**Experimental Analysis on the Thermal Management of Lithium-Ion Batteries Based on Phase Change Materials**

**Mingyi Chen 1,\*, Siyu Zhang 1, Guoyang Wang 1, Jingwen Weng 2, Dongxu Ouyang 2, Xiangyang Wu 1, Luyao Zhao <sup>1</sup> and Jian Wang <sup>2</sup>**


Received: 10 September 2020; Accepted: 19 October 2020; Published: 21 October 2020

**Abstract:** Temperature is an important factor affecting the working efficiency and service life of lithium-ion battery (LIB). This study carried out the experiments on the thermal performances of Sanyo ternary and Sony LiFePO4 batteries under different working conditions including extreme conditions, natural convection cooling and phase change material (PCM) cooling. The results showed that PCM could absorb some heat during the charging and discharging process, effectively reduce the temperature and keep the capacity stable. The average highest temperature of Sanyo LIB under PCM cooling was about 54.4 ◦C and decreased about 12.3 ◦C compared with natural convection in the 2 C charging and discharging cycles. It was found that the addition of heat dissipation fins could reduce the surface temperature, but the effect was not obvious. In addition, the charge and discharge cycles of the two kinds of LIBs were compared at the discharge rates of 1 C and 2 C. Compared with natural convection cooling, the highest temperature of Sanyo LIB with PCM cooling decreased about 4.7 ◦C and 12.8 ◦C for 1 C and 2 C discharging respectively, and the temperature of Sony LIB highest decreased about 1.1 ◦C and 2 ◦C.

**Keywords:** lithium-ion battery; thermal management; phase change material; temperature; heat dissipation fins; capacity

#### **1. Introduction**

The ways to deal with the energy crisis and environmental pollution and develop new energy of safety and cleanness have become the focus of the attention of all countries in the world. It also becomes the core issue to solve the sustainable development of humankind. LIBs, which have the advantages of high specific energy, relatively high operating voltage, long cycle life, low self-discharge rate, small and convenient, are considered to be one of the most promising energy storage devices [1–3]. However, if the operating temperature of LIB is high and the heat dissipation is not timely, it will lead to thermal failure, shorten the service life of LIB and cause safety problems, such as fire and explosion [4,5]. Therefore, the thermal safety of LIB needs to be focused on.

The temperature difference between battery internal and ambient, as well as the temperature difference between the cells inside the battery pack will have a negative impact on the performance, life and safety of the battery [6]. Therefore, it is necessary to conduct a reasonable heat management system to make the LIB working in the normal operating temperature range [7–10]. At present, there are three kinds of mainstream thermal management methods for LIBs including air cooling, liquid cooling

and PCM cooling [11]. Air cooling is divided into natural air cooling and forced air cooling. Pesaran et al. studied the air cooling performance of the battery thermal management system (BTMS). The results showed that the air cooling could effectively reduce the battery temperature and keep the battery temperature consistent in a low rate discharging [12]. Giuliano et al. studied the thermal management system using air cooling of metal foam-based heat exchanger plate. The system showed that the LIB temperature decreased with the increase of airflow. However, the thermal conductivity of air is low and the heat dissipation is weak [13]. Compared with the air cooling method, the liquid cooling method has higher thermal conductivity, which leads to higher cooling performance and is more suitable for cooling large battery packs. Liquid cooling is divided into direct and indirect liquid cooling. Chen et al. compared different liquid cooling systems of LIB, and the results showed that the indirect liquid cooling system had the lowest temperature rise and was more practical than direct liquid cooling [14]. Zhang et al. applied the S-type guide plate to the integrated module of liquid cooling heat dissipation system, and found that the device could avoid heat concentration, improve heat transfer performance and keep the temperature of LIB uniform [15]. However, the traditional battery thermal management method that uses cheap air and water as the cooling medium requires additional energy to drive the cooling medium circulation. In battery thermal management applications, the battery's safe operating temperature is often sacrificed at the expense of battery capacity and power in exchange for longer operating life, and these traditional thermal management methods are complex and occupy a large space [16]. In recent years, researchers have found that PCMs exhibit excellent performance in thermal management of LIB [17,18] since they have large storage density apart of many other advantages [19–21]. Duan et al. conducted the numerical and experimental studies on PCM heat transfer, and found that they have great potential in thermal management due to potential energy storage and controllable temperature stability [22]. PCM battery management system which performed better than traditional thermal management system was first proposed and patented by Al-Hallaj and Selman [23,24]. Mills and Al-Hallaj used the entropy coefficient method to simulate the battery pack, and the results showed that using a PCM could significantly improve the system performance and keep the operating temperature below 55 ◦C, even at high discharge rate [25]. Javani et al. studied the effect of a PCM on LIB, and found that it could make the temperature distribution uniform and keep the battery in a safe temperature range [26]. Weng et al. systematically investigated the cooling behavior and the influence of several detailed factors on the performance of a PCM. The experimental results showed that a PCM module with a thickness of ~10 mm presented the optimal cooling performance [27]. Javani et al. investigated the heat transfer with a PCM in passive thermal management of electric and hybrid electric vehicles. The results showed that the temperature distribution became about 10% more uniform when a PCM was applied in a 3 mm thickness around the cell. The PCM with 12 mm thickness decreased the maximum temperature about 3.04 ◦C [28]. However, it is found that PCM is easy to get heat saturation when absorbing a large amount of heat in the practical application. BTMS based on pure phase-varying materials cannot work for a long time in high-power batteries and effectively control the battery temperature. Commonly used PCM is paraffin wax whose thermal conductivity is very low. The thermal conductivity of PCM is improved by adding high thermal conductivity materials such as expanded graphite, carbon fiber, graphene, aluminum foam, copper foam and so on [29–32].

On the other hand, many researchers combined other cooling methods with PCM-based BTMS in order to improve the cycling stability and thermal management ability [33,34]. The complex PCM based BTMS can effectively reduce temperature rise and temperature difference, and maintain battery performance, particularly in extreme environments [35,36]. Sun et al. proposed a PCM combined with heat-dissipating fins to enhance the heat transfer. The results showed that the performance of PCM-fin system was better than that of pure PCM system [37]. Azizi et al. used a PCM and composite materials of aluminum mesh plates to carry on the thermal management to the LiFePO4 battery pack under the high temperature environment. The results showed that the usage of PCM and aluminum wire mesh could significantly reduce the surface temperature of the batteries and improve the performance of the battery pack [38]. Although the use of PCM either alone or combined with heat dissipation fins had

been extensively studied, there is no optimal solution for the best cooling effect, quantity, and price of PCMs used in LIBs at present. The combination of a PCM and heat dissipation fin will inevitably increase the weight of the BTMS device. As far as we know, a PCM with high thermal conductivity in the battery charging and discharging cycles and the optimization of the coexistence system of PCM and heat dissipation fin also needs further research. In this paper, we first tested the cooling effect of a PCM with higher thermal conductivity whose phase change process is a solid-solid phase change, and then designed a new type of heat dissipation fins. The main purpose of this paper is to study the cooling effect of a PCM with high thermal conductivity on the battery and the effect of a PCM combined with a new type of heat dissipation fins with a relatively small volume. The authors conducted the experiments to investigate the temperature and capacity changing of two kinds of batteries under different conditions.

