Numerical study of integrated latent heat thermal energy storage devices using nanoparticle-enhanced phase change materials

Numerical study of integrated latent heat thermal energy storage devices using nanoparticle-enhanced phase change materials

Solar Energy 194 (2019) 724–741 Contents lists available at ScienceDirect Solar Energy journal homepage: www.elsevier.com/locate/solener Numerical ...

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Solar Energy 194 (2019) 724–741

Contents lists available at ScienceDirect

Solar Energy journal homepage: www.elsevier.com/locate/solener

Numerical study of integrated latent heat thermal energy storage devices using nanoparticle-enhanced phase change materials

T

B. Akhmetova,b, , M.E. Navarroc, A. Seitova,b, A. Kaltayevd, Z. Bakenove, Y. Dingc ⁎

a

Mechanics Department, Al-Farabi Kazakh National University, Almaty, Kazakhstan GreenWell Mechanics, LLP, Almaty, Kazakhstan c Birmingham Centre for Energy Storage, University of Birmingham, Birmingham, UK d Institute of Industrial Engineering, Satbayev University, Almaty, Kazakhstan e School of Engineering, Nazarbayev University, Astana, Kazakhstan b

ARTICLE INFO

ABSTRACT

Keywords: Latent heat thermal energy storage Phase change materials Thermal properties Nanomaterials Numerical modeling CFD

Two sequentially integrated LHTES devices based on paraffin waxes (PW), PW-L and PW-H with different phase change temperature ranges are numerically studied using Comsol Multiphysics for efficient thermal energy storage (TES). Thermal properties of the PWs are characterized and aluminum oxide nanoparticles (nano-Al2O3) are dispersed into the PWs to improve their heat transfer ability. According to the laser flash apparatus results, when the nano-Al2O3 composes 4 wt% of the mass of the PW-L, its thermal diffusivity can be enhanced up to 40%. The same amount of the nano-Al2O3 improves the thermal diffusivity of the PW-H approximately by 25%. Further characterization studies show that the incorporation of the nano-Al2O3 does not significantly change the specific heat capacity, latent heat of melting and cooling of the PCMs, but improves the heat transfer efficiency of the PCMs. Measured thermal properties of the PCMs are considered as input data in the numerical simulation of operating regimes of the devices. The full charging time of the integrated LHTES devices is reduced by 57 min and 106 min when the nano-Al2O3 composed 2 wt% and 4 wt% of the mass of the PCMs respectively. Likewise, the full discharging time of the integrated devices is decreased by 32 min and 74 min by the addition of the nanoAl2O3. Such reductions lead to improved charging and discharging efficiency of the LHTES devices. Moreover, simulation results show that the total amount of the stored energy in the devices fairly approximates the differential scanning calorimetry (DSC) results.

1. Introduction Buildings consume around 32% of world’s total energy with most of it coming primarily from hazardous coal/gas based thermal power plants. Consequently, buildings account for a significant percentage of the world’s greenhouse gas emissions (Ürge-Vorsatz et al., 2015; Boeck et al., 2015). Besides energy efficiency of buildings, other reasons need to be considered in order to reduce the energy consumption of buildings. For instance, occupants’ behavior must be taken into account during the design stage of buildings to avoid the significant gap between the predicted and actual energy consumption of buildings (Delzendeha et al., 2017; Nabizadeh Rafsanjani and Ahm, 2016). Furthermore, renewable energy sources should be considered as the energy source and integrated to buildings by means of decentralized community-scale systems (i.e. micro-grids), thus avoiding conventional centralized grids and district heating systems, which have enormous energy losses during the long-distance transmission of the energy to ⁎

consumers (Reynolds et al., 2017; Werner, 2017). Similar to smart electrical grids (Kolokotsa, 2016), 5th generation district heating and cooling systems will soon operate at advanced and energy efficient level, where futuristic thermal networks permit decentralized community-scale systems as well as consumer substations to interact by selling surplus thermal energy or buying missing capacity (Buffa et al., 2019). Surely, thermal energy storage (TES) device plays main role in such smart thermal networks, providing balanced energy management between production and use at the decentralized community-scale level or at the consumer substation level. Consequently, TES device with fast charging and discharging rates is required for such thermal networks (Heier et al., 2015; Akhmetov et al., 2016). TES devices will certainly be located in densely populated and urban areas. Consequently, besides charging and discharging rates, the size and energy density of TES devices are also important (Hsieha et al., 2017). Comparted to sensible heat storage device, latent heat thermal energy storage (LHTES) device enables significantly higher storage

Corresponding author. E-mail address: [email protected] (B. Akhmetov).

https://doi.org/10.1016/j.solener.2019.10.015 Received 4 August 2019; Received in revised form 30 September 2019; Accepted 9 October 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.

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Nomenclature

cf cP ds Estored

Emax Fz kf kp n pf Qs qchar

qdis qs Tf TP TPC Ts t u ,v ,w uP ,vP ,wP

Greek symbols

specific heat capacity of the heat transfer fluid (J/kg K) effective specific heat capacity of the PCMs (J/kg K) thickness of the layer (m) total amount of the stored thermal energy in the PCM containers (J) maximum amount of the thermal energy that can be stored in the PCM containers (J) gravity force (N/m3) thermal conductivity of the heat transfer fluid (W/m K) effective thermal conductivity of the PCMs (W/m K) normal to the thin layer surface (-) pressure of the heat transfer fluid (Pa) heat source within the thin layer (W/m3) heat flux between the initial and current time of the charging state (W/m2) heat flux between the initial time and current time of the discharging state (W/m2) net outflux of the heat through the top and bottom surfaces of the thin layer (W/m2) temperature of the working fluid (K) temperature of the PCMs in the containers (K) phase change temperature (K) temperature of the layer (K) current charging/discharging time (t) velocity components of the heat transfer fluid (m/s) velocity components of the PCM (m/s)

P

µf char

dis f

p

effective thermal diffusivity (m2/sec) phase indicator dynamic viscosity of the heat transfer fluid (kg/ms) charging efficiency (-) discharging efficiency (-) density of the heat transfer fluid (kg/m3) effective density of the PCMs (kg/m3) volume fraction (-)

Acronyms BC CNT CN-PW CFD DSC LFA LHTES PW PW-L PW-H PCMs PCT TES

boundary condition carbon nanotube copper nanocomposite mixed paraffin wax computational fluid dynamics differential scanning calorimetry laser flash apparatus latent heat thermal energy storage paraffin wax paraffin wax with low phase change temperature range paraffin wax at high phase change temperature range phase change materials phase change temperature thermal energy storage

controlled by the bottom fraction of the PCM, since it took longer time than the top and central fractions of the PCM due to the particular design of the LHTES. Some other types of LHTES devices and their performance depending on design features are discussed in the review works (Li, 2015). Here, the authors propose a novel design of the LHTES device with embedded PCM containers, which can be uniformly charged or discharged during operating regimes. Moreover, the storage efficiency is increased by sequentially integrating two LHTES devices each having own PCM with specific phase change temperature (PCT) range. Paraffin waxes (PW) are studied as PCMs for the sequentially integrated LHTES devices due to their low cost, non-toxicity, substantial amount of latent heat and chemical stability for large number of thermal cycles (Sharma et al., 2015). Moreover, PCT ranges of most PWs are suitable for thermal energy storage for space heating and SHW applications (Kahwaji et al., 2018). Yet their major drawbacks such as significant thermal resistance to heat transfer, low thermal conductivity and thermal diffusivity prevent PWs from using extensively in thermal energy storage devices, which are designed for fast operating regimes (Rathod and Jyotirmay, 2013; Drissi et al., 2019). In the current studies, Al2O3 nanoparticles (nano-Al2O3) are mixed into the PWs with the purpose of enhancing their heat transfer properties. Thermal properties, such as thermal diffusivity, thermal conductivity, specific heat capacity, latent heat of melting and cooling, density changes of the pure and nano-Al2O3 added PWs are experimentally characterized within the operating temperature range of the LHTES device, and the data is further used in the numerical studies to evaluate the design and heat transfer efficiency of the LHTES devices as well as the effect of nanoAl2O3 addition to the charging and discharging duration of the sequentially integrated LHTES devices. In fact, designing and development of LHTES devices based on nanomaterial enhanced PWs and the effect of nanomaterial addition to the energy storage performance of the LHTES devices have not been studied much in detail. Few articles provide research results, where nanomaterial enhanced PWs were tested in a TES system as PCMs. One of the

