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Structural optimization of lithium-ion battery for improving thermal performance based on a liquid cooling system
International Journal of Heat and Mass Transfer 130 (2019) 33–41
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Structural optimization of lithium-ion battery for improving thermal performance based on a liquid cooling system Zhuangzhuang Shang a, Hongzhong Qi b, Xintian Liu a,⇑, Chenzhi Ouyang b, Yansong Wang a a b
School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China Automotive Engineering Institute, Guangzhou Automobile Group Co. LTD, Guangzhou 511434, China
a r t i c l e
i n f o
Article history: Received 19 May 2018 Received in revised form 25 September 2018 Accepted 18 October 2018
Keywords: Lithium-ion battery Thermal management Thermal characteristics Structural optimization Orthogonal test
a b s t r a c t Liquid cooling system is of great significance for guaranteeing the performance of lithium-ion battery because of its good conductivity to keep battery working in a cool environment. In this paper, a liquid cooling system for lithium-ion battery with changing contact surface is designed. Contact surface is determined by the width of cooling plate. Mathematical derivation and numerical analysis are conducted to evaluate cooling performance and the consumption of pump power. The results show that increasing inlet mass flow can effectively limit the maximum temperature, but cannot improve temperature uniformity significantly. The temperature is proportional to the inlet temperature, but inversely proportional to the width of cooling plate. Considering the effect of temperature on thermal properties, the thermal properties will weaken the effect of width of cooling plate, inlet temperature and mass flow rate on temperature performance, specifically the maximum temperature and temperature difference, and cause temperature changes in a nonlinear manner. It is difficult to improve the overall performance of the battery by only optimizing a single factor. Three factors (mass flow rate, inlet temperature, the width of cooling plate) for the thermal performance of battery are optimized by using the single factor analysis and the orthogonal test. The best cooling performance can be obtained when inlet temperature is 18 °C, the width of cooling plate is 70 mm and the mass flow rate is 0.21 kg/s. With the use of the optimization method, the lower bound of temperature and the temperature uniformity of battery are achieved and the pump consumption can be reduced. The strategy adopted in this research can be widely applied to battery thermal management to reduce analysis time. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Lithium-ion battery is widely used as an energy source in electric vehicles in recent years because of its outstanding advantages, such as high specific energy and power densities, long cycle-life and low self-discharge rate [1,2]. The performance of lithium-ion battery modules is significantly affected by working temperature. The heat generated by cells, which are the basic units of battery modules, need to dissipate for safety and reliability purposes of modules. The capacity of battery degrades rapidly at high temperature, while the lifetime and the energy output decrease in a cold environment [3,4]. A bad design of thermal management system usually results in the heat accumulation, which is a serious safety issue, and battery degradation. However, a lithium-ion battery with ideal thermal performance remains to be a challenge [5]. Accurate temperature measurement of cells is critical to the thermal control of power battery pack that is assembled by battery ⇑ Corresponding author. E-mail address: [email protected] (X. Liu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.074 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
modulus to achieve a desired performance [6]. When the lithiumion battery cell is in an operating state, the internal resistances will increase as a result of the electrochemical reactions. If the heat generated inside does not dissipate from the cell, the high temperature will lead to electrolyte burns or battery explodes. With the lithium-ion battery working above 50 °C for a long while, it will accelerate its aging process, thereby leading to the degradation of the battery capacity and the driving range of vehicles. The proper working temperature range for the lithium-ion battery is usually from 20 °C to 45 °C, and the temperature distribution of the whole battery pack should be fine and its difference is normally less than 5 °C [7,8]. Therefore, it is crucial to design an appropriate thermal management system for lithium-ion batteries. The battery thermal management system can be classified into three categories: air cooling system [9,10], liquid cooling system, and phase change material (PCM) system [11,12]. The air cooling system can be further divided into forced air cooling and natural air cooling ones. The effectiveness of the air cooling system is poor, and cannot meet the requirement of a long driving-range electric vehicles and hybrid electric vehicles [13]. The PCM system can
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effectively remove heat away and keep the distribution of internal temperature more uniform [14]; however, its encapsulation is difficult and the volume change restricts its application in engineering field. Compared with the air cooling one and the PCM, the liquid one has a better thermal conductivity. Therefore, the liquid cooling system is much more suitable for the heat dissipation of the lithium-ion battery and large-scale battery in engineering applications [15]. A great number of researchers have paid attention to the heat dissipation of the battery pack. Multi-objective optimal design of lithium-ion battery packs has been reported in many literatures. Bai et al. [16] studied the thermal behavior of lithium-ion battery by establishing numerical models and different airflow duct, employing an optimizing scheme of the orthogonal test. Severino et al. [17] proposed an optimization method for the battery thermal management based on evolutionary algorithms. Plenty of optimization methods have been employed for different heat dissipation of lithium-ion battery packs. Mahamud and Wang [18,19] demonstrated that the use of reciprocating cooling flow can reduce the temperature and non-uniformity in battery pack. Lafdi, Zhang and Zhao [20–22] established a three-dimensional model of PCM and experimental verification, and the results indicated that the thermal management system of battery with PCM has a significant impact on its heat transfer behavior by means of numerical simulation and experimental verification [23].
2. Model description The schematic of battery model is shown in Fig. 1(a). Both the shell of cells and the cooling plate are made of aluminum because of its light weight and good thermal conductivity. In practical assembly, there is a gap between the two aluminum components, and thermal conductivity between them is significantly affected by the air. A solution to this problem is usually that inserting a thermal conductive pad between the cooling plate and the cells. The thermal conductive pad is with properties of good viscosity, flexibility, good compression properties and excellent thermal conductivity, thus it is widely used in liquid cooling system. The air between the electronic components can be fully discharged to achieve sufficient contact. The thickness of aluminum cooling plate is 0.47 mm. Heat is generated from the battery cells and transferred from the thermal conductive pad to cooling plate (filled with mixture of glycol and water). Coolant removes the heat away by flowing fluid inside the cooling plate. There are 15 cells adopted as targets to investigate. Material properties used in the simulation are shown in Table 1. In this paper, a prismatic lithium-ion battery composed of 15 battery cells with three coolant passages is selected as the model for investigation. The main technical parameters are shown in Table 2. The contact area between cooling plate and cells is a main factor to influence the heat transfer for cells. The length of thermal
(a) 3D model of battery module and actual picture of Single cell
(b) Coolant flow channel with different width of cooling plate Fig. 1. Schematic of liquid cooling system for the battery module.
