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.     

Second law analysis of latent thermal storage for solar system

A theoretical model has been developed for analysis and optimization of the solar system using phase change material (PCM). The later consists of a solar air heating collector coupled with a cylindrical storage tank which contains spherical capsules filled with a PCM. Energy and exergy analyses are carried out to understand the behavior of the system using single PCM or multiple PCMs. Numerical results show that the performance of the latent thermal storage system can be ameliored by the judicious choice of the melting temperature of the PCM.     

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.     

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.     

Thermal performance of a solar-aided latent heat store used for space heating by heat pump

In this study, the cylindrical phase change storage tank linked to a solar powered heat pump system is investigated experimentally and theoretically. A simulation model defining the transient behaviour of the phase change unit was used. In the tank, the phase change material (PCM) is inside cylindrical tubes and the heat transfer fluid (HTF) flows parallel to it. The heat transfer problem of the model (treated as two-dimensional) was solved numerically by an enthalpy-based finite differences method and validated against experimental data. The experiments were performed from November to May in the heating seasons of 1992–1993 and 1993–1994 to measure both the mean temperature of water within the tank and the inlet and outlet water temperature of the tank. The experimentally obtained inlet water temperatures are also taken as inlet water temperature of the simulated model. Thus, theoretical temperature and stored heat energy distribution within the tank have been determined. Solar radiation and space heating loads for the heating seasons mentioned above are also presented.     

Discharge mode for encapsulated PCMs in storage tanks

This paper is aimed at analysing the behaviour of encapsulated salt hydrates, used as latent energy storage in a heat transfer system of a domestic hot water tank. The salt is a eutectic mixture of hydrate nitrates of ammonium and magnesium, with low melting temperature, already tested for latent heat storage in domestic applications. In the discharge mode, cold water enters the tank and flows on the encapsulated melted PCM, which is cooled and solidified. In the initial condition the PCM is at its melting temperature. Suddenly its external surface is cooled to a constant temperature T₀; the duration of the solidification represents the time in which the latent heat is released to water. The discharge process of the phase change material (PCM) is analyzed analytically and its effectiveness is assessed, for constant surface temperature conditions, in three different geometrical configurations, i.e. considering the PCM encapsulated in slab, cylindrical or spherical polyethylene containers. The focus is on a model of the moving boundary within the phase-change material during the discharging mode, and the duration of the phenomenon. Results shown include transient position of the moving surface, temperature distribution, amount of solid PCM, energy released, and duration of complete solidification. The influence of the geometry and the Jacob number on the ending time of solidification is investigated. Among different geometrical configurations of the PCM, it is found that the shortest time for complete solidification is matched for small spherical capsules, with high Jacob numbers and thermal conductivity.     

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.     

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.     

Crystallization of supercooled spherical nodules in a flow

The general context of this work concerns the latent heat storage (cold storage) by encapsulated spherical nodules of 7.7 cm in diameter containing a Phase Change Material (PCM) and filling a cylindrical tank (about 2500 nodules per m³). During the storage process, a cold heat transfer liquid flows through the tank to crystallize the PCM inside the nodules. The stored energy is released when a hotter heat transfer liquid flows through the tank to induce the melting of the PCM. As the velocity in the tank is relatively small (a few mm·s⁻¹), natural convection is expected on the coolant when the latent heat is released at the crystallization of the PCM. The present study concerns a single nodule surrounded by a flowing heat transfer liquid at a temperature T_C lower than the melting temperature T_F. This text presents an enthalpic modelling of the phase change inside the nodule coupled with a CFD simulation of the external flow to describe the mutual influence of the natural convection and the kinetics of crystallization. This study is afterwards extended to the case of two superposed nodules to investigate the influence of the crystallization of the lower nodule on the upper one.     

