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.     

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.     

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.     

A numerical investigation into the charge behaviour of a spherical phase change material particle for high temperature thermal energy storage in packed beds

基于高温相变材料,对填充床储热系统中储热单元球体的储热性能进行了模拟研究.研究了不同传热流体温度和球体直径对球体储热性能的影响规律,对导热为主的相变储热过程与导热和自然对流共同作用的相变储热过程进行了比较分析,同时还探讨了高温辐射换热的影响.结果表明,相变时间随球体直径的增大而增大,随传热流体温度的增大而减小.当考虑相变区域自然对流时,总的相变时间显著减少,和单纯导热相比,完全相变时间缩短了近16%.在导热和自然对流的基础上加上辐射传热后可以看出,辐射换热强化了球体内的传热过程,加快了相变材料的熔化速度,强化了自然对流的作用.     

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.     

Analysis of an encapsulated phase change material‐based energy storage system for high‐temperature applications

The capability of an encapsulated phase change material (EPCM)‐based thermal energy storage (TES) system to store a large fraction of latent energy at high temperatures was examined. A 3‐dimensional simulation of a prototype heat exchanger was conducted employing sodium nitrate as the phase change material (PCM). The k‐ω SST model was used to capture the turbulent flow of the HTF, while the melting front was tracked using the enthalpy‐porosity method. The results show that the use of metal deflectors yields a nearly constant heat transfer coefficient over the capsule's surface. Despite this, the presence of the void in the capsule and natural convection within the molten PCM influenced the storage characteristics of the system affecting the shape of the isotherms and melting front. Furthermore, the EPCM capsules consecutively undergo the same heat transfer starting from the capsule closest to the inlet. The EPCM capsules store 80% of the energy lost by the HTF. The 17.7 kg of sodium nitrate stores 14.5 MJ of energy where 20% of the energy stored is via latent heat. Of the energy released by the heat transfer fluid, 80% was absorbed by the EPCM capsules with the remaining energy going into the test section walls. A total of 14.5 MJ of energy was stored by the 17.7 kg of NaNO₃, of which 20% is attributed to the latent heat. The fraction of energy stored as latent heat would be larger if a smaller operating temperature range was used. Thus, an EPCM‐based latent heat TES system is capable of storing a large fraction of the supplied energy and presents efficient means of storing thermal energy for high‐temperature applications. Additionally, the strong agreement between the numerical and experimental works demonstrates that the numerical methods employed can predict the behavior of an EPCM capsule not only within a single capsule but on the system scale as well. Therefore, the applied numerical methods can be used for further design and optimization of EPCM‐based latent heat TES systems.     

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.     

Validation of a CFD model for the simulation of heat transfer in a tubes-in-tank PCM storage unit

A computational fluid dynamics (CFD) model was developed for the simulation of a phase change thermal energy storage process in a 100 l cylindrical tank, horizontally placed. The model is validated with experimental data obtained for the same configuration. The cold storage unit was charged using water as the heat transfer medium, flowing inside a horizontal tube bundle, and the selected phase change material (PCM) was microencapsulated slurry in 45% w/w concentration. The mathematical model is based on the three-dimensional transient Navier–Stokes equations with nonlinear temperature dependent thermo-physical properties of the PCM during the phase change range. These properties were experimentally determined using analytical methods. The governing equations were solved using the ANSYS/FLUENT commercial software package. The mathematical model is validated with experimental data for three different flow rates of the heat transfer fluid during the charging process. Bulk temperature, heat transfer rate and amount of energy stored were used as performance indicators. It was found that the PCM bulk temperatures were predicted within 5% of the experimental data. The results have also shown that the total accumulated energy was within 10% of the observed value, and thus it can be concluded that the model predicts the heat transfer inside the storage system with good accuracy.     

The value of thermal radiation in assessing the charge/discharge rate of high‐grade thermal energy storage using encapsulated phase change materials (PCMs)

The charge/discharge rate of a spherical phase change material (PCM) capsule was assessed in consideration of phase change phenomenon and the combined effect of thermal radiation and heat convection in the charging/discharging processes. The heat transfer model was developed based on a single PCM capsule. The equivalent heat flux was evaluated by using the thermal resistance method. In consideration of the thermal radiation, the equivalent charge/discharge rate was improved, and the temperature rising of the PCM was actually much faster in the charging/discharging processes. It was indicated that the influence of the thermal radiation became more significant for PCM capsules under a small Re number (constant air velocity) and for high‐grade thermal energy storage. The analytical results showed that the highest heat flux contributed by cold thermal radiation occupied 30% and 62% of that by heat convection for PCM capsules with radius of 10 and 40 mm, respectively. This illustrated the crucial value of thermal radiation on the charge/discharge rate of PCM capsules with a large radius. However, for smaller size PCM capsules, the equivalent heat flux was larger under the same fluid flow velocity, and it decreased more promptly with time, because the heat convection that played the dominant role in charge/discharge processes was sensitively affected by the radius of the PCM capsules. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

相变蓄热装置内部温度场的理论与实验研究

对螺旋盘管相变蓄热装置性能和相变材料 (PCM)的传热特性开展理论和试验研究,建立相变蓄热装置物理和数学模型,对蓄热温度场进行了数值模拟和实验测试。结果表明 ：自然对流换热对PCM的熔化过程影响很大,当考虑自然对流时,相变蓄热速率加快,相变分层现象明显;实验实测温度与模拟温度相近,说明所建立的模型适用于相变装置内部温度场的模拟。     

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.     