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Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41 Table 1 Physical properties of lithium-ion battery. Material 3
Density (kg/m ) Thermal conductivity (W/m/K) Specific heat (J/kg/K) Dynamic viscosity (Pa/s)
Al
Cu
Thermal conductive pad
Coolant
2710.0 155.0 890.0 –
8940.0 398.0 386.0 –
2400.0 1.2 2200.0 –
1069.4 0.4 3358.0 0.0034
where qc, cc and kc are the density, specific heat capacity and thermal conductivity of the coolant, respectively. The continuous equation of liquid coolant can be given as:
Table 2 Technical parameters of 49Ah Lithium-ion battery. Parameters
Values
Rated capacity (Ah) Rated voltage (V) Internal resistance (mX) Specific heat capacity (J/kg/K) Density (kg/m3) Size of cell (length width height) (mm) Size of positive and negative electrode (length width height) (mm) Thermal conductivity (X, Z directions) (W/m/K) Thermal conductivity (Y direction) (W/m/K)
49.0 3.7 1.0 1151.0 2277.0 230 73 175 33.6 25.0 15.2 2.7 0.9
conductive pad is constant, but the width is changeable in the simulation. The width size of cooling plate varies from 55 mm to 75 mm, and the interval between them is 5 mm. As shown in Fig. 1, the cooling plate has the same width and length with the thermal conductive pad. 3. Initial boundary conditions
To obtain the temperature distribution in a cell, heat conduction energy conservation equation of the battery can be written as:
ð1Þ
where q and cp are the density and specific capacity of the battery, respectively; kx, ky, and kz are the heat conductivity coefficient in x, y, z directions, respectively, as listed in Table 1; Qv is the volumetric heat source in the cell, which is generated by electrochemical enthalpy change and internal thermal resistance. The specific form of Qv can be written as:
Q v ¼ IðU OC V Þ IT
dU OC dT
In a state of stationary flow, @@tqc ¼ 0, and as coolant is an incom-
pressible fluid so that ddtqc ¼ 0. The continuous equation of incompressible fluid can be ! obtained by r v ¼ 0, ! where v is the velocity vector of coolant. The momentum equation of incompressible liquid is as follows
qc
! dv ! ¼ rp þ lr2 v dt
where p and l are static pressure and dynamic viscosity of coolant, respectively.
In order to obtain the temperature distribution of cells, some initial conditions and boundary condition are necessary for a specific heat conduction problem. The schematic of the modules is shown in Fig. 2, and it can be seen that the coolant flow direction is along a single channel in the x direction, and the cooling plate is filled with liquid coolant. Considering that the heat dissipation on the side of the modules is negligible, and the modules are placed in a steady state and a closed environment, thus, @T ¼ 0 and @T ¼ 0.The @t @x heat flux equation of the battery is given as:
where U is the heat flux along the x, y, z directions; Kr is the thermal heat conductivity coefficient; A is the surface area of the battery and DT is the temperature difference. As the heat flux in the z direction is more than that in the y in Eq. (1) is direction, we can obtain kz > ky. Since the term kz @T @z @T @T greater than ky @y, which means that ky @x can be ignored.
ð2Þ
where I, T and Uoc are the electric current, temperature of the cell and open-circuit voltage, respectively. Theoretically, high temperature and large current cause cells generate much heat.dUdTOC is an entropic coefficient of the cell. Liquid coolant is a mixture of water and glycol in this study. The energy conservation equation of liquid coolant is:
qc
@T c kc ! rT c þ r qc v T c ¼ r @t cc
ð5Þ
U ¼ K r A DT
4. Theoretical model
@T @ @T @ @T @ @T þ þ þ Qv kx ky kz ¼ @ s @x @x @y @y @z @z
ð4Þ
5. Cooling capacity analysis
The boundary conditions of inlet and outlet are set to mass flow rate and pressure outlet, respectively. Inlet mass flow rate is set to 0.17 kg/s, 0.21 kg/s, 0.25 kg/s, and 0.29 kg/s for different cases, while outlet is set to 0.0 pa at all time. Inlet and outlet temperatures are different, the former is equal to environment temperature. Speed-up climbing condition is used, and the initial temperature of the cell is usually 30 °C. As mentioned above, the thermal conductive pad is placed between the module and the cooling plate to increase heat transfer, and its thermal resistance 0.0043 m2/K/W.
qcp
@ qc þ rðqc v Þ ¼ 0 @t
ð3Þ Fig. 2. Schematic of lithium-ion battery with cooling plate.
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With the boundary condition of @T = 0 at the point z = 0 and @z z = Lcell, T = Tb1 can be obtained, where Lcell is the size of the half cell-width, and Tb1 is the boundary temperature between thermal conductive pad and cell.
@ @T kz þ Qv ¼ 0 @z @z
ð6Þ
With some mathematical operations, Eq. (6) can be rearranged as
Q T ¼ v L2cell z2 þ T b1 2kz
ð7Þ
considering the existence of thermal resistance between thermal conductive pad and module, one has
T b1 T b2 ¼ Q v Lcell Rc
ð8Þ
where Tb2 is the surface temperature of the thermal conductive pad. For thermal conductive pad, heat conduction equation in the z direction can be expressed as
T b2 T b3 kp ¼ Q v Lcell Lp
ð9Þ
where Tb3 is the surface temperature of the interface between cooling plate and thermal conductive pad, and Lp and kp are the thickness of cooling plate and thermal conductivity, respectively. According to the Fourier’s law, the convective heat transfer between thermal conductive pad and coolant can be given as
h T b3 T f ¼ Q v Lc
property of coolant at a certain location in y direction. From Eq. (12), with a larger heat transfer coefficient h and a specific heat of the coolant and a mass flow rate, the temperature of modules becomes lower, but the changing trend of module temperature is nonlinear.
ð10Þ
6. Numerical simulation and experiment All calculated result are presented at transiting high-speed climbing conditions (120 kph 3% climbing), and the ambient temperature is 25 °C. The lithium-ion battery is discharged at 1.2C with a constant current by charge-discharge apparatus. The temperature sensors are placed on three different locations (near positive and negative electrode, the middle). Fig. 3 illustrates the measurement points of sensors in the experiment. The battery was placed in a temperature control box. All data is recorded by the Agilent 34972A Data Logger which is connected to a computer. The results of numerical simulation and experiment are compared in Fig. 4. The experimental results take the average value of temperature at the positive and negative electrodes as well as the middle of the battery. It is clear to see that the simulation results agree well with the experimental results, and the maximum discrepancy between the two is less than 0.21 °C. The experimental results indicate the calculation method of heat source is accurate and the CFD numerical model is reliable. 6.1. Effects of the width of cooling plate Fig. 5 illustrates the temperature with different mass flow rate and different contact area between thermal conductive pad and
where h is the conductive heat transfer coefficient and Tf is the temperature of the coolant, which varies along y direction in the model. With the use of the energy conservation equation, it can be calculated as follows
qq ! v dhalf cq T f T in ¼ Q v Lcell y
ð11Þ
where y is the random axis along y direction; dhalf is the half width of the coolant channel; qq and cq are the density and specific heat capacity of the coolant, respectively. Therefore, the following equation can be obtained
T¼
Qv 2 Lp 1 Q Lcell y þ T in þ v! Lcell z2 þ Q v Rc þ þ 2kz kp h qq v dhalf
ð12Þ
where T describes the temperature distribution in the direction normal to the cooling plate. Based on Eq. (12), it indicates that the temperature is inversely proportional to the inlet mass flow rate, proportional to the inlet temperature, all parameters are constant except h and 1/qqvdhalf. Furthermore, it is evident that the temperature is determined by merely the flow situation in y direction and the thermal-physical
Fig. 4. The results from experiments and simulations.
Fig. 3. (a) Temperature control box and pictures of lithium-ion cell with embedded thermocouple (b) Picture of test points of temperature sensors.
Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
a Mass flow rate = 0.17kg/s
37
(b) Mass flow rate = 0.21kg/s
(c) Mass flow rate = 0.25kg/s Fig. 5. Modules temperature variation during the discharge process with different width of cooling plate in a highspeed climbing condiction.
module. The width changes from 55 mm to 75 mm, and the mass flow rates are set to 0.17 kg/s, 0.21 kg/s and 0.25 kg/s, respectively. The time of operating condition is set to 1800 s based on engineering experience. According to Fig. 5, the temperature rises as time increases. Specifically, the temperature goes up fast in the beginning stage of the discharge but slowly in the end stage. This is because the cooling system does not work when the temperature is less than 35 °C, but when the temperature exceeds 35 °C, the battery system enters into the cooling stage so that the temperature gradient turns to be lower. Besides, the larger width of cooling plate is, the faster of cell temperature drops. As shown in Fig. 5, with the increase of cooling plate width, both the maximum temperature and the maximum-temperature difference are reduced. As the value of width varies from 55 mm to 75 mm, the maximum temperature of cells are dropped by 4.02 °C, 3.32 °C and 3.66 °C, and the maximum-temperature difference decreases by about 1.44 °C, 1.46 °C and 1.50 °C. However, the reduction is nonlinear. When size reaches 65 mm, the decreasing trend of temperature becomes gentle, the reduced temperature are 3.1 °C, 2.0 °C, 1.5 °C and 1.0 °C, respectively. Apparently, when the width of cooling plate increased, the maximum temperature and the maximum-temperature difference of cells are decreased, but both the downtrend of them slows down, when the value of width reaches to a certain extent. If the
width continues to increase, it will bring the weight to the battery module, which is harmful to the performance of the vehicle. 6.2. Effects of inlet temperature As shown in Fig. 6, the overall trend of temperature contours are consistent obviously. The inlet temperature has much influence at the entrance position of coolant for battery modules, the hottest position moves from the entrance to the end side of modules which is close to the top. As the inlet temperature rises from 15 °C to 18 °C, the maximum temperature dropped from 41 °C to 38.7 °C, the results show that the inlet temperature of the cooling plate has a significant effect on the maximum temperature. The lower of inlet temperature, the lower of the maximum temperature of cells. The results of simulation also verify the relationship between the temperature of modules and the inlet temperature of the coolant derived from the mathematical analysis. However, the magnitude of the temperature difference is relatively smaller, The changing curve of battery modules with different inlet temperature is shown in Fig. 7, it can be seen that the temperature difference are 5.4 °C,5.5 °C,4.5 °C and 4.9 °C, when the inlet temperature is 15 °C, 18 °C, 21 °C and 24 °C, respectively. So dropping the inlet temperature cannot significantly improve the uniformity of temperature in this temperature range.
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(a) Inlet temperature=15
(b) Inlet temperature=18
(c) Inlet temperature=21
(d) Inlet temperature=24
Fig. 6. The battery modules contour with different inlet temperature of 55 mm width.
Fig. 7. Temperature variation of modules with different inlet temperature of 55 mm width.
6.3. Effects of the inlet mass flow rate Fig. 8 shows that increasing inlet mass flow can reduce maximum temperature, but it is difficult to improve temperature uniformity. Apparently, the maximum temperature reaches to
41.22 °C at the mass flow rate of 0.17 kg/s, which is more than that at the mass flow rate of 0.21 kg/s by 1.28 °C. Moreover, the maximum temperature is smaller at the mass flow rate of 0.25 kg/s when the width of cooling plate is 55 mm. Situation is the same as the case of w = 60 mm, 65 mm, 70 mm, 75 mm, when the mass flow rate is 0.17 kg/s, 0.21 kg/s, 0.25 kg/s. As shown in Fig. 7(b), the temperature difference decreases obviously when increasing the width of cooling plate, but the trend of curves gradually slows down. However, increasing inlet mass flow rate will lead to more pump power consumption, and increasing the width of cooling plate will give rise to mass-increase of the battery pack and battery layout space. By comparing the cases above, the cooling capability of coolant is investigated by the mathematical analysis. Considering the term ! 1=qq v dhalf in Eq. (12), the density of coolant is inversely proportional to the inlet temperature, and according to relationship between volume flow rate and cross-sectional area of inner diameter of cooling plate in Eq. (13), it can be deduced when inlet mass flow rate is constant. wider the flow path in cooling plate is, the smaller the velocity of coolant is. The relationship between them can be written as:
Q ¼v A
ð13Þ
where Q is mass flow rate, A is the cross-sectional area of the flow channel in the cooling plate, v is the velocity of coolant. It can be seen when parameters (v, q) vary with the temperature and the width of cooling plate, the influence of inlet
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Fig. 8. Temperature distribution with different width of aluminium plate: Maximum temperature (b) Temperature difference.
temperature, mass flow rate and the width of cooling plate to temperature performance will be reduced. As shown in Figs. 5 and 6, the changing trend of temperature is not linear. It is not good to obtain better temperature performance only by increasing inlet mass flow rate or contact area between cooling plate and cells.
7. Analysis of multiple-factor 7.1. The design of orthogonal test Increasing the width of cooling plate can greatly reduce the battery module maximum temperature and the temperature difference between the modules, but for large rate electricity, the cells emit more heat. To achieve a good performance and long life, it must be controlled by adjusting the temperature influence parameters to control its temperature and temperature difference in an optimal temperature range. In order to reduce the analysis time, the following orthogonal test is used to make the maximum temperature and temperature difference in a suitable range. The orthogonal test is an effective way to analyze the effectiveness of multiple factors. In order to make sure that results have a certain degree of accuracy and to control the number of experiments, an orthogonal test table with three factors and four levers (L16(45)) is applied to investigate the effectiveness of multiple factors on the cooling performance in Table 3, in which A, B and C are three factors (A is the inlet temperature, B is the inlet mass flow rate and C is the width of the cooling plate). The evaluating indexes are the maximum temperature and the temperature difference, and the results are shown in Table 4. In order to investigate the influence of factors and levels on the results and the importance of each factor, the experimental results are analyzed by the mean value and the range. Table 3 The analysis results according to maximum temperature and temperature difference. Levers
1 2 3 4
