Experimental study on transient thermal characteristics of stagger-arranged lithium-ion battery pack with air cooling strategy

Experimental study on transient thermal characteristics of stagger-arranged lithium-ion battery pack with air cooling strategy

International Journal of Heat and Mass Transfer 143 (2019) 118576 Contents lists available at ScienceDirect International Journal of Heat and Mass T...

5MB Sizes 0 Downloads 9 Views

International Journal of Heat and Mass Transfer 143 (2019) 118576

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Experimental study on transient thermal characteristics of stagger-arranged lithium-ion battery pack with air cooling strategy Xiaoling Yu a, Zhao Lu a, Liyu Zhang b, Lichuan Wei a,c, Xin Cui b, Liwen Jin b,⇑ a

School of Energy and Power Engineering, Xi’an Jiaotong University, 710049, China Institute of Building Environment and Sustainable Technology, Xi’an Jiaotong University, 710049, China c Shenzhen Envicool Technology Co. Ltd., Shenzhen 518129, China b

a r t i c l e

i n f o

Article history: Received 19 June 2019 Received in revised form 25 July 2019 Accepted 12 August 2019 Available online 21 August 2019 Keywords: Lithium-ion battery Heat generation behaviors Transient thermal characteristics Longitudinal airflow

a b s t r a c t The thermal characteristics of lithium-ion battery affect significantly charging/discharging performance, cycle life and safety of electric vehicles (EVs) battery packs. In this study, a stagger-arranged battery pack consisting of three battery modules was developed to explore its transient thermal characteristics in charging/discharging process under the two cooling strategies, i.e., natural cooling and forced air cooling. The investigation of heat generation behavior of the battery with Li(NixCoyAlz)O2 cathode showed that the heat generation rate of the battery remains almost unchanged along the main discharging process, while a rapid increase in heat production is detected at the end of discharging. It was found that the maximum temperature and temperature difference in the battery pack subject to a moderate charging/discharging rate, e.g., 0.5 C, can be maintained within the desirable ranges by natural cooling. The forced air cooling strategy employing longitudinal airflow remarkably improves the battery’s transient thermal characteristics with achieving the depth of discharge (DOD) up to 84.2%, which is capable to prolong the battery pack’s cycle life to a large extent. Lastly, the appropriate air supply velocity of 0.8 ms1 is recommended for the proposed battery pack subject to a higher discharging rate, e.g., 1 C, from the viewpoint of cooling effectiveness. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, the rechargeable lithium-ion battery has become a promising candidate as the power source of electric vehicles (EVs) due to its high energy density, long cycle life and low self-discharging rate, etc [1,2]. It is widely acknowledged that a densely-packed battery module has to be produced by connecting a certain number of batteries in series and/or in parallel to supply the adequate power for EVs, which would result in a severe thermal management issue owing to the heat accumulation inside the battery pack. Therefore, a well-designed battery management system (BMS) plays the crucial role in managing the charging/discharging characteristics of the battery pack [3,4]. It is well-known that the battery temperature and temperature uniformity possess significant effects on the charging/discharging characteristics, cycle life and safety of the battery pack, which are critical to the performance of EVs to a large extent [5–11]. The heat generated by the battery itself is mainly consisted of the reversible heat caused by the entropic change and irreversible heat resulted from ⇑ Corresponding author. E-mail address: [email protected] (L. Jin). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118576 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

the overpotential resistance. The amount of heat generated by the battery pack during the charging/discharging process would significantly elevate the battery temperature, which may lead to a rapid degradation of battery capacity and even thermal runaway or fire hazard [5–8]. On the other hand, the battery charging/discharging capacity would be obviously decreased when the battery operating temperature is lower than 0 °C [9,10]. In addition, some researchers emphasized that the non-uniform temperature distribution inside the battery pack (>5 °C) may result in the inconsistency of batteries and the reduction of battery packs’ performance [11]. These researches further emphasized the need of a properdesigned battery thermal management system (BTMS) to maintain the batteries at the optimum operating range from 25 °C to 40 °C and the temperature uniformity inside a battery pack lower than 5 °C. As a result, all kinds of battery thermal management systems including air BTMS [12–20], liquid BTMS [21–25], phase change material BTMS [11,26–28] or a combination of them [29], have been extensively investigated to improve the charging/discharging characteristics as well as the thermal safety performance for the EVs battery pack. Among these battery thermal management systems, liquid BTMS and phase change material BTMS are more

2

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

Nomenclature Cp,b D Dch Dct Dvh L m q s SD SL ST tf T uA uB uC dTb/dt V  x x, y, z

specific heat of battery (Jkg1K1) diameter of battery (mm) diameter of circular holes on the holding plate (mm) outer diameter of copper tube (mm) diameter of venting holes on the holding plate (mm) height of battery (mm) mass of battery (kg) heat generation rate (W) standard deviation distance between the center of cells (mm) longitudinal pitch of tube (mm) transverse pitch of tube (mm) thickness of fin (mm) temperature (K) random uncertainty systematic uncertainty combined standard uncertainty temperature rising rate (°Cs1) air supply velocity (ms1) average value of measurements directions

Greek symbols D accuracy of experimental instrument DT temperature difference (K)

effective than air BTMS for the extreme conditions, e.g., high charging/discharging rates and high operating or ambient temperatures [23,26]. However, these two BTMS have also several concerns. For the liquid BTMS, the common shortcomings are the potential leakage of liquid coolant, the poor thermal contact between cooling channel and battery, as well as the need for large space and complex cooling system. For the phase change material BTMS, the downsides are the undesirable thermal mass and the significantly decreased energy-density ratio of battery pack. Due to low cost and energy loss, simple structure as well as superior security of an air BTMS, therefore, it is still preferred over both liquid BTMS and phase change material BTMS for most of EVs battery pack with relatively moderate conditions [16,17]. Many studies have been carried out on air supply strategy, cooling condition and battery configuration to improve the thermal characteristics and cooling performance for the EVs battery pack. Panchal et al. [12] conducted a comprehensive study on the transient temperature distributions of a large sized 20Ah-LiFePO4 prismatic battery at different discharging rates under natural cooling condition using both experimentally and theoretically. Li et al. [13] developed a two-dimensional numerical model to explore the thermal characteristics of aligned-arranged battery pack with the crossed airflow, which was validated by experimental data using wind tunnel testing. In addition, a reduced-order model associate with numerical results was established to predict the maximum temperature of aligned-arranged battery pack with the crossed airflow. Wang et al. [14] investigated the thermal performance of cylindrical battery pack with different battery configurations and air supply strategies. Their results could be summarized as follows: (1) the best cooling performance can be achieved when airflow inlet and outlet are located on the top of battery pack and (2) the optimal battery configuration can be obtained based on three key factors, namely, cooling effectiveness, cost and space utilization of battery pack. Mahamud et al. [15] designed a BTMS using a reciprocating airflow and established a two-dimensional