energy density in smaller volumes (Za et al., 2016). As storage media, different types of PCMs have been studied and tested using experimental and numerical approaches (Pielichowska and Pielichowski, 2014). Due to the high heat of fusion, PCMs are capable of storing and releasing a significant amount of thermal energy. However, poor thermal properties of phase change materials (PCM) usually results in relatively long charging and discharging of LHTES devices (Sharma et al., 2015). This is the main reason that LHTES devices still have not been widely used for energy intensive thermal networks, which often require dynamic heat exchange to provide required heating/cooling performance for consumers. There are mainly two ways to increase the charging and discharging performance of the LHTES device: (i) improve the design of the LHTES device (Kalapala and Devanuri, 2016); and (ii) increase the heat transfer ability of the PCM using additional high conductive materials (Qureshi et al., 2018; Leong et al., 2019). According to the previous experience, the improper design of the LHTES device initiated steadystate non-uniform thermal energy distribution in the device, which resulted in long lasting charging and discharging times (Seitov et al., 2016; Akhmetov et al., 2018). It should be noted that the charging or discharging time usually indicates the complete melting or solidification of the PCM at the heating or cooling temperature. In fact, there are many design examples of LHTES devices, where non-uniform thermal energy distribution in the devices led to extended charging and discharging times. For instance, in the case of the LHTES device with single and double spiral coil tubes used as heat exchangers for heat transfer fluid flow, the half and one third of the charging time, respectively, was spent to charge the residue fraction (around 10%) of the non-melted PCM in the LHTES (Zheng et al., 2018). Likewise, shell and tube type LHTES with longitudinal fins was experimentally investigated and readings from the thermocouples at various zones of the storage as well as photographic illustrations of the solidification front of the PCM during the discharging studies showed that the temperature distribution in the LHTES was non-uniform for various inlet temperatures and flow rates (Agarwai and Sarviya, 2016;19). The complete discharging was 725

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studies carried out by Lin and Al-Kayiem (2016) where they experimentally confirmed that utilization of copper (Cu) nanoparticles (1 wt %) dispersed PW in the solar-TES pilot plant, increased the efficiency of the system by 1.7%. Elfasakhany (2016) studied solar distillers integrated with thermal energy storage (TES) tubes filled with PCMs. Fourteen copper tubes with 115 cm length, 16 mm diameter, and 1.5 mm thickness were used as TES in the basin of the solar distiller. The PW and copper nanocomposite mixed PW (CN-PW) were filled into the TES tubes as storage materials. The number of cases were compared: solar distiller (i) without any TES tubes; (ii) with TES tubes filled with the PW and (iii) with TES tubes having the CN-PW. Thus, due to the application of the TES based on the CN-PW, the overall daily productivity of the distiller increased up to 106% and 125% respectively compared to the cases (i) and (ii). Chen et al. (2016) numerically as well as experimentally investigated cylindrical LHTES system with the inner radius of 10 cm and the height of 30 cm and filled with PW/expanded graphite composite PCM. The storage has a spiral coil tube functioning as heat exchanger between PCM and the heat carrier fluid. The research was mainly dedicated to investigate the influence of the heat carrier fluid temperature and the Reynolds number of the flow on the performance of the LHTES device, as well as, to optimize its design. The authors did not discuss the efficiency difference between the application of pure and expanded graphite added PWs in the LHTES device. A shell and tube heat exchanger based LHTES filled with paraffin as PCM was experimentally and numerically studied and the impact of nano-additives such as aluminum oxide (Al2O3), aluminum nitride (AIN) and graphene nano-platelets (GnP) to the LHTES performance was investigated. It was noticed that the nano-additives improved both charging and discharging rates, although, the addition of these materials into PCM more than 3% (volume fraction) resulted in significant reduction of the storage capacity and the decrease of the natural convection rate in the device, thus adversely influencing to its thermal performance (Khan and Ahmad Khan, 2018). Prior to prototyping, the use of CFD methods for the development of thermal energy systems has substantial advantages such as the brevity of the time consumed to study the thermo-physical processes and the easiness of carrying out design and geometry optimization at both the system and component levels. But, CFD modeling should fully describe transport phenomena in the system and it must take into account the thermal properties of the materials related to the system to achieve reasonable results. According to the review paper on CFD studies of LHTES devices (Al-abidi et al., 2013), almost all of the numerical studies were limited to simple rectangular, cylindrical or spherical forms of LHTES devices while computational domains were mainly 1D, 2D and 2D axisymmetric, meaning that the geometries of LHTES devices were purposefully simplified to reduce computational costs and avoid the modeling of time-dependent heat transfer and fluid flow processes in complicated domains. Very few authors have published recently their works with the simulation results obtained in 3D computational domain, which numerically studied heat transfer and fluid flow processes in designed LHTES devices. Niyas et al. (2017) studied a shell-and-tube type of LHTES device. Applying 3D CFD studies to the discharging process of the LHTES, the number of embedded tubes and fins on the tubes were optimized. Youssef et al. (2018) conducted 3D CFD modeling of charging and discharging modes of the PCM heat exchanger with spiral-wired tubes. Based on the numerical studies, the influence of the various inlet flow rates and inlet temperature of the heat transfer fluid on the PCM melting/solidification times were analyzed. Allouchen et al. (2016) investigated the phase change processes within horizontally placed, 100 l cylindrical storage device, by means of CFD in 3D computational domain. The aim of the research was to validate the numerical approach by comparing the results with experimental data obtained from the charging of the storage device for three different flow rates of the heat transfer fluid. The PCM bulk temperature and accumulated energy in the storage device were numerically predicted within 5% and 10% of the experimental data.

Even though the aforementioned CFD studies (Niyas et al., 2017; Youssef et al., 2018; Allouchen et al., 2016) take into account transport phenomena in the LHTES devices, none of them included the temperature dependency of the properties of the PCMs in the modeling. Instead, the thermal properties of the studied PCMs were considered to be constant in solid and liquid states. Thus, besides development of the novel design of the sequentially LHTES devices, the current work also considers the combination of the PCM thermal characterization with 3D numerical simulations to achieve accurate numerical results. In other words, temperature dependent thermal properties of the pure and nanoAl2O3 added PWs both in the solid and liquid states, are used together with the continuity and energy equations for accurate numerical simulation of operating regimes of the sequentially integrated LHTES devices. Thus, the CFD simulation results showed that the sequential integration of two LHTES devices having various PCT can efficiently store thermal energy. Moreover, the results demonstrated that the addition of the nano-Al2O3 significantly improves the charging and discharging efficiency of the LHTES devices, thereby keeping their energy storage capacity nearly unchanged. 2. Experimental studies of the PCMs 2.1. Materials and preparation Two fully refined paraffin waxes, PW-L and PW-H were studied as PCMs, where letters L and H indicates low and high phase change temperature ranges of the PCMs respectively. According to the manufacturer (poth-hille.co.uk) the melting/congealing point of the PW-L is around 44–48 °C and it is the mixture of various low melting point paraffin wax components. Furthermore, the melting/congealing point of the PW-H is in the temperature range of 64–66 °C and its composition mostly consists of C18-C40 carbon atoms. The detailed information of the PWs is provided in Table 1. Sigma-Aldrich’s Al2O3 nanopowder (product No.: 718475) with a primary particle size of around 13 nm and a surface area of 85–115 m2/g was added to the PWs with the purpose of improving their thermal properties. In order to disperse Al2O3 nanoparticles into the PWs two techniques were applied in the following order: (1) firstly, nanoparticles were mixed with the PWs by means of an ultrasonic bath for half an hour at the rate of 60 kHz, while keeping the temperature of the PWs above their melting points; (2) then, the composite PCMs were mechanically mixed for 15 min at the medium stirring rate of 300 rpm, while maintaining their liquid state with a hot plate; (3) finally, the samples were sonicated again at the same rate as in the first step for additional 30 min to achieve well-dispersed final composite nano-Al2O3-PWs (Fig. 1). Mass percentages of Al2O3 nanoparticles in the PWs were 2% and 4 wt%. Therefore, the number of PCM samples were six: (i) two pure PWs; (ii) two nano-Al2O3 (2 wt%)-PWs; and (iii) two nano-Al2O3 (4 wt%)-PWs. 2.2. Particles-dispersed composites In certain cases, an approximation of a heterogeneous material as Table 1 Information about the PWs provided by the manufacturer (Poth Hille & Co Ltd).

