are developed for both isothermal and nonisothermal melting behaviours. Axial thermal dispersion effects are modelled, including intraparticle conduction (Biot number) effects. Regenerative thermal storage applications involve flow reversals to recover the stored energy; this aspect of operation is included in the present model. Results from the model for a commercial sized thermal storage bed for both the energy storage and recovery periods are presented. Experimental measurements of transient temperature distributions in a randomly packed bed of uniform spheres containing a PCM for a step-change in inlet air temperature are reported for a range of Reynolds number.     

An Analytical Technique of Transient Phase-Change Material Melting Calculation for Cylindrical and Tubular Containers

In this study, an analytical model for a class of heat storage that utilizes latent heat of a phase-change material (PCM) is developed. Two basic shell-and-tube configurations are considered, one in which the PCM melts inside the tubes while the heat transfer fluid (HTF) flows in the shell along it, and the other in which HTF flows inside the tubes while PCM melts outside. A system of partial differential equations, which describes heat transfer and melting of the PCM and heat transfer in the HTF, is derived with some simplifying assumptions, while still capturing and preserving the essential features of the processes involved. These equations are solved analytically, yielding the overall heat exchange parameters, like instantaneous heat transfer rate, stored energy, and overall operation time of the system. The present work shows that the use of the proposed analytical technique and its modifications for the practical PCM arrangements is beneficial. Proper application of the model makes it possible to obtain the parameters of a real PCM melting process in the form of algebraic formulas, both for the transient values of variables over time, and for the overall process characteristics. A comparison with the results of numerical calculations of transient melting, made using computational fluid dynamics, confirms the validity of analytical findings and allows to assess the degree of accuracy of the results of our analytical method in various practical cases.     

Numerical analysis on the thermal behavior of high temperature latent heat thermal energy storage system

High temperature latent heat thermal energy storage technology is a promising option for future cost reduction in parabolic trough or tower power plant. However, low thermal conductivity of phase-change material (PCM) is the major shortage of latent heat thermal energy storage. This paper proposed a new thermal energy storage system (TESS) that metal foam and fins were used to enhance the effective conductivity of PCM. Three-dimensional physical model was established for representative element extracted from TESS. Considering the natural convection in the liquid part of PCM, volume-averaged mass and momentum equations were employed with the Brinkman–Forchheimer extension to Darcy law to simulate the porous resistance. A local thermal equilibrium model was developed to obtain temperature field. The governing equations were solved with finite-volume approach and enthalpy method was employed to account for phase change. The model was firstly validated against low temperature experiments from the literature and then used to predict the charging and discharging behavior of the present TESS. The position of solid/liquid interface was explored and the effects of design parameters, including that of metal foam pore density and porosity, configuration of fin and Rayleigh number, on melting and solidifying rate and energy stored in each time step were revealed and discussed. The results indicate that metal foam and fins can effectively improve the heat transfer performance for thermal storage system and decrease charging and discharging time.     

Thermal radiation effects in phase-change energy-storage systems

A numerical model was developed to determine the transient temperature distribution, solid/liquid interface location, and energy-storage capacity of a semi-transparent phase-change medium. The medium is bounded between two concentric cylinders and internal energy transfer occurs simultaneously by conduction and thermal radiation. The radiation transport equation was coupled with the energy equation; both enthalpy and temperature were employed as dependent variables. The spherical harmonic approximation (P-N approximation) was used to obtain solutions for the radiative heat flux. The coupled conservation of energy and moment differential equations were solved by using iterative numerical finite-difference schemes with appropriate thermal and radiant boundary and interface conditions. The numerical model was used to study the effects of radiation on solidification (melting), transient temperature distribution and energy-storage capacity of an absorbing, emitting, and isotropically scattering, semi-transparent, gray medium contained in a cylindrical annulus. The results increase our understanding of internal energy transfer and show the effects of optical properties, conduction/radiation parameter, and geometric dimensions and should lead to better designs and optimization of phase-change energy-storage systems.     

高温肋板式蓄热器蓄/放热特性的数值模拟

采用计算流体动力学方法对高温不锈钢肋板式相变蓄热器的蓄/放热特性进行了数值模拟。分析了多孔肋片和锯齿肋片对蓄热器蓄/放热特性的影响以及载热体入口温度和流量对相变材料熔化和凝固速度的影响,计算结果表明:在该新型肋板式相变蓄热器中,多孔翅片的性能优于锯齿肋片;随着蓄热器传热温差的增大和载热体流量的增加,蓄热器的蓄/放热性能越好;肋片作为换热元件可以很好的提高蓄热器的蓄/放热性能。所得结论可为高温肋板式蓄热器的优化设计提供有益的参考。     

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.     

