Numerical heat transfer analysis of the packed bed latent heat storage system based on an effective packed bed model

Due to the complexity of the fluid flow and heat transfer in packed bed latent thermal energy storage (LTES) systems, many hypotheses were introduced into the previous packed bed models, which consequently influenced the accuracy and authenticity of the numerical calculation. An effective packed bed model was therefore developed, which could investigate the flow field as the fluid flows through the voids of the phase change material (PCM), and at the same time could account for the thermal gradients inside the PCM spheres. The proposed packed bed model was validated experimentally and found to accurately describe the thermo-fluidic phenomena during heat storage and retrieval. The proposed model was then used to do a parametric study on the influence of the arrangement of the PCM spheres and encapsulation of PCM on the heat transfer performance of LTES bed, which was difficult to perform with the previous packed bed models. The results indicated that random packing is more favorable for heat storage and retrieval as compared to special packing; both the material and the thickness of the encapsulation have the apparent effects on the heat transfer performance of the LTES bed.     

柱状颗粒填充床的储能性能分析

填充床储能是一种很有发展前景的热能储存技术,它具有可降低存储成本和提高太阳能热系统开发效率等优点。研究人员多采用球形的储能单元,而圆柱体在储能填充床换热中有其独特的优势,因此基于圆柱形和拉西环形两种柱状颗粒,建立了一种潜热储能填充床的三维模型,采用数值模拟的方法分别研究两种柱状颗粒组成的填充床的储能性能,分析了储能填充床的直径比对其性能的影响。研究表明,填充床直径比越大,其储能性能越好。同时研究了圆柱形储能单元高度和拉西环形储能单元孔径对储能性能的影响。结果表明,在研究范围内,由高度为3 mm的圆柱形储能单元和孔半径1.50 mm的储能单元分别组成的填充床储能速率最高。     

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.     

Granular phase change materials for thermal energy storage: Experiments and numerical simulations

The present paper reports on the utilization of granular phase change composites (GPCC) of small particle diameter (1–3 mm) in latent heat thermal energy storage (LHTES) systems. The phase changing parameters (phase change temperature, latent heat, and energy storage capacity) of GPCC have been determined using differential scanning calorimeter (DSC) and temperature-history methods. Further analysis of measurement results has been conducted to describe the evolution of latent heat with temperature during phase change in terms of liquid fraction–temperature relationships. Charging and discharging packed bed column experiments have been also carried out for different operating conditions to analyze the potential of GPCC for packed bed thermal energy storage. The present column results clearly demonstrate the dependence of temperature variation along the packed bed and the overall performance of the storage unit on the phase change characteristics of GPCC. Small and non-uniform particles diameters of GPCC and heterogeneity of the bed material complicate the phenomena of heat transfer and evolution of latent heat in the packed bed. Mathematical modeling of the packed bed that considers the GPCC and air as two separate phases with inter-phase heat transfer is presented. Comparisons between experimental and numerical results are used to evaluate the sensitivity of numerical simulations to different model parameters.     

Numerical analysis of latent heat thermal energy storage using encapsulated phase change material for solar thermal power plant

Thermal energy storage improves the load stability and efficiency of solar thermal power plants by reducing fluctuations and intermittency inherent to solar radiation. This paper presents a numerical study on the transient response of packed bed latent heat thermal energy storage system in removing fluctuations in the heat transfer fluid (HTF) temperature during the charging and discharging period. The packed bed consisting of spherical shaped encapsulated phase change materials (PCMs) is integrated in an organic Rankine cycle-based solar thermal power plant for electricity generation. A comprehensive numerical model is developed using flow equations for HTF and two-temperature non-equilibrium energy equation for heat transfer, coupled with enthalpy method to account for phase change in PCM. Systematic parametric studies are performed to understand the effect of mass flow rate, inlet charging system, storage system dimension and encapsulation of the shell diameter on the dynamic behaviour of the storage system. The overall effectiveness and transient temperature difference in HTF temperature in a cycle are computed for different geometrical and operational parameters to evaluate the system performance. It is found that the ability of the latent heat thermal energy storage system to store and release energy is significantly improved by increasing mass flow rate and inlet charging temperature. The transient variation in the HTF temperature can be effectively reduced by decreasing porosity.     

两级填充床蓄热器式绝热压缩空气储能系统变工况特性研究

利用压缩机和透平的变工况模型及填充床蓄热器的非稳态模型,对两级填充床蓄热器式绝热压缩空气储能系统一次完整的充放电循环过程进行模拟,分析系统的热力学性能和各个部件的变工况特性.结果表明,系统的充放电效率可达62.4％.储能时,受洞穴内压力变化影响,两级压缩机压比、效率不断改变,从而引起下游填充床蓄热器进口温度变化;释能时...     