726

PW-L

PW-H

Product name (by manufacturer) Shape Color Melting/Congealing point Content

Low melt point paraffin wax (PHCTW4448) Pellet form Saybolt 44–48 °C Mixtures of the different paraffin wax components

CAS number

8002-74-2

Paraffin wax (PHC6568) Pellet form Saybolt 64–66 °C Mainly consists of C18-C40 carbon atoms 8002-74-2

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Fig. 1. Preparation process of the nano-Al2O3-PWs as PCMs for the LHTES devices.

nearly homogeneous in transient thermal analysis allows to measure its effective thermal properties using appropriate tools. Moreover, based on such approximation it is possible to numerically study heat transfer processes through the heterogeneous material without any difficulties if the size of dispersed particles or fibers are much smaller compared to the size of the sample (Lee and Taylor, 1978). In the current studies, dispersed Al2O3 nanoparticles were significantly smaller than PW sample dimensions and added in small amounts. Therefore, nano-Al2O3 dispersed PWs could be approximated as nearly homogeneous composite PCMs for the transient thermal analysis. Otherwise, due to the discontinuity of the thermophysical properties of the composing materials at the contact interface, the thermal properties of the composite PCMs, couldn’t be evaluated readily even for simple geometric configurations. Thus, by taking into account aforementioned assumptions, the relation between the thermal parameters of the nano-Al2O3-PWs was established using the following formula: P

=

kP ( c )P

LHTES based on PWs, as well as, how the addition of nano-Al2O3 into PWs would influence on the efficiency of the LHTES devices. 2.3. Characterization techniques The specific heat capacity, latent heat of melting and cooling, and phase transition temperature ranges of the pure and nano-Al2O3 added PWs were evaluated by DSC2 (Mettler Toledo). 10 mg samples of PCMs were placed into standard aluminum crucibles. An empty crucible and a crucible with a sapphire were used as the blank and the reference respectively to evaluate the specific heat capacity of the PCMs. The studies were performed in a nitrogen gas environment, starting with the isotherm at 15 °C for 10 min, then heating up at the rate of 5 °C/min till the sample temperature reached 100 °C, and finally providing the isotherm at 100 °C for 10 min. The samples were then cooled down at the rate of 5 °C/min till 15 °C with the final 10 min isotherm at the same temperature. The temperature range of the study, 15–100 °C, was chosen because the LHTES devices need to work in that temperature range to store solar thermal energy for heating applications. The aim of using the DSC was not only to evaluate the cp, latent heat, temperature range and peak of the phase change of the PCMs, but also to understand how these parameters were changed or shifted when Al2O3 nanoparticles were added in different amounts to the PWs. The densities of the pure and nano-Al2O3-PWs were measured by means of a density meter, DMA 4100 (Anton Paar). Assigned temperature range for the density measurements was same as in DSC studies (15–100 °C) and the densities of the PCMs were measured with 5 °C increment within this range. The results were studied together with the results of DSC and LFA to evaluate the thermal properties of the pure and composite PCMs. The thermal diffusivities of the pure and nano-Al2O3-PW samples in the solid and liquid states were measured using a laser flash apparatus, LFA 427 (Fig. 2). The liquid nitrogen cooled furnace, designed to carry out measurements in the temperature range of −70 °C to 400 °C, was used to evaluate the thermal diffusivity of the PCMs in the range of 15–100 °C. A crucible made of platinum-rhodium (Pt/Rh: 90/10) for non-metallic melts, was used to hold the PCM samples in the furnace. In fact, the PCM was placed into the crucible in the solid state and slowly heated until it melted and evenly spread over the bottom of the crucible. The amount of the PCM was measured in advance to make sure

(1) 2

where P – effective thermal diffusivity (m /s), kP – effective thermal conductivity (W/m K), P – effective density (kg/m3), c P – effective specific heat capacity (J/kg K) of the nano-Al2O3-PWs (subscript p represents the variables of the PCMs). In fact, the denominator of Eq. (1), which is effective volumetric heat capacity, can be written for composite materials from the equilibrium expression in the following form (Lee and Taylor, 1978):

( c )P = vPW ( c )PW + vAl2 O3 ( c )Al2 O3

(2)

where v is the volume fraction and the subscripts denote the composing substances of the PCMs. It should be noted that when the nano-Al2O3 is absent in the PCM, Eq. (1) describes the thermal properties of the pure PWs. In most of the cases, the measuring of the density and the specific heat capacity of the pure nanomaterials, such as Al2O3 is challenging. As a result, the effective volumetric heat capacity ( c )P of the composite material can’t be calculated based on the properties of the composing materials, which are Al2O3 and PWs in our case. Alternatively, the effective thermal properties of the PCMs such as nano-Al2O3-PWs could be measured experimentally using appropriate tools, for instance, laser flash apparatus LFA and differential scanning calorimetry (DSC). By experimentally evaluating these properties and further applying them in a numerical model, it is possible to assess the performance of the 727

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devices, which contain pure or nano-Al2O3-PWs (each of them having different phase change temperature (PCT) ranges). When solar thermal energy collected by a heat transfer fluid is available or when there is an excess of energy from the main thermal storage tank of the solar district heating network, the heat is transferred into the LHTES devices. Thus, the heat is firstly transferred into the PCM with higher PCT range (i.e. PW-H). The remaining thermal energy is further sequentially delivered to the LHTES-L device, in which PCM has a lower PCT range (i.e. PW-L). Thus, the heat is gradually transferred into the PCMs and the cooled heat transfer fluid leaves the LHTES-L and returns to the solar collectors (or heat source) to further operate in the closed loop. Once the PCMs in both LHTES devices are fully melted, the charging process is stopped. During the discharging mode, the flow direction is reversed. The heat transfer fluid first flows through the LHTES-L device which contains the PCM with lower PCT range, and then through LHTES-H device, which contains the PCM with higher PCT range. Thus, the heat transfer fluid gradually gains the thermal energy from the sequentially connected LHTES devices to deliver the energy for heating application purposes or send the surplus thermal energy to the main (central) storage of the district heating network. The detailed illustration of the LHTES device and its design features are shown in Fig. 5. The storage vessel with 1.05 m height and 0.74 m diameter has 27 containers filled with PCM. The PCM containers in the LHTES have a circular cross section with a diameter of 0.09 m and a height of 95 cm. 27 PCM containers are placed as three concentric circles: external circle contains 16 of them, while the middle and inner circles have 8 and 3 containers respectively, as shown in Fig. 5. The storage vessel and PCM containers are considered to be made of stainless steel. The inlet apertures at the bottom of each PCM container are designed to evenly deliver the heat transfer fluid into the storage tank. Similarly, the outlet apertures are also located on the top of each PCM containers to extract the heat transfer fluid and deliver it to the next LHTES device. Such distribution of inlet and outlet apertures improves the charging and discharging rate of the PCM containers, as if they are functioning as stand-alone thermal energy storage.

Fig. 2. Illustration of the thermal diffusivity measurement technique using the laser flash apparatus (LFA 427).

that the thickness of the PCM in the container was 0.6 mm according to the sample preparation requirements of the LFA apparatus. Then the crucible was covered with its lid and cooled down to the room temperature to bring the PCM to its solid state. Practically, aforementioned process assures the uniform contact of the PCM with both the inner surface of the lid and the bottom of the crucible. Under these circumstances, the PCM holding crucible is considered as a three-layer model, metal-PCM-metal, as illustrated in Fig. 3, where the thicknesses of the upper and lower layers were 0.305 mm and the thickness of the PCM layer was 0.505 mm with an unknown thermal diffusivity (Lee et al., 1978Maglić and Taylor, 1992). Furthermore, the crucible was coated with a micro-graphite spray to increase the absorbance of the laser energy at the bottom of the container and improve the emission of the infrared light on the surface of the crucible lid, thus, optimizing the signal-to-noise ratio for thermal diffusivity measurement purposes. During the measurements, liquid N2 was poured into the furnace from a dewar with the purpose of cooling down the furnace when necessary. The laser voltage and the pulse width were 450 V and 07 ms respectively. At the assigned temperature values, the laser was shot three times and their average values were taken as the effective thermal diffusivity of the PCM at that temperature value. Actually, the laser shots were performed at different temperature sets for PW-L and PW-H based PCMs since they have various phase transition temperature ranges. In order to obtain accurate measurement results, the temperature difference threshold was set to 1 K, which allowed measuring the effective thermal diffusivity at the required temperature with the deviation of around ± 1 K. The thicknesses of each layer, thermal properties of the upper and lower layers must be known in order to apply the three-layer model (with non-linear regression and consideration of heat loss) for the evaluation of the unknown thermal diffusivity of the mid layer, which is the PCM sample.

