An investigation of heat transfer and capacity fade in a prismatic Li-ion battery based on an electrochemical-thermal coupling model

Journal Pre-proofs An investigation of heat transfer and capacity fade in a prismatic Li-ion battery based on an electrochemical-thermal coupling model Guiwen Jiang, Ling Zhuang, Qinghua Hu, Ziqiang Liu, Juhua Huang PII: DOI: Reference:

S1359-4311(19)36382-3 https://doi.org/10.1016/j.applthermaleng.2020.115080 ATE 115080

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Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

14 September 2019 4 February 2020 12 February 2020

Please cite this article as: G. Jiang, L. Zhuang, Q. Hu, Z. Liu, J. Huang, An investigation of heat transfer and capacity fade in a prismatic Li-ion battery based on an electrochemical-thermal coupling model, Applied Thermal Engineering (2020), doi: https://doi.org/10.1016/j.applthermaleng.2020.115080

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An investigation of heat transfer and capacity fade in a prismatic Li-ion battery based on an electrochemical-thermal coupling model Guiwen Jiang1,2*, Ling Zhuang1, Qinghua Hu1, Ziqiang Liu3, Juhua Huang3 1 School of Physics and Electronic Information, Shangrao Normal College, 2 Research Center of Intelligent Engineering Technology of Electronic Vehicle Parts in Jiangxi Province, Shangrao 334001, China; 3 School of Mechatronics Engineering, Nanchang University, Nanchang 330031 Abstract: A large format lithium-ion (Li-ion) battery significantly suffers from a

nonuniform thermal distribution, which adversely affects the electrochemical reaction inside the battery and accelerates its degradation. In this work, a one-dimensional (1D) electrochemical-three-dimensional (3D) thermal coupling model is developed to investigate the heat transfer of a prismatic Li-ion battery when cooling different external surfaces. Simulation parameters are considered, including a forced convection cooling coefficient, h, the surface area of heat dispersion and the battery size. Despite the side surfaces of the prismatic Li-ion battery being small, the orthotropic thermal conductivity of the prismatic battery improves the planar heat transfer and effectiveness of forced convection cooling on the small side surfaces. It is found that the temperature distribution in the prismatic battery with forced convection cooling on the small side surfaces is more uniform than cooling the large front surfaces. At h=100 W/m2 K, as the battery size increases, the maximum temperature difference of the prismatic battery with small side surface cooling stays at a constant value of 3.18°C. In addition, the effect of operating temperature on the capacity fade of Li-ion batteries during cycling is investigated. It is found that a high operating temperature accelerates the parasitic lithium/solvent reduction reaction, and the above reduction reaction results in the loss of Li ions and increases the rate of capacity fade during the cycling process. *

Corresponding author: E-mail address: [email protected]

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Keywords: Li-ion battery; Electrochemical-thermal coupling model; Temperature distribution; Capacity fade. Highlights 

An electrochemical-thermal coupling model was developed for a large battery.



The orthotropic thermal conductivity improves the planar heat transfer of the battery.



The temperature uniformity is improved by forced convection cooling on the small side surfaces.



The effect of the operating temperature on the electrochemical properties during cycling was discussed.

1. Introduction With the shortage of fossil energy resources and the increasing severity of air pollution, it is urgent that electric vehicles (EVs) replace vehicles with traditional internal combustion engines. Li-ion batteries are the first candidates for emerging EVs due to their superior performance, such as high energy and power density [1, 2], long cycling life and no memory effect [3]. However, the main obstacle to Liion battery operation is the generation of a large amount of heat inside the batteries at high C-rate discharging, which results in the temperature rising too rapidly. Li-ion battery performance is sensitive to the operating temperature. Waldmann et al. [4] pointed out that the decline in battery capacity was accelerated with increasing temperature at operating temperatures higher than 25°C. Several studies [3, 5, 6] have demonstrated that the optimum operating temperature of Li-ion batteries should be controlled within 25~40°C and that battery aging would be intensified for operating temperatures beyond 45°C [7]. Therefore, the thermal management of a Li-ion battery is essential for inhibiting a rapid increase in temperature. A well-designed thermal

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management system should not only maintain the battery pack temperature within an optimum range but also control the temperature difference of each cell in a narrow gap, usually less than 5°C. Many numerical simulation studies [8-12] have been performed on forced air and liquid cooling of Li-ion batteries, which propose different cooling strategies to improve thermal distribution uniformity across each cell in a battery module. Xu and He [13] pointed out that the heat dissipation performance of a battery module was greatly improved by the optimization of battery arrangements and air inlets/outlets. Subsequently, He and Ma [14] asserted that the nonuniform temperature of the battery module was reduced from 4 to 1°C by employing reciprocating cooling flow compared to results with unidirectional cooling flow. Furthermore, Rao et al. [15] developed a novel liquid cooling system with aluminum blocks of variable length attached to battery surfaces, thus improving the temperature uniformity of the battery module. A large battery consists of a multitude of cells connected in parallel to satisfy the desired capacity. Therefore, there exists a great temperature gradient inside the battery resulting from the thermal inertia of the battery and an external cooling system. For instance, An et al. [16] found that the temperature presents a parabolic distribution in the direction of battery thickness and that the temperature gradient increases with cell number and cooling strength. Xu et al. [17] demonstrated that the temperature gradient in the axial direction of a cylindrical battery is higher than that in the radial direction under natural convective cooling conditions due to the heat dissipation effect of the current collecting tabs. As mentioned above, the improvement of the temperature distribution in a battery module has been most investigated in references employing numerical simulation methods; however, few studies have focused on how to improve the uniformity of temperature distribution inside a battery.

