Investigation on lithium-ion battery electrochemical and thermal characteristic based on electrochemical-thermal coupled model

Accepted Manuscript Investigation on lithium-ion battery electrochemical and thermal characteristic based on electrochemical-thermal coupled model Zhoujian An, Li Jia, Liting Wei, Chao Dang, Qi Peng PII: DOI: Reference:

S1359-4311(18)30984-0 https://doi.org/10.1016/j.applthermaleng.2018.04.014 ATE 12011

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

11 February 2018 26 March 2018 3 April 2018

Please cite this article as: Z. An, L. Jia, L. Wei, C. Dang, Q. Peng, Investigation on lithium-ion battery electrochemical and thermal characteristic based on electrochemical-thermal coupled model, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.04.014

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Investigation on lithium-ion battery electrochemical and thermal characteristic based on electrochemical-thermal coupled model Zhoujian An1, 2, Li Jia1, 2*, Liting Wei1, 2, Chao Dang1, 2, Qi Peng1, 2 1. Institute of Thermal Engineering, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China 2. Beijing Key Laboratory of Flow and Heat Transfer of Phase Changing in Micro and Small Scale, Beijing 100044, China

Corresponding author: Li Jia Institute of Thermal Engineering, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, China E-mail: Tel: Fax:

[email protected]

86-10-51684321 86-10-51684321

Investigation on lithium-ion battery electrochemical and thermal characteristic based on electrochemical-thermal coupled model Zhoujian An1, 2, Li Jia1, 2*, Liting Wei1, 2, Chao Dang1, 2, Qi Peng1, 2 1. Institute of Thermal Engineering, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China 2. Beijing Key Laboratory of Flow and Heat Transfer of Phase Changing in Micro and Small Scale, Beijing 100044, China Abstract A lithium-ion battery consists of numerous electrochemical cell units, and is treated as an assembly of one dimensional (1D) cell unit connected in parallel. The electrochemical and thermal characteristics of 1D cell unit have a great influence on battery performance. The thermal behavior and the dynamic evolution of electrochemical reaction in the cell are simulated. At lower discharge rate, reversible heat dominates the heat generation, but the proportion of irreversible heat gradually increases with the discharge rate. Non-uniform distribution of heat generation and electrochemical reaction rate in the cell increase with the discharge rate. Temperature has little effect on average heat generation rate and mainly influences the distribution uniformity of electrochemical reaction rate and heat generation in the cell. The temperature distribution in a battery is researched based on multi-cell 1D model. It is found that temperature in the battery presents a parabolic distribution in the laminated direction and the temperature gradient significantly increases with the cells number, which is mainly induced from the lower heat conductivity in the laminated direction. The bulk temperature will be decreased and safety of battery will be improved with the increase of cooling strength, but the temperature difference within the battery will be significant increased simultaneously. The number of cell can’t exceed 80 for a monomer battery with this electrode thickness and an active battery thermal management system (such as

) is also

indispensable to keep the temperature difference and surface temperature in the reasonable range at 5C discharge rate. At the same time, the thickness of the battery need to be chosen based on the application

Key word: lithium-ion battery; heat generation; electrochemical-thermal couple; discharge rate; temperature

1. Introduction The worldwide energy shortage and environmental pollution stimulated the development of electric vehicles (EVs) and hybrid electric vehicle (HEVs). The trend of vehicle electrification will be to continue with the innovation of battery technology in the future. As the power source, the lithium-ion battery has attracted more attentions with the increasing number of EVs and HEVs. The performance of lithium-ion battery has a significant influence on the driving range, reliability and safety issues of EVs and HEVs. It has been known that the overall performance of battery depends not only on the material and physical parameters, but also on the operating conditions including discharge rate and temperature. Understanding the influence of operating conditions on electrochemical and thermal performance of battery is limited by experimental methods. Conversely, the numerical model and simulation are economic and convenient for understanding the information during the electrochemical process and thermal characteristics, such as the electrochemical reaction rate and heat generation distribution throughout the electrode layers can be obtained numerically while the data can’t be measured by experiment method.

Nomenclature List of symbol a b c c1 c1,max c1,surf c2 Cp Cs D1 D1,ref D2 EaD EaR F f± Iapp j0 jloc

stoichiometric of lithium in the FePO4 stoichiometric of lithium in the C6 mole number of lithium taking part in the electrochemical reaction Li+ concentration in solid phase (mol m-3) maximum Li+ concentration (mol m-3) Li+ concentration on the surface of active material particles (mol m-3) Li+ concentration in liquid phase (mol m-3) heat capacity(J kg-1 K-1) number of cell in the multi-cell model Li+ diffusion coefficient in solid phase (m2 s-1) diffusion coefficient at reference temperature (m2 s-1) Li+ diffusion coefficient in electrolyte phase (m2 s-1) diffusion activation energy (J mol-1) reaction activation energy (J mol-1) Faraday constant (96485C mol-1) average molar activity coefficient applied current density (A m-2) exchange current density (A m-2) local current density (A m-2)

ΔS Sa t t+ T

entropy change (Jmol-1 K-1) specific surface area (m2/m3) time (s) Li+ transference number absolute temperature (K)

Tref

reference temperature (K)

U Greek letters

open circuit potential (V)

αa

transfer coefficient for anodic current

αc γ ε1 ε2

transfer coefficient for cathodic current Bruggeman exponent volume fraction for solid phase volume fraction for liquid phase

η

over potential (V)

ν ρ σ1 σ2 φ1 φ2

thermodynamics factor density (kg m-3) electric conductivity for solid phase (S m-1) electric conductivity for liquid phase (S m-1) solid phase potential (V) liquid phase potential (V)

Subscripts and superscripts

k k0 k0,ref Li Q Qact Qohm Qrea r rp R

thermal conductivity (W m-1 K-1) reaction temperature constant (m2.5 mol-0.5 s-1) reaction temperature constant at reference temperature (m2.5 mol-0.5 s-1) thickness of cell component (μm) heat generation (J) active heat generation (J) ohmic heat generation (J) reaction heat generation (J) radius distance variable of particle (μm) radius of active material particles (μm) universal gas constant (J mol-1 K-1)