3.2. Numerical modeling The simulation of the fluid flow and heat transfer processes within the LHTES devices is based on 3D space and time-dependent numerical analysis. Comsol Multiphysics, version 5.2 was used for this study. In fact, 3D simulation can provide the complete velocity field of the heat transfer fluid, solid-liquid interaction in terms of pressure and temperature within both PCM containers and LHTES devices. Therefore, the dimensions of the computational domain coincide with the actual LHTES design illustrated in Fig. 5. In the numerical studies carried out in this work, depending on the charging/discharging direction, the temperature and velocity of the outlet tubes of the neighboring LHTES

3. CFD studies 3.1. Sequentially integrated LHTES devices Fig. 3. Cut view of the three-layer model, metal-PCM-metal.

Fig. 4 illustrates the concept of sequentially connected LHTES 728

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Fig. 4. Schematic illustration of the sequentially connected LHTES devices.

device are used as the inlet conditions at the inlet tubes of next LHTES device in the sequence. It is assumed that there are no heat losses from the heat transfer fluid coming out from one storage device and entering to the second device (Fig. 4). Temperature dependent thermo-physical properties of the PCMs obtained from DSC, DMA and LFA studies were used in the LHTES performance modeling (Table 2). These properties were defined as functions in Global Definitions node of the model tree of the Comsol and applied together with the fluid flow and heat transfer modules to model the processes in the LHTES devices. The properties of the other materials such as the heat transfer fluid (water) and the LHTES stainless steel container were taken from the inbuilt library of the Comsol. The steps of the CFD modeling in Comsol Multiphysics software program is illustrated in Fig. 6. In order to avoid unnecessary numerical calculations, some physical processes that have minor impact

on the CFD results were not taken into account. Thus, the following assumptions were made: 1. Heat transfer does not occur between LHTES device and its surroundings since the storage vessels are considered to be perfectly insulated; 2. Fluid flow within the LHTES device is considered laminar; 3. Heat transfer through the PCM is conductive without free convection effect. In fact, paraffin waxes present high viscosity when melted, therefore, it assumed that the free convection in both containers does not significantly affect the heat transfer process between the PCM and the heat transfer fluid; 4. In the case of the PCM containers filled with nano-Al2O3-PWs, they are considered as homogeneous composite materials, because

Fig. 5. Design of the LHTES device. 729

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Table 2 Application of characterization results into CFD studies. Properties

Values

CFD domain/boundary

Melting temperature range Solidification temperature range Latent heat Specific heat capacity: solid/liquid Density: solid/liquid Thermal diffusivity/conductivity Thermal properties of heat transfer fluid (water) Thermal properties of stainless steel

From From From From From From From From

PCM containers PCM containers PCM containers PCM containers PCM containers PCM containers LHTES devices Thin layer approximation: PCM containers

Charging regime Initial temperature in LHTES devices Inlet temperature of LHTES-H Inlet temperature of LHTES-L Outlet temperature of LHTES devices Inlet flow rate Outlet flow rate

20 °C 80 °C CFD results at the outlet of LHTES-H Neuman BC 0.1 m/s Pressure BC

PCM containers and LHTES devices Inlet tubes of LHTES-H Inlet tubes of LHTES-L Outlet tubes of LHTES devices Inlet tubes of LHTES devices Outlet tubes of LHTES devices

Discharging regime Initial temperature in LHTESs Inlet temperature of LHTES-L Inlet temperature of LHTES-H Outlet temperature of LHTES devices Inlet flow rate Outlet flow rate

80 °C 20 °C CFD results at the outlet of LHTES-L Neuman BC 0.1 m/s Pressure BC

PCM containers and the storage tank Inlet tubes of LHTES-L Inlet tubes of LHTES-H Outlet tubes of LHTES devices Inlet tubes of LHTES devices Outlet tubes of LHTES devices

DSC results DSC results DSC results DSC results DMA results LFA results built-in material library of Comsol built-in material library of Comsol

Fig. 6. Steps of the CFD modeling in Comsol Multiphysics software program.

discontinuities in terms of the heat transfer across the highly conductive aluminum nanoparticles are negligible due to the number of the nanoparticles, which constitute 2 wt% and 4 wt% of the PCM weight. Consequently, for the transient thermal analysis based on the numerical simulation, the effective thermal properties of the nano-Al2O3-PWs were applied, which were measured by the characterization techniques described above.

f

f cf

=

Laminar Flow module was used to numerically solve the mass and momentum Eqs. (3) and (4) to describe the incompressible flow of the heat transfer fluid in the storage devices. The resulting velocity field is used in the Heat transfer in Fluids module to solve the energy Eq. (5) with the purpose of calculating the thermal field in the LHTES devices:

u v w + + =0 x y z f

u + t

f

u

u u u +v +w = x y z

f

v + t

f

u

v v v +v +w = x y z

pf + µf

2u

x2 2v

x2

+

+

2u

y2 2v

y2

+

+

2u

z2 2v

z2

Tf t x

f

u

+ (k f

w w w +v +w = x y z

f cf

Tf x

u )+

Tf

+v

x y

(k f

Tf y Tf y

+w )+

pf + µf

2w

x2

+

2w

y2

+

2w

z2

+ Fz

Tf z z

(k f

Tf z

)

(5)

where u , v , w – velocity components (m/s), f – density (kg/m3), pf – pressure (Pa), and µ f – dynamic viscosity (kg/ms), cf – specific heat capacity (J/kg K), kf – thermal conductivity (W/m K), and Tf – temperature of the heat transfer fluid (K) and Fz – gravity force (N/m3). Phase change processes in the PCM containers were modelled using the apparent heat capacity method coupled with the Heat Transfer in Fluids module applied for the PCMs (Fig. 6). According to the apparent heat capacity method, the latent heat is included in the heat capacity of the PCM as an additional term, and it is suitable to include solid-solid, solid-liquid and liquid-solid phase transitions in the desired order. Thus, the energy equation for PCM containers is:

(3)

pf + µf

w + t

(4) 730

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p cP

TP + t

=

x

(k p

p cp

uP

compared to the adjacent media. Since the layer is thin and has high thermal conductivity, one can assume that there is no temperature changes along normal direction to the thin layer. Therefore, the layer

TP T T + vP P + wP P x y z

TP T T )+ (k p P ) + (k p P ) x y y z z

(6)

where uP , vP , wP – velocity components of the flow in PCM containers (m/s), p – effective density (kg/m3), cP – effective specific heat capacity (J/kg K), kp – effective thermal conductivity (W/m K), and TP – temperature of the PCMs in the containers (K). Density, specific heat capacity and thermal conductivity equations that takes into account the phase change processes are: P

=

cP =

phase1

1

(

+ (1

phase 1 cp, phase 1

kP = kphase 1 + (1

a=

)

) phase 2 1 (1 2 phase 1 + (1

(7)

phase2

+ (1

)

phase 2 cp, phase 2 )

) kphase 2

+L

da dT

(8) (9)

phase 1

)

phase 2

(10)

T/2 and The phase transition occurs in a transition interval TPC TPC + T/2 , where TPC is the phase change temperature, and T is the difference between the temperature values of the phase transition start and end. In fact, operates as the Heaviside step function, that is, equal to 1 before the phase change temperature TPC and 0 after TPC , while da dT functions as a Dirac pulse. Therefore, the last term in Eq. (8) describes given amount of latent heat, which is released over the phase transition interval T . Moreover, since the convective flow is not taken into account in the PCM containers, convective term in the energy Eq. (6) is not considered. Temperature dependent values of the thermo-physical properties considered in Eqs. (3)–(10) were taken from the results of PCM characterization studies and from the built-in material library of the Comsol during numerical calculations as explained in Table 2. 3.3. Initial and boundary conditions As shown in Table 2, initially the temperatures of the integrated LHTES devices were 20 °C in the charging case and 80 °C in the discharging case respectively, while the velocity of the heat transfer fluid within the fluid flow domains was initially zero in both cases. No-slip boundary condition (BC) was applied to the fluid flow at the solid surfaces of the LHTES device as shown in Fig. 7a. The temperature at the inlet tubes of the LHTES-H was maintained at 80 °C during the charging case and the inlet temperature of the consequent LHTES-L was equal to the outlet temperature of the LHTES-H since they are sequentially connected to each other. In fact, modern solar collectors, especially evacuated tube solar collectors can provide medium and high temperatures in the range of 50–200 °C depending on the weather conditions (Khan and Ahmad Khan, 2018). Therefore, the selected charging temperature (i.e. 80 °C) in the current study was reasonable for the LHTES performance’s numerical simulation. Furthermore, during the discharging case, the inlet temperature of the LHTES-L was set to 20 °C and the temperature at the inlet tubes of the subsequent LHTES-H was considered equal to the outlet temperature of the LHTESL, as shown in Fig. 4. During both charging and discharging studies, the flow velocity at the inlet tubes was set to 0.1 m/s, for both LHTES devices. Outlet BCs for both velocity and temperature were Neumann type. The metal PCM containers were assumed to be highly conductive layers. This allows to efficiently model heat transfer in thin layers without the need of creating a numerical mesh for them, thus drastically reducing the computational time. The part of the geometry where this approximation is applied should satisfy two requirements: (1) the layer is significantly thinner than the thickness of the adjacent geometry; and (2) the considered part is a good conductive material

Fig. 7. (a) Schematic description of the BCs; (b) numerical grid of the LHTES device; (c) numerical grid of the PCM containers. 731

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Fig. 8. a) Illustration of the experimental set-up used in the previous study; and b) Comparison of the numerical and experimental temperature developments in the middle of the rectangular PCM container(the figures are redrawn from Akhmetov et al. (2018)).

can be considered as a boundary rather than a domain, leading to the reduced number of mesh elements in the computational domain. In the current study, the PCM containers are considered to be made of a thin stainless steel sheet, therefore, satisfies the conditions of the thin layer approximation. Thus, the equation that describes general heat flux boundary condition related to the thin layer is considered as:

n · q = d s Qs

ds s cs

Ts t

t ·qs

qs = ds ks t · T

that occupies the fluid flow domain in the LHTES devices as shown in Fig. 7b and the resulting velocity field is coupled with Eq. (5) to obtain the thermal field in the same numerical domain. Furthermore, Fig. 7c shows the meshing of the domain related to the PCM containers, where Eqs. (6)–(9) were solved numerically by taking into account the heat transfer processes between the heat transfer fluid and the PCMs.

