Heat transfer in the dynamic cycling of lithium–titanate batteries

International Journal of Heat and Mass Transfer 93 (2016) 896–905

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

Heat transfer in the dynamic cycling of lithium–titanate batteries Qingsong Wang a,b,⇑, Qiujuan Sun a, Ping Ping a, Xuejuan Zhao a, Jinhua Sun a, Zijing Lin c a

State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, PR China CAS Key Laboratory of Materials for Energy Conversion, University of Science and Technology of China, Hefei 230026, PR China c Department of Physics & Collaborative Innovation Center of Suzhou Nano Science and Technology, University of Science and Technology of China, Hefei 230026, PR China b

a r t i c l e

i n f o

Article history: Received 5 April 2015 Received in revised form 28 October 2015 Accepted 2 November 2015

Keywords: Lithium–titanate batteries Heat dissipation Thermal–electrochemical model Cycling

a b s t r a c t Based on the coupled model of a three-dimensional thermal model and one-dimensional electrochemical model, the thermal behaviors of lithium–titanate battery under the discharge–charge cycling with various current are investigated. The temperature on the surface of battery increases with the increasing cycling rate. Two temperature peaks are observed during the constant-current discharge, constantcurrent and constant-voltage charge process based on the analysis of the heat generation. Additionally, the radiative heat transfer cannot be omitted when the battery is operated under natural convection at 0.5 C cycling rate, in this case, the radiative heat transfer is estimated to contribute 42% to the total heat transfer. The results can provide basic data for the thermal management of the battery pack during the discharging and charging processes. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Batteries play a key role in the development of electric vehicles and hybrid electric vehicles [1]. Progress in the development of lithium-ion batteries with large capacity and high power has been advanced for application to electric vehicle. However, the thermal stability under various operation conditions is one of the most important safety considerations for large-scale lithium-ion batteries. Some thermal models of the lithium-ion battery were proposed in previous studies and the temperature distribution inside the battery was simulated. In general, the models can be classified into three types in dimension: one-dimensional, two-dimensional and three-dimensional models [2]. Bernardi et al. [3] developed a heat-generation model for battery systems concerning the heat contributions from electrochemical reactions, mixing enthalpies and phase changes. Chen et al. [4] embedded the basic equations of Bernardi’s work into a three-dimensional thermal model for the heat source term. As an effective tool, numerical simulation of heat transfer within batteries can be used to obtain the fundamental data on whether the generated heat can be easily dispersed out of batteries, and how to design a proper thermal management policy for ⇑ Corresponding author at: State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, PR China. Tel.: +86 551 6360 6455; fax: +86 551 6360 1669. E-mail addresses: [email protected] (Q. Wang), [email protected] (Q. Sun), [email protected] (P. Ping), [email protected] (X. Zhao), [email protected] (J. Sun), [email protected] (Z. Lin). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.11.007 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

the discharging and charging processes of batteries [5,6]. Jeon and Baek [7] provided the thermal behavior of lithium ion battery at several discharge rates. Based on the finite element method, Kim et al. [8] simulated the thermal behavior of a lithium-ion battery during galvanostatic discharge, constant-current (CC) and constant-voltage (CV) charge. Onda et al. [9] calculated the temperature rise of a small lithium-ion battery during rapid charging and discharging cycles. Most of these thermal models of lithiumion batteries focused on the thermal behavior during galvanostatic discharging. Only few works reported the thermal behavior of lithium ion batteries during dynamic CC and CV charging. However, the lithium ion battery packs used for the electric vehicle application rarely cycle per these simple protocols. It is important to predict accurately the thermal behavior of lithium-ion batteries under various discharge and charge conditions to improve their performance and life, as well as ensuring the thermal safety. The objective of this paper is to provide deeper insight on the heat transfer inside the battery and heat exchange with the environment under various working conditions and boundary conditions. Additionally, the current distribution influence on the temperature distribution of the battery also was investigated by others. Tang et al. [10] used COMSOL Multiphysics to solve the 2D potential and current distribution during galvanostatic charge of lithiumion batteries. Gerver and Meyers [11] developed a 2D electrochemical and 3D thermal model to simulate the current and temperature distributions. However, the novel work in this paper is on the effect of heat transfer not the influence of current distribution on the temperature. Therefore, the heat generation was treated as

Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905

897

Nomenclature as c Cp D E @EOC =@T f F hc hr i0 J k k L R rs T T1 t 0þ

a

specific interfacial area of the electrode lithium ion concentration heat capacity diffusion coefficient of lithium ion cell potential temperature derivative of equilibrium potential mean molar activity coefficient of the electrolyte Faraday’s constant, 96,487 C mol1 convective heat transfer coefficient the emissivity of the cell surface exchange current density of an electrode reaction transfer current resulted from the intercalation or deintercalation of lithium electrochemical reaction rate constant thermal conductivity thickness of the different layers of the cell the gas constant radius of the spherical particle absolute temperature the ambient temperature transport number charge transfer coefficients

uniform throughout the core region of the system to improve the computation efficiency. As one new power cell for electric vehicles, the lithium–titanate battery was investigated in this work. For this type of battery, its positive electrode is nickel-cobalt-manganeseoxide lithium (Li(Ni1/3Co1/3Mn1/3)O2, NCM), and its negative electrode is lithium titanate oxide (Li4Ti5O12, LTO). 2. Model development 2.1. One-dimensional electrochemical model Commercially available lithium-ion cells have three primary functional components, i.e. negative electrode, electrolyte, and positive electrode. Schematic of one-dimensional model of lithium-ion cell is shown in Fig. 1.

j e r

electric conductivity volume fraction of a phase the Stefan–Boltzmann constant, 5.670373  108 kg s3 K4 activation over-potentials of an electrode reaction effective density of the active battery material

g q

Subscripts e the electrolyte phase neg negative electrode pos positive electrode sep electrolyte neg_cc negative current collector pos_cc positive current collector i different layer of active battery material, i.e. neg, pos, sep, neg_cc, pos_cc s the solid phase eff effective oc open circuit rev reversible rxn irreversible j X, Y, Z-direction

During charging, lithium-ions deintercalate from the positive electrode and intercalate into the negative electrode, and the reverse takes place during discharging. During charging and discharging, various chemical and electrochemical reactions occur as well as the transport processes of lithium ions. As limited knowledge on the multi-physics processes were obtained in the lithium-ion batteries, the following assumptions were proposed [4]: (1) positive and negative material are the spherical particles, the particle diffusion behavior follows Fick’s second law of diffusion; (2) spherical particles uniformly distribute in the positive and negative electrodes; (3) the behavior of the electrolyte could be described by the theory of dilute solution; (4) the thermal physical properties in each layer are isotropic and their values equal to the average values within a certain temperature range. The effects of current density, lithium-ion diffusion in solids, average radius on discharge capacity and temperature were studied through the electrochemical models of lithium-ion cells proposed by Cai and White [13]. Lu et al. [14] compared White’s and Newman’s models and found that Newman’s model is more sensitive to current density, lithium-ion diffusion in solids, and average radius than that of White’s model. According to the electrochemical models of Newman, the flux of material balance for the lithiumions in an active solid material particle is governed by Fick’s second law in spherical coordinates [15]:

  @cs Ds @ @cs r2 ¼ 2 @t r @r @r

ð1Þ

The material balance for the binary electrolyte in the liquid phase is given by:

ee Electrolyte

0

Lpos_cc

Lpos

Lsep

L neg

Lneg_cc

Fig. 1. Schematic of one-dimensional model of lithium-ion cell [12].

X'

  @ce @ @ce Deff;i ¼ þ ð1  t0þ Þas J @x @t @x

ð2Þ

The charge balance for the solid and liquid phase is governed by Ohm’s law:

ks;eff

@ 2 /s ¼ as FJ @x2

ð3Þ

898



Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905

@ @x



jeff



@/e @ þ @x @x



jeff D

@ ln ce @x

 ¼ as FJ

ð4Þ

js;eff ¼ js e1:5 s

ð5Þ

jeff ¼ je e1:5 e

ð6Þ

as ¼ 3es =rs

ð7Þ

jeff D ¼

  2RT jeff 0 d ln f ðt þ  1Þ 1 þ d ln ce F

and assumed that the thermal behavior of the core region is analogous to that of a homogeneous material. The Biot number (Bi), characterizes the importance of the internal thermal resistance of the solid as compared to the external thermal resistance of the fluid. As the Biot number approaches zero, the temperature gradient in the solid can be neglected. A rule of thumb for using the Biot number is that if Bi < 0.1, the assumption of uniform temperature introduces an error in the calculations of less than 5% [17].