0 1

initial state solid phase

2

liquid phase

i irr n p re s tol

n/p irreversible negative electrode positive electrode reversible separator total

In recent years, numerical simulation technology played an important role in the research of lithium-ion battery based on electrochemical-thermal coupled model. Compared with experimental method, the electrochemical characteristics (voltage and current density distribution) as well as thermal characteristics (heat generation rate and temperature distribution) can be obtained. The most famous and practical model for lithium-ion battery is the porous electrode model according to the porous-electrode theory

[3]

[1, 2]

, which was established

. Coupling the thermal energy equation

with electrochemical model and the heat generation and temperature-dependent physicochemical properties, an electrochemical-thermal coupled model was presented [4]

. Zhao et al.

[5, 6]

numerically researched the thermal behavior of LiMn2O4 battery

based on electrochemical-thermal coupled model, and they focused on the significance of reversible heat and analyzed the effect active material particle size and thickness of electrode on the heat generation. Most of the other researchers also focused on the battery with LiMn2O4 cathode material for simulating the electrochemical and thermal behavior based on electrochemical-thermal coupled model

[7-10]

. Xu et al. developed two-dimensional

[11]

and three-dimensional

[12]

electrochemical-thermal coupled model of LiFePO4 battery to analyze the electrochemical performance, heat generation and temperature distribution. Du et al. [13]

investigated the irreversible heat generation in lithium-ion battery and their results

showed that the negative electrode particle size had more significant impact on heat production. Ye et al.

[14]

developed an electro-thermal cycle life model by

incorporating the dominant capacity fading mechanism to analyze the capacity fading effect on the battery performance. Although previous work observed that phase change occurred in the LiFePO4 cathode material during lithium-ion intercalated and de-intercalated

process

[15,

16]

,

these

results

demonstrated

that

the

electrochemical-thermal coupled model without considering phase change were appropriate to simulate LiFePO4 battery. A battery can be treated as the assembly of one dimensional (1D) cell unit [17]. As

the basic unit, the thermal behavior and electrochemical behavior of cell unit directly determine performance of battery. In turn, the influence of temperature and discharge rate on battery ultimately showed as the different electrochemical reaction process and distribution in cell unit. Temperature has a significant effect on battery performance. For instance, Waldmann et al.

[18]

demonstrated two different aging mechanisms for

the ranges of -20ºC to 25 ºC and 25ºC to 70ºC. The aging rates increased with decrease of temperature below 25ºC, while above 25ºC aging was accelerated with increase of temperature. The battery performance both degraded when battery operated at higher

[19, 20]

or lower temperature

[21, 22]

. Most of the researches on

temperature-dependent performance of battery were based on experiments in the macroscopic view. However, the mechanism of temperature affecting the electrochemical reaction and thermal behavior of battery in the microscopic view was rarely reported in public literatures. The spatial non-uniformity of current and state of charge (SOC) within a battery monomer, have become the key concern for both manufacturers and designers with the increase of battery size. The larger temperature gradient within battery results from the decrease of surface-to-volume ratio with the increase of battery size, and the higher heat generation rate is another key factor in causing larger temperature non-uniformity. For instance, Xu et al. [11] and Zhang et al. [23] demonstrated that there existed a certain temperature gradient within the battery, and Li et al.

[24]

showed that

the distribution of electrochemical parameters was also location-related. But the interaction of temperature gradient and distribution of electrochemical parameters were not focused on in these researches. A battery is formed by a multitude of cells connected in series or/and in parallel to satisfy the desired power and capacity. The uneven temperature distribution will lead to mismatch of the internal resistance among cells, which induces unbalanced discharging and aging performance. This divergence of different cells will significantly shorten the total deliverable capacity and battery lifespan. It also should be noted that a larger temperature gradient also

would be generated in the cross-plane direction during discharge process even though an external cooling system is installed, because the thermal management system (TMS) only cool the surface of the battery and the thermal conductivity in cross-plane direction is low duo to the layer to layer configuration. The temperature-dependent electrochemical performance is supposed to vary due to the temperature gradient, which makes the cells at different layer operating at different temperature. Meanwhile, the non-uniformity in laminated direction will increase with the increase of thickness of battery. Although plenty of scholars have studied battery performance based on electrochemical-thermal coupled model, they almost focused on the overall electrochemical behavior or the heat generation at a certain temperature. Few of researches concerned about the heat generation distribution and electrochemical reaction process across the cell under different operating temperature and discharge rate, as well as the relationship between heat generation characteristic and electrochemical

characteristic

in

the

cell

unit.

In

addition,

most

of

electrochemical-thermal coupled model studies on lithium-ion battery behavior were based on LiMn2O4 chemistry. For battery with LiFePO4 electrode material, only a handful of kinetic model studies have been conducted, even though these battery have many performance superiority compared with the other battery. For a whole battery, the effect of temperature gradient in the battery on the electrochemical performance also should be investigated due to the sensibility of electrochemical reaction on temperature, and provide suggestions for the design of large scale battery to avoid undesirable loss of battery performance. This study aims to shed some light on the electrochemical reaction process and heat generation characteristic in the cell, as well as the temperature distribution in the laminated direction in a battery monomer. In this study, a one dimensional electrochemical-thermal coupled model was established. The thermal behavior and the dynamic evolution of electrochemical reaction in the cell at different discharge

rate and temperature were simulated and the mechanism of temperature affecting the battery performance were discussed. Furthermore, the relationship between heat generation distribution and electrochemical reaction process in a cell was also analyzed. The one cell model was extended to multi-cells and the temperature distribution in the laminated direction at different discharge rates was obtained. The influence of temperature gradient on the electrochemical performance inside a lithium-ion battery was studied.