Subscript b ch ct f in L max T vh

battery circular holes copper tube fin inlet longitudinal maximum transverse venting holes

Acronyms and abbreviations ARC accelerating rate calorimeter BMS battery management system BTMS battery thermal management system BTS battery testing system CC constant current CV constant voltage DOD depth of discharge DAQ data acquisition EVs electric vehicles NI national instrument SOC state of charge

numerical model to investigate the effect of reciprocation period on the thermal characteristics of aligned-arranged battery pack. The numerical results illustrated that the reciprocating airflow can effectively improve the temperature uniformity and reduce the maximum temperature inside the battery pack. Saw et al. [16] developed the correlation between Nu number and Re number in terms of the steady state numerical results, which could be employed to predict the transient thermal behaviors of alignedarranged battery pack with the longitudinal airflow. The threedimensional numerical model of a stagger-arranged battery pack with the longitudinal airflow was developed to study the effects of cooling channel size and air supply strategy on the thermal characteristics of battery pack in our previous work and the results showed that the appropriate cooling channel size is 1 mm for 18,650 lithium-ion battery pack taking into account three key parameters, i.e., the maximum temperature, the space utilization and the energy efficiency [17]. Some researchers [18–20] explored the effects of cooling conditions and battery configuration on the thermal characteristics of a battery pack and their numerical results showed that the forced parallel airflow cooling is capable of effectively improving the temperature uniformity inside the battery pack because each cooling channel formed by the gaps between batteries has nearly identical mass flow rate and inlet temperature. According to the brief literature review on air BTMS, we could learn that the earlier works focus more on the investigation of the thermal characteristics of aligned-arranged cylindrical battery pack or flat-plat battery pack using the steady-state numerical simulations. It is noted that the steady state numerical simulation based on the average heat amount generated by the battery is able to predict the average temperature of batteries in the battery pack properly at the end of discharging [16], however, the battery temperature rise affecting the cycle life of lithium-ion battery has been overlooked to some extent during the charging/discharging process [14,17]. In addition, since the reduction of cooling capability

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

caused by the temperature rise of air coolant along airflow direction, the existing findings containing only one row of batteries along airflow direction may be inappropriate for extrapolating the thermal characteristics of a densely-packed battery module which is aimed to satisfy higher power density and prolong endurance mileage of EVs [14,16,18–20]. In order to resolve issues mentioned above, the staggerarranged battery pack with three battery modules was established carefully to explore its transient thermal characteristics during the charging/discharging process under the two different cooling conditions, namely, natural convection cooling condition and forced air convection cooling condition. In addition, the heat generation behavior of single lithium-ion battery with Li(NixCoyAlz)O2 cathode used to pack the tested battery modules was studied by adopting an accelerating rate calorimeter (ARC). The major contents of this experimental study include: (1) the heat generation behavior of the commercial lithium-ion battery (Panasonic NCR18650PF) was obtained by ARC during the constant current discharging process; (2) the transient thermal characteristics of the tested battery pack during the charging/discharging process under natural convection cooling condition were explored comprehensively; and (3) much efforts were made to investigate the effects of air supply velocities and charging/discharging rates on the transient thermal characteristics of the tested battery pack with the longitudinal airflow, which could provide a specific instruction for the layout design of the practical battery pack with air BTMS.

2. Experiments 2.1. Configuration of stagger-arranged battery pack In this study, a stagger-arranged battery pack consisted of three battery modules with an electric configuration of 3S22P (3 batteries in series along z direction and 22 batteries in parallel on the x-y plane) was established to explore the modules’ transient thermal characteristics under the above mentioned two cooling conditions, as shown in Fig. 1(a). Each battery module contains 22 commercial NCR18650PF (Panasonic, Japan) lithium-ion batteries with a rated capacity of 2.7 Ah. According to the specification, the active materials of the NCR18650PF lithium-ion battery are made up of three elements of Nickel, Cobalt and Aluminum (NCA) at the cathode and graphite at the anode. The rated capacity and voltage of each battery module are 59.4 Ah and 3.6 V, respectively. The details of cross-section A-A of the stagger-arranged battery pack are shown in Fig. 1(b). It is seen that the staggered arrangement is characterized by the distance between two cell centers (SD), which is set to be 22 mm in this study. The minimum gap between the battery cells is 4 mm and 42 venting holes (Dvh = 4 mm) around the battery cells are evenly created on the holding plate in order to ensure air coolant uniformly flow through the battery surfaces. Fig. 1(c) shows the components of stagger-arranged battery pack mostly containing 3 battery modules, 2 insulating plates and 2 mounting plates. Each battery module is composed of 22 battery cells, 2 holding plates and 2 nickel-copper conductive sheets. It is important to note that both the holding plates have 22 circular holes (Dch = 18.2 mm) to fix the battery cells. In addition, the rather small gaps between the holding plates and battery cells are filled with thermal conductive silicon grease to reduce the interfacial contact resistance. The positive and negative terminals of 22 battery cells are attached to the two nickel-copper conductive sheets using the laser-beam welding machine. At last, three battery modules are connected with screws along z direction (horizontal airflow direction) to form tightly the stagger-arranged battery pack combined with insulating plates and mounting plates. The picture of stagger-arranged battery pack tested in this study is shown in