(11)

3.4. Validity of the numerical approach

(12)

The validity of the numerical approach was previously confirmed with the comparison of the simulation results with the experimental data obtained from a LHTES device (Akhmetov et al., 2018). As it can be seen from the illustration of the experimental setup in Fig. 8, the LHTES device was charged using the thermal energy stored in the water-based storage tank, which was heated by the electrical heater. The aim of the numerical study was to understand the heat transfer processes in the device during the charging regime, where the PCM melts. According to the comparative analysis illustrated in Fig. 8 , the numerical method agrees with the experimental results, showing that the phase change process in the PCM container and the outlet temperature changes were properly simulated. The study concluded that the LHTES device design was not efficient in terms of a uniform charging of the rectangular PCM containers (Akhmetov et al., 2018). With the purpose of optimizing the grid elements of the current numerical study, a grid dependence test was performed on the temperature variation of the PCM as a function of charging time (Fig. 9). Pure paraffin wax (i.e. PW-L) was considered as the PCM in the container and its temperature change was averaged across it to analyze the grid dependence of the numerical results regarding the phase transition of the PCM in the storage device. The test results in Fig. 9 illustrate that the temperature evaluations in the PCM during charging were nearly identical for 399,917 (normal mesh) and 419,314 (fine mesh) number of grid elements, while 363,555 (coarser mesh) number of grid elements could not capture the detailed temperature change in the storage. Thus, based on the test, the total number of grid elements regarding the numerical domains (storage device and PCM containers) was assigned to 419,314.

where n – normal to the thin layer surface, q – net heat flux through the layer, ds – thickness of the layer (m), Qs – heat source within the layer (W/m3), s – density of the layer (kg/m3), cs – specific heat capacity of the layer (J/kg K), Ts – temperature of the layer (K), ks – thermal conductivity of the layer (W/m K), t – nabla operator projected onto the layer, qs – net outflux of the heat through the top and bottom surfaces of the layer (W/m2). For more information about Eqs. (11) and (12), please refer to the help tool of the Comsol Multiphysics: section “Theory for the Heat Transfer in Thin Structures” of the Heat Transfer Module. The flow of the heat transfer fluid takes place within the LHTES devices while the phase change processes take place in the PCM containers. Therefore, Eqs. (3) and (4) were solved at the nodes of the mesh

4. Efficiency of the storages The operating efficiencies of the LHTES devices were studied based on the expressions described by Mawire and McPherson (2008). In order to evaluate the charging efficiency of the devices the following equation was used:

Fig. 9. Grid dependence test. 732

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Table 3 Thermo-physical properties of pure and nano-Al2O3 added paraffin waxes (PW-L and PW-H). Latent heat of melting and melting point

Latent heat of cooling and solidification point

Average thermal diffusivity (in %), P

Average specific heat capacity (kJ/kgK), cP

Average density (kg/m3),

kJ/kg

°C

kJ/kg

°C

Solid state

Liquid state

Solid state

Liquid state

Solid state

Liquid state

PW-L PW-L + Al2O3 (2 wt%) PW-L + Al2O3 (4 wt%)

158.14 ↓152.98 ↓148.33

48.31 ↓47.08 ↓46.92

158.52 ↓153.07 ↓148.23

41.12 ↓41.03 ↓40.64

– ↑ 20% ↑ 41%

– ↑ 29% ↑ 39%

2.12 ↓2.02 ↓1.9

1.68 ↓1.6 ↓1.45

800.65 ↑828.6 ↑872.6

755.4 ↑784.6 ↑828.6

PW-H PW-H + Al2O3 (2 wt%) PW-H + Al2O3 (4 wt%)

183.15 ↓180.97 ↓178.69

66.29 ↓65.77 ↓65.64

183.16 ↓180.08 ↓178.44

59.78 ↓59.30 ↓59.10

– ↑ 11% ↑ 22%

– ↑ 15% ↑ 25%

1.94 ↓1.84 ↓1.66

1.89 ↓1.72 ↓1.56

808.9 ↑836.2 ↑887.5

768.8 ↑797.4 ↑846.9

t

char

0 S

=

Moreover, the studies indicated that the PW-H has a wider phase transition temperature range, around 52–70 °C compared to the PW-L. Similar to the PW-L, the mixing of the nano-Al2O3 with the PW-H also resulted in a moderate decrease of the latent heat and a shift on the melting and solidification peak, as shown in Table 3. According to the LFA studies, the thermal diffusivity of the pure and the nano-Al2O3 dispersed PCMs in the solid state were temperature sensitive while they were relatively constant in the studied liquid region. The results are shown in Figs. 10 and 12 together with the specific heat capacity (cp) curves of the corresponding PCMs through the secondary vertical axis. The average thermal diffusivity enhancement in the solid and liquid states of the PCMs due to the mixing of nano-Al2O3 particles, as well as, average values of cp for the solid and liquid states of the PCMs are provided in Table 3. Since the PCM studies were carried out within the temperature range of 15–100 °C, the solid and liquid states of the PW-L were within the temperature ranges 15–41 °C and 55–100 °C respectively. The highest thermal diffusivity value of the pure PW-L was equal to 0.18 mm2/s at 15 °C and it significantly decreased to 0.091 mm2/s at 40 °C. In the liquid state, the thermal diffusivity of the PW-L was relatively constant compared to the solid region and it was approximately equal to 0.16 mm2/s (Fig. 10). The addition of nano-Al2O3 particles into the PW-L, with a mass fraction of 2 wt% and 4 wt%, resulted in the enhancement of the effective thermal diffusivity within both solid and liquid states as illustrated in Fig. 10. Thus, in particular, due to the addition of 2 wt% of nano-Al2O3 particles, the effective thermal diffusivity of the PW-L increased around 20% in average within the solid state, while in the liquid state nearly 29%. With 4 wt% of nano-Al2O3, the effective thermal diffusivity improved in a similar manner as in the case of 2 wt%, by 41 wt% and 39% in average within the solid and liquid states respectively. The specific heat capacity cp of the pure PW-L was nearly constant in the solid state and equal to 2.12 kJ/kg K, while in the liquid state, it was remained stable around 1.68 kJ/kg K. The addition of 2 wt% of nano-Al2O3 into the PW-L led to a reduction of cp both in the solid and liquid states, thus obtaining values of 2.02 kJ/kg K and 1.6 kJ/kg K. The values of cp in the solid and liquid states continued to slightly decrease down to 1.9 kJ/kg K and 1.45 kJ/kg K respectively when the mass fraction of the nano-Al2O3 in the PW-L increased up to 4 wt% (Fig. 10). Since the modeling related to the charging and discharging of the LHTES, was carried out between the temperature range of 20–80 °C, using the measured results of the specific heat capacity cp, it is possible to calculate how much energy could be stored in the solid and liquid state, including the phase transition energy storage of the PCM per kilogram. Thus, the total energy that could be stored in PW-L within the temperature range of 20–80 °C is 260.4 kJ/kg; but it slightly decreased to 251.2 kJ/kg and 239.6 kJ/kg when nano-Al2O3 constituted 2 wt% and 4 wt% of the PCM’s total mass, respectively (Fig. 11). According to the current studies, the temperature ranges of the solid and liquid state of the PW-H were 15–52 °C and 70–100 °C. The thermal diffusivity of the PW-H in average was improved by 11% and 15% in

qchar dS dt Emax

(13)

where Emax is the maximum amount of the thermal energy (J) that can be stored in the PCM containers of the LHTES device within the operating temperature range of 20–80 °C; qchar is the heat flux (W/m2) that passes through the unit surface area dS of the PCM containers between the initial time and the current time t (s) of the charging regime. Similar expression can be applied to evaluate the discharging efficiency: t

dis

=

0 S

qdis dS dt Estored

P

(14)

where Estored is the total amount of the stored thermal energy (J) in the PCM containers of the LHTES device at 80 °C (usually Estored = Emax ); qdis is the heat flux (W/m2) at current time t (s) of the discharging regime. It should be noted that in the studies of the charging and discharging efficiencies of the LHTES devices based on Eqs. (13) and (14), the storage capacity of the PCM containers were considered only. Therefore, the thermal energy stored in the heat transfer fluid in the LHTES devices were excluded. In this way, it was possible to evaluate the efficiency of the PCM containers as the primary storage medium in the LHTES devices. 5. Results and discussions 5.1. Characterization of thermal properties A summary of the PCM thermal characterization is provided in Table 3. Some of the results are demonstrated by graphical illustrations to better understand the temperature dependency of the PCMs thermal properties. Thus, according to Table 3, the latent heat associated with the melting and solidification of PW-L were nearly the same, around 158 kJ/kg, although, the melting and solidification peaks were 48.31 °C and 41.12 °C respectively. The phase transition temperature range of the PW-L was around 41–55 °C. When nano-Al2O3 with a mass fraction of 2 wt% was mixed with the PW-L material, the latent heat of the melting and cooling process decreased to 152.98 kJ/kg and 153.07 kJ/ kg respectively. Moreover, the phase transition peaks were slightly shifted to 47.08 °C and to 41.03 °C respectively. Furthermore, when the mass fraction of the nano-Al2O3 in the PCM sample was increased up to 4 wt%, the latent heat of melting and solidification decreased and obtained the values of 148.33 kJ/kg and 148.23 kJ/kg respectively. The melting and solidification peaks were further shifted down to 46.92 °C and 40.64 °C. The DSC studies showed that the melting and solidification latent heat of the pure PW-H were nearly equal to the value of 183 kJ/kg, which was higher than the latent heat of the PW-L. The melting and solidification peaks of PW-H were 66.29 °C and 59.78 °C respectively. Therefore, the PW-H was considered as the PCM with higher PCT. 733