2. Electrochemical-thermal model 2.1. Model assumption and calculation domain A 1D

electrochemical-thermal coupled

model

for

a

single

cell

in

LiFePO4/graphite battery was established based on the energy, mass and charge conservation as well as electrochemical kinetics. The main model assumption were showed as follow [1, 2, 7]: Active materials in positive and negative electrodes are considered as spherical shape of uniform sizes; Gas possibly generated in the charge/discharge process is neglected, and only solid and liquid phase in the battery are considered; All kinds of side reactions during operation are neglected; The effect of current collector on heat generation is ignored due to the higher electrical conductivity. Fig. 1 shows the schematic calculation domain of 1D cell unit model. The domain includes five parts: negative current collector, negative electrode, separator, positive electrode and positive current collector. In this model, the electrodes were considered as porous solid matrix. The active material in positive electrode was lithium iron phosphate LiFePO4 particles and negative electrode contained graphite C6. The separator was made up of porous polymer membrane which acted as a physical barrier to separate the negative and positive electrode. Both electrode and separator

were immersed in electrolyte, which ensured the lithium-ion transfer between the two electrodes. The electrolyte in this model was LiPF6 solution, in which the concentration of LiPF6 was 1500 mol/m3 and the solvent was a liquid mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC) (2:1 by volume). The electrochemical reactions occurred at the interface of electrolyte and active electrode material particles during charge/discharge process were: disch arg e

Negative electrode:

LibC6

Positive electrode:

Lia FePO4

ch arg e

Lib-c C6 +cLi++ce-

ch arg e disch arg e

Lia-c FePO4  cLi   ce

(1) (2)

Where, a and b are the stoichiometric of lithium in the FePO4 and C6 respectively; c is the mole number of lithium taking part in the electrochemical reaction.

Fig. 1. Schematic of the lithium-ion battery (a) A battery; (b) multi-cells computational domain; (c) one cell computational domain The simulation was based on prismatic battery, as showed in Fig. 1(a), which

was formed by connecting a number of cells (denoted by Cs) in parallel, as showed in Fig. 1(b). In the multi-cells model, there were only two boundaries, namely the internal boundary 1 (center of battery) and external boundary 2 (outside surface of battery). Because the effect of current collector on heat generation was ignored as mentioned above, there were only four boundaries in the one cell model, which were anode external-face boundary 1, anode / separator interface boundary 2, cathode / separator interface boundary 3 and cathode external-face boundary 4, as showed in Fig. 1(c). 2.2. Model development 2.2.1 Electric charge conservation (a) Solid phase. Electric charge conservation for solid phase can be expressed as follows:





  - 1eff 1   Sa jloc

(3)

3 1 eff  ; 1   1 1 1 rp

(4)

Sa,i 

Where, σ1 is the electric conductivity for solid phase; φ1 is solid phase potential; Sa is the specific surface area; jloc is local current density; ε2 is volume fraction for solid phase; rp is the radius of active material particles; γ1 is the Bruggeman exponent for solid phase. (b) Liquid phase. The transport of lithium-ion in the electrolyte is determined by the following equation:   2RT  2eff   ln f      2eff 2  1   1  t    ln c2   =Sa jloc F  ln c2    

(5)

 2eff = 2 2 2

(6)

Where, σ2 is the electric conductivity for liquid phase; φ2 is liquid phase potential; F is the Faraday constant; R is the universal gas constant; f± is the average molar activity coefficient; c2 is the Li+ concentration in liquid phase; t+ is the Li+ transference number; ε2 is volume fraction for liquid phase; γ2 is the Bruggeman exponent for

liquid phase. As shows in Eq. (5), the ionic current consisted of two terms, namely the first term following Ohm’s law and the ionic concentration gradient accounting for the second terms. The liquid-junction potential, which is the potential in the electrolyte induced from the different diffusion rate of different ions, was showed in Eq. (7) with expression K junc 

2RT   ln f   2RT  1    1  t  = F   ln c2  F

(7)

Where, ν is the thermodynamic factor relating to electrolyte activity, which is temperature and lithium-ion concentration dependent. 2.2.2. Mass conservation (a) Solid phase. The mass conservation of lithium-ion in an intercalation particle of the electrode active material can be expressed by Fick’s law. The mass transfer within the solid phase can be described as c1 c  1   2  2 r D1 1   0  t r  r r 

(8)

The parameter of r is the radial coordinate inside a spherical, as showed in Fig. 1(c); t is the time; c1 the Li+ concentration in solid phase; D1 is the Li+ diffusion coefficient in solid phase. For an electrode material particle, the Li+ flux is set to zero at the center of sphere, namely r=0, because there is no species source. The Li+ concentration on the surface of sphere is coupled with the flux and concentration of Li+ in the electrolyte. (b) Liquid phase. The mass conservation of lithium-ion in the electrolyte is given by Eq. (9) 2





S j c2     D2eff c2  a loc 1  t  t F 

D2eff  D2 2 2 Where, D2 is the Li+ diffusion coefficient in electrolyte phase.

(9) (10)

It can be seen that both diffusion and transference are responsible for the transportation Li+ in electrolyte. 2.2.3. Electrochemical kinetics The local current density is determined by Bulter-Volmer equation as showed below:   F    F  jloc  j0 exp  a,i    exp   c,i    RT   RT

    

(11)

Where, αa and αc is the transfer coefficient for anodic and cathodic current; η is the over-potential; j0 is the exchange current density, which act as the connector between lithium-ion concentration in solid phase and liquid phase. It is calculated by Eq. (12) 



j0  Fk0 c2 a c1,max  c1,surf

a c



(12)

c1,surf

Where, k0 is the reaction temperature constant; c1,max is the maximum Li+ concentration; c1,surf is the Li+ concentration on the surface of active material particles. Local current density, jloc, was driven by the over-potential, η, which is defined as the difference between solid and electrolyte phase potential minus Ui: i  1  2  Ui

(13)

Where, Ui is the open circuit potential of the solid phase electrode. 2.2.4. Energy conservation The heat generation was modeled according to the local heat generation model of Rao and Newman