3

Fig. 1(d). The dimensions of stagger-arranged battery pack’s components are tabulated in Table 1. Consequently, the rated capacity and voltage of the entire battery pack are 59.4 Ah and 10.8 V, respectively, with the frame dimensions of 116 (x)  104 (y)  206 (z) mm. It is important to note that the air coolant will be constricted when it flows through the venting holes, and then expanded to the battery surfaces. Therefore, constriction and expansion of airflow inside the stagger-arranged battery would appear periodically along z direction (horizontal airflow direction) due to the air vents on the holding plates. 2.2. Experimental setup and measurement The schematic diagram of experimental system and the actual pictures of experimental facilities are illustrated in Fig. 2. It is seen that the tested battery pack is placed in the test section [12 (x)  12 (y)  210 (z) mm] of the rectangular wind tunnel with the dimensions of 12 (x)  12 (y)  2300 (z) mm. The rectangular wind tunnel was made of 10 mm thick polycarbonate. The centrifugal fan (HONGKE ELECTRIC, 150FLJ7) placed in the front of wind tunnel was to drive air coolant across the fin-and-tube heat exchanger (outer diameter of copper tube Dct = 9 mm, thickness of fin tf = 0.12 mm and tube pitch ST = SL = 25 mm), uniform flow orifice and stagger-arranged battery pack successively, and finally exit from the outlet of wind tunnel. The frequency convertor (WENFU, GT4000W) was employed to control the centrifugal fan speed which adjusted the air volume through the stagger-arranged battery pack with various air supply velocities. The air supply velocity (Vin) was measured by the hot-wire anemometer (Testo 425). The fin-and-tube heat exchanger was connected with the water thermostat (Julabo F32) with excellent heating/cooling capability to maintain the inlet air temperature at 25 °C during the experimental process. The utilization of the orifice is of significance for maintaining the uniform airflow distribution at the entrance of the stagger-arranged battery pack. Two kinds of thermocouples were used in this study, namely, the T-type armored thermocouple (Watlow, ±0.5 °C), and the T-type wire thermocouple (Omega, ±0.5 °C). Particularly, the three T-type armored thermocouples were placed in the entrance and exit of the tested battery pack to measure the air coolant temperature, while the battery surface temperatures were measured by the nine T-type wire thermocouples attached to the middle of battery surface, as shown in Fig. 3. All thermocouples used in this study were connected to a National Instrument (NI) data acquisition (DAQ) system (NI cDAQ-9184) after careful calibration using a metrology dry-block calibrator (Fluke 9142). The battery testing facility (NEWARE, CT-400130V200A) was controlled by a software of battery testing system (BTS v7.5.6) installed on the computer. The terminal voltages, charging/discharging currents and capacities of the tested battery pack measured by the battery testing facility, were collected by the computer through the Ethernet port. In our experiment, the temperature rising rate of single lithiumion battery (Panasonic NCR18650PF) with Li(NixCoyAlz)O2 cathode was firstly measured using an accelerating rate calorimeter at different discharging rates of 0.5 C and 1 C, which could be employed to determine the heat generation rate and analyze the thermal characteristics of the stagger-arranged battery pack. Noting that the symbol C usually refers to the discharging currents employed to make the rated capacity of battery fully discharged at a specific time period. Based on the definition of the symbol C, therefore, the battery discharging currents of 0.5 C and 1 C are 1.35 A and 2.7 A, respectively. Two different cooling conditions, namely, natural convection cooling condition and forced air convection cooling condition were used to comprehensively explore the transient thermal characteristics of the tested battery pack during the charging/ discharging process, which are discussed in Sections 3.2 and 3.3

4

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

Fig. 1. (a) Schematic diagram of the stagger-arranged battery pack; (b) Details of cross-section A-A; (c) Components of the stagger-arranged battery pack; (d) Actual battery pack.

Table 1 Dimensions of the stagger-arranged battery pack’s components. Components

Dimensions (mm)

NCR18650PF lithium-ion battery Holding plate Nickel-copper conductive sheet Insulating plate Mounting plate

18 (D)  65 (L) 116 (x)  104 (y)  10 (z) 116 (x)  104 (y)  0.5 (z) 116 (x)  104 (y)  2 (z) 116 (x)  104 (y)  2 (z)

respectively. It is important to note that the external wall of wind tunnel in the test section was wrapped tightly with polyvinyl chloride foam for lowering the adverse effect of the room temperature

variation (25 ± 2 °C) during the experimental process. The natural convection cooling condition refers to the special case of forced air convection cooling condition when the centrifugal fan was turned off. The objective of exploring natural convection cooling condition is to discover the effect of the heat generated by battery itself on the transient thermal characteristics during the charging/discharging process. This cooling condition is similar to that of a battery pack without BTMS intervention. Sabbah et al. [30] found that the volume averaged battery temperature at the end of discharging decreases less than 2 °C when the air supply velocity approximately ranges from 0.8 ms1 to 8 ms1, and Wang et al. [31] reported a similar result that there is only a small

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

5

Fig. 2. (a) Schematic diagram of experimental setup; (b) Actual experimental facilities.

variation in the maximum temperature over the entire discharging process for the air supply velocity ranging from 1.0 ms1 to 2.0 ms1. In this study, therefore, the three air supply velocities of 0.6 ms1, 0.8 ms1 and 1 ms1 were investigated to optimize air supply strategy for the forced air convection cooling condition. The charging/discharging schemes of the tested battery pack under the two cooling conditions are identical as follows:

(i) Constant current and constant voltage (CC-CV) charging regime: the battery pack is charged at a constant current (CC) regime of 0.5 C until the terminal voltage reaches 12.6 V, and then charged at a constant voltage (CV) regime of 12.6 V until the current is below 0.4 A; (ii) Constant current (CC) discharging regime: the battery pack is discharged to 7.5 V adopting CC regime at 0.5 C, 0.75 C and 1 C, respectively.

6

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

Fig. 3. Locations of thermocouples inside the stagger-arranged battery pack.

The charging/discharging currents of the tested battery pack corresponding to 0.5 C, 0.75 C and 1 C are tabulated in Table. 2.

3. Results and discussion 3.1. Heat generation behaviors of single lithium-ion battery

2.3. Uncertainty analysis Generally, experimental uncertainties are classified into the random uncertainties and the systematic uncertainties. The timeaveraged method is usually employed to minimize the random uncertainties, while the systematic uncertainties can be minimized with careful experimentation and precision instrumentation. In this study, battery terminal voltage, operating current, battery surface temperature, air supply velocity and temperature, were measured and recorded in the real-time mode. The real-time inlet temperatures and velocities of air coolant during the charging process were used to calculate the random uncertainties of air supply temperature and velocity. The accuracies of thermocouples, hotwire anemometer and battery testing system shown in Section 2.2 were utilized to determine the systematic uncertainties. The uncertainties of direct measurements were determined by the following equation [32]:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uC ¼ u2A þ u2B ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  D 2 s x þ pffiffiffi 3

ð1Þ

where uC, uA and uB represent the combined standard uncertainty, 

random uncertainty and systematic uncertainty, respectively; x  and s x represent the average value and the standard deviation

of the direct measurements, respectively; the symbol D represents the accuracy of experimental instrument. The uncertainties of battery terminal voltage, operating current, battery surface temperature, air supply velocity and temperature are 0.25%, 1.45%, 3.96%, 2.0% and 3.96% respectively.”