#### **2. Experiment**

#### *2.1. Experimental Description*

Experiments were carried out on two different brands of LIB (Sanyo ternary and Sony LiFePO4 battery). The detailed parameters of the batteries were shown in Table 1. The experimental conditions of the battery in extreme conditions (inside the closed aluminum tube), natural convection, pure PCM, and PCM combined with the heat dissipation fins were set up. The experiments were carried out in the carton box (length × width × height, 35 × 20 × 20 cm) for the thermal isolation from environmental influences, and each experimental condition is shown in Figure 1. The aluminum tube size with an inner diameter of 36 mm, the height of 65 mm, and thickness of 6 mm (provided by Yuezhong Metal Material Co., Ltd., Dongguan, China) was used, and its thermal conductivity is 237.2 W/m·K. Figure 1d shows that the fin is composed of two circular fins and three vertical fins. Its material is tin sheet and the thermal conductivity is 150 W/m·K. The design of the fin structure is followed by: (1) The ring is set at the bottom of the battery and in the middle of the battery respectively as the temperature of the middle and low part of the battery is higher. (2) The vertical fin protruding is designed to disperse the generated heat in time and reduce the temperature effect. (3) According to previous studies, the best results are obtained when the distance between the radiator and the battery is 0.2 times the diameter of the battery [39]. So, the circular heat dissipation fin size (outer diameter × inner diameter × height) is ϕ26 × ϕ22 × 4 mm, vertical heat dissipation fin size (length × width × height) is 4 × 2 × 80 mm.

The high thermal conductivity phase change composites with phase change temperature of 52 ◦C (provided by Zhongjia New Material Technology Co., Ltd., Guangzhou, China) were selected due to the higher thermal conductivity than the pure paraffin. In this experiment, the phase change material is wrapped around the battery with a thickness of 9 mm and a weight of about 9.9 g. The main components are phase change wax and expanded graphite, which have the following advantages: solid-solid phase change, high phase change latent heat, insulation, good cycle stability, non-corrosive, and non-toxic. Detailed thermal physical properties are shown in Table 2.



(**a**) Extreme conditions (charge/discharge LQVLGH WKH FORVHG DOXPLQXPWXEH (**b**) Natural convection cooling

(**c**) Phase change material cooling (**d**) Heat dissipation fins, pcm-fin cooling

**Figure 1.** Experimental conditions


**Table 2.** Thermal physical properties of PCM.

#### *2.2. Experimental Facility*

Figure 2 shows the schematic diagram of the experiments. The LIB charging and discharging instrument (provided by Neware Electronics Co., Ltd., Shenzhen, China) is provided for the LIB normal charging and discharging cycles, and the accuracy and stability of the whole range can reach 0.1%. The LIB temperature was measured by T-type thermocouples (provided by OMEGA), and recorded by the temperature data acquisition unit (provided by National Instruments) as shown in Figure 2. According to the factory temperature check, the thermocouple temperature measurement accuracy is controlled within 0.5 ◦C. The thermocouple is patch type, which is attached to the middle of the battery surface. The PCM is wrapped around the battery, and the thermocouple is embedded in the PCM. The thermocouple was calibrated before the experiments. The temperature of the LIB by thermocouple was measured only to analyze the cooling effect of PCM on the LIB, not to study the internal reaction of the LIB in this study. Hence, the T-type thermocouple is attached to the center position of the batteries surface to measure the optimum temperature.

**Figure 2.** Schematic diagram of the experiment.

Before the experiment, the LIBs were discharged to the cut-off voltage, charged to maximum voltage, and then placed 24 h to keep the LIB stable. The temperature in the carton is 25 ◦C, and its environmental temperature error is controlled within the normal range of 0.5 ◦C. The charge and discharge process of the two batteries are shown in Table 3. The cycle of Sanyo LIB can be divided into four stages: (1) discharge stage, with 2 C constant current discharge to 2.5 V. (2) shelving stage for 5 min. (3) charging stage with 1 C constant current and voltage to 4.2 V. (4) shelving stage with 5 min. The Sony LIB is tested in the same charge-discharge cycle as the Sanyo LIB. The only differences are the cutoff discharging voltage of 2.0 V and cutoff charging voltage of 3.6 V because of its relatively small capacity and voltage. Besides, two kinds of cells are placed in the PCM to discharge at a discharge rate of 1 C and 2 C.


**Table 3.** Design of charging and discharging experimental conditions.

#### **3. Results and Discussions**

#### *3.1. Temperature Change during LIB Cycle*

When the LIB is charging and discharging, the reaction occurs inside the LIB, which produces heat and shows the increase of battery temperature. Figure 3 shows the temperature change during charging and discharging of Sanyo LIB under four different working conditions: extreme conditions, natural convection cooling, PCM cooling, and PCM combined with heat dissipation fins cooling at the ambient temperature of 25 ◦C. Figure 3a shows the temperature curve of LIB in two cycles. That can be seen from the figure, the temperature of LIB in the enclosed space rises from 30 ◦C to about 77.3 ◦C during discharging, which obviously exceeds the normal operating temperature of the battery. The high temperature has certain bad influence on the LIB. The long-term working under the extreme condition will cause the LIB internal electrolyte decomposition, the positive and negative electrode reaction, and so on, which may cause the LIB thermal runaway and produce the safety risks. The highest temperature of the LIB is about 54.5 ◦C under PCM cooling, 66.2 ◦C under natural convection, 77.3 ◦C under extreme condition. Compared to the air cooling, the temperature of LIB using PCM cooling has a much smaller increase rate, and the highest temperature drops by 11.7 ◦C. Therefore, the results show that PCM can absorb some heat during the LIB discharging process, effectively reducing the LIB temperature. For the analysis of the cooling condition of the PCM with heat dissipation fins on the LIB, the heat dissipation fins have been adopted. The volume ratio of PCM and heat dissipation fins in the device is about 96%:4%. According to the diagram, the maximum temperature difference between the LIB in this working condition and PCM cooling condition is about 0.2 ◦C. The combination of heat dissipation fins can slightly reduce the temperature of LIB. The reason may be the fin structure cannot dissipate the latent heat in time due to its small volume ratio. In the research on the combination of PCM with heat dissipating fins, while giving full play to the maximum effect of heat dissipating fins, its cost and influence on the whole LIB structure should also be considered. Javani et al. [28] investigated heat transfer with PCMs in passive thermal management of electric and hybrid electric vehicles. Their results showed that the temperature distribution became about 10% more uniform when the PCM was applied in a 3 mm thickness around the LIB. The PCM with 12 mm thickness decreased the maximum temperature about 6.6 ◦C. In this research, the PCM not only has better cooling performance, but also makes the device having the advantages of small size and lightweight. In addition, the PCM in this study has a solid-solid phase change process, which avoids the liquid leakage. The device structure in this study is simpler and more practical, which may has a potential for commercialization.

Figure 3b shows the temperature change curve of LIB during six cycles. The temperature of LIB tends to be stable under various working conditions. However, the average of the maximum temperatures for the six cycles of LIB reaches about 77.8 ◦C in the enclosed space, which is in an unsafe state. It may cause great damage to the internal structure of the LIB and seriously affect the cycle service life of LIB. The PCM can have a good cooling effect on the temperature and make the average of the maximum temperatures for the six cycles of LIB keep at about 54.4 ◦C. The average of the maximum temperatures for the six cycles of LIB under the experimental condition of the combination of PCM and heat dissipating fins is about 54.3 ◦C, which is not significantly different compared to PCM cooling condition. The result shows that the effect of heat dissipation fins is not significant and the pure PCM cooling is the best choice due to the cost and complexity of the device structure. On the other hand, the LIB temperature rose at a slower rate and the temperature curve shifted slightly to the right as the cycle progressed. The heat generated inside LIB consisted of five parts: electrochemical reaction heat, ohmic internal resistance heat, polarization heat, electrolytic decomposition heat, and SEI decomposition heat. The electrolytic and SEI decomposition heat were very small and could be ignored when LIB was in the normal operating temperature range. The LIB would produce heat during the charging and discharging cycles. For discharging condition, the total chemical reaction was an exothermic reaction and the temperature rose theoretically, and for charging condition, the total chemical reaction was an endothermic reaction and the temperature drops theoretically. However, in the case of natural convection in Figure 3b, the temperature remains unchanged or even rises within a short period of time (region A) during the battery charging process. In the LIB charge process, although it is an endothermic process, the LIB generated heat such as ohmic internal resistance heat, polarization internal resistance heat, and electrochemical reaction heat more than itself heat dissipation, so that the temperature remains stable or even slightly rises.