[25]

using the formulation of Gu and Wang

[4]

. The total heat

generation of cell unit included the heat generated in the two electrodes and separator, and the heat generated in the current collector was neglected duo to the higher electrical conductivity. There were three parts of heat sources in the battery during charge and discharge process according to the type of heat generation, including reaction heat, Qrea, active polarization heat, Qact, and ohmic heat, Qohm. The energy conservation in the battery is governed by the following equation: C p

T  k 2T  Qrea  Qact  Qohm t

Reaction heat is

(14)

Qrea  Sa jlocT

U S  Sa jlocT T F

(15)

Active polarization heat is Qact  Sa jloc

(16)

Ohmic heat is 

Qohm   1eff 1  1+  2eff 2 

 2RT  2eff   ln f    1   1  t    ln c2   2 F    ln c2 

(17)

The reaction heat Qrea is reversible, while the active polarization heat Qact and ohmic heat Qohm are irreversible, which can be categorized as following: Qre  Qrea

(18)

Qirr  Qact  Qohm

(19)

Where, ρ is the density; Cp is the heat capability; k is the thermal conductivity; ΔS is the entropy change. 2.2.5 Boundary and initial condition As showed in Fig. 1(b), there were two boundaries in multi-cells model. Only half of the battery was simulated considering symmetry, namely the boundary 1 was the center of the battery and boundary 2 was the outside surface of battery. So, the thermal boundary condition at boundary 1 was adiabatic and the boundary condition was convective cooling at boundary 2 with different convective heat transfer coefficient h in order to investigate the effect of cooling conditions on the temperature and electrochemical gradient in the battery. The initial temperature of all the cells was 298.15K for the multi-cells model. The electrochemical boundary conditions at each cells in multi-cells model was same to one cell model as showed below. There were four boundaries in the one cell model as showed in Fig. 1(c), and different boundary and initial conditions were given in the different boundaries. For the interface of electrode and current collector, namely boundary 1 and 4, the solid phase potential was arbitrarily set to be zero at boundary 1; the charge flux was set to equal to the average current density of the cell at boundary 4, which were expressed as Eq. (20).

1

x 0

 0;   1eff

1 x

x  Ln +Ls +Lp

  I app

(20)

At boundary 2 and 3, namely the interface between electrode and separator, there was no electronic charge flux as defined in Eq. (21), and the boundary condition was set as isolation for electron and the ion could pass through the interfaces.  1eff

1 x

  1eff

x  Ln

1 x

x  Ln +Ls =0

(21)

There were no ionic charge flux and only electron could pass through the interface at boundary 1 and boundary 4, which was describes as Eq. (22). At the same time, the liquid phase potential was considered to be continuous at boundary 2 and boundary 3. 2 x

x 0



2 x

x  Ln +Ls +Lp

0

(22)

At the battery surface boundary 1 and 4, the convective cooling boundary condition was considered -k

T x

x 0

 -k

T x

x  Ln +Ls +Lp

 h(T-Tamb )

(23)

where h is the convective coefficient and its value is set as low as 0.1Wm-2 K-1 [6]. This simulates a condition with a very poor heat transfer rate (e.g., aerospace applications) and can lead to a dramatic temperature rise in batteries, which facilitates a clearer inspection on the quantification of battery total heat generation and electrochemical characteristic distribution in the cell. It’s also should be noted that all the boundary condition equations were expressed as 1D format because the model in this research was also 1D. The Ln, Ls and Lp in the boundary condition equation were only used to describe the boundary location in the single layer cells. The multi-layer cell was just the single layers connected in parallel and the electrochemical boundary condition for different layers in the multi-layers was same to the single layer. 3. Model parameters and validation 3.1. Model parameters The

parameters

in

the

model

included

constant

parameters

and

temperature/concentration dependent parameters, which were from literature and estimation. All the parameters used in this model were summarized in Table 1 [11, 24, 26, 27]

. The temperature/concentration dependent parameters will be analyzed below. 3.1.1. Electrode kinetics parameters In the model, the reaction rate constant and open circuit potential were important

parameters related to electrode kinetics, which were all temperature/concentration dependent parameters. The reaction rate constant fitted into the following Arrhenius formula [28]:  EaR,i  1 1  k0,i  k0,ref ,i exp      R  Tref T  

(24)

The open circuit potential depended on both temperature and the local SOC on the surface of active material particles. The open circuit potential approximately was expressed as Taylor’s first order expansion around a reference temperature: Ui  U ref,i +



dUi T  Tref dT



(25)

Firstly, the reference potential under the given reference temperature (25ºC) Uref,i was a function of electrode SOC [26] : U ref ,n  0.6379  0.5416 exp( 305.5309b ) b  0.1958 b  1.0571 )  0.1978 tanh( ) 0.1088 0.0854 b  0.0117 b  0.5692 0.6875 tanh( )  0.0175 tanh( ) 0.0529 0.0875 0.044 tanh( 

(26)

U ref , p  3.4323  0.4828 exp( 80.2493( 1  a )1.3198 ) 3.2474  10 6 exp( 20.2645( 1  a )3.8003 ) 6

3.2482  10 exp( 20.2646( 1  a )

3.7995

(27)

)

Where, b and a are the negative and positive electrode SOC, respectively. Their curves were showed in Fig. 2.

Table 1 Critical battery parameters used in the 1D model Parameters

Unit

Al foil

ε1 ε2 Li rp c1,0 c1,max c2,0 αa αc D1,ref D2 EaD EaR σ1 σ2 k0,ref t+ γ k1 k2 ρ1

--μm μm mol m-3 mol m-3 mol m-3 --m2 s-1 m2 s-1 J mol-1 J mol-1 S m-1 S m-1 m2.5 mol-0.5 s-1 --W m-1 K-1 W m-1 K-1 kg m-3

--16 ---------------160 -8700

Cathode (positive ) 0.435 0.28 92 1.15 3900 22806 -0.5 0.5 1.18×10-18 -20000 4000 0.5 -1.4×10-12 -1.5 1.48 2660

Separator -0.4 20 ---1500 ---Eq. (32) ---Eq. (31) 0.363 1.5 0.334 0.099 492

Anode (negative) 0.56 0.3 59 14.75 16361 31370 0.5 0.5 3.9×10-14 -4000 4000 100 -3×10-11 -1.5 1.04

Cu foil

Ref.