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average densities in solid and liquid state were 808.9 and 768.8 kg/m3. Similar to the PW-L, the addition of 2 wt% of nano-Al2O3 into the PW-H PCM resulted in a density increase, thus, having an average value of 836.2 and 797.4 kg/m3 in solid and liquid states respectively. These average density values increased to 887.5 and 846.9 kg/m3 when the mass ratio of nano-Al2O3 particles within the PW-H increased up to 4% (Table 3). The thermal conductivity of the pure and nano-Al2O3-PWs were calculated using the Eq. (3) and the results are shown in Figs. 16 and 17. It can be seen that the thermal diffusivity of the PWs was also improved due to the addition of nano-Al2O3 particles. The experimentally measured values of the latent heat, melting and solidification points, specific heat capacity, thermal diffusivity, density and thermal conductivity changes in relation with the paraffin waxes, PW-L and PW-H, were applied in Eqs. (6)–(10) in order to numerically study the charging and discharging performance of the sequentially connected LHTES devices, and to understand how the dispersion of nano-Al2O3 in the PWs could influence on the LHTES performance.

Fig. 10. Thermal diffusivity and specific heat capacity of the pure and nanoAl2O3 added PW-L measured by DSC and LFA respectively.

the solid and liquid states respectively when it contained 2 wt% nanoAl2O3. When the amount of the nano-Al2O3 in the PW-H increased up to 4 wt%, its thermal diffusivity further improved by 22% in the solid state and by 25% in the liquid state (Fig. 12). Unlike PW-L, the specific heat capacity values of the pure PW-H in the solid and liquid states were nearly same and equal to 1.94 kJ/kg K and 1.89 kJ/kg K respectively. These values slightly decreased to 1.84 kJ/kg K and 1.72 kJ/kg K respectively, when the PW-H mixed with the nano-Al2O3 (2 wt%). Increasing the mass ratio of the nano-Al2O3 within the PW-H by 4 wt% resulted in further moderate decrease of cp values till 1.66 kJ/kg K and 1.56 kJ/kg K in solid and liquid states respectively. The possible amounts of thermal energy that could be stored in pure and nano-Al2O3 added PW-H per kg, within the temperature range of 20–80 °C were calculated based on cp measurement results and they are illustrated in Fig. 13. It can be noticed that the amount of the stored energy was moderately reduced due to the nano-Al2O3 addition to the PW-H. Density changes of the current PCMs as function of temperature within the range of 15–100 °C and mass ratio of PW/nano-Al2O3 were also studied and the results are shown in Figs. 14 and 15, and an average density values within solid and liquid states of PCMs were provided in Table 3. Figs. 14 and 15 contains also the DSC curves to illustrate the density changes with respect to the phase transition temperature ranges. Thus, while being in their solid states, the density values of both pure and nano-Al2O3-PWs were highly temperature dependent. Higher values of PCM densities were measured at lower temperatures, whereas towards the phase transition temperature range, they significantly decreased. In liquid state, density was relatively stable and insignificantly decreased with increasing temperature. In particular, the highest density value of pure PW-L was about 809.7 kg/m3 at the temperature of 15 °C, and it decreased down to the value of 790.5 kg/m3 when the temperature was increased up to 40 °C. Hence, the average density of pure PW-L in solid state (15–40 °C) was 800.6 °C. On the contrary, in the liquid state (55–100 °C), the density of pure PW-L moderately changed from 758.3 to 753.5 kg/m3 when temperature increased from 55 °C up to 100 °C. Therefore, liquid state average density of PW-L was 755.4 kg/m3. The increase of the PW-L density was observed both in the solid and liquid states due to the addition of the nano-Al2O3 with 2 wt%. Thus, the average densities became 828.6 and 784.6 kg/m3 in solid and liquid states respectively. Increasing the mass ratio of nano-Al2O3 up to 4 wt% in the PW-L resulted in a further density increase, both in the solid and liquid states (Fig. 14). Consequently, the average density of the PW-L obtained were 872.6 and 828.6 kg/m3 respectively (Table 3). The density of the PW-H was higher compared to the PW-L since it had the values between 815.3 and 806.1 kg/m3 within solid state (15–52 °C), and the values between 804.8 and 767.5 kg/m3 within liquid state (70–100 °C) respectively, as shown in Fig. 15. Therefore, the

5.2. Modeling results: Design validation The LHTES device was designed in a way that every PCM container in the device could function as a stand-alone thermal energy storage tank. Therefore, the number of inlet and outlet tubes arranged at the bottom and on the top of the storage device were made equal to the number of the PCM containers in order to provide a uniform flow distribution around them. To validate the design of the LHTES device, the numerical simulation results of the LHTES filled with the pure PW-L was considered. Streamlines of the heat transfer fluid in the device shows that the fluid temperature achieves steady-state condition within 30 min (Fig. 18). It can be seen that the flow passes through the PCM containers uniformly and delivers the thermal energy into the storage device in a steady manner. Further, the heat transfer efficiency of the design was carried out by numerically studying the temperature evolutions within the PCM containers. Temperature changes as a function of the charging time were compared at the midpoints of the PCM containers (midpoint - the central point respect to the height and diameter of the container) and the results are illustrated in Fig. 19 (10 min interval is used). According to the data analysis of the midpoints, the maximum deviation from the mean temperature change was about 2.09 °C, which means all the PCM containers could be almost uniformly charged or discharged at the same time. Consequently, each embedded PCM container in the LHTES device may function as stand-alone thermal energy storage, without significant thermal interaction with the surrounding containers because of the proposed design.

Fig. 11. Amounts of the stored thermal energy within solid, phase change and liquid states of the PW-L based on DSC results. 734

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Fig. 12. Thermal diffusivity and specific heat capacity of the pure and nanoAl2O3 added PW-H measured by DSC and LFA respectively.

Fig. 15. Density of the pure and nano-Al2O3 added PW-H as a function of temperature.

Fig. 16. Thermal conductivity of the pure and nano-Al2O3 added PW-L as a function of temperature.

Fig. 13. Thermal energy stored within solid, phase change and liquid states of the PW-H based on DSC results.

Fig. 17. Thermal conductivity of the pure and nano-Al2O3 added PW-H as a function of temperature.

Fig. 14. Density of the pure and nano-Al2O3 added PW-L as a function of temperature.

various times of charging and discharging regimes of the sequentially integrated LHTES devices. It should be noted that the simulation results illustrated in Figs. 20–23 are based on the thermal properties of the pure PWs. According to Fig. 20, and after 15 min of charging, the surface temperature of the PCM containers in the LHTES-H device was significantly high due to the inflow of the heat transfer fluid (80 °C). At this charging time, the surface temperature of the PCM containers of the neighboring LHTES-L device did not have enough time to get heated by the heat transfer fluid that was coming from the LHTES-H device. The cut views in Fig. 20 show that the temperature of the PCMs in the containers was still around the pure PW initial temperature (i.e. 20 °C).

5.3. Modeling results: Integrated LHTES devices The numerical model was further applied to study the heat transfer processes and energy performance of the sequentially integrated LHTES devices. Also the effects of the nano-Al2O3 dispersed PWs on the charging and discharging efficiencies were evaluated. Thus, Figs. 20–23 show: (i) the surface temperature over the PCM containers that thermally interacts with the heat transfer fluid, and (ii) cut views of the temperature field within both PCM containers and the storage device at 735

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Fig. 18. Streamlines of the flow field in the LHTES device during charging.

Fig. 20. (a) Temperature over the surface of the PCM containers and (b) Cut view of the temperature within both PCM containers and the tank after 15 min of charging time.

flow direction parallel to the PCM containers, due to the high inlet temperature and the convective flow of the heat transfer fluid. However, the temperature of the PWs in the PCM containers increased relatively slow depending on their thermal properties. Melting of the PWs in the containers occurred in a circular manner being nearly identical in all LHTES containers as shown in the cut views of Figs. 20 and 21. Since the heat transfer fluid flows into the LHTES devices through the inlet tubes at the bottom of the devices and leaves via the outlet tubes located over the devices, the lower part of the PCM in the

Fig. 19. (a) Midpoints within PCM containers; (b) temperature evolutions at the midpoints of the PCM containers.