(**a**) Change of charging and discharging temperature of Sanyo LIB

(**b**) The temperature changing of Sanyo LIB cycle

**Figure 3.** The temperature changing of LIBs during charging and discharging.

Figure 4 shows the temperature changes of LiFePO4 battery in charging and discharging cycles under four different working conditions. It can be found that the highest temperature of the LIB under extreme conditions is about 40.6 ◦C and the lowest temperature is about 35.1 ◦C when the LIB is shelved after charging. The temperature of LiFePO4 LIB will not be too high compared with Sanyo LIB when it works for a short time under extreme conditions due to its smaller LIB capacity, and lower internal polarization and ohmic resistance heat. The maximum temperature of Sony LIB is about 35.1 ◦C under PCM cooling, 37.5 ◦C under natural convection, 40.6 ◦C under extreme condition. It is found that the LIB temperature under PCM cooling decreases by 2.4 ◦C compared with the natural convection. In the case of the combination of PCM and heat dissipation fins, the temperature decreases 0.4 ◦C than PCM cooling due to the temperature of battery itself is low. In addition, the Sony LIB temperature in extreme conditions cannot be lowered to the level of other conditions during charging and shelving due to the heat is not dispersed in time. It can accelerate the degradation of the LIB and influence the LIB performance in extreme condition for a long time, which further prove the necessity of BTMS.

**Figure 4.** The temperature changes of LiFePO4 battery during charging and discharging.

#### *3.2. The Influence of Temperature on Battery Performance*

Temperature is an important factor affecting battery performance parameters. Too high or low temperature will affect LIB capacity, charging and discharging efficiency, safety performance and result in battery performance degradation. Figure 5a shows the current change of the LIB in the charging and discharging cycle, and Figure 5b shows the voltage change. For the convenience of statistics, the x-coordinate in the figure represents the time step, and each step is 10 s. That can be seen from the figures, the current and voltage curves of the LIB have the same trend in each working condition. The current and voltage can reach the set rating in each charging and discharging cycle. However, as the cycles progresses, compared with the LIB under extreme conditions, the LIB curves in other conditions shift to the right, which is very similar to Figure 3b. The reason is related to the battery charging and discharging time. Under constant current conditions, the total flux of lithium ions should be roughly similar (both as diffusion in the electrolyte, and total flux into and out of the active material particles), and environmental conditions have little effect on it. However, at lower temperatures, a higher concentration gradient is required to overcome the slower diffusivity to meet the required flux. The higher concentration gradient leads to higher over potential and uneven utilization of electrodes. In turn, this leads to faster reaching of the cut-off voltage when working at lower temperatures. It can be clearly seen in Figure 5a that the LIBs in PCM and PCM-Fin cooling experiments seem to be faster reaching the cutoff voltage than the extreme condition and air cooling experiments in the first discharge cycle when all batteries start at the same state of charge (SOC). On the contrary, a higher temperature of LIB means that a constant current can be provided for a longer period of time. That can be seen in Figure 5b, the voltage drop of LIBs at higher temperature is smaller. In addition, according to Figure 3, it is found that in the constant current charging stage of the battery, the temperature of the battery decreased rapidly in the extreme condition and air cooling experiments, and the temperature is lower

than the other cases in a period of time due to the latent heat effect of PCM. It seems that the LIBs under PCM and PCM-Fin cooling conditions can be charged for a longer time in the later cycles than the other cases.

(**b**) Voltage curves

**Figure 5.** The current and voltage curves of Sanyo LIB.

Figure 6 shows the current and voltage changes in the LiFePO4 battery during charging and discharging cycles. The current and voltage changes of LiFePO4 LIB have the same trend under four different working conditions. Since the operating temperature of LiFePO4 LIB under four working conditions is around 30–40 ◦C, the LIB is in a normal working state and its current and voltage will not change much.

#### (**b**) Voltage curves

**Figure 6.** The current and voltage curves of Sony LIB.

Table 4 shows the capacity changes of Sanyo LIB charging and discharging cycles under different working conditions. It is found from the table that the LIB capacity has some changes in each working cycle. The average charging capacity of six cycles is 2414.6 mAh under the extreme conditions, 2399.4 mAh under natural convection, 2397.7 mAh under PCM cooling, and 2403.6 mAh under PCM combined with heat dissipation fins working condition. The average discharging capacity of six cycles

is 2412.7 mAh under the extreme conditions, 2398.3 mAh under natural convection, 2398.4 mAh under PCM cooling, and 2383.3 mAh under PCM combined with heat dissipation fins working condition. Table 5 shows the capacity changes of LiFePO4 battery charging and discharging cycles under different working conditions. The average charging capacity of six cycles is 1022.6, 1034.9, 1031.6, and 1034.5 mAh, and the average discharging capacity is 1026.8, 1035.9, 1030.4, and 1032.1 mAh, under the extreme conditions, natural convection, PCM cooling, and PCMcombined with heat dissipation fins working condition, respectively. The LIB capacity changes are related to the temperature. The battery capacity does not change significantly, which indicated that the LIB capacity is not significantly affected by short cycles even at high temperatures. Compared with the natural convection condition, the LIB discharging capacity under PCM cooling and PCM combined with heat dissipation fins decreased slightly. In the case of higher temperature, the battery reaches the cut-off voltage more slowly during the charging and discharging process, and the constant current charging and discharging time is longer, so the charging and discharging efficiency is higher, and the maximum capacity value is larger. However, the high temperature has a great influence on the capacity degradation rate of LIB [40]. The higher temperature leads to a quicker rate of various side reactions in the battery and faster the capacity degradation. Due to the low number of battery cycles in the experiments, the internal damage or possible side reactions that might have occurred at high temperatures had not yet become apparent. In the current application of LIB with the high efficiency and capacity, reducing the impact of itself side reaction and temperature are particularly critical, which is also a hurdle for the current LIB technology breakthrough.

**Table 4.** Capacity curve of Sanyo LIB in charge and discharge cycles.


**Table 5.** Capacity curve of LiFePO4 LIB in charge and discharge cycles.


*3.3. The PCM Influence on LIB Temperature under Di*ff*erent Discharging Ratios*

Figure 7 shows the temperature curves of Sanyo and Sony LIB under the conditions of natural convection and PCM cooling. It is found that the PCM has a good effect to decrease the LIB temperature no matter it is discharged at a rate of 1 C or 2 C. Compared with natural convection cooling, the highest temperature of Sanyo LIB decreases about 4.7 ◦C and 12.8 ◦C for 1 C and 2 C discharging, respectively, and the highest temperature of Sony LIB decreases about 1.1 ◦C and 2 ◦C. The temperature reduction

effect of PCM on high rate discharge LIB is more obvious. In the charging and discharging cycles, Sanyo LIB generates more heat due to its large capacity, and PCM absorbs more latent heat. The PCM has the most obvious effect on the Sanyo battery ina2C discharging rate among all experiments.

(**b**) The temperature curves of Sony LIB

**Figure 7.** The temperature curves of Sanyo and Sony LIB under 1 C, 2 C discharging.

#### **4. Conclusions**

PCM has been widely used in the thermal management of LIB due to itself advantages. In this paper, the changes of LIB temperature and capacity under different working conditions and discharge ratios are analyzed in order to further analyze the PCM influence of LIB thermal management and design an effective BTMS. The conclusions are as follows:

(1) The LIB temperature rises during the discharge process, and the PCM can effectively reduce the LIB temperature and keep its capacity stable. The average highest temperature of Sanyo LIB under the PCM cooling is about 54.4 ◦C in the 2 C discharge rate especially, and it is about 12.3 ◦C decrease compared with the natural convection cooling.

(2) The heat dissipation fins can reduce the LIB temperature, but the current effect is not very significant. Further optimization of the combination with heat dissipation fins and PCM is also an important direction in the thermal management of LIB.

(3) The LIB capacity changes are related to the temperature. In the discharge rate cycles, the LIB temperature of PCM cooling and PCM combined with heat dissipation fins decreased slightly, and the capacity decreases compared with the natural convection condition. The battery temperature and capacity increase slightly under extreme conditions.