--9 ---------------400

[26] [27] [27] [27] [11] [11] [11] [11] [11] [11] [11] [27] [27] [24] [11] [24] [11] [24] [11] [11]

1500

2700

[11]

ρ2 Cp,1 Cp,2 F

kg m-3 J kg-1 K-1 J kg-1 K-1 C mol-1

-385 -96487

-1437 --

1210 1978 1518

-1260 --

-903 --

[11] [11] [11]

Fig. 2. The reference open circuit potential (a) Negative electrode; (b) positive electrode The entropy of electrode was ΔS=nF(dU/dT). The dUn/dT and dUp/dT under the given reference temperature (25ºC) were also the function of electrode SOC. Their curves were depicted in Fig. 3, and were expressed by Eq. 27 and Eq. 28 [8, 29, 30] dU n exp( 32.9633287b  8.316711484 )  344.1347148  dT 1  749.0756003 exp( 34.79099646b  8.887143624 )

(28)

0.8520278805b  0.362299229b  0.2698001697 dU p  0.35376a8  1.3902a 7  2.2585a 6  1.9635a5  0.98716a 4 dT

(29)

2

0.28857a  0.046272a  0.0032158a  1.9186  10 3

2

5

The SOC of both negative and positive electrode has the same expression showed as below: SOCi 

c1,i

(30)

c1,max,i

Fig. 3. The fitting curves of the entropy term (dU/dT) (a) Negative electrode; (b) positive electrode

3.1.2. Electrolyte parameters The diffusion coefficient D2, thermodynamics factor ν and ionic conductivity σ2 were all temperature and concentration dependent parameters. But there lack of experimental data about the temperature dependence of Li+ transport in LiPF6 in EC/DMC (2:1 by volume), it was assumed to follow the trends of similar electrolyte systems. Valøen et al.

[31]

experimentally investigated the transport properties for LiPF6 in

PC/EC/DMC (10:27:63 by volume). Combining the parameter for LiPF6 in EC/DMC (2:1 by volume) at 25ºC [31]

[32]

and the experimental results in the PC/EC/DMC system

, the following expressions were obtained [10]:

 2  c2 ,T   1.2544c2  104 (8.2488  0.053248T  2.9871  105 T 2  0.26235c2

(31)

9.3063  103 c2T  8.069  106 c2T 2  0.22002c22  1.765  104 c22T 2 D2  c2 ,T   1  10

4

 10

4.43

54.0  2.2104 c2 T 229.00.005c2

(32)

  c2 ,T   0.601  0.24   0.001c2  +0.982  1  0.0052  T  294    0.001c2  0.5

1.5

(33)

3.1.3. Solid phase parameters The temperature dependence of the Li+ diffusion coefficient D1 in the solid phase follows the Arrhenius relationship, as expressed in Eq. (34)

[28, 33]

. Additionally,

although the D1 was also depend on SOC of electrode, it was not considered in the model due to the lack of data.  EaD,i D1,i  D1,ref exp   R

 1 1      Tref T    

(34)

3.2 Model validation The calculation of the model was performed with the finite element commercial software, COMSOL multi-physics 5.1. A given applied current density Iapp was used at the terminal boundary. The discharging process was stopped when the voltage of the battery decreased to 2V in the simulation. Before discussing the simulation results of lithium-ion batteries, the validation of the established model should be performed. The battery used to validate the model

was a commercial type LiFePO4 power batteries (180 mm in length, 70 mm in width and 27 mm in height) with normal capacity 20 Ah. A Neware battery test station (BTS-60V100A) was used to control the discharge and charge of battery. Nine T-type thermal-couples were evenly fixed on the one side surface of the battery to record the temperature, the average temperature of the nine thermal-couples measured was used to valid the model. The cutoff voltage of this battery was 2V according to the manufacturer. The concrete test method was presented in our previous work [34]. Fig. 4 shows the temperature profile of the average temperature on battery surface and voltage obtained by both experiment and simulation at 1C, 3C and 5C discharge rate with 25±2 ºC ambient temperature, which was controlled by the thermo-tank. It can be seen that the results obtained from the developed model were basically consistent with the data acquired from the experiment and the simulation results can describe the actual thermal and electrochemical behavior inside the battery. It also should be noted that the discharging capacity of battery was slightly larger than 20Ah, which mainly because the discharging time was larger than 3600s, 1200s and 720s for 1C, 3C and 5C respectively. However, there were still small degree of discrepancy between the simulation and experiment results. An explanation may come from 4 aspects: (a) most of the parameters used in this model were obtained from references, which maybe slightly different from the actual parameters of the battery used in the experiment; (b) the neglect of radiation and convection in simulation may cause the subtle difference although the experiment results were also acquired under adiabatic condition by wrapping the battery with thermal insulation material; (c) the unclear additives used in the commercial battery was another factor

[5]

, and (d) the

assumption mentioned in section 2.1 may not exist in the process of discharge

[13]

. If

all these aspects can be comprehensively taken into account, the discrepancy between the experimental and simulative results would be reduced. Overall, it was demonstrated that the coupled model was effective in simulating the thermal behavior and electrochemical behavior associated with the operation of

lithium-ion battery.