太阳辐射填料床储热特性研究

针对给定太阳日辐射曲线,研究集成蓄热单元的太阳光热系统的整体能量的动态转化特性及关键参数影响规律。结果表明：填料床总储热量与传热流体进口流速呈非线性变化,当传热流体进口流速 u_f =0.006 m/s时,填料床总储热量最大;在给定填料总容量和u_f =0.006 m/s的条件下,填料床高径比为5的填料床具有更高的储热能力;在该计算条件下,u_f =0.006 m/s、填料床高径比为5及填料量相对值为1时,太阳光热能实现最大程度上的转化和储存。     

Thermal characteristics of packed bed storage system

The thermal behaviour of a packed bed storage system charged with hot air is modelled using two partial differential equations representing the energy conservation in the air and solid phases constituting the bed. These two equations are coupled through the heat exchange process between the two phases. A fully implicit numerical scheme based on forward, upwind and central differencing for the time, first and second space derivatives, respectively, is used to solve the modelling equations. Marching technique is used for the air equation and a tri-diagonal matrix solver is employed to solve the solid equation. The solution yields the thermal structure of the bed, namely the air and solid temperature distribution inside the bed at any particular time, and the variation of total energy stored in the bed with time. The effect of bed length, solid diameter and void fraction on the thermal characteristics of the packed bed is studied. Further, the performance of the bed under variable inlet air temperature and mass flow rate is investigated.     

相变胶囊堆积形态对蓄热系统性能的影响分析

建立相变蓄热胶囊的三维有序及无序堆积模型,在此基础上分析相变蓄热胶囊有序及无序对蓄热系统特性的影响。通过对蓄热系统的蓄热量、蓄热用时、蓄热效率及系统内温度分布等关键性能指标情况分析,提出一种判定蓄热终点的新方法。结果表明:当采用有序堆积时系统的各项性能指标最优,叉排堆积时蓄热效率最低,而无序堆积时蓄热总量最少。另外,换热流体流速增加可加快蓄热过程,但此时蓄热系统蓄热效率较低。     

Thermal performance simulations of a packed bed cool thermal energy storage system using n-tetradecane as phase change material

The objective of this paper is to study the thermal performance of latent cool thermal energy storage system using packed bed containing spherical capsules filled with phase change material during charging and discharging process. According to the energy balance of the phase change material (PCM) and heat transfer fluid (HTF), a mathematical model of packed bed is conducted. n-tetradecane is taken as PCM and aqueous ethylene glycol solution of 40% volumetric concentration is considered as HTF. The temperatures of the PCM and HTF, solid and melt fraction and cool stored and released rate with time are simulated. The effects of the inlet temperature and flow rate of HTF, porosity of packed bed and diameter of capsules on the melting time, solidification time, cool stored and released rate during charging and discharging process are also discussed.     

Nusselt number and friction factor correlations for packed bed solar energy storage system having large sized elements of different shapes

In order to investigate the effect of system and operating parameters on heat transfer and pressure drop characteristics of packed bed solar energy storage system with large sized elements of storage material, an extensive experimental study has been conducted and reported in the present paper. Five different shapes of elements of storage material have been investigated. Correlations have been developed for Nusselt number and friction factor as function of Reynolds number, sphericity and void fraction. The present correlations can be used to predict the performance of the actual packed bed solar energy storage system having packing material elements of different shapes and bed porosities within the range of parameters investigated.     

Heat conduction in a packed bed with wall effects

The nonuniform porosity effect (wall effect) on steady one-dimensional heat conduction in a packed bed between parallel plates, concentric cylinders and concentric spheres at different temperatures is considered in this paper. The heat conduction characteristics in the bed is shown to be a function of γ (the ratio of particle diameter to the characteristic length of the geometry) and λ (the ratio of the thermal conductivity of the fluid phase to that of the solid phase). Dimensionless temperature distributions at different values of γ are obtained for fluid-saturated porous media composed of water/glass-beads, silicon oil/glass-beads, air/glass-beads and water/steel-balls.     