(4) The PCM have a bigger temperature impact on Sanyo LIB. Sanyo LIB generates more heat due to its large capacity, and PCM absorbs more latent heat. The temperature reduction effect of PCM on high rate discharge LIB is more obvious.

In the future study, PCM combined with other cooling way efficiently and developing the PCM of higher latent heat, better heat conduction performance will be an important direction of battery BTMS.

**Author Contributions:** Conceptualization, M.C., S.Z., and J.W. (Jingwen Weng); Methodology, M.C., D.O. and J.W. (Jian Wang); Investigation, L.Z., S.Z., and G.W.; Writing-Review & Editing, M.C., S.Z., and X.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research and Development Program of China (2018YFC0808600), the Open Project of State Key Laboratory of Fire Science (HZ2020-KF08), Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (19KJB620003), and the Double Innovation Plan of Jiangsu province.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**


#### **References**


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## *Article* **Comparison of Heat Transfer Enhancement Techniques in Latent Heat Storage**

#### **William Delgado-Diaz, Anastasia Stamatiou \*, Simon Maranda, Remo Waser and Jörg Worlitschek**

Competence Center Thermal Energy Storage (CCTES), Lucerne University of Applied Sciences and Arts, 6048 Horw, Switzerland; williamorlando.delgadodiaz@hslu.ch (W.D.-D.); simon.maranda@hslu.ch (S.M.); remo.waser@hslu.ch (R.W.); joerg.worlitschek@hslu.ch (J.W.)

**\*** Correspondence: anastasia.stamatiou@hslu.ch

Received: 22 June 2020; Accepted: 3 August 2020; Published: 10 August 2020

**Abstract:** Latent Heat Energy Storage (LHES) using Phase Change Materials (PCM) is considered a promising Thermal Energy Storage (TES) approach as it can allow for high levels of compactness, and execution of the charging and discharging processes at defined, constant temperature levels. These inherent characteristics make LHES particularly attractive for applications that profit from high energy density or precise temperature control. Many novel, promising heat exchanger designs and concepts have emerged as a way to circumvent heat transfer limitations of LHES. However, the extensive range of experimental conditions used to characterize these technologies in literature make it difficult to directly compare them as solutions for high thermal power applications. A methodology is presented that aims to enable the comparison of LHES designs with respect to their compactness and heat transfer performance even when largely disparate experimental data are available in literature. Thus, a pair of key performance indicators (KPI), Φ*PCM* representing the compactness degree and NHTPC, the normalized heat transfer performance coefficient, are defined, which are minimally influenced by the utilized experimental conditions. The evaluation procedure is presented and applied on various LHES designs. The most promising designs are identified and discussed. The proposed evaluation method is expected to open new paths in the community of LHES research by allowing the leveled-ground contrast of technologies among different studies, and facilitating the evaluation and selection of the most suitable design for a specific application.

**Keywords:** heat transfer; high power; latent heat; energy storage; heat exchanger

#### **1. Introduction**

On the path to the integration of an ever-increasing share of variable renewable energy sources (VRES) into the current energy system, energy storage (ES) technologies play a fundamental role. Energy transformation and consumption globally account for more than 60% of the total green house gas emissions [1]. Additionally, in Switzerland and the European Union in general, over 50% of the total energy consumed is ultimately used as thermal energy for both industry and domestic applications [2,3]. Considering this, the development of thermal energy storage (TES) systems has become a priority for directly pure thermal applications and heat management systems, as well as combined electro-thermal storage initiatives, such as pumped thermal energy storage systems [4] and its potential for alternative use and flexibility for recovered waste heat from already existing sources at large scales [5].

Within the spectrum of TES technologies, Latent Heat Energy Storage (LHES) systems using Phase Change Materials (PCM) allow for thermal energy storage and release within narrow temperature differences with high energy density when compared to the sensible energy storage (SES) approach. These characteristics ultimately allow for the implementation of TES systems with a

high degree of compactness. The heat transfer performance of LHES systems is however hindered by the time-dependent nature of its charging and discharging processes. During crystallization, the heat transfer and phase change processes are thus dominated by conduction under increasing resistance imposed by the moving liquid-solid front, making them a function of the state of charge of the unit [6]. Thus, the widespread application of LHES units on processes that require high heat transfer rate and quick response time relies on the many novel promising technological approaches that have emerged as a way to bypass LHES heat transfer limitations. These technologies include plain tube and finned tube bundle configurations [7–14], carbon composites and dispersions [15–20], metal foams [21–26], macroencapsulation techniques [27–31], and addition of conductive nanoparticles [32–34], among others.

The extensive range of experimental conditions (e.g., inlet temperature and mass flow rate of heat transfer fluid, phase change temperature, size of storage unit, etc.) used to characterize these technologies in literature make it difficult to directly compare and cross-correlate various performance features. This variability makes heat transfer performance and the degree of compactness especially hard to assess without leveled Key Performance Indicators (KPI). Some KPIs have been proposed to evaluate different aspects of an LHES unit. For instance, Energy density (ED) as proposed by Romani et al. [35] provides an indication of the amount of energy stored in relationship to the volume or mass of the unit. ED allows for valuable comparison of TES technologies in terms of overall capacity and required space and material resources, but most relevantly in the case of LHES, it equally considers sensible and latent contributions. By considering the sensible part of the energy stored in the PCM, the result is dependent on the operation temperature levels on the unit and not only the materials and amounts. Alternatively, the energy efficiency ratio described by Wang et al. [36] concerns the ratio of energy required to pump the HTF through the LHES unit to the stored energy. In addition, in a similar approach, Li et al. [37] also proposed the performance analysis of a wide range of LHES operational and material parameters, as both energetic and exergetic efficiencies. Even though the previously described KPIs provide very valuable information about an LHES unit, they address particular aspects and consider mostly capacity and efficiency perspectives, but provide no indication on the rates of heat transfer and the required material to achieve it.

Directly addressing the thermal response, Gasia et al. [38] proposed various KPI for both short and long term scales: Average power, 5 min-peak-power, 5 min peak power-energy ratio (based on 5-min-peak-power over total capacity of the unit), and finally the discharge time. The set of KPIs was intended for the evaluation of four LHES units of very similar scales, operating at uniform conditions and equal PCM. Although useful while the experimental conditions and the geometry remain similar enough, they remain intrinsically connected to the current operation conditions and scale. This leads to non-representative results, especially when comparing across different studies and applications. Similarly, Guo et al. [39] consider the specific charging rate (*γ*[1/h]) and specific energy loss rate. The specific charging rate directly addresses the heat transfer performance of the unit, but it is ultimately an average power to capacity ratio, without any normalization with respect to the driving forces.

Similar analyses include, for instance, the use of the average temperature effectiveness (*εavg*) by Nomura et al. [40] and Krimmel et al. [41] to represent the efficiency of the heat exchange. Additionally, Nomura et al. [40] present a NHTPC (*hv*), directly addressing the heat transfer performance of the units. It considers the average heat transfer rate divided by the average temperature difference (which ultimately can be interpreted as the enthalpy flow of the HTF), with respect to the volume of PCM only in the unit. Although it directly addresses the heat transfer capability of a unit, it still remains dependent on the HTF conditions, and thus varies with different mass flow and temperature difference.

The Effectiveness-NTU Method (*ε*-NTU) allows the calculation of the heat transfer rate and temperature profiles in a heat exchanger using the enthalpy flows, and defining a heat exchanger effectiveness based on the actual heat transfer rate over the maximum achievable by the system [42]. It has been previously used to analyze LHES systems as performed by Tay et al. [43,44] as design and sizing tool on specific designs.