After 30 min of charging, it was observed that the fluid temperature in the LHTES devices significantly got elevated and became nearly uniform with few degrees of temperature difference (Fig. 21a) along the 736

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the temperature evolutions in the upper parts of the PCM containers, the durations required for the complete charging of LHTES devices were evaluated and these results are explained in the next section. Similar analysis can be carried out for the discharge regime of the LHTES devices (Figs. 22 and 23). In this case, it can be said that the LHTES devices is completely charged and the stored thermal energy is ready for user applications. Thus, the initial temperature in both devices was equal to 80 °C in discharging studies (Table 2). In order to discharge the thermal energy from the devices, the heat transfer fluid (20 °C) firstly entered through the bottom inlet tubes of the LHTES-L to extract the thermal energy from its PCM containers, and it further flowed through the LHTES-H to discharge the thermal energy at higher temperature from its PCM containers. It can be noticed from Figs. 22 and 23 that the fluid temperature in the devices was significantly reduced because of the flow of the low temperature heat transfer fluid. On the other hand, the temperature in the containers was still high even after 30 min of discharging and it was due to the slow release of the thermal energy from the PCMs. The complete discharging time of the LHTES devices were also studied based on the temperature decrease of the upper level of the PCM containers. 5.4. Charging/discharging efficiency Thus, for the complete charging of the LHTES-H device, which had the pure PW-H, 493 min was required, as it can be seen from Fig. 24, while it took 451 min for the full charging of LHTES-L device with pure PW-L (Fig. 25). It means that the LHTES-L got fully charged 42 min earlier than LHTES-H, even though the thermal energy was firstly delivered to the LHTES-H and then to the LHTES-L, where inlet tubes of the LHTES-L was considered to be connected to the outlet tubes of LHTES-H in the numerical studies. This can be explained by the thermal properties of the PWs. According to the characterization studies explained above, the melting of PW-L takes place at lower temperatures and it has a narrower PCT range (41–55 °C) compared to PW-H, with wider PCT range (52–57 °C). Moreover, PW-L has better thermal conductive properties than PW-H in both solid and liquid states. Therefore, once the phase transition process was completed in the PCM containers, the temperature of the PW-L was increased quickly. Meanwhile, the solid-liquid phase change of the PW-H took longer time because of its wider PCT range. Even when it achieved its liquid state, the quick elevation of the temperature was not noticed due to its lower thermal diffusivity compared to PW-L. The dispersion of the nano-Al2O3 in the PWs allowed to decrease the full charging time of the sequentially connected LHTES devices, thus increasing their charging rate. In particular, the addition of the nanoAl2O3 with the amount of 2 wt% into the PW-H decreased the charging duration of the LHTES-H till 436 min and it was further reduced down to 387 min when the amount of the nano-Al2O3 increased up to 4 wt%. The numerical studies show that similar reductions took place with the full charging time of the LHTES-L due to the nano-Al2O3 addition into PW-L. Thus, the full charging time of the LHTES-L device was decreased from 451 min to 346 min as a result of nano-Al2O3 addition with 2 wt% amount. A further decrease towards 308 min was noticed when the amount of the nano-Al2O3 was 4 wt% in PW-L. The discharging of the sequentially connected LHTES devices was also numerically modelled and the results are shown in Figs. 26 and 27. The cool water with a temperature of 20 °C first enters the LHTES-L device and then flows through the LHTES-H device to discharge the accumulated thermal energy from the PCM containers. Thus, the complete discharge of the LHTES-L filled with the pure PW-L lasted approximately 429 min while it took nearly 437 min for the LHTES-H having pure PW-H. The application of the nano-Al2O3 in the PWs, reduced also the full discharging duration. Hence, the effect of the nanoAl2O3 addition with the amount of 2 wt% resulted in the reduction of the discharging time of the LHTES-L from 429 min down to 344 min, and it was further reduced till about 318 min when the amount of the

Fig. 21. (a) Temperature over the surface of the PCM containers and (b) Cut view of the temperature within both PCM containers and the tank at 30 min charging time.

Fig. 22. (a) Temperature over the surface of the PCM containers and (b) Cut view of the temperature within both PCM containers and the tank at 15 min discharging time.

containers started to melt earlier than the upper part of the PCM containers. Therefore, the complete charging was achieved when the temperature of the upper part of the PCM in the containers was identical with the inlet temperature, which maintained at 80 °C. Analyzing 737

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Fig. 25. Average temperature change throughout the PCM containers during the charging regime of LHTES-L and influence of the nano-Al2O3 addition to the full charging time.

In both LHTES devices, the phase change of the PWs takes place earlier than 300 min, meaning that the most of the thermal energy is stored within 5 h, which is suitable for accumulating the daytime solar thermal energy for the nighttime heating applications. The addition of the nano-Al2O3 affects differently to the efficiencies of both storage devices and it can be noticed from the efficiency calculations using Eqs. (13) and (14) for two different operating times, particularly 200 min and 300 min. These operating times were chosen based on the results presented in Figs. 24–27, from which it can be seen that the addition of the nano-Al2O3 have significant impact at these times. Thus, using equation (12), the charge efficiency of the LHTES devices were calculated and compared (Fig. 28). According to Fig. 28, the efficiency of the LHTES-H at 200 min was not notably improved when the nano-Al2O3 were added, although they significantly improved the performance of the LHTES-L device at this operating time, thus, increasing its charging efficiency from 66.5% up to 95.5%. At further operating time, 300 min, the charging efficiency of the LHTES-L was not improved notably since it was already above 90%, but the efficiency of the LHTES-H device was improved from 69.5% until 97.3%. Thus, based on the numerical studies it was observed that the addition of the nano-Al2O3 in PWs has time dependent impact to the charge efficiency of the storages: (a) in the case of the LHTES-L filled with the PW-L, the efficiency boost was achieved right after the phase transition; (b) for the LHTES-H filled with PW-H, the efficiency improvement was achieved towards the charging time of 300 min. These variations related to the efficiency improvements of the LHTES devices are mostly due to the temperature dependency of the thermal properties of the PWs. Hence, it can be seen that the charging of the sequentially integrated LHTES devices enhanced with the nano-Al2O3 could be stopped at earlier times than their

Fig. 23. (a) Temperature over the surface of the PCM containers and (b) cut view of the temperature within both PCM containers and the tank at 30 min discharging time.

Fig. 24. Average temperature change throughout the PCM containers during the charging regime of LHTES-H and influence of the nano-Al2O3 addition to the full charging time.

nano-Al2O3 in the PW-L increased up to 4 wt%. Similar reductions were obtained regarding the full discharging time of the LHTES-H device. Thus, the addition of the nano-Al2O3 by the amounts of 2 wt% and 4 wt% decreased the charging duration of the LHTES-H from 437 min to 405 min and 363 min respectively. The duration of the complete charging and discharging regimes of the LHTES devices filled with pure and nano-Al2O3 added PWs are summarized in Table 4. Such improvements of the charging and discharging rates allow to accumulate into or receive from the PCM containers in shorter times. In the case of the charging regime of the sequentially integrated LHTES devices, the LHTES-L device was fully charged earlier than the LHTES-H device, and this did not influence the overall performance of the LHTES-L device since it was located after the LHTES-H. Therefore, the charging of the integrated LHTES devices was further continued till full charging of the LHTES-L.

Fig. 26. Average temperature change throughout the PCM containers during the discharging regime of LHTES-L and influence of nano-Al2O3 addition to the full discharging time. 738

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Fig. 27. Average temperature change throughout the PCM containers during the discharging regime of LHTES-H and influence of nano-Al2O3 addition to the full discharging time. Fig. 28. Efficiency improvements of the LHTES devices at 200 min and 300 min charging times.

complete charging time, for instance at nearly 300 min, to save the time and fluid pumping power since the charging efficiencies of the devices had reached already 90% at 300 min. The discharging efficiency was also studied for the same operating times, 200 min and 300 min using Eq. (14). According to the CFD results, the complete discharging time of the thermal energy from the PCM containers of the LHTES devices was faster than the complete charging time. The following processes in the PCM containers can be further explained. Once the discharging regime was initiated providing the inflow of the heat transfer fluid at low temperature (20 °C) through the LHTES devices, the solidification process of the PWs was started at the inner wall of the PCM containers. Since the thermal diffusivity of the solid state of the PWs is slightly larger than the liquid state, (this is also true for the thermal conductivity of the PWs), the solidified layers of the PWs together with the thin layer of the stainless steel become good thermal conductive media between the convective flow of the heat transfer fluid and the liquid fraction of the PWs in the containers. The mass fraction of the solid state is further increased in the radial direction towards center of the PCM containers, thus allowing to escape the accumulated thermal energy from the PCM containers at higher rate. This can be confirmed by the results of the discharge efficiency. According to Fig. 29, both LHTES devises achieved their discharge efficiencies up to 80% at approximately at 200 min, and the addition of the nanomaterials lead to their increase over 90%. Towards 300 min, the storage devices were almost completely discharged.

