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.     

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.     

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.     

Drastic enhancement of effective thermal conductivity of a metal hydride packed bed by direct synthesis of single-walled carbon nanotubes

Low heat conductivity restricts the rate of hydrogen absorption into a metal hydride, and this leads to a mismatch of the required absorption rate. The use of fin systems is standard in such cases, and the use of several different materials has been attempted. This includes high thermal conductivity carbon brushes and carbon nanotube. Unfortunately, such efforts have not been effective because the boundary thermal resistance has not been addressed. In this study, we focused on the direct synthesis of a single-walled carbon nanotube (SWCNT), which has high thermal conductivity, on particles in a packed bed, for reducing boundary thermal resistance and estimated effective thermal conductivity. Referring to Raman spectra, we succeeded in growing SWCNT on a metal hydride and effective thermal conductivity was estimated as a function of the filling ratios of the metal hydride and the SWCNT. Consequently, the effective thermal conductivity can satisfy the required value.     

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

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Numerical analysis of melting with constant heat flux heating in a thermal energy storage system

Melting in a finite slab with a second kind boundary condition is studied numerically in order to simulate the charging process of a thermal energy storage system. A dimensionless model is given, from which it is concluded that the main factors that influence the melting process are the dimensionless heating flux, the modified Stefan number, the relative thermal diffusivity and the relative thermal conductivity. The influence of preheating or solid subcooling is studied. It is found that though preheating does not have very important effects on the melting time, it does influence the interface marching velocity significantly. The melt fraction and the melting time are calculated extensively for various dimensionless numbers. The numerical results show that the ratio of the thermal conductivity of the solid to that of the liquid has little effect on the melting time, and the time for finishing melting can be expressed as a function of the dimensionless heating flux, the modified Stefan number and the relative thermal diffusivity, and the possible function form is suggested.     

Performance enhancement in latent heat thermal storage system: A review

Phase change material (PCM) based latent heat thermal storage (LHTS) systems offer a challenging option to be employed as an effective energy storage and retrieval device. The performance of LHTS systems is limited by the poor thermal conductivity of PCMs employed. Successful large-scale utilization of LHTS systems thus depends on the extent to which the performance can be improved. A great deal of work both experimental and theoretical on different performance enhancement techniques has been reported in the literature. This paper reviews the implementation of those techniques in different configurations of LHTS systems. The influence of enhancement techniques on the thermal response of the PCM in terms of phase change rate and amount of latent heat stored/retrieved has been addressed as a main aspect. Issues related to mathematical modeling of LHTS systems employing enhancement techniques are also discussed.     

Simplified analysis of coupled heat and mass transfer processes in packed bed liquid desiccant-air contact system

One-dimensional model is frequently used to describe the coupled heat and mass transfer processes in the packed bed liquid desiccant dehumidifier/regenerator. In this paper, within relatively narrow range of operating conditions which are usually encountered in practical dehumidification/regeneration processes, the linear approximation was made to find out the dependence of equilibrium humidity ratio on solution temperature. New parameters were defined and the original equations were rearranged to obtain two coupled ordinary differential equations. For the general cases with different values of Lewis factor, approximations of constant properties and coefficients were further made to render the coupled equations linear. Roots of the characteristic equation were determined algebraically and analytical solution to the linear coupled equations was obtained. Analytical expression for the tower efficiency was further developed based on the analytical solution. The way for obtaining the averaged overall heat and mass transfer coefficients from experimental data in a coupled heat and mass transfer manner was finally indicated. Coefficients obtained in this manner can be used in finite difference model to produce more accurate outlet conditions.     

Solar multi-mode heating system based on latent heat thermal energy storage and its application

为克服太阳能间断性和不稳定性的缺点进而实现太阳能集热与采暖的能量供需调节和全天候连续供热,提出了基于相变储热的太阳能多模式采暖方法（太阳能集热直接采暖、太阳能集热采暖+相变储热、太阳能相变储热采暖）,并在西藏林芝市某建筑搭建了太阳能与相变储热相结合的采暖系统,该系统可根据太阳能集热温度和外界供热需求实现太阳能多模式采暖的自动控制和自动运行。实验研究表明：在西藏地区采用真空管太阳能集热器可以和中低温相变储热器很好地结合,白天储热器在储热过程中平均储热功率为10.63 kW,储热量达到92.67 kW·h,相变平台明显;晚上储热器在放热过程中供热量达85.23 kW·h,放热功率和放热温度平稳,储放热效率达92%,其储热密度是传统水箱的3.6倍,可连续供热时间长达10 h,从而实现了基于相变储热的太阳能全天候连续供热,相关研究结果对我国西藏地区实施太阳能采暖具有一定的指导作用。     