Bi ¼ hLc =k ð8Þ

Butler–Volmer electrode kinetics serves as the link term between charge balance and material balance. It describes the fundamental relationship between electrical current on an electrode, the electrode potential and the local specie concentration at the interface between electrode and electrolyte. The Butler–Volmer relation is given as [16]

     aF gi bF gi  exp J ¼ i0;i exp RT RT

ð9Þ

where h is the convective coefficient, h = 2 W m K ; Lc is the characteristic length, Lc = V/S, V is the volume of the battery, S is the surface area. (For a 945 mA h lithium–titanate battery, Lc = 5.33 mm); k is the thermal conductivity, and k = 1.0437 W m2 K1 is the minimum conductivity of battery among the three-dimensional coordinate direction. Based on the above values, Bi = 0.0102 < 0.1. Therefore, the lumped-capacitance method is applied to simulate the temperature variation here, which means the temperature inside the battery is spatially uniform at any time in the transient process. The transient three-dimensional conductive heat transfer equation is as follows:

The exchange current density is given by

i0;i ¼ k0;i ðc2i;max Þ

1b

ðc2i;max  c2i;surf Þ

1b

b

ðc2i;surf Þ

ð10Þ

The overpotential is given by

gi ¼ ju2;i  u1;i  Ej

ð11Þ

The boundary conditions for the equations in the electrochemical model are listed in Table 1. 2.2. Three-dimensional thermal model Heat can be transferred in three ways: conduction, convection, and radiation. Chen et al. [4] thought that conduction is the only significant contributor to heat transfer in the inner of the cell,

Table 1 The boundary condition for the electrochemical model. Boundary conditions Lithium ion flux

Mass flux

On the surface of the particle, the flux is equal to the consuming/producing rate of lithium ions due to the electrochemical reaction occurring at the solid/liquid interface. There is no flux at the center of the particle @cs s Ds @c @r jr¼R ¼ J; Ds @r jr¼0 ¼ 0 At the two ends of the cell in the x-direction, there is no mass flux @ce e Deff;p @c @x jx¼0 ¼ Deff;n @x jx¼Lneg

Continuous

cc þLneg þLsep þLpos þLpos cc

¼0

Electrolyte and its flux are continuous cs jx¼ðLpos cc þLpos þLsep þLneg Þ ¼ cn jx¼ðLpos cc þLpos þLsep þLneg Þþ cp jx¼ðLpos cc þLpos Þ ¼ cs jx¼ðLpos cc þLpos Þþ @c

s þ Deff;p @xp jx¼ðLpos cc þLpos Þ ¼ Deff;s @c @x jx¼ðLpos cc þLpos Þ @cn s  Deff;s @c @x jx¼ðLpos cc þLpos þLsep þLneg Þ ¼ Deff;n @x jx¼ðLpos

Charge flux

cc þLpos þLsep þLneg Þ

þ

At the interface of the current collector and the positive electrode, the charge flux is equal to the current density applied to the cell kp;eff

@/p @x jx¼Lpos

cc

¼ Iapp

At the interfaces of the positive electrode/separator and separator/negative electrode and At two ends of the cell, there is no charge flux @/p @/n @x jx¼0 ¼ 0; kn;eff @x jx¼Lpos cc þLpos þLsep þLneg þLneg cc @/p n kp;eff @x jx¼Lpos cc þLpos ¼ kn;eff @/ @x jx¼Lpos ccþLpos þLsep ¼ 0

kp;eff Potential

¼0

The potential of the solid phase at the right end is set to zero, and the potential of the solid phase at x = 0 is equal to the cell voltage /s;p jx¼0 ¼ Ecell ; /s;n jx¼Lpos cc þLpos þLsep þLneg þLneg cc ¼ 0

ð12Þ 1 1

qC p

! ! @T ¼ rðK T;j r TÞ þ Q @t

ð13Þ

The thermal conductivity is calculated with the method proposed by Chen et al. [4]. In addition, the heat-generation of a lithium-ion battery during operation is composed of reversible heat generation (Qrev) and irreversible heat generation (Qrxn). The overpotential is an indicative parameter of irreversibility’s such as ohmic losses, charge-transfer overpotential and mass-transfer limitations. The overpotential multiplied by the current is termed the polarization heat. The following heat-generation equation developed by Bernardi et al. [3] is adopted

Q total ¼ Q rev þ Q rxn ¼ as JFðu2;i  u1;i  E  T@Eoc =@TÞ

ð14Þ

The values for the equilibrium potential were determined experimentally as the open-circuit voltages for each state of charge and taken from Ref. [18]. The convective and radiative heat transfers on the surface were considered to be the boundary conditions. The stagnant layer of air in contact with the surface is warmed by conduction and then the heat is transported away by convection currents in the air further from the surface. The convection at the boundary according to Newton’s law of cooling is expressed as follows