Factors A (mm)
B (°C)
C (kg/s)
55 60 65 70
15 18 21 24
0.17 0.21 0.25 0.29
Table 4 The schemes and results. Test number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Test factors
Test results
A (mm)
B (°C)
C (kg/s)
Tmax (°C)
DT (°C)
55 55 55 55 60 60 60 60 65 65 65 65 70 70 70 70
15 18 21 24 15 18 21 24 15 18 21 24 15 18 21 24
0.17 0.21 0.25 0.29 0.21 0.25 0.29 0.17 0.25 0.29 0.17 0.21 0.29 0.17 0.21 0.25
38.85 37.64 36.79 36.02 39.77 37.98 36.88 35.97 39.94 38.72 37.59 36.73 41.22 39.65 38.39 37.60
5.42 6.01 6.95 7.01 5.33 5.94 6.42 6.92 4.52 4.95 5.19 5.88 4.22 4.50 5.31 6.21
7.2. Analysis results of the maximum temperature and temperature difference The maximum temperature and temperature difference are the most important evaluating parameters for battery module. Table 6 shows results of the range according to the following expressions
K ij ¼
X T max ij
ð14Þ
j¼1
kij ¼
1 K ij n
Rj ¼ max k1j min k1j
ð15Þ ð16Þ
where Kij is the sum of four maximum temperatures for the same level; kj is the mean value for each factor at the same level (j represents the column number three factors in Table 3); and n is the maximum number of lever. Rj is the range of kj and indicates the magnitude of the change of the test indicator within this range. The influence of the factor is more obvious and significant with a bigger Rj. As shown in Table 8, because of RjB > RjA > RjC, the importance of factors for maximum temperature is in the following order:
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Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
B > A > C, in which, the factor B is the first one to select, and the factor A should be considered secondly, and lastly factor C is selected. Thus, to obtain the maximum temperature, the optimal design of the width of cooling plate is A = 70 mm, the corresponding inlet temperature is 18 °C, the mass flow rate is 0.25 kg/s. When the width of cooling plate is 60 mm, the inlet temperature is 18 °C, and the mass flow rate is 0.17 kg/s, the better temperature difference can be obtained. The range analysis for temperature difference is shown in Tables 5 and 6. The range analysis only reflects the importance of the factors, which cannot provide an accurate quantitative estimate of the significance of the factors. To compensate the lack of intuitive analysis, variance analysis is used and the results of the variance are presented in Table 7, as calculated by the following equations n X ¼1 T max k T n k¼1
ð17Þ
1 Ti ¼ K ij s
ð18Þ
ð19Þ
SA =f A Se =f e
ð20Þ
is the mean value of the sum of all test results; n is the where T number of the orthogonal test (n = 16); s is the test number of each factor; r is the levels of factors; SA is the sum of the square of deviation of the average deviation caused by the change of level of each factor; Se is the sum of square error; fA is the degree of freedom of SA; fe is the degree of freedom of Se; Fj is the observed value of factor j. Because of FB > F0.05 (3,16), the maximum temperature is influenced by the factors A and B, the Fj of factor C is lower than 1, so the significance is negligible. The variance analysis of temperature difference is listed in Table 8, where the FA and FC > F0.025(3,16). From the analysis, it is clear to see that the factors A and C are significant to the temperature difference. The orthogonal design method is used to optimize the liquid cooling system of lithium-ion battery. From the range analysis, the significance of three factors on temperature is following by B, Table 5 The range analysis of maximum temperature.
Tmax (°C) DT (°C)
Factors
SA
fA
Se
fe
Fj
FA
A B C
33.15 3.5 43.2
3 3 3
24.20 38.05 32.08
12 12 12
5.53 – 5.37
F0.05(3,16) = 3.24 F0.025(3,16) = 4.08
A, C. Inlet temperature is the first level to choose, and the width of cooling plate should be chosen secondly, and the final influencing factor is the mass flow rate. For another evaluating parameter, the importance of three factor on temperature difference is C > A > B. That is, the mass flow rate should be considered firstly, and the width of cooling plate is chosen as the level two, and the inlet temperature has very little effect on temperature difference. The variance analysis is carried out to examine the significance of each factor. From the analysis results, the maximum temperature and the temperature difference are dropped by 12.61% and 20.83%, respectively. 8. Conclusions
r r X 2 1 X T2 s Tl T ¼ K 2ij Sj ¼ s n i¼1 i¼1
Fj ¼
Table 8 The variance analysis of the temperature difference.
Range
A (mm)
B (°C)
C (kg/s)
Rj Rj
1.89 3.59
3.38 2.48
0.20 3.62
Table 6 Optimal design for single index. Indexes
Best solution
Importance of factors
Tmax (°C) DT (°C)
A4B2C3 A2B2C1
B>A>C C>A>B
This work focus on the optimal choice of multiple factors for influencing liquid cooling based on thermal management of lithium-ion battery. Different aspects are compared by simulation and experiments. The model was numerically formulated and put into simulation, and the accuracy of the simulation model was verified by experiments. The obtained results show that when the width of cooling plate changes from 55 mm to 75 mm, and the inlet temperature drops from 24 °C to 15 °C, the maximum temperature changes obviously; however, the trend gradually slows down as the factors change to a certain value. Therefore, among the multiple influencing factors, it is difficult for battery to obtain the improvement of comprehensive performance by optimizing a single factor. Meanwhile, considering the pump consumption and the weight of the battery pack requirements, a better solution needs to be found from these influencing factors. Three factors (the width of cooling plate, the inlet temperature, the inlet mass flow rate) are studied by means of the orthogonal test. From the variance analysis, when considering the temperature range from 15 °C to 24 °C, and the mass flow rate ranging from 0.17 kg/s to 0.25 kg/s, the lowest maximum temperature is obtained with the width of the cooling plate being of 70 mm, the inlet temperature being of 18 °C and the mass flow rate being of 0.25 kg/s. The optimal solution for temperature difference is achieved when the width of the cooling plate is 60 mm, and the inlet temperature is 18 °C, and the mass flow rate is 0.21 kg/s. Analysis by the orthogonal test, the maximum temperature and temperature difference are dropped by 12.61% and 20.83%, respectively. Long-term hightemperature operation will accelerate battery aging process. More seriously, it will cause a safety incident. Therefore, the best combination must be given prior to the highest temperature, the lowest value of maximum temperature can be obtained under the conditions of 18 °C inlet temperature, 70 mm width of cooling plate and 0.21 kg/s mass flow rate. Conflict of interest None.
Table 7 The variance analysis of the maximum temperature.
Acknowledgements
Factors
SA
fA
Se
fe
Fj
FA
A B C
34.17 34.05 8.90
3 3 3
27.71 34.81 35.10
12 12 12
9.08 3.91 –
F0.05(3,16) = 3.24 F0.025(3,16) = 4.08 F0.01(3,16) = 9.01
This work is supported by the key project of Science and Technology Commission of Shanghai Municipality (15110501100) and the National Natural Science Foundation of China (51675324).
Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2018.10.074.