Fig. 4. Validation between experimental results and simulative results (a) Thermal performance; (b) electrochemical performance. 4. Results and discussion The discharge rate and operating temperature play an important role on battery electrochemical behavior and heat generation characteristic, and they determines the local current density in the electrode, lithium-ion concentration distribution in liquid and solid phase and the process of electrochemical reaction. The simulated heat distribution and the constitution of heat generation in cell unit combined with the electrochemical behavior were analyzed in detail. 4.1. The effect of discharge rate on cell performance As one of the important factors affecting battery performance, discharge rate directly determines the current density in the electrode. The local current density and heat generation rate in the electrode layer were simulated with 298.15K initial temperature. The curves of local current density at 1C and 5C were showed in Fig. 5. The local current density showed similar regularity at anode and cathode, which the local current density increased severely at the electrode/separator interface at the beginning of discharge. The peak of local current density moved from electrode/separator interface to the electrode/current collector interface with the proceeding of discharge. Notably, the local current density ultimately closed to zero near the separator/cathode interface at the end of discharge process for 5C discharge rate. It means that the electrochemical reaction rate was not uniform across the

electrode layer and it was more obvious for lager discharge rate. This non-uniform distribution

of

electrochemical

intercalation/de-intercalation

reaction Li+

of

rate

was

showed also

that

uneven.

the The

intercalation/de-intercalation rate of Li+ was drastic near the electrode/separator interface at the beginning of discharge process and moved to electrode/current collector

interface

with

discharge

proceeding.

The

drastic

intercalation/de-intercalation of Li+ in local domain might lead to local mechanical stress, which would become more obvious with the increase of discharge rate and accelerate the aging rate of cell. As shown above,

the peak

of local current

density

moved

from

electrode/separator interface to electrode/current collector interface. However, it was opposite to the results in Ref.

[35]

, in which the peak moved from electrode/current

collector interface to electrode/separator interface with the process of discharge. This was depend on the comparison between electric conductivity in solid phase (σ1) and electric conductivity in liquid phase (σ2). When σ1 > σ2, the moving direction of local current density peak was from electrode/separator interface to electrode/current collector interface, but the moving direction was opposite when the σ1 < σ2 [36]. In this research, the solid phase conductivity σ1 was larger than liquid phase conductivity σ2, so, the local current density peak moved from electrode/separator interface to electrode/current collector interface. It can be explained that the Li+ de-intercalated from negative electrode move through the separator and then reach to separator/positive electrode interface to react with positive electrode. When the Li+ reach to separator/positive electrode interface, it will immediately react with LiFePO4 material particle than continuously move forward when the solid phase electric conductivity is higher than liquid phase electric conductivity and a peak occur near the separator/positive electrode interface as a result. It’s mainly because the higher electric conductivity signify the lower electric resistance, namely the resistance of Li + intercalate into LiFePO4 electrode material particles is lower than the resistance of Li+

transfer in electrolyte.

Fig. 5. The local current density at different time during the discharge (a) 1C rate; (b) 5C rate The discharge rate was directly related to the heat generation rate, as showed in Eq. (15)-(17). To investigate the discharge rate on the heat generation characteristic and the proportion of different mechanism heat to total heat, the heat generation rate at 1C and 5C were also studied.

Fig. 6. The heat generation rate at 1C discharge rate (a) Total heat; (b) reaction heat; (c) polarization heat; (d) ohmic heat Fig. 6(a) shows the total heat generation rate across the cell at 1C discharge rate

and for seven time intervals. It was indicated that the heat generation rate at negative electrode and positive electrode were different and exhibited certain regularity. The local heat generation rate nearly reached to 59 kW/m3 and 20 kW/m3 for negative electrode and positive electrode respectively at the end of discharge process. The heat generated in negative electrode dominated the total heat generation in the cell. At the initial period, the heat generation rate increased rapidly, which was responsible by the rapidly increase of reaction heat, as showed in Fig. 6(b). Similarly, the heat generation also showed a slightly rapid increase at the later stage of discharge. The main reason was that the polarization heat rapidly increased due to the intensification of polarization at the later stage of discharge process. In the view of heat generation mechanism, the reaction heat, namely reversible heat, played the most important role in the heat generation, which nearly reached to 40 kW/m3 and 16 kW/m3 for negative and positive electrode respectively. LiMn2O4 battery presented similar law as investigated by Zhao et al.

[6]

, because the reversible heat was non-ignorable. The

ohmic heat was relatively small compared with the other kinds of heat. Another phenomena was the distribution of heat generation rate across the cell. The heat generation distribution was basically uniform in the negative electrode and positive electrode and only there was a slight fluctuation, which was owing to the even distribution of local current density at lower discharge rate (1C). As the discharge rate reached to 5C, the heat generation characteristic showed different regularity. As showed in Fig.7, the local heat generation rate nearly reached to 450 kW/m3 and 100 kW/m3 respectively. Although the reaction heat still occupied the dominant position for the cell heat generation in the view of heat generation mechanism, the proportion of the reaction heat to the total heat reduced. This was mainly due to the drastic increase of ohmic heat which follows an i2R type of heating scheme and the rapid rise of polarization heat because of the intensification of polarization at higher discharge rate. Additionally, the heat generation distribution across the cell showed a significant

non-uniformity at 5C rate. The non-uniform distribution of heat generation rate was similar to the distribution of local current density as showed in Fig. 5 and Fig. 7 (a). The uneven distribution of heat generation rate across the electrode might lead to local thermal non-uniformity, which would become more obvious with the increase of discharge rate and accelerate the aging rate of the cell. As mentioned above, the discharge rate mainly affected the proportion of different mechanism heat and distribution non-uniformity of electrochemical reaction. The severe distribution non-uniformity of electrochemical reaction and heat generation at higher discharge rate would lead to uneven mechanical stress and thermal response, these were the reason why higher discharge rate will accelerate the fading rate of battery. Zhao et al.

[5]

found that decrease of the thickness of electrode layer could

improve the uniformity of heat generation distribution. For the design of battery, the application, electrode structure, technology and cost should be comprehensively considered to improve the performance and lifespan of battery.