Q c ¼ hc ðT s  T 1 Þ ¼ f jT s  T 1 jn ðT s  T 1 Þ

ð15Þ

The heat transfer coefficient hc is a function of both location and temperature. For natural convection, f = f1/pn, where p denotes the characteristic length of the surface, and f1 and n are the coefficients. For the vertical plate, the values of f1 and n is 0.9415 W mn2 Kn1 and 0.35, 0.4151 W mn2 Kn1 and 0.33 for the horizontal plate. Since is in the laminar airflow, the environmental temperature is 298 K, and the velocity of the airflow is assumed equals zero. Furthermore, the temperature variation of the battery is small under the natural cooling condition. Hence, the heat transfer coefficient along the vertical length varies little, and can be treated as a constant average value [19]. Therefore, the heat transfer coefficient of this 945 mA h punch cell is calculated to 2 W m1 K1 at the cycling rate of 0.5 C. Cells can also radiate heat at their surfaces. The radiative heat depends on the surface geometry, the material, the texture of the surface and so on. The radiative heat transfers at the boundary according to Stefan–Boltzmann law, which is expressed as follows

Q R ¼ hr rðT 41  T 4 Þ

ð16Þ

899

Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905

experiment is one where heat is neither lost from nor added to the system during the test. In this experiment, the cell was placed inside the ARC cavity using a specially designed cell holder and connected to a LAND cycler channel using extensive nickel straps, and the thermocouple was attached to the cell surface. In the adiabatic calorimeter, the temperatures of the cell and container are continually monitored. The temperature can be changed to follow the cell temperature within the calorimeter. The experiments data were compared with the simulation results. Both the simulation and the experimental cells were cycled in the following sequence of operation modes: (1) CC discharge with 0.5 C, 1.0 C, or 1.5 C current until the cell voltage drops below 1.5 V, (2) rest for 1 min, (3) CC with 0.5 C, 1.0 C, or 1.5 C current until the cell voltage exceeds 2.8 V, (4) CV charge at 2.8 V until the charging current drops below 20 mA, (4) rest for 1 min, (5) go to the first step, and then continue cycling.

Table 2 Information about the geometry of the lithium–titanate battery. Parameters

Value

Size of a pouch cell (L  W  H) Thickness of the propene polymer separator Thickness of lithium–titanate electrode Thickness of copper foil Thickness of lithium electrode Thickness of aluminum foil Thickness of the exterior aluminum layer

36 mm  7 mm  68 mm 0.030 mm 0.066 mm 0.007 mm 0.056 mm 0.10 mm 2 mm

The COMSOL Multiphysics includes a set of predefined user interfaces with associated modeling tools, referred to as physics interfaces, for modeling common applications. Any number of modules can be seamlessly combined to handle challenging Multiphysics applications. Therefore, the above coupled model was embedded into COMSOL Multiphysics software, and then was used to simulate the thermal response of the battery. The model parameters used in this study were collected from the literature [9]. Tables 2 and 3 presents the values of model parameters used to describe the Li(Ni1/3Co1/3Mn1/3)O2/Li4Ti5O12 chemistry at full charged state.

3.1. Temperature variation with different current rates under different operation conditions In order to fully validate the effectiveness of this thermal model, the predicted and measured cells both cycled twice at a cycling rate of 0.5 C under the adiabatic condition. The experimental current and simulated current are under the same voltage variation in Fig. 2(a), the variation curves of temperature for the experiment and simulation are compared in Fig. 2(b). The comparison on the experimental and simulated current under the same voltage variation shows that there is some discrepancy in the process of constant voltage charging. The simulated current is lower than the experimental current in this process due to the characteristic of the lithium ion diffusion in the active material. Some resistance lies in the lithium-ions’ deintercalate/intercalate process on the electrodes, while no diffusion resistance exists in the numerical

3. Results and discussion In this work, a finite element method (COMSOL Multiphysics software) was used to simulate the temperature variation of lithium-ion batteries. The thermal behavior of a soft package 945 mA h lithium–titanate battery was examined. Besides, Accelerating Rate Calorimeter (ARC) experiments [21] were carried out to analyze the thermal behavior of lithium–titanate battery under the adiabatic condition. The adiabatic condition for this ARC Table 3 Thermal and physical properties of each material used in the mathematical model. Parameters

LTO electrode

NCM electrode

Electrolyte

Cu foil

Al foil

Average particle radius (lm) Diffusion coefficient (m2 s1) Electric conductivity (S m1) Reaction rate constant (m4 mol1 s1) Density (g cm3) Heat capacity (J kg1 K1) Thermal conductivity (W m1 K1)

0.01075 [7] 6.8  1015 [7] 100 [7] 3.0  103 [7] 3.510 [7] 1.4374 1.04

1.2 [20] 2.50  1016 [20] 139 [7] 2.0  1012 [20] 1.5 [20] 0.7 [20] 5 [18]

– 2.0  1010 – – 1.00898 1978.16 0.33

– – – – 8.933 385 398

– – – – 2.702 903 238

‘‘–” means no such property needed.