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[11] F.F. Bai, M.B. Chen, W.J. Song, et al., Thermal management performances of PCM/Water cooling-plate using for lithium-ion battery module based on nonuniform internal heat source, Appl. Therm. Eng. 126 (2017) 17–27. [12] J.H. Xie, Z.J. Ge, M.Y. Zang, et al., Structural optimization of lithium-ion battery pack with forced air cooling system, Appl. Therm. Eng. 126 (2017) 583–593. [13] N. Javani, I. Dincer, G.F. Naterer, et al., Modeling of passive thermal management for electric vehicle battery packs with PCM between cells, Appl. Therm. Eng. 73 (2014) 307–316. [14] W.Q. Li, Z.G. Qu, Y.L. He, et al., Experimental and numerical studies on melting phase change heat transfer in open-cell metallic foams filled with paraffin, Appl. Therm. Eng. 37 (2012) 1–9. [15] Z.H. Rao, Z. Qian, Y. Kuang, et al., Thermal performance of liquid cooling based thermal management system for cylindrical lithium-ion battery module with variable contact surface, Appl. Therm. Eng. 123 (2017) 1514–1522. [16] F. Bai, M. Chen, W. Song, Z. Feng, Design and optimization of air-cooled structure for lithium-ion battery pack, Adv. New Renew. Energy 4 (2016) 358– 363. [17] B. Severino, F. Gana, R. Palma-Behnke, P.A. Estevez, W.R. Calderon-Munoz, M.E. Orchard, J. Reyes, M. Cortes, Multi-objective optimal design of lithium-ion battery packs based on evolutionary algorithms, J. Power Sources 267 (2014) 288–299. [18] R. Mahamud, C. Park, Reciprocating air flow for Li-ion battery thermal management to improve temperature uniformity, J. Power Sources 196 (2011) 5685–5696. [19] F. He, H. Wang, L. Ma, Experimental demonstration of active thermal control of a battery module consisting of multiple Li-ion cells, Int. J. Heat Mass Transfer 91 (2015) 630–639. [20] K. Lafdi, O. Mesalhy, S. Shaikh, Experimental study on the influence of foam porosity and pore size on the melting of phase change materials, J. Appl. Phys. 102 (2007) 759. [21] C.Y. Zhao, W. Lu, Y. Tian, Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs), Solar Energy 84 (2010) 1402–1412. [22] Z.Q. Zhang, J. Cheng, X.D. He, Numerical simulation of flow and heat transfer in composite PCM on the basis of two different models of open-cell metal foam skeletons, Int. J. Heat Mass Transfer 112 (2017) 959–971. [23] H.Y. Huang, Y.S. Chen, J.S. Chen, Optimizing the heat dissipation of an electric vehicle battery pack, Adv. Mech. Eng. 7 (2014) 204131–204142.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Structural optimization of lithium-ion battery for improving thermal performance based on a liquid cooling system Zhuangzhuang Shang a, Hongzhong Qi b, Xintian Liu a,⇑, Chenzhi Ouyang b, Yansong Wang a a b
School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China Automotive Engineering Institute, Guangzhou Automobile Group Co. LTD, Guangzhou 511434, China
a r t i c l e
i n f o
Article history: Received 19 May 2018 Received in revised form 25 September 2018 Accepted 18 October 2018
Keywords: Lithium-ion battery Thermal management Thermal characteristics Structural optimization Orthogonal test
a b s t r a c t Liquid cooling system is of great significance for guaranteeing the performance of lithium-ion battery because of its good conductivity to keep battery working in a cool environment. In this paper, a liquid cooling system for lithium-ion battery with changing contact surface is designed. Contact surface is determined by the width of cooling plate. Mathematical derivation and numerical analysis are conducted to evaluate cooling performance and the consumption of pump power. The results show that increasing inlet mass flow can effectively limit the maximum temperature, but cannot improve temperature uniformity significantly. The temperature is proportional to the inlet temperature, but inversely proportional to the width of cooling plate. Considering the effect of temperature on thermal properties, the thermal properties will weaken the effect of width of cooling plate, inlet temperature and mass flow rate on temperature performance, specifically the maximum temperature and temperature difference, and cause temperature changes in a nonlinear manner. It is difficult to improve the overall performance of the battery by only optimizing a single factor. Three factors (mass flow rate, inlet temperature, the width of cooling plate) for the thermal performance of battery are optimized by using the single factor analysis and the orthogonal test. The best cooling performance can be obtained when inlet temperature is 18 °C, the width of cooling plate is 70 mm and the mass flow rate is 0.21 kg/s. With the use of the optimization method, the lower bound of temperature and the temperature uniformity of battery are achieved and the pump consumption can be reduced. The strategy adopted in this research can be widely applied to battery thermal management to reduce analysis time. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Lithium-ion battery is widely used as an energy source in electric vehicles in recent years because of its outstanding advantages, such as high specific energy and power densities, long cycle-life and low self-discharge rate [1,2]. The performance of lithium-ion battery modules is significantly affected by working temperature. The heat generated by cells, which are the basic units of battery modules, need to dissipate for safety and reliability purposes of modules. The capacity of battery degrades rapidly at high temperature, while the lifetime and the energy output decrease in a cold environment [3,4]. A bad design of thermal management system usually results in the heat accumulation, which is a serious safety issue, and battery degradation. However, a lithium-ion battery with ideal thermal performance remains to be a challenge [5]. Accurate temperature measurement of cells is critical to the thermal control of power battery pack that is assembled by battery ⇑ Corresponding author. E-mail address: [email protected] (X. Liu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.074 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
modulus to achieve a desired performance [6]. When the lithiumion battery cell is in an operating state, the internal resistances will increase as a result of the electrochemical reactions. If the heat generated inside does not dissipate from the cell, the high temperature will lead to electrolyte burns or battery explodes. With the lithium-ion battery working above 50 °C for a long while, it will accelerate its aging process, thereby leading to the degradation of the battery capacity and the driving range of vehicles. The proper working temperature range for the lithium-ion battery is usually from 20 °C to 45 °C, and the temperature distribution of the whole battery pack should be fine and its difference is normally less than 5 °C [7,8]. Therefore, it is crucial to design an appropriate thermal management system for lithium-ion batteries. The battery thermal management system can be classified into three categories: air cooling system [9,10], liquid cooling system, and phase change material (PCM) system [11,12]. The air cooling system can be further divided into forced air cooling and natural air cooling ones. The effectiveness of the air cooling system is poor, and cannot meet the requirement of a long driving-range electric vehicles and hybrid electric vehicles [13]. The PCM system can
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Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
effectively remove heat away and keep the distribution of internal temperature more uniform [14]; however, its encapsulation is difficult and the volume change restricts its application in engineering field. Compared with the air cooling one and the PCM, the liquid one has a better thermal conductivity. Therefore, the liquid cooling system is much more suitable for the heat dissipation of the lithium-ion battery and large-scale battery in engineering applications [15]. A great number of researchers have paid attention to the heat dissipation of the battery pack. Multi-objective optimal design of lithium-ion battery packs has been reported in many literatures. Bai et al. [16] studied the thermal behavior of lithium-ion battery by establishing numerical models and different airflow duct, employing an optimizing scheme of the orthogonal test. Severino et al. [17] proposed an optimization method for the battery thermal management based on evolutionary algorithms. Plenty of optimization methods have been employed for different heat dissipation of lithium-ion battery packs. Mahamud and Wang [18,19] demonstrated that the use of reciprocating cooling flow can reduce the temperature and non-uniformity in battery pack. Lafdi, Zhang and Zhao [20–22] established a three-dimensional model of PCM and experimental verification, and the results indicated that the thermal management system of battery with PCM has a significant impact on its heat transfer behavior by means of numerical simulation and experimental verification [23].
2. Model description The schematic of battery model is shown in Fig. 1(a). Both the shell of cells and the cooling plate are made of aluminum because of its light weight and good thermal conductivity. In practical assembly, there is a gap between the two aluminum components, and thermal conductivity between them is significantly affected by the air. A solution to this problem is usually that inserting a thermal conductive pad between the cooling plate and the cells. The thermal conductive pad is with properties of good viscosity, flexibility, good compression properties and excellent thermal conductivity, thus it is widely used in liquid cooling system. The air between the electronic components can be fully discharged to achieve sufficient contact. The thickness of aluminum cooling plate is 0.47 mm. Heat is generated from the battery cells and transferred from the thermal conductive pad to cooling plate (filled with mixture of glycol and water). Coolant removes the heat away by flowing fluid inside the cooling plate. There are 15 cells adopted as targets to investigate. Material properties used in the simulation are shown in Table 1. In this paper, a prismatic lithium-ion battery composed of 15 battery cells with three coolant passages is selected as the model for investigation. The main technical parameters are shown in Table 2. The contact area between cooling plate and cells is a main factor to influence the heat transfer for cells. The length of thermal
(a) 3D model of battery module and actual picture of Single cell
(b) Coolant flow channel with different width of cooling plate Fig. 1. Schematic of liquid cooling system for the battery module.