Table 2 Charging/discharging rates and currents tested in this study. Charging/discharging rate

Charging/discharging current

0.5 C 0.75 C 1C

29.7 A 44.6 A 59.4 A

It is important to note that the thermal characteristics of the battery pack under different cooling conditions are primarily dependent on the heat generated by battery cells. As a result, study on the heat generation behaviors of the lithium-ion battery with Li (NixCoyAlz)O2 cathode is of significance for exploring further the transient thermal characteristics of the battery pack which is discussed in Sections 3.2 and 3.3 respectively. Generally, the heat generation rate of the battery could be determined using the following equation [14]:

q ¼ C p;b mb

dT b dt

ð2Þ

where q (W) is the heat generation rate; Cp,b (Jkg1K1), mb (kg) and dTb/dt (°Cs1) are the specific heat, mass and temperature rising rate of the battery, respectively. Therefore, it is clear that the temperature rising rate could be used to evaluate the heat generation behavior using Eq. (2), since the specific heat and mass of the battery remain constants during the charging/discharging process. The discharging curves and temperature rising rates of the tested battery in the ARC at different discharging rates of 0.5 C and 1 C are illustrated in Fig. 4. It can be observed that the terminal voltages of the tested battery decrease greatly at the beginning of discharging test caused mainly by the ohmic resistance, and then linearly decrease along the discharging process, and drop suddenly at the end of discharging test due to the rapid increase of overpotential resistance. As expected, the terminal voltage at high discharging rate (1 C) is lower than that at low discharging rate (0.5 C) during the discharging process. The variations of discharging curves of the tested battery in ARC could be employed to quantitatively evaluate the accuracy of the temperature rising rates measured by the ARC shown in Fig. 4(b). It is seen that the temperature rising rate at high discharging rate (1 C) is obviously higher than that at low discharging rate (0.5 C). In addition, the temperature rising rates of the battery almost remain constant along the discharging process except for the end of discharging, especially for 0.5 C discharging rate. The significant increase in the temperature rising rate observed at the end of discharging is mainly due to the remarkable increase of the overpotential resistance. Based on the above discussion, it can be concluded that

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

7

Fig. 4. (a) Discharging curves of the tested battery in ARC; (b) Temperature rising rates of the tested battery in ARC.

the heat generation rate of the lithium-ion battery with Li(NixCoyAlz)O2 cathode almost remains constant along the main discharging process, while a rapid increase in the heat generation rate occurs at the end of discharging process. 3.2. Thermal characteristics of battery pack under natural convection cooling condition As described in Section 2, the natural convection cooling condition refers to the particular case compared to the forced air convection cooling condition when the air supply velocity Vin = 0 ms1. The objective is to discover the effect of the heat generated by batteries on the transient thermal characteristics of the tested battery pack during the charging/discharging process, which is capable to provide a specific guidance for a battery pack without BTMS intervention. The charging curve and temperature curves of the tested battery pack at charging regime of 0.5 C under natural convection cooling condition are illustrated in Fig. 5. It is observed that the transition point from CC regime to CV regime occurs at the state of charge (SOC) equalling to 92.6% for the tested battery pack. As expected, the terminal voltage gradually increases and reaches 12.6 V until the transition point, while the terminal voltage is held at 12.6 V during CV regime (after the transition point occurs). It is

Fig. 5. Charging curve of the battery pack and temperature curves of selected points inside the battery pack under natural convection cooling condition.

noted that the thermal characteristics of the battery pack are largely dependent on the charging characteristics under natural convection cooling condition. We find that the battery surface temperatures (from Tb1 to Tb9 shown in Fig. 3) inside the tested battery pack gradually increase and reach the maximum value until the SOC is equal to 96.8%, and then drop sharply at the end of CV regime due to the rapid decrease of charging current. The SOC at the maximum temperatures is obviously larger than that at the transition point from CC regime to CV regime, which is mainly attributed to the reason that the heat generated by the battery pack is still higher than the heat dissipated to the ambient at the beginning of CV regime. In addition, it is found that the measuring point (Tb,6) inside the tested battery pack nearly maintain a higher temperature over the entire discharging process. This is due to the effect of buoyancy effect under natural convection cooling condition. The maximum temperature Tmax (Tb,6) and temperature difference DTmax (Tb,6  Tb,1) of the tested battery pack at charging regime of 0.5 C almost occur simultaneously at the SOC equal to 96.8%, which are 37.3 °C (a temperature rise of 12.3 °C) and 1.1 °C, respectively. The results clearly illustrate that the maximum temperature is within the optimum operating temperature range from 20 °C to 40 °C, and the maximum temperature difference is below 5 °C. On the other hand, some researchers have shown that the cycle life of lithium-ion battery could be shortened by about two months for every degree of temperature rise in the optimal temperature range of 20 °C to 40 °C [33]. This indicates that a temperature rise of 12.3 °C inside the tested battery pack should be decreased as much as possible to prolong the lifespan of the battery. Therefore, we achieved that although the maximum temperature and temperature difference of the tested battery pack at charging regime of 0.5 C can be maintained within the desirable range under natural convection cooling condition, however, the significant temperature rise must be reduced to prolong the lifespan of the EVs battery pack through switching on an efficient BTMS, e.g., the forced air cooling strategy discussed in Section 3.3. Figure 6 shows the discharging curves of the tested battery pack at different discharging rates of 0.5 C, 0.75 C and 1 C under natural convection cooling condition. As expected, the terminal voltages decrease sharply at the beginning of discharging test, and then linearly decrease along the discharging process, and drop suddenly at the end of discharging test. The variations of terminal voltage with the discharging capacity of the tested battery pack are resemblance to that discussed in Section 3.1. In addition, it is observed that the

8

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

Fig. 6. Discharging curves of the tested battery pack under natural convection cooling condition.