Fig. 7. The heat generation rate at 5C discharge rate

(a) Total heat; (b) reaction heat; (c) polarization heat; (d) ohmic heat 4.2. The effect of temperature on cell performance The temperature also is an important factor affecting the electrochemical process and thermal behavior inside the battery. The decrease of temperature can lower the activity of electrolyte and electrode material. Conversely, the increase of temperature will cause higher thermal effect in the battery [18]. In order to investigate the influence of temperature on the thermal and electrochemical behavior, the simulation under four ambient temperature conditions (273.15K, 283.15K, 298.15K and 313.15K) at 5C discharge rate were carried out.

Fig. 8. The average heat generation rate of negative electrode (NE) and positive electrode (PE) at different temperature during 5C discharging process Fig. 8 shows the average heat generation rate of negative electrode and positive electrode at difference temperature during discharge process. According to Eq. (15)-(19), the reversible heat was directly related to temperature and temperature indirectly affected the heat generation of battery because the distribution of electrolyte potential, over-potential and local current collector were temperature-dependent. However, it was found that temperature had little effect on average heat generation rate especially for positive electrode. Only the average heat generation rate in

negative electrode increased with the increase of temperature at later stage of discharge

process.

The

electrolyte

and

electrode

characteristic

were

all

temperature-dependent. Because temperature had little effect on cell average heat generation rate, the temperature affecting cell electrochemical and thermal behavior may be in other ways. As

mentioned

above,

the

diffusion

and

transfer

of

Li+

was

temperature-dependent and the local current density showed significant difference at different temperature, as showed in Fig. 9. Although the local current density was location-related for all temperature conditions and showed remarkable gradient, it was more severe at lower temperature. For instance, at 120s within negative electrode, the difference of local current density reached to 6.6 A/m2, 3.7 A/m2, 2 A/m2 and 1.3 A/m2 for 273.15K, 283.15K, 298.15K and 313.15K, respectively. The results indicated that the gradient of local current density was larger at lower temperature and distribution non-uniformity decreased with the increase of temperature. For positive electrode, the maximum local current density was at electrode/separator interface at the initial stage of discharge process. Subsequently, a peak appeared in the positive electrode and then the local current density was closed to 0 at the electrode/separator interface as the proceeding of discharge process. In these simulations, the cell was discharged under constant current condition. The amount of Li+ intercalated into the particles of electrode material must be constant per unit time, so the integral of local current density across the positive electrode was also a constant relative to applied current density. When the particle near the electrode/separator interface approximately reached to the fully charge state, Li+ would be hardly intercalated continuously, which resulted in a lower local current density and eventually reached to zero during the later discharge process. When the temperature was lower, the diffusion and transfer of Li+ was slow and the intercalation/de-intercalation of Li+ was more intensive at the electrode/separator interface compared to higher temperature at the beginning of discharge process. So

the gradient of local current density was larger under lower temperature conditions to satisfy the charge balance condition during the discharge process. As a result, the local current density near the cathode electrode/separator interface at lower temperature reached to 0 earlier than that for higher temperature and became a more non-uniform distribution across the cathode. This intensive intercalation/de-intercalation of Li+ in local domain resulting from lower temperature will give rise to mechanical stress in the local domain and accelerate the aging rate of battery.

Fig. 9. The local current density at 5C discharge rate (a) 273.15K; (b) 283.15K; (c) 298.15K; (d) 313.15K At the same time, the total thermal distribution presented similar trend with local current density, as showed in Fig. 10. The non-uniformity of thermal distributions were severe at lower temperature, which were mitigated with the increase of temperature. Although the maximum local heat generation rate was large at lower temperature, the average heat generation rate of cell, namely integral of the local heat generation rate, had no obvious difference due to larger gradient at lower temperature. So, there were little effect of temperature on average heat generation rate of cell, as

showed in Fig. 8. Temperature significantly affected the distribution uniformity of heat generation rate as far as thermal characteristic. Although the thermal distribution was improved with the increase of temperature, the battery would reach to a higher temperature and exceed the safe operating temperature. So, the operating temperature must be within an appropriate range as pointed in Ref. [37]. Overall, temperature affected the performance of battery by influencing the distribution uniformity of electrochemical reaction rate and heat generation rate across the electrode in the view of cell unit. Lower temperature would lead to uneven mechanical

stress

and

thermal

response

due

to

the

intensive

intercalation/de-intercalation of Li+ in local domain, which would accelerate the aging of battery in mechanical and thermal ways.

Fig. 10. The total heat generation distribution at 5C discharge rate (a) 273.15K; (b) 283.15K; (c) 298.15K; (d) 313.15K 4.3. Temperature distribution within a battery monomer It has been a consensus that the electrochemical performance and state of health

of lithium-ion battery is temperature-related. However, many of the numerical and experimental researches only focused on the overall performance and the total heat generation amount during the discharge process. For a laminated battery, as showed in Fig. 1(b), the battery was electrically equivalent to a number of cell unit (positive current collector, positive electrode, separator, negative electrode and negative current collection) collected in parallel. The electrochemical and thermal characteristic of different cells were prone to be non-uniform due to the large temperature gradient within the battery, especially in cross-plane because of the lower thermal conductivity. It is interesting and of great significance to research the thermal non-uniformity in laminated direction and the effect of this thermal non-uniformity on electrochemical performance of battery. In this research, only a half of battery was simulated based on symmetry and the cell number showed below was only the cell number of half battery. The cell at the center of battery (left side in Fig. 1(b)) was numbered cell 1 and the cell at the outside surface (right side in Fig. 1(b)) was cell Cs successively, as showed in Fig. 1(b). In this section, it mainly focused on the temperature gradient within the battery which resulted from the outside battery thermal management system, heat generation and lower thermal conductivity within the battery. The ambient temperature was set to be constant, namely 298.15K. It’s assumed that the battery operated under different thermal management systems with different convection heat transfer coefficient h at the outside surface of the battery. Three kinds of thermal management condition were simulated. The first, h=7.17 W/m2K was considered as the natural convection heat transfer

[38]

. The second,

h=50W/m2 K was assumed that a high-velocity forced air cooling system was used [39]. Thirdly, the h=100 W/m2K and 150 W/m2 K was supposed liquid cooling system was implemented on the battery surface as showed in our previous work