Novel approach to optimize the dimensions of phase change material thermal storage heat exchanger in refrigeration systems

The present study aims to develop an approach to define the optimal dimensions of a phase change material (PCM) packed bed heat exchanger used as a cold thermal energy storage system in a conventional refrigerator. The heat exchanger is used to extend the daily refrigerator downtime and to ensure effective temperature control to contribute to the improved performance of the refrigerator. The mathematical model has been developed according to the technical characteristics and operating conditions of the refrigerator, the technical characteristics of the ventilator, and the thermo‐physical properties of the PCM. The model parameters that have been analyzed are the PCM melting time, air velocity range for tolerable efficient operating conditions, and the pressure drop through the PCM heat exchanger. As a case study, the approach was applied to a 600‐L conventional refrigerator equipped with a 63‐W ventilator. It has been found that over the tolerated velocity range of [2.5‐3.7 m/s], the optimal dimensions of the PCM heat exchanger are defined for an optimal velocity of 3.495 m/s. This is equivalent to an optimum sphere diameter of 0.071 m, a PCM heat exchanger length of 0.213 m, and a width of 0.148 m. The PCM heat exchanger ensures an extended compressor downtime of 12.6 hours for an ice‐PCM mass of 7.15 kg and occupies only 1.2% of the useful volume of the refrigerator.     

Thermal performance of PCM thermal storage unit for a roof integrated solar heating system

The thermal performance of a phase change thermal storage unit is analysed and discussed. The storage unit is a component of a roof integrated solar heating system being developed for space heating of a home. The unit consists of several layers of phase change material (PCM) slabs with a melting temperature of 29 °C. Warm air delivered by a roof integrated collector is passed through the spaces between the PCM layers to charge the storage unit. The stored heat is utilised to heat ambient air before being admitted to a living space. The study is based on both experimental results and a theoretical two dimensional mathematical model of the PCM employed to analyse the transient thermal behaviour of the storage unit during the charge and discharge periods. The analysis takes into account the effects of sensible heat which exists when the initial temperature of the PCM is well below or above the melting point during melting or freezing. The significance of natural convection occurring inside the PCM on the heat transfer rate during melting which was previously suspected as the cause of faster melting process in one of the experiments is discussed. The results are compared with a previous analysis based on a one dimensional model which neglected the effect of sensible heat. A comparison with experimental results for a specific geometry is also made.     

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.     

Eutectic compound (KNO3/NaNO3 : PCM) quasi‐encapsulated into SiC‐honeycomb for suppressing natural convection of melted PCM

The phase change eutectic compound, KNO₃/NaNO₃ (50/50 mol%) (phase change material (PCM)), which is used as the thermal energy storage material in the solar thermal power plant, was quasi‐encapsulated into the SiC‐honeycomb (SCH) for suppressing the natural convection occurring at the liquid state of PCM. The performance of the SCH as the material suppressing natural convection of PCM was investigated experimentally. PCM with three kinds of mixing ratios of SCH of 10%, 20%, and 30%, was prepared and packed in their respective stainless can with oil‐flowing pipe in the center, which is called thermal energy storage unit (TESU). Three units were linked together and stacked vertically by the connector at the inlet/outlet oil pipe. The time variation of temperature at the fixed positions inside the TESU in charging/discharging process and temperature gradient in the radial direction inside TESU when PCM was liquid state were investigated. It is concluded that the natural convection is suppressed by mixing the SCH with PCM up to around 30% in weight, because the PCM is quasi‐encapsulated into cell holes and porous structures of SCHs. And thus, the heat transfer of the PCM + 30%SCH composite is controlled mainly by its thermal conduction, which is also supported through comparison of simulation result with experimental one. And so, we conclude that SCH has a function as the quasi‐encapsulating material for suppressing the natural convection of PCM. Copyright © 2015 John Wiley & Sons, Ltd.     

Non-thermal equilibrium model of the coupled heat and mass transfer in strong endothermic chemical reaction system of porous media

A two dimension mathematical model has been developed to simulate the coupled heat and mass transfer in a porous medium undergoing a strong endothermic chemical reaction. Differing from the traditional two phase equation model, just the temperature field of bulk flow is known from the solution of energy equation. The temperature distribution of the solid matrix is solved according to the reaction kinetics of the decomposition of calcium carbonate. The coupling of these two equations is given by the item of chemical reaction. The fluid flow is modeled by the Ergun–Forchheimer–Brinkman equation. This model is solved numerically by the alternate dimension implicit method, and the numerical results are validated by comparing with the experimental data in literature. The influence of the strongly endothermic chemical reaction on the heat and mass transfers in the porous medium is discussed. The reaction features of the packed bed of pellets are analyzed under different conditions by varying the key parameters.     

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.     

Analysis of hydrogen storage performance of metal hydride reactor with phase change materials

Using phase change materials (PCM) as thermal energy storage material in metal hydride reactor bed is an effective method to store the heat emitted during hydrogen charging and retrieving it later during discharging. The present work examines the effect of a PCM on the behaviour of the metal hydride in the reactor bed. A two-dimensional model was developed to describe the mass and heat transfer inside the metal hydride and the PCM as well as the interaction between them. The results were compared with other numerical simulation and experimental data. In the simulations, thermal conductivity and the latent heat were varied in order to evaluate the effect of these parameters on the kinetics of absorption, desorption and melting of the phase change material.