0.5 C is 38.6 °C (lower than 40 °C), thus the available capacity of 63.3 Ah was chosen for comparison with those at different discharging rates of 0.75 C and 1 C. In other words, the maximum temperatures of the battery pack at 0.75 C and 1 C exceed 40 °C when the DODs are larger than 99.2% and 74.1%, respectively, as shown in Fig. 8(a). The maximum temperature differences (Tb,6 - Tb,1) of the battery pack are shown in Fig. 8(b). It is seen that the maximum temperature differences at 0.5 C, 0.75 C and 1 C are within 2 °C. The above results showed that the temperature distribution inside the battery pack is relatively uniform, comparatively, the natural convection cooling condition is not sufficient to dissipate a large amount of heat generated at high discharging rate, especially for 1 C discharging rate, and cannot maintain the battery pack within the proper temperature range from 25 °C to 40 °C. Noting that the excessive temperature may accelerate the battery capacity degradation and result in a thermal runaway during cycling. Therefore, switching on an efficient BTMS is of significance to maintain batteries at optimum conditions for the EVs battery pack at higher discharging rate. 3.3. Thermal characteristics of battery pack under forced air convection cooling condition

terminal voltages gradually decrease with the increase of the discharging rate when the DOD is lower than 84.2%, while the terminal voltages according to the different discharging rates (0.5 C, 0.75 C and 1 C) are almost identical at the end of discharging test. Meanwhile, we also found an interesting result that the discharging capacities of the tested battery pack under natural convection cooling condition are independent on the discharging rates and nearly equivalent to 63.3 Ah that is larger than the nominal capacity of 59.4 Ah. The above results are in agreement with our previous observation [34] that the discharging capacities of the tested battery under near-adiabatic condition are nearly independent on the discharging rates ranging from 0.5 C to 2 C on account of the temperature rise resulted from the heat generated by battery itself. It is conceivable that the discharging rates ranging from 0.5 C to 2 C have little effect on the discharging capacities of the tested battery pack under natural convection cooling condition due to the effect of the battery temperature rise inside the tested battery pack. It is noted in the current study that the maximum temperature of the tested battery pack at 1 C discharging rate under natural convection cooling condition is about 49 °C which is beyond the optimal temperature range of 25–40 °C (as shown in Fig. 8). This implies that higher discharging rates, e.g., 2 C or 3 C may cause thermal safety issue that is usually prohibited in the laboratory test. Therefore, three discharging rates, namely 0.5 C, 0.75 C and 1 C are used for the tested battery pack in order to avoid any thermal issues. The temperature curves of the tested battery pack at different discharging rates of 0.5 C, 0.75 C and 1 C under natural convection cooling condition are illustrated in Fig. 7. It is noted that the maximum temperature limit of 40 °C for the tested battery pack is employed to ensure battery high efficiency, safety operation and cycle life of lithium-ion battery. As expected, the battery surface temperatures (from Tb1 to Tb9) increase gradually along the discharging process and become more significant with the increase of the discharging rates, which is due to the reason that the heat generated by the battery pack is larger than the heat dissipated to the ambient environment. On the other hand, we found that the available capacities gradually degrade with the increase of discharging rate when the maximum temperatures (Tb,6) inside the battery pack at 0.5 C, 0.75 C and 1 C reach the temperature limit (40 °C) of the lithium-ion battery. For example, the available capacities at 0.5 C, 0.75 C and 1 C are 63.3 Ah, 58.9 Ah (DOD = 99.2%) and 44.1 Ah (DOD = 74.1%) respectively. It is noted that the maximum temperature (Tb,6) of the battery pack at the discharging rate of

Based on the above discussion, the forced air convection cooling strategy is recommended to deal with the serious thermal issues of the tested battery pack, which are unable to be managed by natural convection cooling for ensuring battery high efficiency and safety operation, as well as prolonging the cycle life of lithium-ion battery. The effects of air supply velocities and discharging rates on the transient thermal characteristics of the stagger-arranged battery pack with longitudinal airflow were then explored in detail with attempting to provide the specific instructions for the layout of practical battery pack with air BTMS. The charging curve and temperature curves of the tested battery pack at charging regime of 0.5 C under forced air convection cooling condition are shown in Fig. 9. It is noted that the air supply velocity is held at 0.8 ms1 in the charging test. We find that the charging curve under forced air convection cooling condition is almost the same with that of the battery under natural convection cooling condition, which has been discussed in Section 3.2. The reason is that the battery could possess the similar charging characteristics under the operating temperature range from 20 °C to 40 °C [34]. Comparatively, the variations of the battery surface temperatures (from Tb1 to Tb9) inside the tested battery pack under forced air convection cooling condition differ from those of the tested battery pack under natural convection cooling condition, although the thermal characteristics of the battery pack are closely related to the charging characteristics. The battery surface temperatures markedly increase at the beginning of charging test (SOC < 16.8%), and then slightly increase and reach the maximum value until the SOC equals to 94.3%, and finally decrease rapidly at the end of charging test (SOC >94.3%). In addition, it is observed that the battery surface temperatures gradually increase along z direction (horizontal airflow direction from Tb1 to Tb9) caused by the temperature rise of air coolant, and the temperatures of three measuring points in each battery module almost remain the same due to uniform airflow distribution in the vertical airflow direction. Taking example from the three measuring points (T1, T2 and T3) in the first battery module near the inlet of air coolant, the temperatures are nearly equal to 27.2 °C at the SOC = 94.3%. The results indicate that 22 batteries connected in parallel in each battery module have almost identical cooling conditions. Therefore, it is considered that the uniformly-distributed venting holes around the battery cells on the holding plate are capable of ensuring air coolant evenly flow through the stagger-arranged battery pack. At last, the maximum temperature Tmax (Tb,9) and temperature

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

9

Fig. 7. Temperature curves of selected points inside the battery pack under natural convection cooling condition: (a) 0.5 C discharging rate; (b) 0.75 C discharging rate; (c) 1 C discharging rate.

Fig. 8. Effects of discharging rate on the maximum temperature (Tmax) and temperature difference (DTmax) inside the battery pack under natural convection cooling condition: (a) Maximum temperature (Tmax); (b) Maximum temperature difference (DTmax).