Exergy analysis of latent heat storage systems with sensible heating and subcooling of PCM

The effect of sensible heating of the phase-change material (PCM) before melting and subcooling after solidification, on the performance of the latent heat storage system (LHSS), is studied in terms of first- and second-law efficiencies for the overall charge–discharge cycle. The external heat transfer irreversibilities on account of the interaction between the heat transfer fluid and the storage element are characterized and the optimum phase-change temperature for maximum second-law efficiency is studied. The performance of the LHSS operation is assessed with and without sensible heating before melting and subcooling after solidification. It is observed that the optimum phase-change temperature is higher, and, the overall second-law efficiency is greater for LHSS with sensible heating and subcooling beyond a certain phase-change temperature compared to latent heat storage alone. In addition, the first-law overall efficiency is found to exhibit a minimum and a pre-heated discharge stream is shown to result in a substantial improvement of the second-law efficiency. © 1998 John Wiley & Sons, Ltd.     

Performance analysis of phase-change material storage unit for both heating and cooling of buildings

Utilisation of solar energy and the night ambient (cool) temperatures are the passive ways of heating and cooling of buildings. Intermittent and time-dependent nature of these sources makes thermal energy storage vital for efficient and continuous operation of these heating and cooling techniques. Latent heat thermal energy storage by phase-change materials (PCMs) is preferred over other storage techniques due to its high-energy storage density and isothermal storage process. The current study was aimed to evaluate the performance of the air-based PCM storage unit utilising solar energy and cool ambient night temperatures for comfort heating and cooling of a building in dry-cold and dry-hot climates. The performance of the studied PCM storage unit was maximised when the melting point of the PCM was ～29°C in summer and 21°C during winter season. The appropriate melting point was ～27.5°C for all-the-year-round performance. At lower melting points than 27.5°C, declination in the cooling capacity of the storage unit was more profound as compared to the improvement in the heating capacity. Also, it was concluded that the melting point of the PCM that provided maximum cooling during summer season could be used for winter heating also but not vice versa.     

Heat Transfer Enhancement for PCM Thermal Energy Storage in Triplex Tube Heat Exchanger

Thermal energy storage is critical for reducing the discrepancy between energy supply and energy demand, as well as for improving the efficiency of solar thermal energy systems. Among the different types of thermal energy storage, phase-change materials (PCM) thermal energy storage has gained significant attention recently because of its high energy density per unit mass/volume at nearly constant temperature. This study experimentally investigates the using of a triplex tube heat exchanger (TTHX) with PCM in the middle tube as the thermal energy storage to power a liquid desiccant air-conditioning system. Four longitudinal fins were welded to each of the inner and middle tubes as a heat transfer enhancement in the TTHX to improve the thermal performance of the thermal energy storage. The average temperature of the PCM during the melting process in the TTHX with and without fins was compared. The PCM temperature gradients in the angular direction were analyzed to study the effect of the natural convection in the melting process of the thermal storage. The energy storage efficiency of the TTHX was determined. Results indicated that there was a considerable enhancement in the melting rate by using fins in the TTHX thermal storage. The PCM melting time is reduced to 86% by increasing of the inlet heat transfer fluid. The average heat storage efficiency calculated from experimental data for all the PCMs is 71.8%, meaning that 28.2% of the heat actually was lost.     

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.     

HEAT TRANSFER ENHANCEMENT IN A LATENT HEAT STORAGE SYSTEM

Commercial acceptance and the economics of solar thermal technologies are tied to the design and development of efficient, cost-effective thermal storage systems. Thermal storage units that utilize latent heat storage materials have received greater attention in the recent years because of their large heat storage capacity and their isothermal behavior during the charging and discharging processes. One major issue that needs to be addressed is that most phase-change materials (PCM) with high energy storage density have an unacceptably low thermal conductivity and hence heat transfer enhancement techniques are required for any latent heat thermal storage (LHTS) applications. In the present paper the various heat transfer enhancement methods for LHTS systems are discussed. Three different experiments to augment heat transfer were conducted and the findings are reported.     

增强石蜡相变材料传热性能的实验研究

添加高导热颗粒和增大换热面积是当前增强石蜡相变材料传热性能的主要研究方向。以此为基础搭建试验台结合数据采集系统对石蜡在圆管外的熔化凝固过程进行了实验测试,并对各测点的温度变化趋势进行分析,研究了添加不同纳米颗粒和加入金属肋片对换热过程的影响。结果表明:在石蜡溶液中添加纳米颗粒能够起到减小过冷度的效果同时有效增强相变材料的传热性能,添加纳米氧化铜颗粒的传热性能增强效果要优于添加氧化锌颗粒和二氧化硅颗粒;在储热系统中加入肋片能够显著提高相变储能系统的热性能,强化换热过程。     

Phase-change heat transfer during cyclic heating and cooling with internal radiation and temperature-dependent properties

This paper contains the results of a numerical investigation of the effects of internal radiation on heat transfer during cyclic heating and cooling of a phase-change energy–storage system. The effects of internal radiation, temperature distribution and energy stored and extracted were investigated. An absorbing, emitting, and isotropically scattering, finite, and semi-transparent, gray, phase-change medium bounded between two concentric cylinders was studied. The phase-change medium was a fluoride salt with LiF (41.27%), MgF₂ (48.76%) and KF (8.95% by weight). Radiative heat transfer affects the dynamics of phase changes significantly for low values of the conduction–radiation interaction parameter.     