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An uneven temperature distribution inside batteries will result in the mismatch of performance parameters such as the internal resistance, diffusion coefficient and electrochemical reaction rate of the cells at different layers. The divergence of cells at different layers induces unbalanced charge-discharge, accelerating the capacity fade and shortening the life span of the overall battery [16,18]. In recent years, an electrochemical-thermal coupling model has played an important role in research on Li-ion battery performance [18-25]. For instance, Panchal et al. [21-23] developed an empirical battery thermal model and an electrochemical battery thermal model for a large prismatic Li-ion battery, which was validated with experimental data. Mastali et al. [24] developed a simplified electrochemical multiparticle model and a homogenous pseudo-two-dimensional model, and both models could more accurately predict the operating voltage of half-cells and cost much less simulation time compared to the standard Newman pseudo-two-dimensional model. Tran et al. [25] presented a 1Dcoupled degradation-electrochemical-thermal model for a large format cylindrical Liion cell. Using these models mentioned above, valuable information about heat generation power, capacity fade and temperature-dependent electrochemical performance is available, which is not easily accessible through experiments. In this work, a prismatic Li-ion battery with different sizes is considered for a thermal management study. A 1D electrochemical-3D thermal coupling model is developed to investigate the heat transfer behavior inside a prismatic Li-ion battery with different convection cooling coefficients h on different outer surfaces. More innovatively, an orthotropic thermal conductivity, as a new parameter, has been incorporated into the heat transfer computation. We also develop an electrochemicalthermal aging model of a Li-ion cell and investigate the influence of operating temperature on the capacity fade of the cell. The models described above are

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numerically solved in a COMSOL Multiphysics 5.2 platform using a Finite Elements Method. The numerical computations are conducted on a desktop computer with a 3.0 GHz core processor and 8 GB random access memory.

2. Simulation model The sample image of the prismatic Li-ion battery is presented in Fig. 1, using Li[Ni1/3Co1/3Mn1/3]O2 as the positive electrode, graphite as the negative electrode and LiPF6/EC:EMC=2:1 (by volume) as the electrolyte. The prismatic battery has a nominal capacity of 50 Ah, nominal voltage of 3.65 V, width of 148 mm, thickness of 26 mm and height of 96 mm.

side surface

front surface Fig. 1 Sample image of a prismatic Li-ion battery. 2.1. Electrochemical model A Li-ion battery consists of many cells in parallel, and the electrochemical model of each cell can be simplified as a 1D model due to Li-ion transfer mainly in the direction perpendicular to the cell laminated structure. Fig. 2 shows a 1D electrochemical model of a Li-ion cell that involves five parts: a positive electrode collector, a positive electrode, a separator, a negative electrode and a negative electrode collector. A 1D electrochemical model was established by Newman et al. [26] on the basis of porous electrode theory and the principles of mass, charge conservation and electrochemical kinetics.

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Fig. 2 Schematic illustration of the 1D electrochemical model.

(a) Mass conservation Solid phase: The Li-ion conservation equation of the electrode particles is based on Fick's diffusion law, and can be expressed as follows:

c cs 1   2 ( Ds r 2 s ) r t r r

(1)

Solution phase: Li-ion transfer in the electrolyte is determined by Fick’s diffusion law and concentrated solution theory, and can be expressed as follows:

 ( e ce )  c S j  ( Deeff e )  a loc (1  t ) t x x F

(2)

Deeff  De e e

(3)

where cs and ce are the Li-ion concentration in the solid phase (electrode active material) and solution phase (electrolyte), respectively; Ds and De are the Li-ion diffusion coefficients in the solid phase and electrolyte, respectively; εe is the volume fraction of the electrolyte; Sa is the specific surface area; jloc is the local current density of the electrode/electrolyte interface; F is Faraday's constant; t+ is the transference number of Li ions in the electrolyte; and γe is the Bruggeman exponent for the electrolyte.

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The concentration gradient of lithium is zero in the center of solid phase spherical particles because there is no lithium source at this position, while it is related to jloc on the surface of spherical particles. In the solution phase, the ionic flux at the interface of the electrode/current collector is also set to zero due to the impermeability of the current collectors for the electrolyte. Therefore, the boundary conditions for the Li-ion transport process in the solid phase and solution phase are shown below:

cs r Ds

ce x

r 0

cs r

0

r  rp

x  0, x  L

(4)



jloc Sa F

(5)

0

(6)

(b) Charge conservation Solid phase: The charge conservation equation for electron transport in the solid phase is governed by ohm’s law: is   seff

 s x

 seff   s s 

(7) (8)

s

where is is the electron current density in the solid phase,  seff is the effective electrical conductivity of the solid phase, φs is the solid phase potential, εs is the solid phase volume fraction, and γs is the Bruggeman coefficient for the solid phase. Solution phase: The charge balance equation for Li-ion transfer in the electrolyte is given below: ie   eeff

e 2 RT  eeff d ln f  ln ce  (1  t )(1  ) x F d ln ce x

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(9)

 eeff   e e

e

(10) where ie is the Li-ion current density in the electrolyte, φe is the liquid phase potential,

 eeff is the effective electrical conductivity of the electrolyte, R is the universal gas constant, T is the battery temperature, and f is the molecular activity coefficient of the electrolyte. At the electrode/separator interface, the insulation boundary condition is set for the electron current because electrons cannot pass through the separator. The current collector presents an impermeable wall to ionic flux, so the boundary condition at the electrode/current collector interface for ionic current is insulated. The negative terminal is grounded, and the positive terminal is applied to the working current of the battery. Therefore, the boundary conditions for charge conservation are described as follows:

 seff

 s x

e x

s

x  Ln , x  Ln  Lsep

x  0, x  L

x 0

0

(11)