10

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

Fig. 9. Charging curve of the battery pack and temperature curves of selected points inside the battery pack under forced air convection cooling condition.

difference DTmax (Tb,9  Tb,1) are achieved concurrently at the SOC of 94.3%, which are 28.4 °C (a temperature rise of 3.1 °C) and 1.2 °C, respectively. A temperature rise of 3.1 °C under forced air convection cooling condition is considerably lower than that under natural convection cooling condition (a temperature rise of 12.3 °C). These results certainly demonstrate that the forced air convection cooling strategy employing longitudinal airflow could effectively improve the thermal characteristics of stagger-arranged battery pack at charging regime of 0.5 C. The discharging curves of the tested battery pack at different discharging rates of 0.5 C, 0.75 C and 1 C under forced air convection cooling condition are illustrated in Fig. 10. It is found that the discharging curves under forced air convection cooling condition are similar to those under natural convection cooling condition when the DOD is lower than 84.2%. However, a visible difference is observed at the end of discharging test. The specific details are shown as follows. The terminal voltages are dependent on the discharging rates under forced air cooling condition, while the tested discharging rates hardly affect the terminal voltages at the end of discharging test under natural convection cooling condition that has been discussed in Section 3.2. This phenomenon largely arises from the different thermal characteristics under the two tested cooling conditions.

Fig. 10. Discharging curves of the tested battery pack under forced air convection cooling condition.

Figure 11 illustrates the temperature curves of the tested battery pack at different discharging rates of 0.5 C, 0.75 C and 1 C under forced air convection cooling condition. It is noted that the air supply temperature and velocity are fixed at 25 °C and 0.8 ms1 respectively in order to explore the effect of discharging rates on the thermal characteristics of the tested battery pack with longitudinal airflow. As expected, it is found from Fig. 11 that the battery surface temperatures gradually rise up along z direction (from Tb1 to Tb9) and the temperatures of three measuring points in each battery module are approximately the same. These observations are resemblance to the variations of the battery surface temperatures of the tested battery pack at charging regime of 0.5 C under forced air convection cooling condition. The maximum temperature (Tb,9) and temperature difference (Tb,9  Tb,1) of the tested battery pack along with the discharging process are shown in Fig. 12(a) and 12(b). It is observed that the maximum temperature and temperature difference of the tested battery pack at 0.5 C, 0.75 C and 1 C could be maintained within the desirable range under forced air convection cooling condition. Taking example from the maximum temperature shown in Fig. 12(a), it is seen that the maximum temperatures of the tested battery pack at the end of 0.5 C, 0.75 C and 1 C discharging test are 30.8 °C, 32.7 °C and 35.1 °C, and are decreased by 7.3 °C, 9.8 °C and 12.8 °C against natural convection cooling condition, respectively. In addition, we find that for a given discharging rate, the maximum temperatures significantly increase at the beginning of discharging (DOD < 16.8%), and then slightly increase at the DOD varying from 16.8% to 84.2%, and finally increase sharply again at the end of discharging (DOD > 84.2%). This phenomenon can be supported by the heat generation behaviors of the tested battery shown in Fig. 4. The high heat generation rates at the beginning and end of discharging test would result in the rapid increase in the battery surface temperature, while the relative low heat generation rate may cause only a slight temperature rise at the DOD ranging from 16.8% to 84.2%. It is noted that the temperature rises at 0.5 C, 0.75 C and 1 C are 1.45 °C, 2.88 °C and 4.76 °C respectively for the DOD ranged from 0 to 84.2%, while those are 3.58 °C, 4.11 °C and 4.57 °C respectively for the DOD larger than 84.2% (i.e., approaching the end of discharging test). Therefore, we achieved that although the discharging capacities at 0.5 C, 0.75 C and 1 C are up to 84.2% of the rated capacity of 59.4 Ah, the battery surface temperatures at the DOD ranging from 0 to 84.2% merely increase by 1.45 °C, 2.88 °C and 4.76 °C, accounting for 28.8%, 41.2% and 51% of the whole discharging process respectively. These findings indicate that the forced air convection cooling strategy employing longitudinal airflow is capable of dissipating effectively the heat generated by the staggerarranged battery pack when the DOD is lower than 84.2%, while it is not sufficient enough to dissipate the excess amount of heat caused by the rapid increase of overpotential resistance at the end of discharging, even for the moderate discharging rates, e.g., 0.5 C. It is important to note that the cycle performance of the lithium-ion battery is largely dependent on the range of DOD during the charging/discharging process [35,36]. Their experimental results demonstrated that the capacity degradation of the battery cycled at the DOD ranging from 0 to 100% is much faster than that at the DOD ranging from 0 to 70%. Thus, these studies have put forward a general discharging strategy for the EVs battery pack that the lithium-ion battery should include a limit in the discharge to 70% or 80% DOD in order to prolong the cycle life of EVs. For similar reasons, Karimi et al. [18] investigated the thermal characteristics of the prismatic lithium-ion battery with LiCoO2 cathode for the DOD ranged from 0 to 80% under various cooling strategies, and Sabbah et al. [30] explored the heat generation behaviors and thermal characteristics of the commercially available lithium-ion battery with LiCoO2 cathode in the DOD range from 0 to 85%. Based on the above discussion, we learnt that the 0–84.2% DOD range

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

11

Fig. 11. Temperature curves of selected points inside battery pack under forced air convection cooling condition: (a) 0.5 C discharging rate; (b) 0.75 C discharging rate; (c) 1 C discharging rate.

Fig. 12. Effects of discharging rates on maximum temperature (Tmax) and maximum temperature difference (DTmax) inside battery pack under forced air convection cooling condition: (a) Maximum temperature (Tmax); (b) Maximum temperature difference (DTmax).

12

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

Fig. 13. Effects of air supply velocity on maximum temperature (Tmax) and maximum temperature difference (DTmax) inside battery pack under forced air convection cooling condition: (a) Maximum temperature (Tmax); (b) Maximum temperature difference (DTmax).