相变蓄热式家用太阳热水系统国外研究进展

综述了国外相变蓄热材料在家用太阳热水系统中的应用研究进展情况;指出相变蓄热材料的应用可以提高系统的集热效率;能量蓄积密度和太阳能保证率。材料的性质（如导热系数、熔点、比热容,相变潜热、密度等）、设计参数（蓄热材料的体积、换热管的数量和位置）以及材料的包装方式（形状和大小）影响系统性能（包括效率、出水温度、热水可用时间、热损及蓄放热速率）。     

Laminar film condensation driven latent thermal energy storage in rectangular containers

This paper focuses on numerically analyzing the thermal transport phenomena in the transient conjugate problem of melting and laminar film condensation. The key focus is to identify an optimum container aspect ratio/shape and conditions for which the heat storage time and the storage capacity are minimum and maximum respectively. Since most solid–liquid phase change materials (PCMs) suffer from poor thermal conductivities, the major resistance to heat transfer comes from PCM. Hence, high thermal conductivity, low-cost metal foam is suggested for use along with PCM to minimize this resistance. The conjugate transient problem of film condensation driven solid–liquid phase change of PCM impregnated inside porous metal foam is numerically analyzed. An effective heat capacity formulation is employed for modeling the transient PCM phase change in porous foam and is solved using finite element method. It is coupled with laminar film condensation on the outside of the storage container. The model is then used for selecting the best aspect ratio for thermal energy storage (TES) containers that enables to store comparatively the maximum heat. The results of the developed model showed that the major resistance to heat transfer and hence efficient thermal energy storage depends strongly on the aspect ratio of the PCM storage containers.     

Enhanced thermal performance analysis of buried heat transfer tubes thermal storage system filled with microcapsule particles

The heat transfer enhancement performance of a phase change buried tubes thermal storage system is influenced by major parameters such as arrangement of heat transfer tubes, fin structure and fin geometry size. We developed a three-dimensional numerical model with two different arrangements and five different enhanced heat transfer structures respectively. For the sake of analysis the effects of arrangement of heat transfer tubes, fin structure and fin geometry size. In addition, we applied the enthalpy-transforming model to obtain the liquid fraction and location of the solid-liquid interface at different time in the phase change process. The numerical results show that the melting time of the thermal storage system model with a triangle arrangement is about 6.1% longer than that of the model with a square arrangement. Besides, the melting time of the model with 55 mm tube pitch is about 16.7% shorter than that of tube pitch with 60 mm. Moreover, the buried tube thermal storage system models with circle fins have the shortest melting time, which is 18 seconds. Melting time of the model with circle fins is about 40% shorter than that of the model with smooth tube. In addition, the melting time of the model with 3 mm fin thickness is 10 seconds, which is the shortest. The model with thicker fins means the shorter time of melting process. Moreover, the melting time of the model with 10.5 mm fin spacing is about 23.5% shorter than that of the model with 12.5 mm fin spacing, which is 13 seconds. In conclusion, the main factor of the melting time is the heat transfer area. It provides a guidance for the design and reconstruction of the type of heat storage structure.     

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.     

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.     

考虑热惯性的居民楼宇综合能源系统日前运行优化

针对居民楼宇中部分热负荷的热惯性特征,提出了一种考虑热惯性的居民楼宇综合能源系统日前运行优化方法。首先,建立了居民楼宇综合能源系统的典型结构和数学模型,探究能源供给、转换、分配、存储的机理;其次,基于线性能量平衡法,采用微分方程描述楼宇制冷采暖系统和生活热水系统的热惯性特征,并将上述方程差分化;再次,以综合成本最小为目标,考虑购能约束、功率平衡约束、热惯性约束、备用容量约束等,建立日前运行优化模型,并将上述模型转化为混合整数二次规划,通过Yalmip调用Cplex求解;最后,通过实际算例分析热惯性对居民楼宇综合能源系统运行优化的影响。结果表明,利用热惯性能够对冷热负荷进行平移或削减,从而降低运行成本。     

Melting in Cylindrical Enclosures: Numerical Modeling and Heat Transfer Correlations

A finite volume model for analyzing melting with natural convection in vertical cylindrical enclosures is developed. The model is verified through detailed comparison with previous experimental and numerical results. Based on the modeling results of outward melting around isothermal cylinders, correlations for the transient heat transfer rate and the total thermal energy stored in the melt are proposed for a wide range of Rayleigh numbers and several representative aspect ratios. Furthermore, a theoretical relationship between the latent energy storage and the total thermal energy storage in the melt is derived and shown to agree well with the numerical results.