Numerical and experimental study of spherical capsules packed bed latent heat storage system

A numerical model to simulate a storage system composed of spherical capsules filled with PCM placed inside a cylindrical tank fitted with a working fluid circulation system to charge and discharge the storage tank. The simplified transient one-dimensional model is based on dividing the tank into a number of axial layers whose thickness is always equal or larger than a capsule diameter. It is also assumed that the temperature of the working fluid is uniform and equal to the average temperature of the layer. The solidification process inside the spherical capsule is treated by using a conductive one-dimensional phase change model with convective boundary condition on the external surface. The convection present in the liquid phase of the PCM is treated by using an effective heat conduction coefficient in the liquid region of the PCM. The solution of the differential equations is realized by the finite difference approximation and a moving grid inside the spherical capsules. The geometrical and operational parameters of the system are investigated both numerically and experimentally and their influence on the charging and discharging times was investigated.     

A model for latent heat energy storage systems

In this study, a theoretical approach is proposed for the prediction of time and temperature during the heat charge and discharge in the latent heat storage of phase changed materials (PCM). By the use of the average values of the mean specific heat capacities for the phase‐changed materials, analytical solutions are obtained and compared with the available experimental data in the literature. It is shown that decreasing the entry temperature of the working fluid from ?4 to ?15°C has a very dominant and strong effect on the PCM solidification time. The effect of the working fluid flow rate and the material of PCM capsules on the time for complete solidification and total charging is also investigated. The agreement between the present theoretical model results and the experimental data related to the cooling using small spheres and the heat storage using rectangle containers is very good. The largest difference between the present results and the experimental data becomes about 10% when the fluid temperature approaches the phase change temperature at high temperatures. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Numerical analysis and parameters optimization of shell-and-tube heat storage unit using three phase change materials

In this paper, a mathematical model of shell-and-tube latent heat thermal energy storage (LHTES) unit of two-dimension of three phase change materials (PCMs) named PCM1, PCM2 and PCM3 with different high melting temperatures (983 K, 823 K and 670 K, respectively) and heat transfer fluid (HTF: air) with flowing resistance and viscous dissipation based on the enthalpy method has been developed. Instantaneous solid–liquid interface positions and liquid fractions of PCMs as well as the effects of inlet temperatures of the air and lengths of the shell-and-tube LHTES unit on melting times of PCMs were numerically analyzed. The results show that melting rates of PCM3 are the fastest and that of PCM1 are the slowest both x, r directions. It is also found that the melting times of PCM1, PCM2 and PCM3 decrease with increase in inlet temperatures of the air. Moreover, with increase in inlet temperatures of the air, decreasing degree of their melting times are different, decreasing degree of the melting time of PCM1 is the biggest and that of PCM3 is the smallest. Considering actual application of solar thermal power, we suggest that the optimum lengths are L₁ = 250 mm, L₂ = 400 mm, L₃ = 550 mm (L = 1200 mm) which corresponds to the same melting times of PCM1, PCM2 and PCM3 are about 3230 s and inlet temperature of the air is about 1200 K. The present analysis provides theoretical guidance for designing optimization of the shell-and-tube LHTES unit with three PCMs for solar thermal power.     

Thermal performance of packed bed thermal energy storage units using multiple granular phase change composites

The present article reports on the utilization of multiple granular phase change composites (GPCC) with different ranges of phase change temperatures in a packed bed thermal energy storage system. Small particle diameter of GPCC allows simple mixing of two or three ranges of GPCCs in a packed bed for enhancement of storage unit performance. Experiments have been carried out to characterize the phase changing characteristics of two GPCCs chosen for this purpose. Packed bed column experiments have been carried out to provide basic understanding of the heat transfer process in the composite bed consisting of a mixture of GPCCs at different values of mixing ratio. A mathematical model has been developed for the analysis of charging and discharging process dynamics. Once validated, the model has been used to perform a parametric study to investigate the overall bed performance at different values of mixing ratio and Reynolds number. An optimization of the value of mixing ratio has been obtained based on the overall charging and discharging times as well as the exergy efficiency. It has been demonstrated that, as compared to the use of single GPCC, careful choice of the mixing ratio of GPCCs in a composite bed can result in a significant enhancement of the overall storage unit performance. As compared to the use of multiple sequential layers of GPCCs, using units composed of a mixture of GPCCs with an optimized mixing ratio results in a remarkable improvement of the unit performance without limitations on the charging and discharging directions during practical applications.     