should be appropriate for the practical EVs battery pack produced by the lithium-ion batteries with Li(NixCoyAlz)O2 cathode under forced air convection cooling condition employing longitudinal airflow from the viewpoints of cooling effectiveness and cycle life. In other words, battery management system (BMS) should maintain the battery with Li(NixCoyAlz)O2 cathode at an appropriate operating DOD range from 0 to 84.2% to concurrently satisfy the requirement of high cooling effectiveness and long cycle life for the practical EVs battery pack with longitudinal airflow. The variations of maximum temperature Tmax (Tb,9) and temperature difference DTmax (Tb,9-Tb,1) of the tested battery pack at 1 C discharging rate under three air supply velocities of 0.6 ms1, 0.8 ms1 and 1 ms1 are shown in Fig. 13(a) and 13(b), respectively. It is observed that the maximum temperature Tmax and temperature difference DTmax are nearly independent on the air supply velocity when the DOD is lower than 16.8%, while these two factors exhibit different variations for the DOD larger than 16.8%. It is found from Fig. 13(a) that the maximum temperature gradually decreases with the increase of air supply velocity, but an extremely slight reduction is observed in the maximum temperature when the air supply velocity ranges from 0.8 ms1 to 1.0 ms1. For example, at the DOD of 84.2%, the maximum temperatures subject to the three air supply velocities (0.6 ms1, 0.8 ms1 and 1 ms1) are 31.8 °C, 30.5 °C and 30.1 °C respectively. This implies that continuous increase of air supply velocity is not an effective method for lowering the maximum temperature inside the battery pack with longitudinal airflow. Therefore, it is concluded that the appropriate air supply velocity is about 0.8 ms1 for the current battery pack configuration from the viewpoint of cooling effectiveness. Surprisingly, it is found from Fig. 13(b) that the smallest temperature difference DTmax is achieved by the moderate air supply velocity of 0.8 ms1 instead of the highest velocity of 1 ms1. Taking example from a DOD of 84.2%, the maximum temperature differences at three air supply velocities (0.6 ms1, 0.8 ms1 and 1 ms1) are 2.7 °C, 2.0 °C and 2.2 °C respectively. It is noted that this observation agrees well with the findings reported by Sabbah et al. [30]. The above phenomenon may be explained as follows: (1) the cooling effect of air coolant on the first battery module is better than that of the last battery module along airflow direction, therefore, the difference between Tb,9 and Tb,1 refers to the maximum temperature difference inside the tested battery pack; (2) when the air supply velocity increases from 0.8 ms1 to 1.0 ms1, the heat transfer performance between air coolant and the first battery

module could be significantly improved, while that between air coolant and the last battery module is less enhanced due to the temperature rise of air coolant along airflow direction, which can be supported by the maximum temperature shown in Fig. 13(a).

4. Conclusions In this study, a careful-designed experimental system and scheme are employed to explore the heat generation behaviors of a single lithium-ion battery with Li(NixCoyAlz)O2 cathode by the ARC, and the transient thermal characteristics of the staggerarranged battery pack consisting of three battery modules under the two cooling conditions. The major findings are summarized below: (1) Heat generation rate of the battery with Li(NixCoyAlz)O2 cathode almost remains constant along with the main discharging process, while a rapid increase in the heat generation rate is detected at the end of discharging process. (2) Although the maximum temperature and temperature difference of the tested battery pack at moderate charging/discharging rates, e.g., 0.5 C can be maintained within the desirable range under natural convection cooling condition, however, the significant temperature rise should be effectively controlled to prolong the lifespan of the battery pack through switching on an efficient BTMS. (3) The forced air cooling strategy employing the longitudinal airflow can significantly reduce the maximum temperature and battery temperature rise in the proposed battery pack. It is recommended that battery management system should maintain the DOD of battery with Li(NixCoyAlz)O2 cathode below 84.2% to concurrently satisfy the requirements of high cooling effectiveness and long cycle life for the practical EVs battery pack cooled by the longitudinal airflow. In addition, the appropriate air supply velocity is about 0.8 ms1 for the current battery configuration subject to a higher discharging rate, e.g., 1 C from the viewpoint of cooling effectiveness.

Declaration of Competing Interest The authors declared that there is no conflict of interest.

X. Yu et al. / International Journal of Heat and Mass Transfer 143 (2019) 118576

Acknowledgement The authors are grateful for the support by the National Natural Science Foundation of China (51676150), the Key Science Research Innovation Team Project of Shaanxi Province (2016KCT-16) and the National Key Research & Development Program of China (2016YFC0802405). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118576. References [1] R. Xiong, F.C. Sun, X.Z. Gong, C.C. Gao, A data-driven based adaptive state of charge estimator of lithium-ion polymer battery used in electric vehicles, Appl. Energy 113 (2014) 1421–1433. [2] R. Xiong, F.C. Sun, Z. Chen, H.W. He, A data-driven multi-scale extended Kalman filtering based parameter and state estimation approach of lithium-ion polymer battery in electric vehicles, Appl. Energy 113 (2014) 463–476. [3] H.W. He, R. Xiong, H.Q. Guo, Online estimation of model parameters and stateof charge of LiFePO4 batteries in electric vehicles, Appl. Energy 89 (2012) 413– 420. [4] F.C. Sun, R. Xiong, H.W. He, W.Q. Li, J.E.E. Aussems, Model-based dynamic multiparameter method for peak power estimation of lithium–ion batteries, Appl. Energy 96 (2012) 378–386. [5] Z.H. Rao, S.F. Wang, A review of power battery thermal energy management, Renew. Sustain. Energy Rev. 15 (2011) 4554–4571. [6] J. Lindgren, P.D. Lund, Effect of extreme temperatures on battery charging and performance of electric vehicles, J. Power Sources 328 (2016) 37–45. [7] A. Hausmann, C. Depcik, Expanding the Peukert equation for battery capacity modeling through inclusion of a temperature dependency, J. Power Sources 235 (2013) 148–158. [8] Y. Wu, P. Keil, S.F. Schuster, A. Jossen, Impact of temperature and discharge rate on the aging of a LiCoO2/LiNi0.8Co0.15Al0.05O2 lithium-ion pouch cell, J. Electrochem. Soc. 165 (2017) A1438–A1445. [9] Z. Lei, C. Zhang, J. Li, G.C. Fan, Z.W. Lin, A study on the low-temperature performance of lithium-ion battery for electric vehicles, Automot. Eng. 35 (2013) 927–933. [10] L.X. Liao, P.J. Zuo, Y.L. Ma, X.Q. Chen, Y.X. An, Y.Z. Gao, G.P. Yin, Effects of temperature on charge/discharge behaviors of LiFePO4 cathode for Li-ion batteries, Electrochim. Acta 60 (2012) 269–273. [11] S.A. Khateeb, S. Amiruddin, M. Farid, J.R. Selman, S. Al-Hallaj, Thermal management of Li-ion battery with phase change material for electric scooters: experimental validation, J. Power Sources 142 (2005) 345–353. [12] S. Panchal, I. Dincer, M. Agelin-Chaab, R. Fraser, M. Fowler, Transient electrochemical heat transfer modeling and experimental validation of a large sized LiFePO4/graphite battery, Int. J. Heat Mass Transf. 109 (2017) 1239–1251. [13] X.S. Li, F. He, L. Ma, Thermal management of cylindrical batteries investigated using wind tunnel testing and computational fluid dynamics simulation, J. Power Sources 238 (2013) 395–402. [14] T. Wang, K.J. Tseng, J. Zhao, Z. Wei, Thermal investigation of lithium-ion battery module with different cell arrangement structures and forced aircooling strategies, Appl. Energy 134 (2014) 229–238. [15] R. Mahamud, C. Park, Reciprocating air flow for Li-ion battery thermal management to improve temperature uniformity, J. Power Sources 196 (2011) 5685–5696. [16] L.H. Saw, Y.H. Ye, A.A.O. Tay, W.T. Chong, S.H. Kuan, M.C. Yew, Computational fluid dynamic and thermal analysis of lithium-ion battery pack with air cooling, Appl. Energy 177 (2016) 783–792.