0

(12)

 0 ;  seff

 s x

xL

 iapp

(13)

where iapp is the applied current density of the cell. (c) Electrochemical kinetics During the electrochemical reaction process, the local current density jloc on the surface of the electrode is given by the Butler-Volmer equation [27]:

  F   F   jloc  j0 exp[ a ]  exp[ c ] RT RT   (14) where j0 is the exchange current density provided by Eq. (15):

j0  Fk0 (ce ) a (cs ,max  cs , surf ) a (cs , surf )c

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(15)

and the local overpotential η is defined as follows:

   s  e  U oc

(16)

where k0 is the reaction rate constant;  a and  c are the charge transfer coefficients of the anode and cathode, respectively; cs ,max and cs , surf are the maximum concentration and surface concentration of lithium in the solid phase, respectively; and Uoc is the open circuit voltage of the cell. The electrochemical parameters and some temperature-dependent transmission parameters are listed in Tables 1 and 2, respectively. Table 1 Electrochemical parameters used in the 1D model [28-30] Parameters

Unit

εs εe Li rP cs,max SOCmax SOCmin c0 αa αc γ Ds De Ea,i σs σe k0 t+ Uref F Tref

μm μm mol/m3 mol/m3 m2/s m2/s kJ/mol s/m s/m m2.5mol-0.5s-1 V C mol-1 °C

Al foil 7 -

Cathode Li[Ni1/3Co1/3Mn1/3]O2 0.43 0.40 55 1.7 29000 0.975 0 29000*0.975 0.5 0.5 3.15 Eq. (17) 30 3.8 5×10-10 Eq. (23) -

Separator 0.37 30 1200 Eq. (19) Eq. (20) 0.363 96487 298.15

Anode graphite 0.384 0.444 55 2.5 31507 0.98 0 31507*0.98 0.5 0.5 3.15 Eq. (18) 20 100 2×10-11 Eq. (24) -

Cu foil 10 -

Table 2 Temperature-dependent transmission parameters used in the 1D model [31-34]

Parameters Diffusion coefficient of Li-ions in the electrode

Equations Ds , p  1014  exp[

30000 1 1 (  )] 8.314 T Tref

Ds ,n  1.4523 1013  exp[

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20000 1 1 (  )] 8.314 T Tref

(17) (18)

Diffusion coefficient of Li-ions in the electrolyte

De  10

Ionic conductivity

( 4.43

54.0  0.220.001ce )  4 T  229.0  0.005 ce

σe=1.2544ce×10-4(-8.2488+0.053248T-2.9871×10-5T2 +0.26235ceT2+0.22002ce2-1.765×10-4ce2T)2

(20)

ce,i

, (i  p, n)

(21)

U oc ,i

(22)

State of charge (SOC)

i 

ce,i ,max

U oc ,i  U ref ,i  (T  Tref ) Open circuit potential

(19)

T

U ref , p  10.27 p4  23.88 p3  16.77 p2  2.595 p  4.563 (23) U ref ,n  0.1493  0.8439 exp(61.79 n )  0.3824 exp(665.8 n )  exp(39.42 n  41.92)  0.0313arctan(25.59 n  4.099) 0.009434 arctan(32.49 n  15.74) (24)

2.2. Thermal model In the 3D thermal model, the energy conservation equation based on the basic principle of heat transfer can be expressed as:

C p

T  2T  2T  2T   x 2   y 2  z 2  q t x y z

(25)

where λx, λy and λz are thermal conductivities in the x, y and z directions of the battery, 

respectively. The value of q refers to heat generation in the cell, which includes 





reversible heat q re and irreversible heat q irr . The value of q re is mainly related to the entropy change of the electrode active material and is formulated as [35]: 

q re  S a jlocT

U oc T

(26)





The value of q irr consists of the active polarization heat (also called reaction heat) q act 



and ohmic heat q ohm . q act arising from the electrochemical reaction, which is given by [35]: 

q act  S a jloc

(27)

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

is mainly caused by electron and ionic charge transfer in the

The value of q ohm

electrode material and electrolyte, which is expressed as follows [31,36]: 

q ohm  is 

 s   ie  e x x

(28)

The thermal conductivity λy is the same as λz because their directions are parallel to the electrode plate, while the x direction indicates the cell thickness direction, which is perpendicular to the electrode plate. The equivalent thermal conductivities of the cell in the x, y, and z directions are calculated based on a thermal resistance model in parallel and series, which can be expressed as the following:

 y  z 

x 

Al LAl   p Lp  sep Lsep  n Ln  Cu LCu LAl  L p  Lsep  Ln  LCu

LAl  L p  Lsep  Ln  LCu LAl L p Lsep Ln LCu    

Al

p

sep

n

(29)

(30)

Cu

Without considering the thermal radiation of the battery, the boundary condition of the thermal model based on Newton’s cooling law is expressed as:  （

     )T  h(T  Tamb ) x y z

(31)

where h is the heat transfer coefficient and Tamb is the ambient temperature. The thermophysical property parameters of the battery are listed in Table 3. Table 3 Thermophysical property parameters used in the 3D thermal model [28] Parameters

Density (kg/m3)