The methodology presented in this paper is inspired on the previous (*ε*-NTU) analyses and the view of LHES units as a heat exchanger core acting as boiler or condenser. It focuses on two KPIs, which represent the normalized heat transfer performance and degree of compactness of the LHES design. This new approach allows the comparison of LHES systems reported in literature in terms of their heat transfer capabilities and compactness regardless of their geometry, scale, and operation conditions. The developed KPIs are applied to several technologies reported in literature and the results of this comparison are presented and discussed. Based on the authors' knowledge, this is the first time such an extensive quantitative comparison across different LHES technologies with a focus on high power applications has been performed.

#### **2. Methodology**

#### *Definition of Proposed KPIs*

The main focus of this study is to allow the simplified and quick evaluation of the heat transfer capabilities in a LHES unit regardless of scale and operating conditions. Achieving this goal requires the usage of the most readily available information able to represent a highly transient process through averaged properties. The methodology proposed in this study uses this information adapted around the (*ε*-NTU) method. Two KPI are proposed representing both the heat transfer performance of a LHES unit as well as the degree of compactness and an indication of the energy density attainable by the system.

Regarding the degree of compactness, the volume fraction of the major contributor to the storage capacity of the LHES unit, PCM to total volume of the unit, (Φ*PCM*) is suggested as an indicator of the energy density attainable by the system. Φ*PCM* provides an indication of the compactness degree attainable, but also information on the required trade-off of PCM storage volume for heat exchanger material to achieve certain heat transfer performance, and it is the ratio of PCM volume in the storage (*VPCM*) to the total outer volume of the unit (*VTOT*). See Equation (1)

$$
\Phi\_{PCM} = \frac{V\_{PCM}}{V\_{TOT}} \tag{1}
$$

The total volume (*VTOT*) was calculated considering the geometry of the outermost layer of the unit while excluding the additional volume used for insulation. The container wall thickness as well as additional volume dedicated to manifolds (flow development) and the like were all taken into account.

From a heat exchanger perspective, an LHES unit can be regarded as a heat exchanger, the performance of which is defined by a static heat sink or source, or an analog case of a heat exchanger operating as a boiler or condenser. The average NTU (*NTUavg*) represents the added effects of the heat exchanger tubes and growing layer of solid through the discharge process. It is defined as the ratio of the heat transfer rate capacity of the heat exchanger (product of the overall heat transfer coefficient (U) and the heat exchange surface (A)), and the heat capacity rate of the HTF (*m*˙ *HTF*·*cp*,*HTF*) [45].

Additionally, the average NTU can be easily estimated as it is directly related to the average effectiveness (*εavg*) of the heat exchange, and under the assumptions of a phase change, similarly to boiler/condenser operation, the heat exchanger effectiveness relations can be simplified [45] as described in Equation (2):

$$NTUL\_{avg} = \frac{U \cdot A}{\dot{m}\_{HTF} \cdot \mathcal{C}\_{p,HTF}} = -\ln(1 - \varepsilon\_{avg}) \tag{2}$$

*Appl. Sci.* **2020**, *10*, 5519

This equation can be rearranged and divided by the total volume *VTOT* to calculate the normalized heat transfer performance coefficient (NHTPC) as shown below in Equation (3):

$$\textbf{NHTPC} = \frac{\textbf{U} \cdot \textbf{A}}{\textbf{V}\_{TOT}} = \frac{-\ln\left(1 - \varepsilon\_{\text{avg}}\right) \cdot \dot{m}\_{HTF} \cdot \varepsilon\_{p,HTF}}{V\_{TOT}}\tag{3}$$

Thus, the proposed KPI on the heat transfer side, NHTPC, can be seen as the product of the overall heat transfer coefficient (U) and the heat exchange surface (A) normalized by the total volume of the LHES unit (*VTOT*). Considering the transient nature of the solidification process due to the increasing resistance and changing surface, it is useful to express an average U·A for the whole process. Dividing this product by the total volume of the LHES unit (*VTOT*) excluding insulation enables comparison of the heat transfer behavior regardless of the final dimensions, operation conditions, and overall scale.

Where *εavg* represents the average heat exchanger effectiveness during discharge, *m*˙ *HTF* and *cp*,*HTF*, the mass flow rate and specific heat capacity of the HTF, respectively, and finally *VTOT* the total outer volume of the container without considering any insulation.

In this case, the effectiveness of the heat transfer (*εavg*) is defined by the relation of the actual average (over the discharge time) temperature difference between inlet (*THTF*,*In*) and outlet (*THTF*,*Out*), and the theoretical maximum temperature difference achievable, with respect to the phase change temperature (*TPC*) as shown in Equation (4) [43,45].

The *TPC* values were reported by the individual studies, and are usually obtained through differential scanning calorimetry (DSC) measurements:

$$
\varepsilon\_{\text{avg}} = \frac{\overline{T\_{HTF,In}} - \overline{T\_{HTF,Out}}}{\overline{T\_{HTF,In}} - T\_{PC}} \tag{4}
$$

This relation allows access to the average product "U·A", or the average heat rate capacity of the heat exchange geometry in the core of the unit. This quantity can be considered independent of the operation conditions, but remains an intrinsic characteristic of the heat exchanger geometry, design, and material combination (PCM and heat exchanger materials).

During the solidification process, the conductive resistance between the HTF and the solidifying (liquid) PCM increases as solid PCM builds up around the HEX structure surface. This also generates a changing solid–liquid PCM heat transfer surface throughout the process. With this in mind, it can be especially handy to consider the product U·A averaged through time, since both the heat transfer surface, and heat transfer coefficient, vary throughout the discharge process with the state of charge of the unit.

Even though the main required information pertaining to the geometry, materials, and amounts are uniformly available, how and which experimental results are readily displayed in literature remains very dependent on the authors and the focus of the studies. Some additional considerations to the definition of the pair of the previously discussed KPIs are suggested for an even representation with the proposed KPIs:

The average HTF outlet temperature (*THTF*,*Out*) was preferably estimated by fitting a polynomial function to the reported data and calculating a mean function value between the beginning of the discharge process up to an arbitrary point. For practical purposes, and considering that once a high degree of solidification is attained the power sharply decreases, a 90% solidification or melting is considered as a standard for a completed process and thus is defined as discharge time (*tDisch*).

For the few cases in which outlet temperature or power profiles were not provided, *THTF*,*Out* can be approximated as shown in Equation (5) derived from the simplified steady-flow thermal energy equation [45]:

$$\overline{T\_{HTF,Out}} = \overline{T\_{HTF,In}} + \frac{\dot{Q}\_{d\text{avg}}}{\dot{m}\_{HTF} \cdot \mathcal{C}\_{p,HTF}} \tag{5}$$

Knowing *tDisch* conveniently allows for indirectly representing the average output power-to-capacity ratio as it represents the inverse of the time required to achieve a certain amount of PCM solidification, and thus the average discharge power (*Q*˙ *avg*) can be approximated using Equation (6) [46] and the energy balance based on material properties and temperature levels:

$$\frac{\hat{Q}\_{\text{av}\underline{\text{v}}}}{E\_{\text{st},90}} = \frac{1}{t\_{D\text{isch.}}}\tag{6}$$

The energy associated with the defined standard degree of solidification (*Est*,90) is estimated assuming the complete contribution of the sensible heat from container (*mCont*·*cp*,*Cont*) and heat exchanger materials (*mHEX*·*cp*,*HEX*) and PCM (*mPCM*·*cp*,*PCM*) from the initial temperature of the unit *Tinit* up to the phase change temperature of the PCM *TPC* in addition, to 90% of the latent contribution from the PCM, as shown in Equation (7):

$$E\_{st,90} = (m\_{HEX} \cdot c\_{p,HEX} + m\_{\text{Cont}} \cdot c\_{p,\text{Cont}} + m\_{\text{PCM}} \cdot c\_{p,\text{PCM}}) \cdot (T\_{\text{init}} - T\_{\text{PC}}) + (90\% \cdot m\_{\text{PCM}} \cdot \Delta h\_{\text{PC}}) \tag{7}$$

Using these considerations and assumptions allows for the calculation of the proposed NHTPC with minimal representative information. The results of the preliminary analysis are shown and discussed subdivided in similarity classes, with a specific focus on the heat transfer performance and the potential of the different approaches for applications that require high power LHES systems.