Similarity and generalized analysis of efficiencies of thermal energy storage systems

This paper examined the features of three typical thermal storage systems including: 1) direct storage of heat transfer fluid in containers, 2) storage of thermal energy in a packed bed of solid filler material, with energy being carried in/out by a flowing heat transfer fluid which directly contacts the packed bed, and 3) a system in which heat transfer fluid flows through tubes that are imbedded into a thermal storage material which may be solid, liquid, or a mixture of the two. The similarity of the three types of thermal storage systems was discussed, and generalized energy storage governing equations were introduced in both dimensional and dimensionless forms. The temperatures of the heat transfer fluid during energy charge and discharge processes and the overall energy storage efficiencies were studied through solution of the energy storage governing equations. Finally, provided in the paper are a series of generalized charts bearing curves for energy storage effectiveness against four dimensionless parameters grouped up from many of the thermal storage system properties including dimensions, fluid and thermal storage material properties, as well as the operational conditions including mass flow rate of the fluid, and the ratio of energy charge and discharge time periods. Engineers can conveniently look up the charts to design and calibrate the size of thermal storage tanks and operational conditions without doing complicated individual modeling and computations. It is expected that the charts will serve as standard tools for thermal storage system design and calibration.     

Dynamic discharging characteristics simulation on solar heat storage system with spherical capsules using paraffin as heat storage material

The dynamic characteristics of solar heat storage system with spherical capsules packed bed during discharging process are studied. According to the energy balance of solar heat storage system, the dynamic discharging processes model of packed bed with spherical capsules is presented. Paraffin is taken as phase change material (PCM) and water is used as heat transfer fluid (HTF). The temperatures of PCM and HTF, solid fraction and heat released rate are simulated. The effects of inlet temperature of HTF, flow rate of HTF and porosity of packed bed on the time for discharging and heat released rate are also discussed. The following conclusion can be drawn: (1) the heat released rate is very high and decreases rapidly with time during the liquid cooling stage, it is stable at the solidification cooling stage, then it decreases to zero at the solid cooling stage. (2) The time for complete solidification decreases when the HTF flow rate increases, but the effect is not so obvious when the HTF flow rate is higher than 13 kg/min; (3) compared to the HTF inlet temperature and flow rate, the influence of porosity of packed bed on the time for complete solidification is not so significant.     

Natural convective heat transfer of heated packed beds

Natural convection heat transfer of heated packed bed was investigated. Experiments were performed for a single heated sphere buried in unheated packed beds varying its locations and for packed beds with all heated spheres varying the heights of packed beds from 0.02 m to 0.26 m. Mass transfer experiments using a copper electroplating system were performed based upon the analogy between heat and mass transfer. The diameter of sphere was 0.006 m, which corresponds to Ra_d of 1.8 × 10⁷. For the single heated sphere cases, the measured results agreed well with the existing natural convection heat transfer correlations for packed beds and even with those for a single sphere in an open channel. For all heated sphere cases, the average heat transfers decrease with increasing packed bed heights.     

Comparison of energy and exergy efficiencies of an underground solar thermal storage system

In this experimental study, solar energy was stored daily using the volcanic material with the sensible heat technique. The external heat collection unit consisted of 27 m² of south‐facing solar air collectors mounted at a 55° tilt angle. The dimensions of the packed‐bed heat storage unit were 6 × 2 × 0.6 m deep. The packed‐bed heat storage unit was built under the soil. The heat storage unit was filled with 6480 kg of volcanic material. Energy and exergy analyses were applied in order to evaluate the system efficiency. During the charging periods, the average daily rates of thermal energy and exergy stored in the heat storage unit were 1242 and 36.33 W, respectively. Since the rate of exergy depends on the temperature of the heat transfer fluid and surrounding, the rate of exergy increased as the difference between the inlet and outlet temperatures of the heat transfer fluid increased during the charging periods. It was found that the average daily net energy and exergy efficiencies in the charging periods were 39.7 and 2.03%, respectively. The average daily net energy efficiency of the heat storage system remained nearly constant during the charging periods. The maximum energy and exergy efficiencies of the heat storage system were 52.9 and 4.9%, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Thermal performance of a single-layer packed metal pebble-bed exposed to high energy fluxes

It is difficult to accurately measure the temperature of the falling particle receiver since thermocouples may directly be exposed to the solar flux. This study analyzes the thermal performance of a packed bed receiver using large metal spheres to minimize the measurement error of particle temperature with the sphere temperature reaching more than 700°C in experiments in a solar furnace and a solar simulator. The numerical models of a single sphere and multiple spheres are verified by the experiments. The multiple spheres model includes calculations of the external incidence, view factors, and heat transfer. The effects of parameters on the temperature variations of the spheres, the transient thermal efficiency, and the temperature uniformity are investigated, such as the ambient temperature, particle thermal conductivity, energy flux, sphere diameter, and sphere emissivity. When the convection is not considered, the results show that the sphere emissivity has a significant influence on the transient thermal efficiency and that the temperature uniformity is strongly affected by the energy flux, sphere diameter, and sphere emissivity. As the emissivity increases from 0.5 to 0.9, the transient thermal efficiency and the average temperature variance increase from 53.5% to 75.7% and from 14.3% to 27.1% at 3.9 min, respectively. The average temperature variance decreases from 29.7% to 9.3% at 2.2 min with the sphere diameter increasing from 28.57 mm to 50 mm. As the dimensionless energy flux increases from 0.8 to 1.2, the average temperature variance increases from 13.4% to 26.6% at 3.4 min.     