Separator Cathode Anode Copper foil Al foil

1009 2328.5 1347.3 8933 2770

Heat capacity (J/kg·K) 1978 1269.2 1437.4 385 875

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Thermal conductivity (W/m·K) 0.334 1.58 1.04 398 170

2.3. Electrochemical-thermal coupling model A 1D electrochemical model proposed by Newman et al. [26] was adapted to calculate the heat generation of Li-ion cells. The heat generation rate by the 1D model, as a heat source, is coupled to the 3D thermal model to calculate the temperature distribution inside the battery. In turn, the obtained average temperature from the 3D model is fed back to the 1D electrochemical model, as shown in Fig. 3. As a result, the heat generation rate of the 1D model is influenced by temperature-dependent electrochemical parameters due to increasing temperature. The electrochemical parameters related to temperature are derived by the Arrhenius equation [37]:

 0 (T )= 0, ref exp[

Ea ,i

1 1  )] R Tref T (

(32)

where χ0(T) is the temperature-dependent parameter, Ea,i is the activation energy, and χ0,ref is the parameter at reference temperature Tref =25°C.

Fig. 3 Coupling between electrochemical model and thermal model using average values for the temperature and generated heat.

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2.4 . Capacity fading model Li ions intercalate and deintercalate in the anode active material during the charging and discharging process, with a corresponding solvent reduction side reaction occurring at the anode/electrolyte interface that forms a passivation layer on the anode. A passivation layer film is also known as a solid/electrolyte interphase (SEI), which will continue to grow as the cycling process proceeds, leading to a capacity fade mechanism with Li-ion cells. To date, although much research has been performed on the SEI growth model, a simple, kinetics-driven SEI film growth model proposed by Ramadass et al. [38] is adopted to simulate capacity fade, which is expressed as:

S  2 Li   2e   P

(33)

where S stands for the solvent and P denotes the product formed in the reaction. The production of P results in a loss of cyclical lithium, causing cell capacity fade. The side reaction kinetics can be described by the following kinetics equation [39] for the local side reaction current density jside on the anode particle surface: jside   jside,0 exp(

F s ) 2 RT

where jside,0 is defined as the exchange current density and  s

(34) refers to the

overpotential of the side reaction, which is described as follows:

 s   s  e  U side  jRsei

(35)

where Rsei is the SEI layer resistance, which rises with an increase in the thickness of the SEI layer; and j is the total reaction current in the anode, which includes the main reaction current of Li-ion intercalation jloc and the side reaction current jside. The rate of increase of the SEI layer thickness δsei on the negative electrode is determined by Faraday’s law:

 sei j M   side sei t 2 F  sei

(36)

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where Msei and ρsei are the molar weight and density of the product P (SEI layer). The resistance of the SEI layer is related to δsei, which can be calculated with Eq. (37):

Rsei 

 sei  sei

(37)

where κsei is the electrical conductivity of the SEI layer. The parameters used in the capacity fading model are listed in Table 4. Table 4 Parameter values used for the side reaction [28, 39, 40] Parameter jside,0 (A/m2) Uside (V) Msei (kg/mol) ρsei (kg/m3) κsei (s/m)

Value 10-3 0.4 0.1 2100 3.97×10-7

3. Results and discussion 3.1 Temperature distribution in a prismatic battery monomer A large battery is prone to nonuniform thermal and electrochemical properties due to the temperature gradient in the battery. Obviously, the temperature gradient increases with increasing cooling strength and heat generation power of the battery. For a prismatic battery, a cooling medium can be attached to the front surfaces or the small side surfaces. Although the front surface of the prismatic battery has a much larger area for heat dissipation, the high thermal conductivity in the planar direction of the prismatic battery makes the heat generation inside the battery transfer more easily to the small side surfaces of the battery. It is interesting and of great importance to investigate the thermal distribution inside the battery with forced air or liquid cooling on the different outer surfaces of a battery. For the thermal management of a battery monomer, forced air or liquid cooling can be considered as having different convection heat transfer coefficients h. High-velocity forced air cooling is assumed to have a convection heat transfer coefficient of h=50 W/m2 K [41], and h=100 or 150 W/m2 K

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is considered for a liquid cooling system [42]. The ambient temperature was set to 298.15 K, and three kinds of thermal management conditions (i.e., h=50, 100, 150 W/m2 K) were considered. The discharge rate of the battery, generally defined as the C-rate, is the degree of discharge speed. If it takes 1 h to discharge the battery completely, the discharge rate is 1C. Similarly, if the battery completely discharging needs 0.2 h, it is called a 5C discharge. Fig. 4 shows the minimum, maximum and average temperature responses of the battery with h=100 W/m2 K during the 5C charge-discharge cycling process (cycle time=600 s). As shown in Fig. 4, the difference in the rate of temperature increase between the charging and discharging processes is attributed to the difference in entropy change for the charging and discharging electrochemical reactions. The temperature difference with forced convection cooling on the small side surfaces of the battery is significantly lower than cooling the large front surface due to the higher thermal conductivity in the planar direction. At a charging-discharging time of 900 s, the temperature difference with small side surface cooling is 1.5°C; however, it reaches 4.8°C with large front surface cooling, as shown in Fig. 4 (a) and (b). The maximum temperature of the battery reaches approximately 47°C and 43°C with small side surface cooling and large front surface cooling, respectively, which is attributed to the larger area for heat dissipation of the large front surface than that of the small side surface.

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Fig. 4 Temperature responses of the battery with different outer surfaces being cooled during the 5C discharge-charge cycling process: (a) small side surfaces and (b) large front surfaces.