In summary, Φ*PCM* represents the ratio of main energy storage material to the total volume of the unit, excluding insulation. It provides a general idea on the compactness degree of the system and energy density potential by remaining independent of the temperature levels. Additionally, it can be regarded as a representation of the required HEX material to attain a certain heat transfer performance. It only requires the overall dimensions of the unit and the total amount of PCM inside for its calculation.

NHTPC represents the average heat transfer performance of an LHES unit regardless of the operation conditions (HTF flowrate and temperature levels) used by the authors of the different studies but remaining an intrinsic characteristics of the heat exchange structure geometry, and material combinations (PCM, HEX, container, etc). The calculation requires, in principle, information on both inlet and outlet temperatures on the unit and material properties of PCM and the different components (HEX and container). Temperature profiles are preferably used to estimate directly the average temperatures by using fitting techniques, mean function values, and the previously defined *Est*,90 from the energy balance. Alternatively, if this information is not presented directly, average discharge power or the discharge time can be used to compute close approximations, as shown in Equations (5)–(7).

#### **3. Results and Discussion**

Only the studies that provided sufficient information to perform the calculations with minimal assumptions are shown and discussed in this study. The analysis of the different cases is presented subdivided in four subclasses, namely, finned tube bundle heat exchanger structures, composites of different natures as Thermal Conductivity Enhancers (TCE), macro encapsulation based systems, and experiments using automotive heat exchanger structures and capillary tube bundles.

#### *3.1. Robustness Testing*

In order to corroborate the relative independence of the proposed KPIs with regard to the operation conditions and scale of the LHES unit under scrutiny, a sensitivity analysis incorporating results from a sample of studies in which different inlet temperatures (*THTF*,*In*) and HTF mass flow rate (*m*˙ *HTF*) were used.

The influence of the inlet temperature on the final NHTPC was examined using data from Waser et al. [7] and considering three *THTF*,*In* levels between 15 ◦C and 40 ◦C in both a tube bundle (Unit 1) with 0.02 m3 (20 kg of PCM, CH3COONa·3H2O), and the equivalent finned tube bundle (Unit 2) under a constant 360 kg/h of flowing water as HTF. The mass flow rate effect was considered using data from two different sources and consistent temperature levels. On a larger scale, the data gathered by Zauner et al. [47] for a storage of 0.4 m3 total outer volume (170 kg of PCM, HDPE) operating with thermal oil (Marlotherm SH) as HTF between 2088 kg/h up to 6984 kg/h (Unit 3) was used. On the smaller side, the unit shown by Amagour et al. [13] is considered (Unit 4) with a total outer volume of 0.009 m3 (2.3 kg of PCM, organic blend) with water as HTF and flow rates ranging between 24 kg/h and 62 kg/h.

Figure 1 shows the obtained results for the analysis of the ability of the KPIs to describe system performance independently of experimental conditions.

**Figure 1.** Sensitivity analysis. Calculated NHTPC vs. Φ*PCM* at different temperature levels and HTF mass flow rates in logarithmic scale.

The tight spread of the final results for all four cases corroborates the relative independence of the proposed KPI to the operation conditions. Even though small variations were found for the different experiments, an average coefficient of variation (defined as the standard deviation over the average value) of less than 6% was calculated for every case, which is considered satisfactory for the purpose of this study.

#### *3.2. Finned Tube Bundles*

Finned Tube Bundle (FTB) geometries are the most widely studied Heat Exchanger (HEX) configuration for LHES applications. They consist of fixed-fin geometries, of different topologies and configurations, generally protruding from the tubes used to carry the HTF, into the PCM mass. Highly conductive metals such as copper and aluminum are the most commonly used. The disposition of the fins, packing fraction, thickness, and amount determine the performance of a finned tube bundle.

The selection of analyzed studies which addressed the addition of fins to a tube bundle (TB) heat exchanger geometry to enhance the heat transfer rates of a LHES unit is summarized in Table 1. It includes reference numbers, notation, some descriptive information, and a representative picture or scheme of the discussed units. All additional data required for the calculation of NHTPC are presented in Table A1. The outer volumes of the units V*TOT* , including the container tank surrounding the TB or FTB (and additional manifolds if required) without considering any insulation, were for the most part explicitly reported along with container material and properties. In the cases were information

was missing in this regard, it could be approximated from additional reported geometrical parameters and conservative assumptions. Figure 2 presents the estimated performance indicators. Experiments performed in the framework of the same study with different geometries are indicated with the same letter but different numbering.


**Table 1.** References pertaining to tube bundles (TB) and finned tube bundles (FTB).


**Table 1.** *Cont.*

**Figure 2.** Calculated NHTPC vs. Φ*PCM* for the references concerning tube bundles (TB) and finned tube bundles (FTB) in LHES unit configurations in logarithmic scale.

The most commonly found arrangements pertain fixed fins embedded in the PCM bulk, oriented perpendicularly (A.2, B.1, D, G, H) or longitudinally (C, E, F, I, J) to the HTF flow inside the tubes. Some interesting alternative variations see longitudinal fins used such as in triplex heat exchanger configurations by Al-Abidi et al. [9] (C), complex geometries to fit specific applications by Laing et al. [10] (E) or even fixed on the side of the flowing HTF, as presented by Raul et al. [12] (J). Regarding performance, the study carried out by Waser et al. [7] provided data for a finned copper tube bundle (A.2) and additional in-house data from the same study was used for the analog plain tube bundle (A.1). The addition of aluminum fins traded an additional 3% of PCM volume fraction for a

significant discharge time reduction of around 50% and a total threefold improvement in the calculated NHTPC. However, it is necessary to highlight the performance of the tube bundle structure (A.1) as it exceeds most of the FTB designs. Taking the unit used by Khan et al. [49] (I) as comparison point, the sheer difference in heat transfer surface could explain this behavior. Even though A.1 presents no fins, the heat transfer surface to volume ratio of unit A.1 is over two times higher (63 m2/m3) than that of unit I (27 m2/m3).

In a similar comparison approach, Medrano et al. [48] (B.2) achieved a sevenfold increase (when compared to B.1) in heat transfer performance by trading an approximate 7% of PCM volume to accommodate circular radial fins.

The FTB unit presented by Shon et al. [14] (D.1) attained the higher performance in this case with an additional 4% of the total volume dedicated to the analog copper finned tubes than the FTB unit investigated by Waser et al. [7]. The heat exchange structure with a higher packing fraction could explain the differences in performance.

In the case of Amagour et al. [13] (H), it is interesting to note that around 65% of the total LHES unit volume was dedicated to heat exchange elements as well as additional empty space above the heat exchanger. It directly affects the overall energy density of the unit with around 29 kWh/m3, but achieves a thermal response around the average for the category. This is evidence of the intricacies of the container, heat exchanger design, and chosen materials. A high share of heat exchanger material, or consequently a low PCM fraction, does not necessarily translate into improved heat transfer behavior. A similar situation was found on some other cases leading to a low Φ*PCM* was caused by a large volume occupied by the HTF, and additional head space in the units which could potentially be optimized.

#### *3.3. Automotive Heat Exchangers and Polymer Based Capillary Scale Tube Bundles*

This entire subsection is dedicated to particularly interesting systems as they are in principle extreme variations of finned and simple tube bundles. On one hand, Automotive HEX (AHEX), conceived from the idea of finned tubes for gas-to-liquid heat exchange, are mass produced on a wide variety of configurations usually completely made out of braced aluminum and seek to maximize the heat transfer surface. On the other hand, without additional material, very large heat transfer surfaces can be achieved by driving the diameter of a tube bundle to the capillary scale (below 5 mm). Additionally, the consequent thin walls produced at this scale minimize the influence of the material conductivity, opening the door to the utilization of polymers for a wide range of applications when temperature levels allow. These systems will be finally referred to as capillary tube bundles (CTB). Table 2 gathers the notation and representative schemes of the studies treated in this section. All additional data required for the calculation of NHTPC are presented in Table A1. The outer volumes of the units V*TOT* , including the container tank surrounding the HEX without considering any insulation, were for the most part explicitly reported in the different studies along with container material and properties. In the cases where information was missing in this regard, it could be approximated from additional reported geometrical parameters and conservative assumptions.

