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.     

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.     

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.     

An analysis of a packed bed latent heat thermal energy storage system using PCM capsules: Numerical investigation

This paper is aimed at analyzing the behavior of a packed bed latent heat thermal energy storage system. The packed bed is composed of spherical capsules filled with paraffin wax as PCM usable with a solar water heating system. The model developed in this study uses the fundamental equations similar to those of Schumann, except that the phase change phenomena of PCM inside the capsules are analyzed by using enthalpy method. The equations are numerically solved, and the results obtained are used for the thermal performance analysis of both charging and discharging processes. The effects of the inlet heat transfer fluid temperature (Stefan number), mass flow rate and phase change temperature range on the thermal performance of the capsules of various radii have been investigated. The results indicate that for the proper modeling of performance of the system the phase change temperature range of the PCM must be accurately known, and should be taken into account.     

Analysis and optimization of a latent thermal energy storage system with embedded heat pipes

Latent thermal energy storage system (LTES) is an integral part of concentrating solar power (CSP) plants for storing sun’s energy during its intermittent diurnal availability in the form of latent heat of a phase change material (PCM). The advantages of an LTES include its isothermal operation and high energy storage density, while the low thermal conductivity of the PCM used in LTES poses a significant disadvantage due to the reduction in the rate at which the PCM can be melted (charging) or solidified (discharging). The present study considers an approach to reducing the thermal resistance of LTES through embedding heat pipes to augment the energy transfer from the heat transfer fluid (HTF) to the PCM. Using a thermal resistance network model of a shell and tube LTES with embedded heat pipes, detailed parametric studies are carried out to assess the influence of the heat pipe and the LTES geometric and operational parameters on the performance of the system during charging and discharging. The physical model is coupled with a numerical optimization method to identify the design and operating parameters of the heat pipe embedded LTES system that maximizes energy transferred, energy transfer rate and effectiveness.     

Experimental investigation on a combined sensible and latent heat storage system integrated with constant/varying (solar) heat sources

The objective of the present work is to investigate experimentally the thermal behavior of a packed bed of combined sensible and latent heat thermal energy storage (TES) unit. A TES unit is designed, constructed and integrated with constant temperature bath/solar collector to study the performance of the storage unit. The TES unit contains paraffin as phase change material (PCM) filled in spherical capsules, which are packed in an insulated cylindrical storage tank. The water used as heat transfer fluid (HTF) to transfer heat from the constant temperature bath/solar collector to the TES tank also acts as sensible heat storage (SHS) material. Charging experiments are carried out at constant and varying (solar energy) inlet fluid temperatures to examine the effects of inlet fluid temperature and flow rate of HTF on the performance of the storage unit. Discharging experiments are carried out by both continuous and batchwise processes to recover the stored heat. The significance of time wise variation of HTF and PCM temperatures during charging and discharging processes is discussed in detail and the performance parameters such as instantaneous heat stored and cumulative heat stored are also studied. The performance of the present system is compared with that of the conventional SHS system. It is found from the discharging experiments that the combined storage system employing batchwise discharging of hot water from the TES tank is best suited for applications where the requirement is intermittent.     

相变储能堆积床传热特性的研究

基于多孔介质传热理论,建立了储能堆积床的传热模型.在此基础上分析了换热流体流量、温度、单元尺寸、相变材料导热系数和孔隙率等参数对堆积床传热特性的影响.研究表明,提高相变材料的导热系数,增大换热流体温差或减小单元尺寸对堆积床传热速率有明显提高,而提高换热流体流量,增大对流换热系数对传热速率的影响不明显.因而强化相变材料侧的传热过程是提高堆积床传热速率的有效途径.     

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.     

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.     

Comparative study of different numerical models of packed bed thermal energy storage systems

This paper presents, compares and validates two different mathematical models of packed bed storage with PCM, more specifically the heat transfer during charge of the PCM. The first numerical model is a continuous model based on the Brinkman equation and the second numerical model treats the PCM capsules as individual particles (energy equation model). Using the Brinkman model the flow field inside the porous media and the heat transfer mechanisms present in the packed bed systems can be described. On the other hand, using the energy equation model the temperature gradient inside the PCM capsules can be analysed. Both models are validated with experimental data generated by the authors. The experimental set up consists mainly of a cylindrical storage tank with a capacity of 3.73 L full of spherically encapsulated PCM. The PCM used has a storage capacity of 175 kJ/kg between ?2–13 °C. The results from the energy equation model show a basic understanding of cold charging. Moreover, three different Nu correlations found in the literature were analysed and compared. All of them showed the same temperature profile of the PCM capsules; hence any of them could be used in future models. The comparison between both mathematical models indicated that free convection is not as important as forced convection in the studied case.     

A review on packed bed solar energy storage systems

Because of intermittent nature of solar energy, storage is required for uninterrupted supply in order to match the needs. Packed beds are generally used for storage of thermal energy from solar air heaters. A packed bed is a volume of porus media obtained by packing particles of selected material into a container. A number of studies carried out on packed beds for their performance analysis were reported in the literature. These studies included the design of packed beds, materials used for storage, heat transfer enhancement, flow phenomenon and pressure drop through packed beds. This paper presents an extensive review on the research carried out on packed beds. Based on the literature review, it is concluded that most of the studies carried out are on rocks and pebbles as packing material. A very few studies were conducted on large sized packing materials. Further no study has been reported so far on medium sized storage elements in packed beds.     