Exergetic and performance analyses of two-layered packed bed latent heat thermal energy storage system

In concentrating solar power (CSP) plant, a novel method involving the use of thermocline can be employed to augment the capability of the thermal energy storage system (TES). The rate of thermocline degradation can be reduced by packing encapsulated phase change material (PCM) in the TES. The thermal performance of the packed bed latent heat thermal energy storage system (PBTES) can be further enhanced by employing different diameters of PCM capsules arranged in multiple layers. In this paper, the thermal and exergetic performance of single-layered and two-layered PBTES is evaluated for varying mass flow rate, PCM capsule diameter and bed height of larger PCM capsules using a dynamic model based on simplified energy balance equations for PCM and heat transfer fluid (HTF). The single-layered PBTES has a lower TES latent charging rate than the two-layered PBTES. The charging efficiency and charging time of two-layered PBTES are increased by 15.85% and 16.85%, respectively for reducing the HTF mass flow rate by 14.29%. A higher stratification number can be achieved by using a two-layered PBTES instead of a single-layered PBTES filled with the corresponding larger diameter PCM capsules. The second law efficiency of the two-layered PBTES is found to be less than that of the single-layered PBTES. A decrease in the bed height of larger PCM capsules decreases the exergetic efficiency of the two-layered PBTES by 3.27%. The findings from this study can be used in further designing and optimising the multi-layered PBTES.     

Exergy‐based performance analysis of packed‐bed solar air heaters

This paper presents an experimental investigation of the thermal performance of a solar air heater having its flow channel packed with Raschig rings. The packing improves the heat transfer from the plate to the air flow underneath. The dimensions of the heater are 0.9 m wide and 1.9 m long. The aluminium‐based absorber plate was coated with ordinary black paint. The characteristic diameter of the Raschig rings, made of black polyvinyl chloride (PVC) tube, is 50 mm and the depth of the packed‐bed in flow channel is 60 mm. Energy and exergy analyses were applied for evaluating the efficiency of the packed‐bed solar air heater. The rate of heat recovered from the packed‐bed solar air heater varied between 9.3 and 151.5 W m^?2, while the rate of thermal exergy recovered from the packed‐bed solar air heater varied between 0.04 and 8.77 W m^?2 during the charging period. The net energy efficiency varied from 2.05 to 33.78%, whereas the net exergy efficiency ranged from 0.01 to 2.16%. It was found that the average daily net energy and exergy efficiencies were 17.51 and 0.91%, respectively. The energy and exergy efficiencies of the packed‐bed solar air heater increased as the outlet temperature of heat transfer fluid increased. Copyright © 2004 John Wiley & Sons, Ltd.     

Operation strategies guideline for packed bed thermal energy storage systems

Packed bed thermal energy storage (TES) systems have been identified in the last years as one of the most promising TES alternatives in terms of thermal efficiency and economic viability. The relative simplicity of this storage concept opens an important opportunity to its implementation in many environments, from the renewable solar‐thermal frame to the industrial waste heat recovery. In addition, its implicit flexibility allows the use of a wide variety of solid materials and heat transfer fluids, which leads to its deployment in very different applications. Its potential to overcome current heat storage system limitations regarding suitable temperature ranges or storage capacities has also been pointed out. However, the full implementation of the packed bed storage concept is still incomplete since no industrial scale units are under operation. The main underlying reasons are associated to the lack of a complete extraction of the full potential of this storage technology, derived from a successful system optimization in terms of material selection, design, and thermal management. These points have been evidenced as critical in order to attain high thermal efficiency values, comparable to the state‐of‐the‐art storage technologies, with improved technoeconomic performance. In order to bring this storage technology to a more mature status, closer to a successful industrial deployment, this paper proposes a double approach. First, a low‐cost by‐product material with high thermal performance is used as heat storage material in the packed bed. Second, a complete energetic and efficiency analysis of the storage system is introduced as a function of the thermal operation. Overall, the impact of both the selected storage material and the different thermal operation strategies is discussed by means of a thermal model which permits a careful discussion about the implications of each TES deployment strategy and the underlying governing mechanisms. The results show the paramount importance of the selected operation method, able to increase the resulting cycle and material usage efficiency up to values comparable to standard currently used TES solutions.