The temperature distributions within the battery at different charge-discharge times (t=200, 400, 600, 800 s) are shown in Fig. 5. For large front surface cooling, the temperature distribution curve in the thickness direction presents a parabolic shape, and the temperature difference is significantly larger than that when cooling the small side 16

surfaces. The temperature difference in the thickness direction of the battery obviously increases during charging-discharging, and at t=600 and 800 s, the maximum temperature difference reaches approximately 4.3°C and 5.1°C, respectively. For small side surface cooling, the temperature distribution in the planar (width) direction is basically uniform and presents little difference for t=200 and 400 s. With increasing charge-discharge time, the temperature difference slightly increases, and at t=600 and 800 s, the maximum temperature difference reaches approximately 1.1°C and 1.3°C, respectively. The thermal conductivity in the planar direction of the battery is much higher than that in the cross-plane (thickness) direction, which makes it easier to transfer the heat generation inside the battery to the small side surfaces. Therefore, the temperature gradient in the battery with forced convection cooling on the small side surfaces is significantly lower than cooling the large front surfaces.

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Fig. 5 Temperature distributions in the X (thickness) and Y (width) directions of the battery at a 5C discharge-charge rate and cooling different external surfaces: (a) large front surfaces and (b) small side surfaces.

It is desirable to design a large Li-ion battery to improve the energy density of the battery; however, a large battery size may result in a large temperature gradient. As mentioned above, the 3D sizes of the battery in the simulation are assumed to be 148 mm (width), 26 mm (thickness) and 96 mm (height); the batteries in the simulation are scaled up by a factor of 1.5, 2, 2.5 and 3 to investigate the temperature distribution inside the battery. Fig. 6 demonstrates the maximum and minimum temperatures of batteries with different sizes during the 5C discharging-charging process at t=800 s. When the battery thickness is increased from 26 to 39 mm, the minimum temperature of the battery with small side surface cooling or large front surface cooling increases slightly. As the size of the battery increases further, the minimum temperatures of the small side and large side surfaces remain almost constant at approximately 41°C and 31°C, respectively. The maximum temperature with small side surface cooling increases with an increase in the battery size, but the rate of increase decreases

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accordingly. When the battery thickness increases from 65 to 78 mm, the maximum temperature only increases by 0.32°C. For large front surface cooling, the variation trend of the maximum temperature is the same as that with small side surface cooling. Interestingly, the same maximum temperature inside the battery is observed with the cooling of either external surface when the thickness of the battery increases to 78 mm. The rate of increase of the temperature difference decreases with increasing battery size, and the maximum temperature difference is close to a stable value of 3.18°C when cooling the small side surfaces; however, it reaches 10.26°C when cooling the large front surfaces. Obviously, in comparison with large front surface cooling, forced convection cooling on the small side surfaces of the battery is beneficial for providing uniformity to the temperature distribution within the battery.

Fig. 6 Maximum and minimum temperature dependence of the battery on battery size when cooling the different surfaces.

Fig. 7 shows the temperature field of the battery (thickness of 26 mm) with the different surfaces being cooled for t=800 s. The temperature distribution of the battery when cooling the small side surfaces is basically uniform, and its maximum temperature

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difference is less than 2°C. When cooling the large front surfaces, a large temperature difference is observed, and the maximum temperature difference reaches approximately 5°C. (b)

(a)

Fig. 7 Temperature field of the battery with forced convection cooling on the different surfaces: (a) small side surfaces and (b) large front surfaces.

There is no doubt that enhancing the forced convection cooling coefficient h will significantly decrease the battery operating temperature, thus improving the thermal safety of the battery. Moreover, it will also result in a large temperature gradient in the battery due to the active cooling of the outer surfaces of the battery. To evaluate the effect of cooling strength on the maximum temperature and temperature distribution within the battery, three kinds of convection cooling coefficients h=50 W/m2 K, 100 W/m2 K and 150 W/m2 K were considered for a large prismatic battery (3D size is 39 mm, 144 mm and 222 mm, respectively). The temperature distribution inside the battery with different h values on the external surfaces is demonstrated in Fig. 8. With small side surface cooling, the maximum temperature in the battery decreases by approximately 1.73°C when h increases from 50 to 150 W/m2 K, and the temperature difference only increases to approximately 2.7°C. However, with the same convection

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cooling coefficient h on the large front surfaces, the maximum temperature also decreases by approximately 1.7°C, but the temperature difference increases to approximately 9°C. Pesaran [43] pointed out that it was desirable to have a relatively uniform temperature distribution with a temperature difference less than 5°C to decrease the nonuniformity of the electrochemical reaction rate. Obviously, for a large battery (thickness of 39 mm) with high convection cooling (h=150 W/m2 K) on the small side surface, the maximum temperature difference inside the battery remains at a relatively low value of less than 5°C.

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Fig. 8 Temperature distribution within batteries with different convection cooling coefficients on the different surfaces: (a) small side surfaces and (b) large front surfaces.

3.2. Capacity fade during cycling The terminal voltage of the cell with 5C discharging gradually decreases with an increase in the number of cycles, as shown in Fig. 9. The terminal (operating) voltage of the cell is equal to the open circuit voltage minus the voltage loss caused by the internal resistance. As described previously, the parasitic lithium/solvent reduction reaction forms an SEI film layer during the charging process, which occurs on the surface of the anode. The loss of lithium during cycling and the increase in the SEI layer resistance, which arises from the growth of the SEI, results in a capacity fade and a decline in the open circuit voltage.

