Thermal performance of a solar latent heat storage unit using rectangular slabs of phase change material for domestic water heating purposes
Introduction
Solar energy has become a reliable and popular alternative source of energy in several applications, especially in solar water heating systems which use a solar collector area to collect and convert solar radiation into thermal energy for water heating. Because the availability of solar radiation is irregular and intermittent in nature, the coupling of thermal storage systems with solar thermal collection systems is essential. It can improve the reliability and the generation capacity of solar systems as well as the reduction of the electricity consumption costs during periods of sunlight lack. Among the thermal storage systems, latent heat storage systems using phase change materials (PCMs) are at the center of focus due to their high thermal storage capacity and their isothermal behavior during phase change process. The research efforts on latent heat storage systems include numerical [1], [2], [3], experimental [4], [5] and analytical [6], [7] studies. PCMs have been employed in many practical applications, including solar cooling and heating [8], [9], [10], [11], building envelopes [12], [13], [14] and electric cooling [15], [16], [17].
In recent years, a number of numerical and experimental studies have been conducted to investigate the thermal performance of solar latent heat storage systems. Sharif et al. [18] presented a review of the previous studies on the thermal energy storage systems used in different parts of domestic hot water (DHW) systems and heating networks, including storage tanks, solar collector, packed beds, and specific heat exchangers. Seddegh et al. [19] conducted a review of the thermal energy storage technologies integrating phase change material (PCM) for solar DHW applications. Yang et al. [20] studied numerically a packed bed heat storage system connected with a flat-plate solar collector. The storage system consisted of spherical capsules filled with three kinds of PCM placed in series based on their melting point. They conducted numerical calculations to compare the storage performance of their proposed multiple-type PCM packed bed with the traditional single-type packed bed. The results revealed that the multiple-type PCM packed bed has higher exergy and energy transfer efficiencies compared to the single-type packed bed. El Qarnia [21] investigated numerically the thermal behavior and performance of a shell-and-tube latent heat storage unit (LHSU) coupled with a flat-plate solar collector during charging and discharging processes. Numerical calculations were conducted for three marks of PCM (n-octadecane, Paraffin wax, and Stearic acid) to get the optimum designs of the LHSU that maximize the thermal storage efficiency. Nallusamy and Velraj [22] studied experimentally and theoretically the storage performance of a packed bed thermal storage system connected with a flat-plate solar collector during charging process. They evaluated the influence of HTF mass flow rate and porosity of the bed on the system performance. The results showed that the variation in the HTF mass flow rate affects significantly the charging rate of the thermal storage system. However, the results revealed that the variation in the bed porosity has less effect on the charging time of the storage system. Ledesma et al. [23] developed a numerical model based on the enthalpy method and the finite volume approach to study the thermal behavior of a LHSU consisted of a packed bed combined with a flat-plate solar collector situated in the south of Spain. The packed bed storage system is made of spherical capsules filled with PCM usable for a solar DHW system. The numerical simulations were conducted for the meteorological data of several months in Malaga city to investigate the storage performance of the LHSU. Li et al. [24] developed a mathematical model based on finite-time thermodynamics to investigate the overall exergetic efficiency of a thermal storage system composed of two PCMs (named PCM1 and PCM2) combined with a concentrating solar collector. They examined the effects of the melting temperatures and the number of heat transfer units of the both PCMs on the overall exergetic efficiency. The results showed that the use of two PCMs instead of a single PCM can lead to an increase of the overall exergetic efficiency between 19% and 53.8%. Osterman et al. [25] carried out an experimental and numerical study of a LHSU composed of 30 plates of PCM (Paraffin RT22HC) co-operating with a solar air collector for space heating during morning and evening hours in winter. The results revealed that due to the large amount of heat available in March, the important energy savings are obtained at this month. Saman et al. [26] developed a mathematical model to analyze the thermal performance of a LHSU composed of a number of horizontally arranged PCM slabs during charging and discharging processes. The studied LHSU is a part of a roof-integrated solar heating system where air delivered by the flat-plate solar collector passes through the gap between the slabs and transfers heat to PCM. The results showed that the increase in the inlet temperature and the augmentation of air flow rate decrease the melting and solidification times during charging and discharging processes, respectively. Wu and Fang [27] investigated numerically the thermal characteristics of a LHSU composed of a packed bed filled with spherical capsules of myristic acid as PCM integrated into a solar heat storage system. They evaluated the effects of the HTF mass flow rate, HTF inlet temperature and packed bed initial temperature on the storage performance of the LHSU during the discharging process. The results showed that the increase in the HTF inlet temperature and the mass flow rate enhances the heat release rate and reduces the time required for the complete solidification. Navarro et al. [28] presented an experimental study of a LHSU composed of a prefabricated concrete slab incorporating PCM in its hollows and coupled to a solar air collector. The results showed the high potential of the proposed LHSU to reduce the energy consumption and the environmental impact. Tao and He [29] developed a two-dimensional mathematical model to investigate the thermal performance of a shell-and-tube LHSU under non-steady state characteristics of HTF at the inlet. They evaluated the effect of the non-steady state inlet temperature and mass flow rate of HTF on the solid-liquid interface, melting fraction, thermal energy storage capacity, HTF outlet temperature, and heat transfer rate. The results showed that the time required for the complete melting of PCM decreases with increasing initial HTF inlet temperature and mass flow rate. Elbahjaoui and El Qarnia [30] investigated the thermal performance of a shell-and-tube LHSU heated by a pulsed HTF flow during melting process. The effects of the pulsation frequency, pulsation amplitude, Reynolds number, and Stefan number on the thermal characteristics of the storage unit were numerically evaluated. The results showed that the pulsating parameters of HTF flow affect the melting time of PCM and the shorter melting time is obtained for a low pulsating frequency and high pulsating amplitude. Elbahjaoui et al. [31], [32], [33] studied the melting of PCM (Paraffin wax P116) dispersed with nanoparticles in a rectangular LHSU heated by a laminar HTF flow. The storage unit is made of a number of vertically arranged slabs of nanoparticle-enhanced phase change material (NEPCM) separated by a laminar flow of HTF (water). They investigated the effects of the volumetric fraction of nanoparticles, aspect ratio of NEPCM slabs, Reynolds number, and Rayleigh number on the storage performance and flow characteristics of the storage unit. They also developed a correlation including all the investigated parameters to estimate the time required for the complete melting of the storage unit.