44

3.0 600

2.8

Voltage T_ex T_si

2.8

400

2.6

40

2.2

0

2.0 -200

1.8

2.4

Voltage, V

200

2.4

Current, mA

Voltage, V

2.6

36

2.2 32

2.0 1.8

28

1.6

-400

1.6 1.4

1.4 0

100

200

300

400

500

600

-600 700

o

3.0

Temperature, C

The voltage The experimental current The simulated current

24 0

100

200

300

400

500

Time, min

Time, min

(a) Current vs voltage

(b) Voltage vs temperature

600

700

Fig. 2. The comparison of experimental current and simulated current under the same voltage variation, temperature profiles at current rates of 0.5 C under the adiabatic condition.

Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905

simulation. For the temperature variation, it can be seen that the average temperatures of the cell increased in a stepwise manner. For the current rate of 1.0 C and 1.5 C, the comparisons of the simulated and experimental temperature corresponding to the voltage are shown in Fig. 3(a) and (b). From Figs. 2(b) and 3(a), it can be seen that the simulation results agree well with the experimental data for the current rates of 0.5 C and 1.0 C. While for the current rate of 1.5 C, no constant current charging process exists in the experimental curve of voltage and current in the cycling, hence, the cycling time of the simulation is longer than the experiment. The predicted temperatures and currents may not agree with the experimental results for 1.5 C. Additionally, the variation curve of voltage is not stable for the first CC discharging at 1.0 C. Nevertheless, the results show that this lithium–titanate battery model can simulate the dynamic changes of temperature and voltage especially for the cycle at 0.5 C. The natural convection with radiation (the emissivity is 0.25 [22]) is the default cooling condition at the boundaries. The profile of voltage and corresponding temperature variations at the current rate of 0.5 C, 1.0 C and 1.5 C under the natural cooling condition in the simulation are shown in Fig. 4(a)–(c), respectively. Fig. 4(d) shows the temperature comparison under different current rates. The temperature increases with the increasing current rate significantly. The temperature rise originates from the electrochemical reactions and ohmic heat when the current pass through the battery. The generation rate of reaction heat is proportional to the current rate, while the ohmic heat generation rate is proportional to the square of current rate according to the Joule’s law [23]. Therefore, the maximum temperatures that the batteries could achieve at the cycling rate of 0.5 C, 1.0 C and 1.5 C under the natural cooling condition are 27.35 °C, 28.04 °C and 30.09 °C, respectively. Based on the numerical result under the adiabatic condition as verified by the ARC experiment results in Fig. 2, the simulation under the radiative condition can be used to obtain the radiation heat loss. As a result, the radiative heat transfer was found to contribute 42% to the total heat transfer when the battery is operated under natural convection at 0.5 C cycling current. For the higher cycling rates, such as higher than 1.5 C, more attentions should be paid on the thermal management of the battery pack, such as assembling phase change materials, to ensure the normal operating condition. Additionally, there are two temperature peaks in one cycle as presented in Fig. 4. Furthermore, the first peak is greater than the second one, and the difference of the two peak values diminished with the increase of current rates. However, the temperature profiles show the similar tendency at different current rates during

To analyze the two temperature peaks more clearly, Figs. 5 and 6 shows the detailed temperature variation and the heat source in a process of discharge and charge at 0.5 C. As shown in Figs. 5 (a) and 6(a), the simulated discharge voltage agrees well with the experimental result, but the simulated charge voltage is 0.05 V higher than the experimental result. In the simulation, the diffusion resistance is ignored in the model, then the total resistance is smaller than the experimental one, under the same given power, less energy is lost in the simulation, which causes the battery has higher voltage than the experimental voltage. The electrochemical impedance exists at electrode/electrolyte interfaces during electrochemical processes. When lithium ion transferred through the insertion/desertion process in the intercalation electrode, the electrode polarization such as the charge transfer resistance, the electronic resistance of activated material and the resistance of SEI film that lithium ion transferring through cannot be ignored for lithium ion battery. Although the discrepancy may be nonnegligible, the simulation result is credible as long as the precision being in a reasonable range. The polarization effect can be seen in Figs. 5(b) and 6(b). It can be seen that the overpotential at the start and stop points of both discharge and charge cycle are very large. An electrochemical reaction is a combination of two half-cells and multiple elementary steps. Each step is associated with multiple forms of overpotential. The overall overpotential is the summation of many individual losses. When current flow through the electrodes, an electrolytic cell’s anode is more positive using more energy than thermodynamics require, and an electrolytic cell’s cathode is more negative using more energy than thermodynamics require. The overpotential increases with growing current density. Therefore, the higher overpotential is required to maintain the current flow inside the battery at the beginning of discharge and charge, and the same reason to the end of discharge and charge. In addition, the irreversible heat curves and the profile of the overpotential shows the similar trends, due to the dominant role of the polarization heat on the irreversible heat sources. As shown in Figs. 5(c) and 6(c), the generation rates of reversible and irreversible heat are of the similar order of magnitude at 0.5 C rates in the process of CC discharge and CC–CV charge, except for two beginning of discharge and charge. The heat generation of a