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Fig. 9 Cell voltage response at 1C discharging for different cycling amounts.

Fig. 10 shows the temporal history of the cell operating voltage during the 50th cycle at different operating temperatures. It is found that the operating voltage of the cell decreases with an increase in operating temperature, showing that the high operating temperature will accelerate the capacity fade of the cell. For example, at t=1000 s, the operating voltage of the cell deceases to 3.88 V, 3.84 V and 3.80 V for operating temperatures of 25°C, 35°C and 45°C, respectively. A fresh cell that is discharged continuously at a 1C rate will theoretically take one hour to completely discharge the cell. The discharging time decreases gradually with increasing operating temperature, and it is 3218 s, 2900 s and 2800 s for operating temperatures of 25°C, 35°C and 45°C, respectively. The operating voltage drop caused by the SEI film layer is defined as the operating current multiplied by the resistance of the SEI film, as shown in Fig. 11. The potential drop over the film increases with increasing operating temperature and cycle number due to the growth of the SEI film.

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Fig. 10 Cell voltage response vs. operating temperature at a 1C discharging rate.

Fig. 11 Potential drop of the SEI layer during a 1C discharge (100 s). The SOC of the cell is defined as the ratio of the quantity of lithium to the maximum

quantity of lithium in the negative electrode of a fully charged cell, which is expressed below:

24

 c ds s

SOC 

n

cs ,max  Ln

(38)

where cs is the Li-ion concentration in the negative electrode and cs,max is the maximum concentration of the intercalated lithium in the negative electrode of a fresh battery. The SOC value (i.e., cell capacity) decreases linearly with an increase in the cycling number of the cell, as shown in Fig. 12. At an operating temperature of 25°C, the capacity loss is approximately 0.198% during the second ten cycles of the cell; however, at 45°C, the equivalent value is increased to approximately 0.362%. The current density of the side reaction that causes the loss of lithium during cycling in the cell is related to the operating temperature, as described by Eq. (34). It can be seen from Eq. (34) that the current density of the side reaction increases exponentially with increasing temperature. As shown above, parallel-connected cells in a prismatic battery operate at different temperatures, which results in an unbalanced electrochemical reaction and an increasing rate of capacity fade during the cycling process. The capacity difference of the cells in a battery increase with an increasing number of charge-discharge cycles, which decreases the capacity of the overall battery.

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Fig. 12 SOC of the negative electrode after discharging at different operating temperatures.

4. Conclusions In comparison with forced convection cooling on the large front surfaces of Li-ion batteries, small side surface cooling significantly improves the temperature distribution uniformity of the battery. With small surface cooling, the maximum temperature difference of the battery, whose size is increased by 3 times, still stays at a relatively low value of 3.18°C; however, it reaches 10.26°C with large front surface cooling for h=100 W/m K. It is strongly advised that forced convection cooling should be applied to the small side surfaces of a prismatic battery in a large format battery, thus providing a high convection cooling coefficient h. The operating voltage of the Li-ion battery decreases with increasing cycle number and operating temperature. A parasitic lithium/solvent reduction reaction occurs on the surface of the anode and is related to the operating temperature. Therefore, a high operating temperature accelerates the loss of lithium and increases the rate of capacity fade during the cycling process.

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Acknowledgement This work was supported by Natural Science Foundation of Jiangxi Province Scientific Department and Technological Project of Shangrao city, Jiangxi, China (Grant No. 20181BAB206032 and 18B005), and National Natural Science Foundation of China (Grant No. 51762034). Nomenclature cs lithium concentration in solid phase [mol/m3] ce lithium concentration in electrolyte phase [mol/m3] c0 lithium initial concentration in solid phase [mol/m3] r radial coordinate along solid particle [μm] rP radius of solid particle [μm] x spatial coordinate along cell thickness [μm] t time [s] Ds diffusion coefficient of lithium in solid phase [m2/s] De diffusion coefficient of lithium in electrolyte [m2/s] Sa specific surface area [1/m] jloc F t+ is ie f R T L Ln Ls iapp j0 k0 cs,max cs,surf Uoc Ea,i 

q

local reaction current density [A/m2] Faraday's constant [96487C/mol] lithium transference number in electrolyte electron current density in solid phase [A/m2] ionic current density in electrolyte [A/m2] molecular activity coefficient of electrolyte universal gas constant 8.3143 [J/mol·K] battery operating temperature [K] overall length of cell [μm] negative electrode thickness [μm] separator thickness [μm] applied current density of the cell [A/m2] exchange current density [A/m2] reaction rate constant maximum concentration of Li-ion in solid phase [mol/m3] surface concentration of Li-ion in solid phase [mol/m3] cell open circuit voltage [V] reaction activation energy [J/mol] heat generation rate [W/m3]

Cp specific heat capacity [J/kg·K] h transfer heat coefficient [W/m2·K] M molecular weight [mol/kg3] Rsei SEI film resistance [Ω·m2] Subscripts and superscripts εs volume fraction of solid phase εe volume fraction of electrolyte

γs γe σs

Bruggeman exponent for solid phase Bruggeman exponent for electrolyte electrical conductivity of solid phase [s/m]

σe

electrical conductivity of electrolyte [s/m]

φs φe f η αa

solid phase potential [V] electrolyte phase potential [V] molecular activity coefficient of electrolyte local surface overpotential [V] charge transfer coefficients of anode

αc

charge transfer coefficients of cathode

ρ

density [kg/m3]