In most of the studies published previously on latent heat storage systems coupled with solar collectors, the rectangular configuration of storage tanks using vertically oriented PCM slabs has not been researched before. Furthermore, in most of the previous works on the thermal performance of latent heat storage tanks co-operating with flat-plate solar collectors, the effect of natural convection in the liquid PCM has been neglected or described by an effective thermal conductivity in order to consider only the thermal conduction in the PCM and simplify the numerical modeling. In the proposed study, the thermal performance of a rectangular latent heat storage unit composed of several PCM slabs exchanging heat with a heat transfer fluid heated in a flat-plate solar collector has been numerically investigated. The effect of natural convection is taken into account by resolving the momentum equations in the liquid PCM.
The objectives of the proposed study are threefold. First, a two-dimensional numerical model has been presented for predicting the heat transfer and flow characteristics in the LHSU and flat-plate solar collector. Moreover, the developed numerical model has been validated by comparing the predicted results with the experimental, numerical and theoretical results available in literature. Second, the numerical calculations were carried out to evaluate the effect of the geometrical and operational control parameters for three commercial phase change materials having different melting temperatures. This parametric study aims to determine the number of HTF channels, total mass of PCM and mass flow rate of HTF circulating in the solar collector that maximize the latent storage efficiency under the meteorological conditions of a representative day of the month of July in Marrakesh city, Morocco. Therefore, the optimal geometric design and operational parameters depending on the kind of PCM are given. Third, the thermal performance and flow characteristics of the optimal designs of LHSU have been investigated during charging and discharging processes. In addition, the effect of the mass flow rate of HTF on the thermal performance of the optimal storage units has been also evaluated during discharging process.
Section snippets
System description
Fig. 1 shows the schematic diagram of the coupled solar collector LHSU investigated in the present study during charging and discharging processes. It consists of a flat-plate solar collector which is combined with a thermal storage tank containing vertical arranged slabs filled with PCM (Fig. 2a). The height of the PCM slabs, thickness of the HTF channels and collector area of the solar collector are fixed at 0.5 m, 6 mm and 2 m2, respectively. During the charging process, the water heated by
Modeling of flat-plate solar collector
In steady state, the useful energy collected by a flat-plate solar collector is defined as the difference between the absorbed solar radiation and thermal losses. It is expressed as follows [34]:where Ac is the collector area, FR is the collector heat removal factor, IT is the total incident radiation on solar collector, (τα) is the average transmittance-absorptance product, UL is the collector overall heat loss coefficient, Tf, o is the water inlet temperature to
Numerical solution and validation
The set of governing equations are integrated using the finite volume approach over each control volume. The convection terms in governing equations are treated adopting the power law scheme. The pressure-velocity coupling in momentum equations is resolved using the SIMPLE algorithm. And the resulting algebraic equations are solved using the iterative Tri-diagonal Matrix Algorithm (TDMA).
The developed numerical model has been implemented into an in-house Fortran code to carry out the numerical
Results and analysis
The numerical calculations were performed to investigate the storage performance and thermal behavior of the LHSU coupled with a flat-plate solar collector for three kinds of PCM: RT42, RT50 and RT60. The melting temperature of the PCMs used in this study for storing collected solar energy are 41°C, 49°C and 60°C for RT42, RT50 and RT60, respectively. The thermo-physical properties of PCMs are obtained from the manufacturer [45], and they are displayed as well as those of HTF [36], [46] in
Conclusion
The thermal performance of a rectangular latent heat storage unit coupled with a flat-plate solar collector was studied numerically for three kinds of PCM (RT42, RT50 and RT60). A numerical model based on the finite volume approach and the conservation equations of mass, momentum, and energy was developed and validated by comparing the present simulation results with the experimental, numerical and theoretical results previously published in the literature. The developed numerical model was
Conflict of Interest
The authors declare no conflict of interest.
Acknowledgement
We extend our sincere thanks to the Joint International Laboratory LMI-TREMA (http://trema.ucam.ac.ma) for providing us the meteorological data.
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