13

[17] Z. Lu, X.L. Yu, L.C. Wei, Y.L. Qiu, L.Y. Zhang, X.Z. Meng, L.W. Jin, Parametric study of forced air cooling strategy for lithium-ion battery pack with staggered arrangement, Appl. Therm. Eng. 136 (2018) 28–40. [18] G. Karimi, X. Li, Thermal management of lithium-ion batteries for electric vehicles, Int. J. Energy Res. 37 (2013) 13–24. [19] H.B. Zhou, F. Zhou, L.P. Xu, J.Z. Kong, Q.X. Yang, Thermal performance of cylindrical lithium-ion battery thermal management system based on air distribution pipe, Int. J. Heat Mass Transf. 131 (2019) 984–998. [20] K. Chen, M.X. Song, W. Wei, S.F. Wang, Structure optimization of parallel aircooled battery thermal management system with U-type flow for cooling efficiency improvement, Energy 145 (2018) 603–613. [21] S. Panchal, M.H. Akhoundzadeh, K. Raahemifar, M. Fowler, R. Fraser, Heat and mass transfer modeling and investigation of multiple LiFePO4/graphite batteries in a pack at low C-rates with water-cooling, Int. J. Heat Mass Transf. 135 (2019) 368–377. [22] S. Panchal, I. Dincer, M. Agelin-Chaab, R. Fraser, M. Fowler, Experimental and theoretical investigations of heat generation rates for a water cooled LiFePO4 battery, Int. J. Heat Mass Transf. 101 (2016) 1093–1102. [23] S. Panchal, I. Dincer, M. Agelin-Chaab, M. Fowler, R. Fraser, Uneven temperature and voltage distributions due to rapid discharge rates and different boundary conditions for series-connected LiFePO4 batteries, Int. Commun. Heat Mass Transf. 81 (2017) 210–217. [24] S. Panchal, I. Dincer, M. Agelin-Chaab, R. Fraser, M. Fowler, Experimental temperature distributions in a prismatic lithium-ion battery at varying conditions, Int. Commun. Heat Mass Transf. 71 (2016) 35–43. [25] L.W. Jin, P.S. Lee, X.X. Kong, Y. Fan, S.K. Chou, Ultra-thin minichannel LCP for EV battery thermal management, Appl. Energy 113 (2014) 1786–1794, https:// doi.org/10.1016/j.apenergy.2013.07.013. [26] N. Javani, I. Dincer, G.F. Naterer, G.L. Rohrauer, Modeling of passive thermal management for electric vehicle battery packs with PCM between cells, Appl. Therm. Eng. 73 (2014) 307–316. [27] X.H. Yang, S.S. Feng, Q.L. Zhang, Y. Chai, L.W. Jin, T.J. Lu, The role of porous metal foam on the unidirectional solidification of saturating fluid for cold storage, Appl. Energy 194 (2017) 508–521. [28] J. Qu, Z.Q. Ke, A.H. Zuo, Z.H. Rao, Experimental investigation on thermal performance of phase change material coupled with three-dimensional oscillating heat pipe (PCM/3D-OHP) for thermal management application, Int. J. Heat Mass Transf. 129 (2019) 773–782. [29] Z.Y. Ling, F.X. Wang, X.M. Fang, X.N. Gao, Z.G. Zhang, A hybrid thermal management system for lithium-ion batteries combining phase change materials with forced-air cooling, Appl. Energy 148 (2015) 403–409. [30] R. Sabbah, R. Kizilel, J.R. Selman, S. Al-Hallaj, Active (air-cooled) vs. passive (phase change material) thermal management of high power lithium-ion packs: Limitation of temperature rise and uniformity of temperature distribution, J. Power Sources 182 (2008) 630–638. [31] T. Wang, K.J. Tseng, J.Y. Zhao, Development of efficient air-cooling strategies for lithium-ion battery module based on empirical heat source model, Appl. Therm. Eng. 90 (2015) 521–529. [32] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1988) 3–17. [33] C.G. Motloch, J.P. Christopheresen, J.R. Belt, R.B. Wright, G.L. Hunt, R.A. Sutula, T. Duong, T.J. Tartamella, H.J. Haskins, T.J. Miller, High-power battery testing procedures and analytical methodologies for HEV’s SAE Technical Paper 200201-1950, 2002. [34] Z. Lu, X.L. Yu, L.C. Wei, F. Cao, L.Y. Zhang, X.Z. Meng, L.W. Jin, A comprehensive study on temperature-dependent performance of lithium-ion battery, Appl. Therm. Eng. 158 (2019) 113800. [35] S. Watanabe, M. Kinoshita, T. Hosokawa, K. Morigaki, K. Nakura, Capacity fading of LiAlyNi1-x-yCoyO2 cathode for lithium-ion batteries during accelerated calendar and cycle life tests (effect of depth of discharge in charge-discharge cycling on the suppression of the micro-crack generation of LiAlyNi1-x-yCoxO2 particle), J. Power Source 260 (2014) 50–56. [36] K.A. Striebel, J. Shim, E.J. Cairns, R. Kostecki, Y.J. Lee, J. Reimer, T.J. Richardson, P.N. Ross, X. Song, G.V. Zhuang, Diagnostic analysis of electrodes from highpower lithium-ion cells cycled under different conditions, J. Electrochem. Soc. 151 (2004) A857–A866.