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Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41 Table 1 Physical properties of lithium-ion battery. Material 3
Density (kg/m ) Thermal conductivity (W/m/K) Specific heat (J/kg/K) Dynamic viscosity (Pa/s)
Al
Cu
Thermal conductive pad
Coolant
2710.0 155.0 890.0 –
8940.0 398.0 386.0 –
2400.0 1.2 2200.0 –
1069.4 0.4 3358.0 0.0034
where qc, cc and kc are the density, specific heat capacity and thermal conductivity of the coolant, respectively. The continuous equation of liquid coolant can be given as:
Table 2 Technical parameters of 49Ah Lithium-ion battery. Parameters
Values
Rated capacity (Ah) Rated voltage (V) Internal resistance (mX) Specific heat capacity (J/kg/K) Density (kg/m3) Size of cell (length width height) (mm) Size of positive and negative electrode (length width height) (mm) Thermal conductivity (X, Z directions) (W/m/K) Thermal conductivity (Y direction) (W/m/K)
49.0 3.7 1.0 1151.0 2277.0 230 73 175 33.6 25.0 15.2 2.7 0.9
conductive pad is constant, but the width is changeable in the simulation. The width size of cooling plate varies from 55 mm to 75 mm, and the interval between them is 5 mm. As shown in Fig. 1, the cooling plate has the same width and length with the thermal conductive pad. 3. Initial boundary conditions
To obtain the temperature distribution in a cell, heat conduction energy conservation equation of the battery can be written as:
ð1Þ
where q and cp are the density and specific capacity of the battery, respectively; kx, ky, and kz are the heat conductivity coefficient in x, y, z directions, respectively, as listed in Table 1; Qv is the volumetric heat source in the cell, which is generated by electrochemical enthalpy change and internal thermal resistance. The specific form of Qv can be written as:
Q v ¼ IðU OC V Þ IT
dU OC dT
In a state of stationary flow, @@tqc ¼ 0, and as coolant is an incom-
pressible fluid so that ddtqc ¼ 0. The continuous equation of incompressible fluid can be ! obtained by r v ¼ 0, ! where v is the velocity vector of coolant. The momentum equation of incompressible liquid is as follows
qc
! dv ! ¼ rp þ lr2 v dt
where p and l are static pressure and dynamic viscosity of coolant, respectively.
In order to obtain the temperature distribution of cells, some initial conditions and boundary condition are necessary for a specific heat conduction problem. The schematic of the modules is shown in Fig. 2, and it can be seen that the coolant flow direction is along a single channel in the x direction, and the cooling plate is filled with liquid coolant. Considering that the heat dissipation on the side of the modules is negligible, and the modules are placed in a steady state and a closed environment, thus, @T ¼ 0 and @T ¼ 0.The @t @x heat flux equation of the battery is given as:
where U is the heat flux along the x, y, z directions; Kr is the thermal heat conductivity coefficient; A is the surface area of the battery and DT is the temperature difference. As the heat flux in the z direction is more than that in the y in Eq. (1) is direction, we can obtain kz > ky. Since the term kz @T @z @T @T greater than ky @y, which means that ky @x can be ignored.
ð2Þ
where I, T and Uoc are the electric current, temperature of the cell and open-circuit voltage, respectively. Theoretically, high temperature and large current cause cells generate much heat.dUdTOC is an entropic coefficient of the cell. Liquid coolant is a mixture of water and glycol in this study. The energy conservation equation of liquid coolant is:
qc
@T c kc ! rT c þ r qc v T c ¼ r @t cc
ð5Þ
U ¼ K r A DT
4. Theoretical model
@T @ @T @ @T @ @T þ þ þ Qv kx ky kz ¼ @ s @x @x @y @y @z @z
ð4Þ
5. Cooling capacity analysis
The boundary conditions of inlet and outlet are set to mass flow rate and pressure outlet, respectively. Inlet mass flow rate is set to 0.17 kg/s, 0.21 kg/s, 0.25 kg/s, and 0.29 kg/s for different cases, while outlet is set to 0.0 pa at all time. Inlet and outlet temperatures are different, the former is equal to environment temperature. Speed-up climbing condition is used, and the initial temperature of the cell is usually 30 °C. As mentioned above, the thermal conductive pad is placed between the module and the cooling plate to increase heat transfer, and its thermal resistance 0.0043 m2/K/W.
qcp
@ qc þ rðqc v Þ ¼ 0 @t
ð3Þ Fig. 2. Schematic of lithium-ion battery with cooling plate.
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With the boundary condition of @T = 0 at the point z = 0 and @z z = Lcell, T = Tb1 can be obtained, where Lcell is the size of the half cell-width, and Tb1 is the boundary temperature between thermal conductive pad and cell.
@ @T kz þ Qv ¼ 0 @z @z
ð6Þ
With some mathematical operations, Eq. (6) can be rearranged as
Q T ¼ v L2cell z2 þ T b1 2kz
ð7Þ
considering the existence of thermal resistance between thermal conductive pad and module, one has
T b1 T b2 ¼ Q v Lcell Rc
ð8Þ
where Tb2 is the surface temperature of the thermal conductive pad. For thermal conductive pad, heat conduction equation in the z direction can be expressed as
T b2 T b3 kp ¼ Q v Lcell Lp
ð9Þ
where Tb3 is the surface temperature of the interface between cooling plate and thermal conductive pad, and Lp and kp are the thickness of cooling plate and thermal conductivity, respectively. According to the Fourier’s law, the convective heat transfer between thermal conductive pad and coolant can be given as
h T b3 T f ¼ Q v Lc
property of coolant at a certain location in y direction. From Eq. (12), with a larger heat transfer coefficient h and a specific heat of the coolant and a mass flow rate, the temperature of modules becomes lower, but the changing trend of module temperature is nonlinear.