Energy analysis of space solar dynamic heat receivers

Energy analysis of space solar dynamic heat receivers employing solid–liquid phase change storage is developed. The heat receiver is a critical component of a solar dynamic system. Phase change thermal energy storage is used in the heat receiver. The energy analysis presented here can be used to understand the energy transfer in the heat receiver and thermal energy storage in phase change materials (PCM). The heat receiver cavity radiation mathematical model and the working fluid tube heat model are established. Energy loss, energy absorbed by gas, the latent and sensible thermal energy storage in PCM, maximum tube temperature, gas outlet temperature and liquid PCM fraction were calculated. The results are analyzed and could be used in heat receiver design.     

Thermal Energy Storage Module Design Using Energy and Exergy Analysis

In this paper, irreversibility of a thermal energy storage system is numerically investigated. The system consists of two concentric cylinders. The outer cylinder is filled with phase change material (PCM), while working fluid flows inside the inner pipe. The system works periodically. The related governing equations are solved by a control volume-based finite difference method. The effects of different parameters such as PCM size and melting point temperature are examined on the irreversibility of the system. The results show that the irreversibility of thermal storage module is strongly affected by the size of PCM (diameter and length of the external cylinder) and melting temperature. Based on the obtained results, the irreversibility of the system can be reduced by proper selection of PCM size and melting temperature.     

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.     

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.     

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.     

矩形腔内相变材料接触熔化的分析

对矩形腔内相变材料紧密接触熔化过程进行了理论分析。应用努谢尔特液体边界层理论，求得了便于工程计算用的接触熔化传热过程的理论解。分析结果与实验数据进行了比较，吻合程度良好。     

Experimental validation of a CFD model for tubes in a phase change thermal energy storage system

A computational fluid dynamic (CFD) model for tubes in a phase change thermal energy storage system has been developed and validated with experimental results. The heat transfer fluid (HTF) flows in tubes which are configured in a unique arrangement during the charging and discharging processes. Water was used as the phase change material (PCM) which was contained in a cylindrical tank with four tubes coiled inside it. Experiments were conducted for both freezing and melting processes. A three-dimensional CFD model using Ansys code was developed and validated with experimental results. This model endeavoured to describe both the freezing and melting processes of the PCM. The inlet and outlet HTF temperatures as well as nine temperature locations in the PCM were compared with the CFD results. The average effectiveness as well as the duration of the phase change process of each experimental point was also compared with results from the CFD. From this study, it was concluded that the CFD model developed can accurately predict the behaviour of the thermal storage system during charging and discharging. The paper gives details of the CFD model and compares results from the model and experiments.     

Experimental study on the discharge characteristics of two eutectic solder packed bed latent heat storage systems

Metallic solder based PCMs possess higher thermal conductivities, larger storage masses and exhibit lower subcooling effects compared to their organic or inorganic counterparts. It is thus justified to investigate their potential usage for medium temperature applications. These solders are relatively expensive and can be combined with cheaper PCMs in cascaded storage systems which are more thermodynamically efficient compared to single PCM systems as reported recently. The aim of the research is thus to compare two packed bed storage systems during discharging cycles using eutectic solder (Sn63/Pb37), that is widely available worldwide. The single PCM system (40 capsules) consists of encapsulated spheres of eutectic solder, whereas the second cascaded system consists of encapsulated spheres of eutectic solder and erythritol in an equal storage ratio in the tank. For the cascaded system, the eutectic solder capsules are placed at the top and erythritol at the bottom of the storage tank (20 capsules at the top and 20 at the bottom). The effect of the discharging flow-rates of 4 mL/s, 6 mL/s and 8 mL/s is investigated in relation to the temperature profiles, energy rates and exergy rates. Increasing the flow-rate, increases heat transfer rate thus shortening the discharging time as well as increasing thermal profile reversals during discharging. The peak energy and exergy rates increase with the increase in the flow-rate for the two storage systems. The single PCM system shows slightly higher average energy and exergy rates compared to the cascaded system possibly due to its higher thermal conductivity. The cascaded PCM system shows higher average stratification numbers at all the flow rates considered. The non-cascaded system exhibited slightly higher exergy recovery efficiencies compared to the cascaded PCM system possibly due to its higher thermal conductivity at all flow-rates considered. The effect of the initial discharging temperature is also investigated with a discharging flow-rate of 6 mL/s after charging with set heater temperatures of 260°C, 280°C and 300°C, respectively. Comparable thermal profiles are seen for both systems for the three set temperatures; however, the single PCM system shows slightly higher storage temperatures. The single PCM shows slightly higher but comparable peak and average discharging energy rates compared to the cascaded system. The exergy rates for the two systems are also comparable. However, the cascaded system shows slightly higher exergy rate values for the lowest set temperature whereas the single PCM system shows slightly higher exergy rate values for the other two set temperatures. Energy and exergy rates are almost independent of the initial storage tank temperatures induced by different set charging temperatures. The average stratification number shows no correlation with set temperature for both storage systems. The cascaded system shows slightly higher average stratification numbers at different set temperatures. Exergy recovery efficiencies for different set heater temperatures are comparable for the two storage systems and vary only marginally with the increase in the set temperature. Overall, the effect of the flow-rate is more pronounced than the effect of the set heater temperature.     