Fig. 29. Efficiency improvements of the LHTES devices at 200 min and 300 min discharging times.

seconds) of the complete charging time to evaluate the total stored thermal energy in the storage device. As stated previously, the charging said to be completed when the temperature of the upper part of the PCM containers reached the inlet temperature, which was maintained at 80 °C. Thus, the heat flux calculations were carried out either choosing in the expression “Total heat flux” or “Total heat flux magnitude” after selecting the surface of the PCM containers, using the postprocessing tool of Comsol, namely “Surface Integration” in the “Derived Values”, as illustrated in Fig. 30. On the other hand, previously the amounts of the thermal energy, which could be stored within solid, phase change and liquid states of the PCMs, were calculated per PCM kilogram using experimental results of DSC (Figs. 11 and 13). Thus, knowing the dimensions and number of the PCM containers, and the density of the PCMs, the total masses of the PCMs in each LHTES were

5.5. Storage capacity The total amount of the thermal energy that can be stored in the PCM containers of the LHTES devices at the temperature range of 20 and 80 °C are provided in Table 5. These numbers in Table 5 were obtained from the numerical results as well as from the results of DSC studies illustrated in Figs. 11 and 13. In the case of the numerical calculations, the amount of the heat flux (J/s) that passed through total surface area of the PCM containers (Fig. 30) for each storage device was calculated and the total heat flux was multiplied by the duration (in

Table 4 Full charging and discharging durations of the sequentially integrated LHTES devices. Full charging duration (min)

Pure PWs PWs + Al2O3 (2 wt%) PWs + Al2O3 (4 wt%)

Full discharging duration (min)

LHTES-H

LHTES-L

Difference

LHTES-L

LHTES-H

Difference

493 436 387

451 346 308

42 90 79

429 344 318

437 405 363

8 61 45

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Table 5 Total amount of the stored thermal energy in the integrated LHTES devices based on the numerical and DSC studies.

LHTES-L LHTES-H Sequentially integrated LHTES-L and LHTES-H devices

Numerical calculations DSC based calculations Relative error Numerical calculations DSC based calculations Relative error Numerical calculations DSC based calculations Average relative error

estimated, and the total amount of the thermal energy was easily calculated using DSC results (Table 5). Based on the relative error provided in the table, it can be calculated that, the numerical calculations were highly accurate since they approximated the DSC results. In fact, the high accuracy was expected since experimentally measured specific heat capacitates of the PCMs were used as input data for numerical studies. Thus, in the case of the sequentially integrated LHTES devices filled with the pure PWs the total amount of the thermal energy was 72.40 MJ. The addition of 2 wt% of nano-Al2O3 particles resulted in an improved (i.e. reduced) complete charging time of the LHTES-L and LHTES-H, by 106 min and 57 min respectively, as shown in Table 4. However, the overall thermal storage capacity of the LHTES devices was reduced by around 5% compared to pure PWs case, 69.16 MJ. The increase of the nano-Al2O3 mass ratio in the PCM up to 4 wt%, led to a further decrease of the overall storage capacity of the integrated devices, 66.16 MJ (i.e. 9% reduction compared to pure PWs). Although the full charging durations of the LHTES-L and LHTES-H were further improved by 143 min and 106 min respectively (Table 4). Similar improvements of the discharging time with the same decrease of the overall storage capacity of the LHTES devices due to the addition of nano- Al2O3 can be noticed from Table 4.

Pure PWs

Pure PWs + Al2O3 (2 wt%)

Pure PWs + Al2O3 (4 wt%)

33.32 MJ 32.92 MJ 1.21% 39.08 MJ 38.17 MJ 2.38% 72.40 MJ 71.09 MJ 1.80%

32.04 MJ 32.43 MJ 1.23% 37.12 MJ 37.47 MJ 0.93% 69.16 MJ 69.55 MJ 0.56%

30.25 MJ 31.13 MJ 2.82% 35.91 MJ 37.19 MJ 3.44% 66.18 MJ 68.32 MJ 3.16%

energy storage (LHTES) devices with phase change materials (PCM) with high and low phase transition temperature (PCT) ranges were proposed as an effective system for solar thermal energy storage applications. Paraffin waxes, PW-H and PW-L, were studied as PCMs and Al2O3 nanoparticles (nano-Al2O3) were dispersed into them in small amounts to improve the thermal properties of the PWs. The validity of the numerical approach was previously confirmed with the comparison of the simulation results with the experimental data obtained from a LHTES device. The design of the LHTES device was introduced and its efficiency was confirmed by computational fluid dynamics (CFD) simulations based on Comsol Multiphysics. Thus, based on the results, the following conclusions were obtained:

• According to the characterization studies, both PW-H and PW-L



6. Conclusion In the current paper, sequentially integrated latent heat thermal

showed relatively low thermal conductive properties. Although, the addition of the nano-Al2O3 with the mass ratio of 2 wt% and 4 wt% resulted in the improvement of the thermal properties of the PWs, while keeping their thermal storage capacity relatively stable with minor decreases. In particular, it should be noted that the thermal diffusivity of the PWs was significantly improved both in solid and liquid states, facilitating a better heat transfer. The results of the thermal characterization of the PCMs were used as input data for the numerical simulation of the LHTES devices. Since, the input data considered the temperature dependence of the PCM thermal properties in the charging and discharging temperature range, the CFD results regarding the heat transfer in the LHTES

Fig. 30. Illustration of the PCM containers, through which the surface integration of the heat flux was carried out, and steps of the postprocessing for calculations of the heat flux. 740

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devices can be considered reasonable and accurate for storage design and development purposes. The design of the LHTES device with embedded PCM containers was studied using 3D CFD methods. The results showed that the proposed design of the LHTES is efficient in terms of delivering thermal energy to the embedded PCM containers in a uniformly distributed manner. It was numerically illustrated that each PCM container in the LHTES device functioned as a stand-alone thermal storage, without significant thermal interaction with the neighboring containers. Hence, the proposed design of the device allows to charge or discharge embedded PCM containers without a significant time delay with respect to each other. Moreover, sequentially integrated LHTES-H and LHTES-L devices filled with PW-H and PW-L respectively were numerically studied for effective solar thermal energy storage applications. Their performance were numerically modeled, and their charging and discharging efficiencies were analyzed. It was shown that the LHTES devices filled with PWs having high (around 65–70 °C) and low (about 45–55 °C) PCT ranges can effectively store solar thermal energy if they are serially connected to each other. The effect of the nano-Al2O3 addition to the complete charging and discharging durations was studied. It was shown that the nanoAl2O3 nanoparticles, which enhanced the heat transfer properties of the PWs, improved the charge and discharge performance of the sequentially connected LHTES devices, without significant reduction of the overall thermal energy storage capacity of the system.

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Fast chargeable or dischargeable LHTES devices discussed here are key developing strategies for the next generation decentralized community-scale district heating networks, since they can quickly communicate with a central or seasonal thermal energy storage (STES) system in terms of sharing the excess energy or receiving the thermal energy demand initiated by the users. Thus, using the characterization studies and numerical results of the current work, the authors have the framework to develop the pilot installation of the LHTES device soon. The new demonstrator aims to integrate a STES system based on borehole thermal energy storage (BTES) with the sequential LHTES system and experimentally study the heat exchange between both. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The authors would like to thank the Newton Funding for providing Researcher Links Travel Grant (No. 216398976) for the first author. Moreover, the research within the scope of the paper is also supported by the joint project of the Government of Kazakhstan and the World Bank “Fostering Productive Innovation”, under the subproject JRG-160071. References Agarwai, A., Sarviya, R.M., 2016. An experimental investigation of discharge/solidification cycle of paraffin in novel shell and tube with longitudinal fins based latent heat storage system. Eng. Sci. Technol. Int. J. 191, 619–631. Akhmetov, B., Georgiev, A., Kaltayev, A., Dzhomartov, A.A., Popov, R., Tungatarova, M., 2016. Thermal energy storage systems – review. Bulgarian Chem. Commun. 48 (Special Issue E), 31–40. Akhmetov, B., Seitov, A., Popov, R., Georgiev, A., Kaltayev, A., 2018. Experimental and numerical studies of PCM-based storage for solar thermal energy storage applications. KazNU Bull. Math., Mech., Comput. Sci. Series 93 (1), 55–68. Al-abidi, A., Mat, S., Sopian, K., Sulaiman, M.Y., Mohammed, A., 2013. CFD applications for latent heat thermal energy storage: a review. Renew. Sustain. Energy Rev. 20, 353–363.

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