ð10Þ
6. Numerical simulation and experiment All calculated result are presented at transiting high-speed climbing conditions (120 kph 3% climbing), and the ambient temperature is 25 °C. The lithium-ion battery is discharged at 1.2C with a constant current by charge-discharge apparatus. The temperature sensors are placed on three different locations (near positive and negative electrode, the middle). Fig. 3 illustrates the measurement points of sensors in the experiment. The battery was placed in a temperature control box. All data is recorded by the Agilent 34972A Data Logger which is connected to a computer. The results of numerical simulation and experiment are compared in Fig. 4. The experimental results take the average value of temperature at the positive and negative electrodes as well as the middle of the battery. It is clear to see that the simulation results agree well with the experimental results, and the maximum discrepancy between the two is less than 0.21 °C. The experimental results indicate the calculation method of heat source is accurate and the CFD numerical model is reliable. 6.1. Effects of the width of cooling plate Fig. 5 illustrates the temperature with different mass flow rate and different contact area between thermal conductive pad and
where h is the conductive heat transfer coefficient and Tf is the temperature of the coolant, which varies along y direction in the model. With the use of the energy conservation equation, it can be calculated as follows
qq ! v dhalf cq T f T in ¼ Q v Lcell y
ð11Þ
where y is the random axis along y direction; dhalf is the half width of the coolant channel; qq and cq are the density and specific heat capacity of the coolant, respectively. Therefore, the following equation can be obtained
T¼
Qv 2 Lp 1 Q Lcell y þ T in þ v! Lcell z2 þ Q v Rc þ þ 2kz kp h qq v dhalf
ð12Þ
where T describes the temperature distribution in the direction normal to the cooling plate. Based on Eq. (12), it indicates that the temperature is inversely proportional to the inlet mass flow rate, proportional to the inlet temperature, all parameters are constant except h and 1/qqvdhalf. Furthermore, it is evident that the temperature is determined by merely the flow situation in y direction and the thermal-physical
Fig. 4. The results from experiments and simulations.
Fig. 3. (a) Temperature control box and pictures of lithium-ion cell with embedded thermocouple (b) Picture of test points of temperature sensors.
Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
a Mass flow rate = 0.17kg/s
37
(b) Mass flow rate = 0.21kg/s
(c) Mass flow rate = 0.25kg/s Fig. 5. Modules temperature variation during the discharge process with different width of cooling plate in a highspeed climbing condiction.
module. The width changes from 55 mm to 75 mm, and the mass flow rates are set to 0.17 kg/s, 0.21 kg/s and 0.25 kg/s, respectively. The time of operating condition is set to 1800 s based on engineering experience. According to Fig. 5, the temperature rises as time increases. Specifically, the temperature goes up fast in the beginning stage of the discharge but slowly in the end stage. This is because the cooling system does not work when the temperature is less than 35 °C, but when the temperature exceeds 35 °C, the battery system enters into the cooling stage so that the temperature gradient turns to be lower. Besides, the larger width of cooling plate is, the faster of cell temperature drops. As shown in Fig. 5, with the increase of cooling plate width, both the maximum temperature and the maximum-temperature difference are reduced. As the value of width varies from 55 mm to 75 mm, the maximum temperature of cells are dropped by 4.02 °C, 3.32 °C and 3.66 °C, and the maximum-temperature difference decreases by about 1.44 °C, 1.46 °C and 1.50 °C. However, the reduction is nonlinear. When size reaches 65 mm, the decreasing trend of temperature becomes gentle, the reduced temperature are 3.1 °C, 2.0 °C, 1.5 °C and 1.0 °C, respectively. Apparently, when the width of cooling plate increased, the maximum temperature and the maximum-temperature difference of cells are decreased, but both the downtrend of them slows down, when the value of width reaches to a certain extent. If the
width continues to increase, it will bring the weight to the battery module, which is harmful to the performance of the vehicle. 6.2. Effects of inlet temperature As shown in Fig. 6, the overall trend of temperature contours are consistent obviously. The inlet temperature has much influence at the entrance position of coolant for battery modules, the hottest position moves from the entrance to the end side of modules which is close to the top. As the inlet temperature rises from 15 °C to 18 °C, the maximum temperature dropped from 41 °C to 38.7 °C, the results show that the inlet temperature of the cooling plate has a significant effect on the maximum temperature. The lower of inlet temperature, the lower of the maximum temperature of cells. The results of simulation also verify the relationship between the temperature of modules and the inlet temperature of the coolant derived from the mathematical analysis. However, the magnitude of the temperature difference is relatively smaller, The changing curve of battery modules with different inlet temperature is shown in Fig. 7, it can be seen that the temperature difference are 5.4 °C,5.5 °C,4.5 °C and 4.9 °C, when the inlet temperature is 15 °C, 18 °C, 21 °C and 24 °C, respectively. So dropping the inlet temperature cannot significantly improve the uniformity of temperature in this temperature range.
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Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
(a) Inlet temperature=15
(b) Inlet temperature=18
(c) Inlet temperature=21
(d) Inlet temperature=24
Fig. 6. The battery modules contour with different inlet temperature of 55 mm width.
Fig. 7. Temperature variation of modules with different inlet temperature of 55 mm width.
6.3. Effects of the inlet mass flow rate Fig. 8 shows that increasing inlet mass flow can reduce maximum temperature, but it is difficult to improve temperature uniformity. Apparently, the maximum temperature reaches to
41.22 °C at the mass flow rate of 0.17 kg/s, which is more than that at the mass flow rate of 0.21 kg/s by 1.28 °C. Moreover, the maximum temperature is smaller at the mass flow rate of 0.25 kg/s when the width of cooling plate is 55 mm. Situation is the same as the case of w = 60 mm, 65 mm, 70 mm, 75 mm, when the mass flow rate is 0.17 kg/s, 0.21 kg/s, 0.25 kg/s. As shown in Fig. 7(b), the temperature difference decreases obviously when increasing the width of cooling plate, but the trend of curves gradually slows down. However, increasing inlet mass flow rate will lead to more pump power consumption, and increasing the width of cooling plate will give rise to mass-increase of the battery pack and battery layout space. By comparing the cases above, the cooling capability of coolant is investigated by the mathematical analysis. Considering the term ! 1=qq v dhalf in Eq. (12), the density of coolant is inversely proportional to the inlet temperature, and according to relationship between volume flow rate and cross-sectional area of inner diameter of cooling plate in Eq. (13), it can be deduced when inlet mass flow rate is constant. wider the flow path in cooling plate is, the smaller the velocity of coolant is. The relationship between them can be written as:
Q ¼v A
ð13Þ
where Q is mass flow rate, A is the cross-sectional area of the flow channel in the cooling plate, v is the velocity of coolant. It can be seen when parameters (v, q) vary with the temperature and the width of cooling plate, the influence of inlet
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Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
Fig. 8. Temperature distribution with different width of aluminium plate: Maximum temperature (b) Temperature difference.
temperature, mass flow rate and the width of cooling plate to temperature performance will be reduced. As shown in Figs. 5 and 6, the changing trend of temperature is not linear. It is not good to obtain better temperature performance only by increasing inlet mass flow rate or contact area between cooling plate and cells.