Experimental and computational study of constrained melting of phase change materials (PCM) inside a spherical capsule

An experimental and computational investigation directed at understanding the role of buoyancy-driven convection during constrained melting of phase change materials (PCM) inside a spherical capsule is reported. The computations are based on an iterative, finite-volume numerical procedure that incorporates a single-domain enthalpy formulation for simulation of the phase change phenomenon. A Darcy’s Law-type porous media treatment links the effect of phase change on convection. Paraffin wax n-octadecane was constrained during melting inside a transparent glass sphere through the use of thermocouples installed inside the sphere. The melting phase front and melting fraction of the PCM are analyzed and compared with numerical solution obtained from the CFD code Fluent. Following a short period of symmetric melting due to prominence of diffusion, expedited phase change in the top region of the sphere and a wavy surface at the bottom of the PCM are observed. The computational predictions point to the strong thermal stratification in the upper half of the sphere that results from rising of the molten liquid along the inner surface of the sphere thus displacing the colder fluid. The waviness and excessive melting of the bottom of the PCM is shown to be underestimated by the experimental observation. This discrepancy is linked to the use of a support structure to hold the sphere. Measured temperature data and computational results near the bottom indicate the establishment of an unstable fluid layer that promotes chaotic fluctuations and is responsible for waviness of the bottom of the PCM. On the other hand, the comparison between the measured and computed temperatures in the top half of the sphere show the stable nature of the molten liquid layer. The computational results start to deviate from the thermocouple readings as one moves lower from the top of the sphere. This delay in predicting the melting instant is linked to the thermal stratification within the “constant temperature bath” that encloses the capsule.     

Numerical Analysis on a Latent Thermal Energy Storage System with Phase Change Materials and Aluminum Foam

Abstract

A latent heat thermal energy storage system with phase change material (PCM) is numerically studied. To enhance the heat transfer inside the system, a highly conductive metal foam is employed with ceramic nanoparticles. The latter method of enhancement leads to a new class of material called Nano-PCM. The system under investigation is a 70-L tank filled up with pure PCM or Nano-PCM and several pipes are situated where the heat transfer fluid (HTF) flows. The pipe surfaces are assumed at constant temperature above the PCM melting temperature to simulate the heat transfer from the HTF. The enthalpy-porosity theory is applied to simulate the PCM phase change, while the porous media formulation is assumed to describe the metal foam behavior. The nano-PCM is modeled with single-phase model where the properties are the weighted-average between the fluid base and the nanoparticles. The simulations are accomplished for charging-discharging process at different porosities and nanoparticle concentration. The results are given in term of average melting fraction evolution, average temperature as function of time, average stored energy. The metal foam significantly improves the heat transfer between PCM and HTF respect to the addition of nanoparticles, reducing the charging and discharging time more than one order of magnitude.