λ thermal conductivity [W/m·K] χ0 temperature dependent parameters δsei temperature dependent parameters [μm] κ electrical conductivity of SEI film [s/m] Subscripts s solid phase, side reaction e electrolyte 0 initial i p, n sep separator eff effective oc open circuit re reversible act active ohm ohmic irr

p positive, particle n negative Acronyms EV Li-ion 1D 3D SOC avg C

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irreversible

electric vehicle lithium-ion one dimensional three dimensional State of charge average capacity

References [1] V. Etacheri, R. Marom, R. Elazariet, et al., Challenges in the development of advanced Li-ion batteries: a review, Energy Environ. Sci. 4 (9) (2011) 3243-3262. [2] S. Panchala, M. Mathewb, R. Frasera, et al., Electrochemical thermal modeling and experimental measurements of 18650 cylindrical lithium-ion battery during discharge cycle for an EV, Appl. Therm. Eng. 135 (2018) 123-132. [3] Y.H. Ye, L.H. Saw, Y.X. Shi, et al., Numerical analyses on optimizing a heat pipe thermal management system for lithium-ion batteries during fast charging, Appl. Therm. Eng. 86 (2015) 281-291. [4] T. Waldmann, M. Wilka, M. Kasper, et al., Temperature dependent ageing mechanisms in Lithium-ion batteries-A Post-Mortem study, J. Power Sources 262 ( 2014) 129-135. [5] C. Forgez, D.V. Do, G. Friedrich, et al., Thermal modeling of a cylindrical LiFePO4/graphite lithium-ion battery, J. Power Sources 195(9) (2010) 2961-2968. [6] R. Mahamud, C. Park, Reciprocating air flow for Li-ion battery thermal management to improve temperature uniformity, J. Power Sources 196 (13) (2011) 5685-5696. [7] Q.S. Wang, P.P, Xue, J. Zhao, et al., Thermal runaway caused fire and explosion of lithium ion battery, J. Power Sources 208 (2012) 210-224. [8] W. Tong, K. Somasundaram, E. Birgersson, et al., Numerical investigation of water cooling for a lithium-ion bipolar battery pack, Int. J. Therm. Sci. 94 (2015) 259269. [9] J.Z. Xun, R. Liu, K. Jiao, et al., Numerical and analytical modeling of lithium ion battery thermal behaviors with different cooling designs, J. Power Sources, 233 (2013) 47-61.

28

[10] R. Liu, J.X. Chen, J.Z. Xun, et al., Numerical investigation of thermal behaviors in lithium-ion battery stack discharge, Appl. Energy 132 (2014) 288-297. [11] H.G. Sun, R. Dixon, Development of cooling strategy for an air cooled lithiumion battery pack, J. Power Sources, 272 (2014) 404-414. [12] H. G. Sun, X. H. Wang, B. Tossa, et al., Three-dimensional thermal modeling of a lithium-ion battery pack, J. Power Sources, 206 (2012) 349-356. [13] X.M. Xu, R. He, Review on the heat dissipation performance of battery pack with different structures and operation conditions, Renew. Sustain. Energy Rev. 29 (2014) 301-315. [14] F. He, L. Ma, Thermal management of batteries employing active temperature control and reciprocating cooling flow, Int. J. Heat Mass Transf. 83 (2015) 164172. [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] Z.J. An, L. Jia, L.T. Wei, et al., Investigation on lithium-ion battery electrochemical and thermal characteristic based on electrochemical-thermal coupled model, Appl. Therm. Eng. 137 (2018) 792-807. [17] M. Xu, Z.Q. Zhang, X. Wang, et al., Two-dimensional electrochemical–thermal coupled modeling of cylindrical LiFePO4 batteries. J. Power Sources, 256 (2014) 233-243. [18] F. Bahiraei, M. Ghalkhani, A. Fartaj, et al., A pseudo 3D electrochemical-thermal modeling and analysis of a lithium-ion battery for electric vehicle thermal management applications, Appl. Therm. Eng. 125 (2017) 904-918.

29

[19] Z.B. Wei, T.M. Lim, M. Skyllas-Kazacos, et al., Online state of charge and model parameter co-estimation based on a novel multi-timescale estimator for vanadium redox flow battery, Appl. Energy 172 (2016)169-179. [20] K. Darcovich, D.D. MacNeil, S. Recoskie, et al., Coupled electrochemical and thermal battery models for thermal management of prismatic automotive cells, Appl. Therm. Eng. 133 (2018) 566-575. [21] S. Panchal, I. Dincer, M. Agelin-Chaab, et al., Thermal modeling and validation of temperature distributions in a prismatic lithium-ion battery at different discharge rates and varying boundary conditions, Appl. Therm. Eng. 96 (2016) 190-199. [22] S. Panchal, Experimental investigation and modeling of lithium-ion battery cells and packs for electric vehicles, Ph.D. Thesis, University of Ontario Institute of Technology, Canada, 2016. [23] S. Panchal, M. Rashid, F. Long, et al., Degradation Testing and Modeling of 200Ah LiFePO4 Battery for EV, SAE Technical Paper, 2018-01-0441 [24] M. Mastali, E. Samadani, S. Farhad, et al., Three-dimensional Multi-Particle Electrochemical Model of LiFePO4 Cells based on a Resistor Network Methodology, Electrochim. Acta, 190 (2016) 574-587. [25] N.T. Tran, T. Farrell, M. Vilathgamuwa, et al., A computationally efficient coupled electrochemical-thermal model for large format cylindrical lithium ion batteries, J. Electrochem. Soc. 166 (13) (2019) A3059-A3071. [26] M. Doyle, T.F. Fuller, J. Newman, Modeling of galvanostatic charge and discharge of the lithium polymer insertion cell, J. Electrochem. Soc. 140 (6) (1993) 1526-1533.