7. Analysis of multiple-factor 7.1. The design of orthogonal test Increasing the width of cooling plate can greatly reduce the battery module maximum temperature and the temperature difference between the modules, but for large rate electricity, the cells emit more heat. To achieve a good performance and long life, it must be controlled by adjusting the temperature influence parameters to control its temperature and temperature difference in an optimal temperature range. In order to reduce the analysis time, the following orthogonal test is used to make the maximum temperature and temperature difference in a suitable range. The orthogonal test is an effective way to analyze the effectiveness of multiple factors. In order to make sure that results have a certain degree of accuracy and to control the number of experiments, an orthogonal test table with three factors and four levers (L16(45)) is applied to investigate the effectiveness of multiple factors on the cooling performance in Table 3, in which A, B and C are three factors (A is the inlet temperature, B is the inlet mass flow rate and C is the width of the cooling plate). The evaluating indexes are the maximum temperature and the temperature difference, and the results are shown in Table 4. In order to investigate the influence of factors and levels on the results and the importance of each factor, the experimental results are analyzed by the mean value and the range. Table 3 The analysis results according to maximum temperature and temperature difference. Levers
1 2 3 4
Factors A (mm)
B (°C)
C (kg/s)
55 60 65 70
15 18 21 24
0.17 0.21 0.25 0.29
Table 4 The schemes and results. Test number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Test factors
Test results
A (mm)
B (°C)
C (kg/s)
Tmax (°C)
DT (°C)
55 55 55 55 60 60 60 60 65 65 65 65 70 70 70 70
15 18 21 24 15 18 21 24 15 18 21 24 15 18 21 24
0.17 0.21 0.25 0.29 0.21 0.25 0.29 0.17 0.25 0.29 0.17 0.21 0.29 0.17 0.21 0.25
38.85 37.64 36.79 36.02 39.77 37.98 36.88 35.97 39.94 38.72 37.59 36.73 41.22 39.65 38.39 37.60
5.42 6.01 6.95 7.01 5.33 5.94 6.42 6.92 4.52 4.95 5.19 5.88 4.22 4.50 5.31 6.21
7.2. Analysis results of the maximum temperature and temperature difference The maximum temperature and temperature difference are the most important evaluating parameters for battery module. Table 6 shows results of the range according to the following expressions
K ij ¼
X T max ij
ð14Þ
j¼1
kij ¼
1 K ij n
Rj ¼ max k1j min k1j
ð15Þ ð16Þ
where Kij is the sum of four maximum temperatures for the same level; kj is the mean value for each factor at the same level (j represents the column number three factors in Table 3); and n is the maximum number of lever. Rj is the range of kj and indicates the magnitude of the change of the test indicator within this range. The influence of the factor is more obvious and significant with a bigger Rj. As shown in Table 8, because of RjB > RjA > RjC, the importance of factors for maximum temperature is in the following order:
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Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
B > A > C, in which, the factor B is the first one to select, and the factor A should be considered secondly, and lastly factor C is selected. Thus, to obtain the maximum temperature, the optimal design of the width of cooling plate is A = 70 mm, the corresponding inlet temperature is 18 °C, the mass flow rate is 0.25 kg/s. When the width of cooling plate is 60 mm, the inlet temperature is 18 °C, and the mass flow rate is 0.17 kg/s, the better temperature difference can be obtained. The range analysis for temperature difference is shown in Tables 5 and 6. The range analysis only reflects the importance of the factors, which cannot provide an accurate quantitative estimate of the significance of the factors. To compensate the lack of intuitive analysis, variance analysis is used and the results of the variance are presented in Table 7, as calculated by the following equations n X ¼1 T max k T n k¼1
ð17Þ
1 Ti ¼ K ij s
ð18Þ
ð19Þ
SA =f A Se =f e
ð20Þ
is the mean value of the sum of all test results; n is the where T number of the orthogonal test (n = 16); s is the test number of each factor; r is the levels of factors; SA is the sum of the square of deviation of the average deviation caused by the change of level of each factor; Se is the sum of square error; fA is the degree of freedom of SA; fe is the degree of freedom of Se; Fj is the observed value of factor j. Because of FB > F0.05 (3,16), the maximum temperature is influenced by the factors A and B, the Fj of factor C is lower than 1, so the significance is negligible. The variance analysis of temperature difference is listed in Table 8, where the FA and FC > F0.025(3,16). From the analysis, it is clear to see that the factors A and C are significant to the temperature difference. The orthogonal design method is used to optimize the liquid cooling system of lithium-ion battery. From the range analysis, the significance of three factors on temperature is following by B, Table 5 The range analysis of maximum temperature.
Tmax (°C) DT (°C)
Factors
SA
fA
Se
fe
Fj
FA
A B C
33.15 3.5 43.2
3 3 3
24.20 38.05 32.08
12 12 12
5.53 – 5.37
F0.05(3,16) = 3.24 F0.025(3,16) = 4.08
A, C. Inlet temperature is the first level to choose, and the width of cooling plate should be chosen secondly, and the final influencing factor is the mass flow rate. For another evaluating parameter, the importance of three factor on temperature difference is C > A > B. That is, the mass flow rate should be considered firstly, and the width of cooling plate is chosen as the level two, and the inlet temperature has very little effect on temperature difference. The variance analysis is carried out to examine the significance of each factor. From the analysis results, the maximum temperature and the temperature difference are dropped by 12.61% and 20.83%, respectively. 8. Conclusions
r r X 2 1 X T2 s Tl T ¼ K 2ij Sj ¼ s n i¼1 i¼1
Fj ¼
Table 8 The variance analysis of the temperature difference.
Range
A (mm)
B (°C)
C (kg/s)
Rj Rj
1.89 3.59
3.38 2.48
0.20 3.62
Table 6 Optimal design for single index. Indexes
Best solution
Importance of factors
Tmax (°C) DT (°C)
A4B2C3 A2B2C1
B>A>C C>A>B
This work focus on the optimal choice of multiple factors for influencing liquid cooling based on thermal management of lithium-ion battery. Different aspects are compared by simulation and experiments. The model was numerically formulated and put into simulation, and the accuracy of the simulation model was verified by experiments. The obtained results show that when the width of cooling plate changes from 55 mm to 75 mm, and the inlet temperature drops from 24 °C to 15 °C, the maximum temperature changes obviously; however, the trend gradually slows down as the factors change to a certain value. Therefore, among the multiple influencing factors, it is difficult for battery to obtain the improvement of comprehensive performance by optimizing a single factor. Meanwhile, considering the pump consumption and the weight of the battery pack requirements, a better solution needs to be found from these influencing factors. Three factors (the width of cooling plate, the inlet temperature, the inlet mass flow rate) are studied by means of the orthogonal test. From the variance analysis, when considering the temperature range from 15 °C to 24 °C, and the mass flow rate ranging from 0.17 kg/s to 0.25 kg/s, the lowest maximum temperature is obtained with the width of the cooling plate being of 70 mm, the inlet temperature being of 18 °C and the mass flow rate being of 0.25 kg/s. The optimal solution for temperature difference is achieved when the width of the cooling plate is 60 mm, and the inlet temperature is 18 °C, and the mass flow rate is 0.21 kg/s. Analysis by the orthogonal test, the maximum temperature and temperature difference are dropped by 12.61% and 20.83%, respectively. Long-term hightemperature operation will accelerate battery aging process. More seriously, it will cause a safety incident. Therefore, the best combination must be given prior to the highest temperature, the lowest value of maximum temperature can be obtained under the conditions of 18 °C inlet temperature, 70 mm width of cooling plate and 0.21 kg/s mass flow rate. Conflict of interest None.
Table 7 The variance analysis of the maximum temperature.
Acknowledgements
Factors
SA
fA
Se
fe
Fj
FA
A B C
34.17 34.05 8.90
3 3 3
27.71 34.81 35.10
12 12 12
9.08 3.91 –
F0.05(3,16) = 3.24 F0.025(3,16) = 4.08 F0.01(3,16) = 9.01
This work is supported by the key project of Science and Technology Commission of Shanghai Municipality (15110501100) and the National Natural Science Foundation of China (51675324).
Z. Shang et al. / International Journal of Heat and Mass Transfer 130 (2019) 33–41
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2018.10.074.
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