The summarized KPIs are portrayed in Figure 3. Experiments performed in the framework of the same study with different geometries are indicated with the same letter but different numbering.

Medrano et al. [48] experimented with an AHEX unit embedded in PCM (B.4), and compared it to other common LHES approaches and it achieved an impressive NHTPC, several times higher than the next best performance within the same study, the graphite matrix enhanced tube-and-shell (B.3) unit previously discussed. This effect might be explained mainly by the sheer mass of heat exchanger material in the unit rather than the heat exchanger design as it presents a relatively low performance in both heat transfer and compactness when compared to other AHEX-based units.


**Table 2.** References pertaining to AHEX and CTB based units.

**Figure 3.** Calculated NHTPC vs. Φ*PCM* for the references concerning AHEX and CTB in LHES unit configurations in logarithmic scale.

A similar situation was discussed in the study performed by Shon et al. [14] their initial experiments were performed using a stock automotive HEX immersed in PCM (D.2). Based on their results, an FTB design with a higher capacity was produced and is discussed in Section 3.2 (D.1). Interestingly, their goal was achieved as their FTB custom design (33 [kW/m3·K]) effectively matched the thermal performance of the AHEX-based unit (36 [kW/m3·K]). Their design variations, however, required an additional sacrifice of 10% PCM volume fraction. A second iteration of an analog system for a diesel based system, explored by Park et al. [51] (T), produced a custom heat exchanger with an analog flat pipe and fin configuration, and produced the highest NHTPC reported, reaching around 85 [kW/m3·K] with a similar PCM volume fraction as its predecessor. The LHES unit proposed by Lee et al. [50] (S) constitutes a particular example of how LHES capacity and power are tailored for specific applications. The high performance parameter calculated and the significantly low PCM volume fraction were adjusted to the envisioned application requirements. The unit was manufactured to produce high cooling power for very short periods of time while the car is idle on a red light, as the LHES unit is part of an automotive HVAC system, and is thus adapted to be used with two HTF systems, coolant loops and pure air convection.

These are good examples of the potential of AHEX as highly optimized systems readily available at industrial manufacturing scales in a broad variety of configurations that, although envisioned for a different application, could widen the areas of implementation of an already existing product.

When looking at polymer CTBs, their average performance does not deviate much from the results seen for FTB. They are polymer based and large heat exchange surfaces are achievable while requiring very low volume within the unit, in the order of 90% PCM fraction or more. Helm et al. produced a prototype [53] (V) and posterior improvement [54] (W) as part of a solar heating and cooling system. The heat exchange structure based on polypropylene capillary tubes in the order of 4.3 mm outer diameter was used in both cases and not only its performance, but also its durability, were put to the test in system level experiments and cycling tests.

Similarly, Hejcik et al. [52] (U) presents a special case, studying the use of polypropylene hollow fibers, capillary tubes in the order of 0.8 mm outer diameter as tube bundle arrangements embedded in PCM within a modeling study. The reported performance was calculated based on the simulations carried out by the authors and the PCM volume fraction was calculated based on the model domain used which included only a PCM mass and the hollow fiber bundle. The potential of hollow fiber bundles and, in general, polymer capillary scale systems becomes discernible when contemplating that thermal performances comparable to FTB configurations are attainable using basic geometries that occupy a minimal share of the volume.

Even though the heat transfer performance seems adequate from a KPI perspective, it is necessary to clarify that although a quick discharge can be achieved with CTB based systems, they require special attention in their design as achieving a stable temperature output window requires low mass flow rates, long tubes, or systems in series. The added frictional effects of the HTF flow at low inner diameter conditions must be considered during the optimization to avoid excessive pumping power requirements and affecting the effectiveness of the system.

#### *3.4. Composites*

The use of highly conductive materials to increase the performance of PCM as Thermal Conductivity Enhancements (TCE) has been widely studied. The general goal of this kind of TCE is to allow the creation of a conductive network through the PCM mass and enhance overall conduction in both melting and solidification processes. Table 3 shows the notation and representative figures of the studies considered in this subsection. All additional data required for the calculation of NHTPC are presented in Table A1. The outer volumes of the units V*TOT*, including the container tank surrounding the HEX (and additional manifolds if required) without considering any insulation, were for the most part explicitly reported in the different studies along with container material and properties. In the cases where information was missing in this regard, it could be approximated from additional reported geometrical parameters and conservative assumptions.


**Table 3.** References pertaining to carbon based techniques and metal foams as TCE

Figure 4 summarizes the performance results of carbon and metal based TCE in different configurations, such as carbon dispersions and composites of various forms, and metal foams of different amounts of pores per inch. Each subcategory will be further discussed separately.

**Figure 4.** Calculated NHTPC vs. Φ*PCM* for the references concerning carbon based structures and metal foams as TCE in LHES unit configurations.

#### 3.4.1. Metal Foam Based Composites

Across the metal foams (MF) considered as TCE options for LHES systems, the most widely studied are aluminum [21,22], copper [23–25], and nickel [26] foams.

For instance, Atal et al. [22] considered aluminum foams of different porosities (N.2, N.3) on a shell and tube arrangement and achieved reductions in discharge time of up to 63% and a proportional increase in its heat transfer performance when compared to the case with only PCM (N.1). However, only a marginal increase in performance is observed with decreasing metal foam porosity (FP) (and consequently PCM volume fraction) as shown in Figure 4. An ultimate difference of around 15% additional PCM volume fraction is sacrificed to accommodate the lower porosity foam but little to no effect is shown in terms of heat transfer enhancement. Additionally, the energy density of the system is heavily affected, decreasing from 112 kWh/m<sup>3</sup> in the case of pure PCM (N.1), to 108 kWh/m3 for the 95% porosity foam (N.2) and finally 94 kWh/m<sup>3</sup> in the case of the 77% porosity foam (N.3). It becomes clear that the energy density trade-off when accomodating the higher porosity foam (N.2) is worth it in terms of performance, but, once a sufficient highly conductive network is created, there is no substantial enhancement in increasing the amount of metal in the unit.

Lazzarin et al. [21] also studied the effect of aluminum foams with slightly different porosities and number of pores per inch (PPI) achieving in the best case a reduction of around 90% on the solidification time. In a similar way, Mancin et al. [23] used copper foams of increasing PPI and attained a reduction in charging time of around 27%. Similarly, Xiao et al. [24] used copper and nickel foams of different amounts of PPI to improve PCM conductivity. From the measurements performed by the authors, a great improvement is evident for all cases when compared to the original 0.305 W/m·K. For instance, the copper foams embedded in the PCM produced conductivities of 5 W/m·K and 16 W/m·K for 97% and 88.9% porosity samples, respectively.

The latter examples, although worth mentioning, are not shown in this study since their experimental setup was not conceived as LHES units working with a heat transfer fluid and thus it was not possible to accurately calculate the proposed KPIs without inaccurate assumptions. Similarly, a major share of the considered references pertaining the use of metallic foams concerned effective thermal conductivity measurements, and experimental setups focused towards electronic heat management strategies. In order to compare in terms of the NHTPC methodology, either more

experimental work or validated models that place these materials in a LHES unit configuration are necessary to further study and evaluate their potential.

#### 3.4.2. Carbon-Based Composites

Among the considered references, several of them contained some form of carbon based TCE, in the form of expanded graphite composites and dispersions [15,16,20,48], carbon fiber (CF) [17], carbon foam [18], and even carbon fiber cloth (CC) [19].