Cascaded latent heat storage for parabolic trough solar power plants

The current revival of solar thermal electricity generating systems (SEGS) unveils the still existing need of economic thermal energy storages (TES) for the temperature range from 250 °C to 500 °C. The TES-benchmark for parabolic trough power plants is the direct two tank storage, as it was used at the SEGS I plant near Barstow (USA). With the introduction of expensive synthetic heat transfer oil, capable to increase the operating temperature from former 300 °C up to 400 °C, the direct storage technology became uneconomical. Cascaded latent heat storages (CLHS) are one possible TES alternative, which are marked by a minimum of necessary storage material. The use of a cascade of multiple phase change materials (PCM) shall ensure the optimal utilization of the storage material.This paper reports experimental and numerical results from the investigation of cascaded latent heat storages with alkali nitrate salts like NaNO₃, KNO₃ and others more. The experiments were conducted with vertical shell and tube type heat exchanger devices under realistic operation parameters. The experimental results were used for a numerical model to simulate different CLHS configurations. Dymola/Modelica was used to conduct the simulation. The outcome of this work shows on the one hand, that the design of CLHS for this temperature range is more complex than for the temperature range up to 100 °C. And on the other hand, the low heat conductivity of available PCM is an obstacle which must be overcome to make full use of this promising storage technology.     

Semi-analytical method for heat and moisture transfer in packed bed of silica gel

A semi-analytical model for the heat and mass transfer of adsorption and desorption processes of the vertical solid desiccant packed bed dehumidifier is presented on the basis of quasi-steady state assumption, and is solved using close form integration with the limits equivalent to bed and time increments, and numerically by Runge-Kutta Fehlberg and forward scheme finite difference techniques. The most important parameters during the dehumidifier operation, namely, (i) exit air temperature and humidity, (ii) axial temperature distribution in the bed and (iii) water content are evaluated. Stability of the semi-analytical method is investigated and found that the main parameters affecting the model stability are the bed and time increments size. A dimensionless parameter combining time and bed increments size and air velocity named velocity ratio is defined and investigated. It is found that when the velocity ratio equals the ratio of particle diameter to bed length, the method is stable, and as the velocity ratio is made smaller beyond the stable velocity ratio, the results remain unchanged. The results of semi-analytical and numerical models agree well with the experimental results for both desorption and adsorption processes. Using the proposed semi-analytical model, the minimum and maximum relative errors for exit air temperature are 2.24% and 11.78%, respectively and for exit air humidity the minimum and maximum errors are 3.79% and 27.17% respectively.     

Properties of some salt hydrates for latent heat storage

For the utilization of low-grade heat the latent storage of thermal energy is of great advantage because the heat can be preserved at a constant temperature perfectly matched to the special purpose of application. Investigations on the heat capacities, enthalpies of fusion, densities, crystallization behaviour and other chemical and physical properties have shown that the following salt hydrates are especially suitable media for storing low-grade heat. The eutectic mixture of water and 3.92% by weight of sodium fluoride, melting point (MP) = - 3.5°C, is extremely convenient and cheap for refrigerating or other cooling purposes. Lithium chlorate trihydrate, LiClO₃. 3H₂O, MP = +8.1°C has an extremely high storage capacity and other advantageous properties as a storage medium in cooling systems, but a very high price will limit its application. Calcium chloride hexahydrate, CaCl₂. 6H₂O, MP = + 29.2°C, is a suitable and cheap storage medium for heating purposes. For the same application disodium hydrogen phosphate dodecahydrate, Na₂HPO₄. 12H₂O, MP = + 35.2°C, is even better because of the larger storage capacity per unit volume and other advantages which largely compensate the higher material cost. the unique properties of potassium fluoride tetrahydrate, KF. 4H₂O, MP = +18.5°C, make it especially suitable for storing low-grade heat. It can directly function as an energy sink and as an energy reservoir in heat collecting and consuming systems. Examples of the practical applicability for residential heating, temperature levelling and cooling are described.     

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.     

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。     

Modeling and validation of heat transfer in packed bed with internal heat generation

Several researchers have modeled the heat transfer in a packed bed, heated externally, and determined its effective thermal conductivity ( $k_{\mathit{eff}}$). But till date, very few researchers have studied the heat transfer of the pebble bed, where the heat is generated inside the bed; and the effective thermal conductivity of the packed bed with internal heat generation has not yet been reported. In the present work, heat generation inside the bed has been imitated by inductively heating randomly placed steel balls with lithium titanate ( ${\text{Li}}_2{\text{TiO}}_3$) pebbles. The system has been modeled and validated with experimental results. The $k_{\mathit{eff}}$ of the ${\text{Li}}_2{\text{TiO}}_3$ pebble bed is determined for various process conditions. A correlation has been developed to calculate the $k_{\mathit{eff}}$ based on various process parameters such as pebble diameter, air flow rate, and induction temperature. The result presented in this study will be used for the design and scale‐up studies of future fusion reactors.