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.     

An analytical model to predict the thermal performance of a novel parallel flow packed bed solar air heater

A design of a parallel flow solar air heater with packed material in its upper channel and capable of providing a higher heat flux compared to the conventional non-porous bed double flow systems is presented. An analytical model describing the various temperatures and heat transfer characteristics of such a parallel flow packed bed solar air heater (PFPBSAH) has been developed and employed to study the effects of the mass flow rate and varying porosities of the packed material on its thermal performance. The model employs an iterative solution procedure to solve the governing energy balance equations describing the complex heat and mass exchanges involved. To validate the proposed analytical model, comparisons between theoretical and experimental results showed that good agreement is achieved with reasonable accuracy. Also, PFPBSAH is found to perform more efficiently than the conventional non-porous double flow solar air heaters with 10–20% increase in its thermal efficiency. Furthermore, the effect of the fraction of mass flow rate in the upper or lower flow channel of PFPBSAH device on its performance, has also investigated theoretically. The fraction of the mass flow rate in the respective channels of the PFPBSAH is shown to be dominant parameter in determining the effective thermal efficiency of the heater.     

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。     

CFD modeling and experimental validation of sulfur trioxide decomposition in bayonet type heat exchanger and chemical decomposer for different packed bed designs

The growth of global energy demand during the 21st century, combined with the necessity to master greenhouse gas emissions has lead to the introduction of a new and universal energy carrier: hydrogen. The Department of Energy (DOE) Nuclear Hydrogen Initiative was investigating thermochemical cycles for hydrogen production using high-temperature heat exchangers. In this study a three-dimensional computational model of high-temperature heat exchanger and decomposer for decomposition of sulfur trioxide by the sulfur–iodine thermochemical water-splitting cycle with different packed bed designs has been done. The decomposer region of the bayonet heat exchanger also called as silicon carbide integrated decomposer (SID) is designed as the packed bed region. Cylindrical, spherical, cubical and hollow cylindrical pellets have been arranged inside the packed bed. The engineering design of the packed bed was very much influenced by the structure of the packing matrix, which was governed by the shape, dimension and the loading of the constituent particles. Staggered and regular packing methods are used for packing the pellets in the packed bed region. The numerical model is created using GAMBIT and fluid, thermal and chemical analyses were performed using FLUENT. The decomposition percentage of sulfur trioxide is found for the packed bed region with different pellets and the numerical results obtained is compared with the experimental results. A comparison is made for the decomposition percentage of SO₃ for the packed bed approach and the porous media approach.     

Numerical simulation of heat transfer in a gas solid crossflow moving packed bed heat exchanger

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High temperature latent heat thermal energy storage using heat pipes

A thermal network model is developed and used to analyze heat transfer in a high temperature latent heat thermal energy storage unit for solar thermal electricity generation. Specifically, the benefits of inserting multiple heat pipes between a heat transfer fluid and a phase change material (PCM) are of interest. Two storage configurations are considered; one with PCM surrounding a tube that conveys the heat transfer fluid, and the second with the PCM contained within a tube over which the heat transfer fluid flows. Both melting and solidification are simulated. It is demonstrated that adding heat pipes enhances thermal performance, which is quantified in terms of dimensionless heat pipe effectiveness.     

Discharge characteristics of latent heat storage columns packed with cross-linked plastic particles

This investigation deals with experimental and numerical analyses carried out to investigate the discharge characteristics of latent heat storage columns, using cross-linked cylindrical plastic particles as a phase-change type of heat storage material and ethylene glycol as a heat transfer medium. In the experiment, the transient response of the outlet temperature of the heat transfer medium was measured under conditions of varying the initial temperature in the column, the inlet temperature of the heat transfer medium, the mass flow rate of the heat transfer medium, and the mass of the heat storage material packed in the column. In the numerical analysis, the transient temperature distributions in the column was calculated by using an empirical formula for estimating the heat transfer coefficient for a fixed bed, which was recommended in the authors' previous paper. The experimental results were found to be in fair agreement with the numerical results. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(3): 193–206, 1997     

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.     

Thermal and thermo-hydraulic performance investigation of double-pass packed bed solar air heaters under external recycle

In the present investigation, two types (Type A and Type B) of the double-pass packed bed solar air heater under external recycle are investigated theoretically. In Type A, the porous media is considered in the upper channel, whereas in Type B, the porous media is considered in the lower channel. Iron scraps are used as a packed bed material (porous media) to strengthen the convective heat transfer coefficient for air flowing through the packed bed. The mathematical model for these two air heaters operating under forced convection mode is presented. The results revealed that the thermal and thermo-hydraulic efficiencies of Type A are higher as compared to Type B. In order to validate the models, the theoretical results obtained from the conventional model of Type B are compared with the theoretical results obtained from the previous investigation and showed that good agreement is achieved.