Within the selected units, Medrano et al. [48] proposed the highest performance of the carbon based enhancements by placing and expanded graphite and PCM composite in a double pipe heat exchanger configuration (B.3) and compared it to a direct analog unit containing only PCM (B.1) discussed in Section 3.2. The addition of the graphite matrix required the trade of 15% in PCM volume fraction but achieved a seventeen fold increase in terms of NHTPC.

Fukai et al. [19,55] used carbon fiber brushes [55] (K.2) and carbon fiber cloth [19] (L) threaded around a copper tube bundle structure (K.1). Interestingly, both enhancements, under the same experimental conditions, reduced the discharge time by up to 45% by trading a minor share of the volume to accommodate the brushes [55] (K.2) and carbon cloth [19] (L) in both cases. Wu et al. [16] (M) produced a similar performance using shape stabilized 75:25 PCM and expanded graphite composite with a copper tube bundle configuration as heat transfer elements but required an additional 17% PCM volume fraction to achieve it.

#### *3.5. Macro-Encapsulation Solutions*

The considered references pertaining macro encapsulation techniques include both high and low temperature applications. The considered examples are shown in Table 4. All additional data required for the calculation of NHTPC are presented in Table A1. The outer volumes of the units V*TOT*, including the container tank surrounding the bed of capsules (and additional manifolds if required) without considering any insulation, were for the most part explicitly reported in the different studies along with container material and properties. In the cases where information was missing in this regard, it could be approximated from additional reported geometrical parameters and conservative assumptions. The results are available in Figure 5.

Ma et al. [27] (O) and Wickramaratne et al. [28] (P) both presented LHES units using stainless steel encapsulation methods for high temperature applications on a range of temperatures around 550 ◦C. Even though the systems are relatively similar, the difference in performance could be explained in part by the fact that Ma et al. [27] (O) uses Al:Si alloy as PCM and Wickramaratne et al. [28] (P) proposed a eutectic salt mixture. This means that, besides having a much larger PCM phase change enthalpy (432 kJ/kg), in the first case, the most common drawback associated with LHES is minimized by the high PCM thermal conductivity in both phases. This ultimately translates into higher average power, and it is taken into account in the NHTPC, as the average outlet HTF temperature is much closer to the phase change temperature.


**Table 4.** References pertaining to macro encapsulation techniques

**Figure 5.** Calculated NHTPC vs. Φ*PCM* for the references concerning macro encapsulation techniques in LHES unit configurations.

Park et al. [31] presented flexible (Polyethylene, Nylon, Aluminum, and PET) laminated pouches (R.1) as the encapsulation method and compared them to 3D CFD modeled spherical equivalents (R.2). The flexible pouches decreased the discharge time of the system by 62% when compared to the simulated spherical containers, and is reflected on a fivefold increase in its NHTPC while retaining the same PCM fraction in the unit. This is a clear illustration of the importance of the design of the encapsulation structure in the overall heat transfer surface of the system.

Similarly, Nallusamy et al. [30] (Q) showed the highest NHTPC and PCM fraction combination calculated using HDPE spheres in a packed bed configuration.

#### **4. Discussion**

Data on the geometry, thermal properties, and performance under specific conditions of a wide range of technological approaches to LHES were gathered and used to estimate NHTPC and PCM volumetric fractions. Figure 6 summarizes the LHES units in each category to enable comparison of performance across all technologies.

**Figure 6.** NHTPC vs. Φ*PCM* for all units in each category in logarithmic scale.

Considering the overall trends when looking at the calculated KPIs, some general observations can be drawn:


#### *KPI Comparison*

Considering the many already available KPI for LHES systems, Table 5 compiles some of the most relevant KPIs concerning heat transfer performance and compactness degree, as well as the pair presented in this study for three systems at different experimental conditions. Even though the considered KPIs are not intended to represent the same phenomena or were conceived with the same objectives, it is still interesting to see how they vary with experimental conditions and how they compare among each other.

Similarly to the robustness testing section, Units 2, 3, and 4 are used as representative systems, with varying inlet temperature, mass flow rate, and overall size, with the intent to analyze how the KPIs change accordingly.


**Table 5.** Comparison of different KPIs for LHES.

As shown in the table, ED is intrinsically dependent not only on material properties and dimensions, but also on the sensible contributions and thus temperature levels imposed on the unit, as seen in the results for Unit 2 at two temperature levels. With a similar point of view, Φ*PCM* shows a similar trend between the Units, but focusing only on the share of main energy storage material. Although it does not provide the exact same information, it can be useful in representing both the compactness degree of the design, and the potential for energy density of the unit without considering the current experimental temperature differences.

On the heat transfer performance side, specific charging rate *γ* as proposed by Guo et al. [39], and 5 min peak power-energy stored ratio by Gasia et al. [38] seem to agree with the overall trend shown by NHTPC across the units. They provide indications of the average heat transfer behavior with respect to the total energy, but remain dependent on both temperature and HTF mass flow rate differences. In contrast, NHTPC remains almost constant for a given system across different experimental conditions.

Although they all provide very useful information on particular aspects, slightly more drastic variations can be seen with the volumetric heat transfer coefficient *hv* and average temperature effectiveness *εavg* presented by Nomura et al. [40] as well as *tDisch*, *Q*˙ *avg* and 5 min. Peak Power.

#### **5. Conclusions**

A pair of performance indicators to evaluate the heat transfer performance and compactness for latent heat energy storage (LHES) units were presented. These key performance indicators (KPIs) were calculated for several LHES units reported in literature allowing a leveled performance comparison with regard to operating conditions at different scales, while remaining intrinsic to the geometry, heat exchanger structure materials, and PCM. The robustness of the proposed KPIs was confirmed with varying HTF mass flow rate and temperature levels, for units at different size scales, with a coefficient of variance below 6% in every case, and were compared to other reported KPIs for LHES.

Finned tube bundle (FTB) and tube bundle (TB) units showed the widest range of performance, and a great potential mainly dependent on the quality of the HEX design. Composites in general require further experimental work but show very promising potential.

Automotive heat exchanger (AHEX)-based units showed promise especially on their heat transfer performance, and are interesting for further study as they are already mass produced in a very wide range of variations. Capillary tube bundles (CTBs) show great potential especially in terms of compactness, but due to the added practical challenges require some optimization work for ideal operation. For both AHEX and CTBs, material limitations regarding compatibility and operation range are some of the main concerns, and should be thoroughly considered in further studies.

The macro encapsulated (ME)-based systems considered showed in general low performance and compactness, but a very large potential for improvement and flexibility, especially in terms of capsule shape and size optimization to customize their performance, for instance.

It is necessary to highlight that the publications taken into account had clear application-oriented objectives. This implies that achieving the highest possible heat transfer rate was not the focus during their conception, but only the required performance for a specific application under given conditions. It is possible to infer that optimized versions of the mentioned technologies would deliver considerably higher performance indicators. Therefore, the conclusions drawn from this analysis cannot be considered as final in any way regarding the technological approaches but more so as a look at the general potential of each approach.

Additionally, a key aspect of the thermal response is relatively overlooked by the analysis, as the methodology proposed only accounts for the stability of the outlet temperature indirectly, within the approximation of the average outlet temperature. Further dimensionless analysis is required to account for this effect.

**Author Contributions:** Conceptualization, S.M. and R.W.; Formal analysis, W.D.-D.; Funding acquisition, A.S.; Investigation, W.D.-D.; Methodology, W.D.-D.; Project administration, W.D.-D. and A.S.; Resources, A.S.; Supervision, A.S. and J.W.; Writing–original draft, W.D.-D.; Writing–review and editing, A.S., S.M., R.W. and J.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Swiss Competence Center for Energy Research Heat and Electricity Storage (SCCER HaE).

**Acknowledgments:** This work was developed within the framework of the Swiss Competence Center for Energy Research Storage of Heat and Electricity (SCCER HaE).

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Appendix A**


**Table A1.** Additional information.


**Table A1.** *Cont.*

#### **References**


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