Voltage T_ex T_si

3.0

36

2.8

40

32

2.0 1.8

28

32

2.4 2.2

30

2.0 28

1.8 1.6

1.6 1.4

24 0

50

100

150

200

250

300

350

o

36

2.2

Voltage, V

2.4

34

2.6 o

2.6

Voltage, V

3.2. Temperature variation in the case of CC discharge and CC–CV charge at 0.5 C rate

44

Voltage T_ex T_si

2.8

Temperature, C

3.0

CC discharging and CC–CV charging. The reason for the existence of two peaks in the curve of temperature could be made clear in the following Section 3.2.

Temperature, C

900

26

1.4 24 0

25

50

75

100

125

Time, min

Time, min

(a) 1.0 C

(b) 1.5 C

150

175

200

Fig. 3. The comparison of experimental temperature and simulated voltage variation under the adiabatic condition at current rates of (a) 1.0 C and (b) 1.5 C.

901

Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905

2.8 2.6

26.0

2.0 1.8

Voltage, V

26.5 2.2

28.0

2.6

27.0

2.4

27.5

2.4

27.0

2.2 26.5 2.0 26.0

1.8

25.5

1.6 25.0

1.4 0

100

200

300 400 Time, min

500

600

1.6

25.5

1.4

25.0 0

700

100

200

400

500

600

700

500

600

700

(b) 1.0 C

Voltage Temperature

2.6

30

30

29

29

2.4 28 2.2 27

2.0 1.8

Temperature,°C

2.8

o Temperature, C

3.0

300

Time, min

(a) 0.5 C

Voltage, V

28.5

2.8

o Temperature, C

Voltage, V

Voltage Temperature

3.0

27.5

o Temperature, C

Voltage Temperature

3.0

0.5C 1.0C 1.5C

28 27

26

26

25

25

1.6 1.4 0

100

200

300 400 Time, min

500

600

700

(c) 1.5 C

0

100

200

300

400

Time,min

(d) The comparison between 0.5 C, 1.0 C and 1.5 C

Fig. 4. The voltage and temperature variations at the current rate of (a) 0.5 C, (b) 1.0 C, (c) 1.5 C under the natural cooling condition in the simulation and (d) the comparison of temperatures under different current rates.

lithium-ion battery during cycling is composed of reversible heat generation and irreversible heat generation. The variation curves of heat sources and temperature are shown in Figs. 5(d) and 6(d). The triggered chemical exothermic reactions will lead to the heat accumulate inside the battery, if the heat transferred from the battery to the surroundings is not sufficient. The heat generation increased early in the discharge and then decreased as the overpotential diminished. This phenomenon induces a rapid rise at the beginning of discharge and a slowing down increase later in the temperature in the cell. The heat generation rate decreases as current gradually diminish and then increase again as overpotential increased with the exhaustion of active materials. Correspondingly, the cell temperature rise sharply at the end of discharge. As to lithium-ion battery, the reversible heat for charge and discharge reactions are endothermic and exothermic, respectively [9]. Therefore, the heat generation rate during charge is less than that of discharge at the same current rate for the battery [24]. Consequently, the temperature declines during CC charging. As a result, the first temperature peak appears. As the negative electrode approaches saturation during CV charging, the exchange current density decreases and kinetics resistance increases in the cell. Hence, a larger (more negative) overpotential is then required to maintain the current [25], resulting in more irreversible heat released, as shown in Fig. 6(b) and (c). Consequently, the heat generation rate increases sharply, causing the temperature to rise again. After the negative electrode reached the saturated condition, the temperature declines as the overpotential diminished gradually. That is why the second peak exists