30

[27] J. Newman, Optimization of porosity and thickness of a battery electrode by means of a reaction-zone model, J. Electrochem. Soc. 142 (1995) 97-101. [28] One dimensional isothermal Li-ion battery model in COMSOL Multiphysics 5.2, Burlington, MA, USA, 2015. [29] A. Samba, N. Omar, H. Gualous, et al., Impact of tab location on large format lithium-ion pouch cell based on fully coupled three-dimensional electrochemicalthermal modeling, Electrochim. Acta 147 (2014) 319-329 [30] J. Li, Y. Cheng, L.H. Ai, et al., 3D simulation on the internal distributed properties of lithium-ion battery with planar tabbed configuration, J. Power Sources 293 (2015) 993-1005 [31] M. Xu, Z. Zhang, X. Wang, et al., Two-dimensional electrochemical-thermal coupled modeling of cylindrical LiFePO4 batteries, J. Power Sources 256 (2014) 233-243, [32] T. Dong, P. Peng, F. Jiang, Numerical modeling and analysis of the thermal behavior of NCM lithium-ion batteries subjected to very high C-rate discharge/charge operations, Int. J. Heat Mass Transf. 117 (2018) 261-272. [33] M.W. Verbrugge, B.J. Koch, Electrochemical analysis of lithiated graphite anodes, J. Electrochem. Soc. 150 (2003) A374-A384. [34] N. Yabuuchi, Y. Makimura, T. Ohzuku, Solid-state chemistry and electrochemistry of LiCo1/3Ni1/3Mn1/3O2 for advanced lithium-ion batteries III. Rechargeable capacity and cycleability, J. Electrochem. Soc. 154 (2007) 314-321 [35] W. Huo, H. He, F. Sun, Electrochemical-thermal modeling for a ternary lithium ion battery during discharging and driving cycle testing, RSC Adv. 5 (2015) 57599-57607

31

[36] W.X. Mei, H.D Chen, J.H. Sun, et al., Numerical study on tab dimension optimization of lithium-ion battery from the thermal safety perspective, Appl. Therm. Eng. 142 (2018) 148-165. [37] D. Bernardi, E. Powlikowski, J. Newman, A general energy balance for battery systems, J. Electrochem Soc.: Electrochem. Sci. Technol. 132 (1) (1985) 5-12. [38] P. Ramadass, B. Haran, P.M. Gomadam, et al., Development of first principles capacity fade model for Li-ion cells, J. Electrochem. Soc. 151 (2) (2004) A196A203 [39] G. Ning, R.E. White, B.N. Popov, A generalized cycle life model of rechargeable Li-ion batteries, Electrochim. Acta 51 (2006) 2012-2022. [40] T.F. Fuller, Simulation and optimization of the dual lithium ion insertion cell, J. Electrochem. Soc. 141 (1994) 1. [41] S. Goutam, A. Nikolian, J. Jaguemont, et al., Three-dimensional electrothermal model of Li-ion pouch cell: Analysis and comparison of cell design factors and model assumptions, Appl. Therm. Eng. 126 (2017) 796-808. [42] Z. J. An, L. Jia. X.J. Li, et al., Experimental investigation on lithium-ion battery thermal management based on flow boiling in mini-channel, Appl. Therm. Eng. 117 (2017) 534-543. [43] A.A. Pesaran, Battery thermal models for hybrid vehicle simulations, J. Power Sources, 110 (2) (2002) 377-382.

Figure and table captions Fig. 1 Sample image of a prismatic Li-ion battery. Fig. 2 Schematic illustration of the 1D electrochemical model. Fig. 3 Coupling between electrochemical model and thermal model using average values for the temperature and generated heat. 32

Fig. 4 Temperature responses of the battery with different outer surfaces being cooled during the 5C discharge-charge cycling process: (a) small side surfaces and (b) large front surfaces. Fig. 5 Temperature distributions in the X (thickness) and Y (width) directions of the battery at a 5C discharge-charge rate and cooling different external surfaces: (a) large front surfaces and (b) small side surfaces. Fig. 6 Maximum and minimum temperature dependence of the battery on battery size when cooling the different surfaces. Fig. 7 Temperature field of the battery with forced convection cooling on the different surfaces: (a) small side surfaces and (b) large front surfaces. Fig. 8 Temperature distribution within batteries with different convection cooling coefficients on the different surfaces: (a) small side surfaces and (b) large front surfaces. Fig. 9 Cell voltage response at 1C discharging for different cycling amounts. Fig. 10 Cell voltage response vs. operating temperature at a 1C discharging rate. Fig. 11 Potential drop of the SEI layer during a 1C discharge (100 s). Fig. 12 SOC of the negative electrode after discharging at different operating temperatures. Table 1 Electrochemical parameters used in the 1D model Table 2 Temperature-dependent transmission parameters used in the 1D model Table 3 Thermophysical property parameters used in the 3D thermal model Table 4 Parameter values used for the side reaction

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Highlights 

An electrochemical-thermal coupling model was developed for a large battery.



The orthotropic thermal conductivity improves the planar heat transfer of the battery.



The temperature uniformity is improved by forced convection cooling on the small side surfaces.



The effect of the operating temperature on the electrochemical properties during cycling was discussed.

34