in the curve of the temperature. The reason why two peaks appear in the curve of temperature at 1.0 C and 1.5 C is similar to that of the current rate of 0.5 C. Additionally, the experimental temperature curve in the constant current and constant voltage charging shows rising firstly than descending latter tendency in the Ref. [8], the upward trend on the temperature change curves in the process of constant current discharging was well verified in the Ref. [4]. Though the active material and the capacity of the battery are different, the mechanism of heat generation is similar. Furthermore, the heat generation in the discharge is larger than that of the charge process in the cell as shown in Figs. 5(c) and 6(c). Therefore, the existence of two temperature peaks on the simulated temperature curve in the CC discharge and CC–CV charge cycling is reliable. 3.3. Temperature variation under different cooling conditions The temperature variations at 0.5 C discharging and charging cycles at initial temperature of 25 °C under three different cooling conditions are shown in Fig. 7. During the whole cycling, the heat generated in electrochemical process is larger than the heat released to the environment. Therefore, the temperature inside the battery is higher than the initial (ambient) temperature. There are three cooling conditions as shown in Fig. 7, i.e. natural cooling condition (Na.), convection condition (Co.), and radiative heat transfer condition (Ra.). The natural cooling condition refers to the use of ventilation or natural heat sinks for heat dissipation

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Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905 2.8

Voltage,V

2.4 2.2 2.0 1.8 1.6

Qrxn

40

0.03

η

30 0.02 20 0.01 10

Overpotential,V

The irreversible heat, W/m3

Voltage-exp Voltage-sim

2.6

0.00

0

1.4 0

20

40

60

80

100

120

0

140

20

Time,min

40

60

80

100

120

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voltage

simulation 3500

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o

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0

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Fig. 5. The simulated thermal behavior in the process of CC discharge at 0.5 C.

of the battery, and the heat transfer coefficient is calculated to 2 W m1 K1 at the cycling rate of 0.5 C. The convection is the concerted, collective movement of groups or aggregates of molecules within fluids and rheids, through advection or through diffusion or as a combination of both of them. The convection heat transfer coefficient is taken as 2.0 W m2 K1 in the simulation. The radiative heat transfer from one surface to another is equal to the radiation entering the first surface from the other, minus the radiation leaving the first surface. The spectral absorption component is taken as 0.5 in the simulation. The battery can get into thermal balance under these three cooling conditions. The range of the temperature fluctuations in the cells are 0.89 K, 1.36 K, and 1.39 K for natural cooling condition, convection condition, and radiative heat transfer condition, respectively. The natural cooling process includes the convection and radiative heat transfer processes. Therefore, under the natural cooling process, the temperature rise is the least one than that of convection and radiation. The maximum temperature difference is 0.89 K under the natural cooling condition during the dynamic cycling of batteries as shown in Fig. 8. In order to get the same cooling effect, that is the temperature rise is same or very close to each other, the effect of radiation was ignored firstly. Under this condition, the calculated convection coefficient is 3.455 W m2 K1. This coefficient was calculated through a conventional Nusselt number (Nu) correlation [26,27], where the Nu is the ratio of convective to conductive heat transfer across (normal to) the boundary in heat transfer at a boundary (surface). By using this method, the contribution of the cooling effect for different heat transfer ways can be obtained.

Fig. 8 shows that the convective heat transfer coefficient increased to 3.455 W m2 K1, and the temperature variation is close to the cell cycling under natural cooling condition. The heat transfer ratio is calculated based on the ratio of average temperature drop to the total temperature drop during cycling. That is,

f Ra ¼ DT Ra =ðDT Co þ DT Ra þ DT Cd Þ f Co ¼ DT Co =ðDT Co þ DT Ra þ DT Cd Þ where fRa is radiative heat transfer ratio, DT Ra is average temperature drop under radiative heat dissipation condition only, DT Co is average temperature drop under convection heat dissipation condition only. DT Cd is the average temperature drop under conduction heat dissipation condition only, fCo is convection heat transfer coefficient. Ignoring the conduction heat dissipation as the battery is hanged. The average adiabatic temperature rise is obtained from the Fig. 2, and then, the heat transfer ratio can be calculated. Using this method, the radiative heat transfer ratio was calculated contributes 42.11% to the total heat transfer. This implies that the radiative heat transfer cannot be omitted when the battery is cycling under natural convection. 3.4. Temperature distribution under natural cooling condition Based on symmetry characteristics of the battery, one quarter of the battery rather than the whole battery was selected as the computing object for time saving. The temperature distribution at the

903

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Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905

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Fig. 6. The simulated thermal behavior in the process of CC–CV charge at 0.5 C.

Na. Ra. Co.

Na. Ra. -2 -1 hc=3.455 W m K

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Fig. 8. The comparison of different convective heat transfer coefficient.

center X = 10.0 mm and Y = W/2 at cycle times of 335 min with 0.5 C for initial temperature of 25 °C under natural cooling condition is shown in Fig. 9. According to Section 2, the heat conduction is the only significant contributor to heat transfer for the interior of the cell. The arrow means the conductive heat flux transfer

direction. The temperature in the center of the computational domain is higher than that of the other regions. The temperature near the current collector is lower than the temperature inside the battery. However, in Gerver and Meyers’s work [11], the temperature at the collector tab is higher than that of the other parts. This is because that the heat generation inside

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Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905

Fig. 9. The temperature distribution at the cut plane of Y = W/2, X = 10.0 mm at cycle times of 335 min at 0.5 C (the unit is °C).

the battery composed of reversible and irreversible heat is higher than the Joule heat generated by large current flows in the current collector. Under a higher discharge rate, such as 5 C in their work, Joule heat contributes the total heat generation, and at the collector tab a lots of heat was generated and caused the temperature rising more quickly than other place. In lower discharge rate, such as 0.5 C here, the temperature rise is dominated by the heat transfer to the environment, then the center has the higher temperature. The higher conductivity of tabs is responsible for lower Joule heating, and also higher heat dissipation at the tabs contributes to lower temperature. Additionally, because of the existence of the convective and radiative heat transfers on the surface and the bigger cooling surface area, the temperature on the surface is lower than the temperature inside the battery and the current collector. For the current rate of 0.5 C, the maximum temperature difference is 0.027 K inside this battery, the temperature distribution is nearly uniform.

4. Conclusions Numerical simulation of heat transfer within batteries is an effective tool to obtain fundamental data on how heat generation conducted out of the battery and the temperature variation correspondingly. The transient and thermal–electrochemical coupled model was implemented with finite element method. Firstly, the results of the battery cycling at different CC discharging and CC– CV charging rates show that the temperature increase with the increasing current. Furthermore, two temperature peaks were observed in one cycle under different cooling conditions. Secondly, the worse thermal boundary cooling conditions, the bigger the magnitude of the temperature fluctuation inside the battery. Additionally, the temperature in the center of the computational domain is higher than that of the other region. Finally, the radiative heat transfer cannot be omitted when the battery is cycling under natural convection at 0.5 C cycling rates, and the radiative heat

Q. Wang et al. / International Journal of Heat and Mass Transfer 93 (2016) 896–905

transfer contributes 42% to the total heat transfer. The simulation results is beneficial for understanding the thermal behavior of the battery module under various discharging and charging conditions, and may expand the application of lithium titanate battery in hybrid electric vehicles. Conflict of interest None declared. Acknowledgements This study is supported by the National Natural Science Foundation of China (Nos. 51176183 and 11374272), the Fundamental Research Funds for the Central Universities (No. WK2320000034), and CAS-EU Partner Programme – Chinese H2020 Matching Fund from CAS (No. 211134KYSB20150004). Dr. Q.S. Wang is supported by Youth Innovation Promotion Association CAS, China (No. 2013286). References [1] S.G. Chalk, J.F. Miller, Key challenges and recent progress in batteries, fuel cells, and hydrogen storage for clean energy systems, J. Power Sources 159 (1) (2006) 73–80. [2] Q. Wang, P. Ping, X. Zhao, G. Chu, J. Sun, C. Chen, Thermal runaway caused fire and explosion of lithium ion battery, J. Power Sources 208 (2012) 210–224. [3] D. Bernardi, E. Pawlikowski, J. Newman, A general energy balance for battery systems, J. Electrochem. Soc. 132 (1) (1985) 5–12. [4] S.C. Chen, C.C. Wan, Y.Y. Wang, Thermal analysis of lithium-ion batteries, J. Power Sources 140 (1) (2005) 111–124. [5] Y. Chen, J.W. Evans, Heat transfer phenomena in lithium-polymer-electrolyte batteries for electric vehicle application, J. Electrochem. Soc. 140 (7) (1993) 1833–1838. [6] J.N. Harb, R.M. LaFollette, Mathematical model of the discharge behavior of a spirally wound lead-acid cell, J. Electrochem. Soc. 146 (3) (1999) 809–818. [7] D.H. Jeon, S.M. Baek, Thermal modeling of cylindrical lithium ion battery during discharge cycle, Energy Convers. Manage. 52 (8–9) (2011) 2973–2981. [8] U.S. Kim, J. Yi, C.B. Shin, T. Han, S. Park, Modelling the thermal behaviour of a lithium-ion battery during charge, J. Power Sources 196 (11) (2011) 5115– 5121. [9] K. Onda, T. Ohshima, M. Nakayama, K. Fukuda, T. Araki, Thermal behavior of small lithium-ion battery during rapid charge and discharge cycles, J. Power Sources 158 (1) (2006) 535–542.

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