[34]

. It should be

pointed out that the convective heat transfer coefficient h was average h on the battery surface rather than the h in the mini-channel. There is no doubt that the increase of h will significantly improve the thermal

safety of lithium-ion battery. However, it will also lead to a relatively larger temperature gradient in the battery, especially in the laminated direction due to the lower thermal conductivity as showed in Eq. (23). In order to evaluate the non-uniformity in laminated direction within the battery during discharge process, 1C and 5C discharge rate were simulated for different quantity of cells. Fig. 11 shows the temperature distribution in cross-plane at 1C rate for 10-cells and 60-cells, and their thicknesses were 1.835mm and 11.01mm, respectively. Due to the lower heat generation at 1C discharge rate, only natural convection heat transfer thermal management condition was simulated for 1C discharge rate. As showed in Fig. 11, the temperature distribution was basically uniform in the cross plane and presented a smaller temperature difference, namely the difference between cell 1 and cell Cs, which was only 0.028ºC and 0.474ºC for Cs=10 and Cs=60 respectively duo to lower discharge current and heat generation at 1C discharge rate. So the small temperature difference could be neglected and had rarely effect on electrochemical characteristic of different cells. The temperature of battery was only reached to 310K in the adiabatic condition at 1C discharge rate as showed in Fig. 4. Actually, there was no need to cool down the battery at this lower discharge rate because the temperature was within the safe operating temperature range.

Fig. 11. Temperature distribution in cross-plane at 1C rate with h=7.17 W/m2 K (a) 10cells; (b) 60cells With the increase of discharge rate, the heat generation rate of battery drastically

increased, as showed in Fig. 6 and Fig. 7. Effective thermal management method must be used to make sure the battery was operating in the safe temperature range. Fig. 12 shows the temperature distribution in the cross-plane at 5C distribution rate for 60-cells (11.01mm) battery with different convection heat transfer coefficient. It was found that the temperature distribution presented a parabolic distribution and the temperature of cells in the center was larger than that of the cells in the outside of the battery. There was no doubt that the temperature of battery decreased and the safety was improved with the increase of convection heat transfer coefficient. The surface temperatures of battery were decreased to 336.31K, 318.66K, 311.01K and 307.41K respectively. On the contrary, the temperature difference between the first cell and last cell reached to 2.12K, 8.05K, 10.16K and 11.01K for battery with h=7.17 W/m2 K, h=50 W/m2K, h=100 W/m2K, h=150 W/m2 K at the end of discharge process, and the temperature difference showed an increasing trend with the increase of convection heat transfer coefficient. Pesaran

[37]

thought that it was desirable to have a

temperature distribution with temperature difference less than 5ºC to decrease the non-uniformity chemical reaction in the battery and the lithium-ion batteries are best at temperature between 25-40°C. At these temperatures they achieve a good balance between performance and life. Obviously, the cooling capacity of natural convection and forced air cooling system were insufficient for the battery discharged at higher rate. With the increase of convection heat transfer coefficient, surface temperature of the battery was decreased lower than 313K for h=100 W/m2 K and h=150 W/m2 K, however, the central temperature of the battery still stayed at a relatively higher value, which were around at 320K due to the lower thermal conductivity and higher heat generation of battery at higher discharge rate. At the same time, the temperature difference within the battery was also beyond the allowable range.

Fig. 12. Temperature distribution in cross-plane at 5C rate for 60-cells (a) h=7.17 W/m2K; (b) h=50 W/m2K; (c) h=100 W/m2 K; (d) h=150 W/m2K. Electrochemical characteristic was temperature-dependent for cell. The temperature gradient among the parallel-connected cells would aggravates the unbalanced discharging phenomenon in the cells because of the cells operating with different temperature. Fig. 13 showed the electrolyte potential and liquid phase Li+ concentration distribution across first cell and last cell for battery with different convection heat transfer coefficient h. It was found the electrolyte potential and liquid phase Li+ concentration distribution presented a larger gradient across the cell at outside of battery (lower temperature region) compared with the cell at the center of battery (higher temperature region). For example, h=150W/m2 K, the electrolyte potential drop across the cell reached to 0.03226V and 0.03967V for cell 1 and cell 60, respectively, and the Li+ concentration drop across the cell increased from 653.54mol/m3 for cell1 to 760.56mol/m3 for cell 60. The larger electrolyte potential

drop and higher Li+ concentration gradient illustrated the more severe polarization effect across the cell. The reasons of these difference were the temperature gradient within the battery, which led to the cell in the outside part operating under a lower temperature and the cell in the center part operating under a higher temperature. For the cell operating under lower temperature, as the diffusion and migration of Li+ were slower and more difficult than that under higher temperature, the gradient of concentration rose and the ohmic drop rose. Also, Yang et al.

[40]

showed the effect of

temperature difference among the parallel-connected cells on the overall output voltage and discharge capacity was negligible for battery. However, it significantly aggravated the unbalanced discharging phenomenon between the cells. For a long term, this unbalanced electrochemical reaction resulting from different operating temperature for different cells in one battery would accelerate the capacity loss rate. At the same time, the capacity loss rate increased with the temperature difference increasing, especially in the case of lower temperature. Therefore, the temperature gradient in the battery should be well controlled to improve the electrochemical reaction uniformity and minimize the capacity loss.

Fig. 13. Comparison of electrochemical parameter for first cell and last cell at 5C rate (a) electrolyte potential (h=100W/m2 K); (b) electrolyte potential (h=150W/m2 K); (c) liquid Li+ concentration (h=100W/m2 K); (d) liquid Li+ concentration (h=150W/m2K) As showed above, a larger temperature gradient existed within battery, especially in cross-plane due to lower heat conduction in laminated direction. It made the cells in battery operating at different temperature and led to electrochemical unbalance for different cells and accelerated the aging of battery. The temperature difference in the battery mainly resulted from the higher heat generation and lower heat conductivity of battery in the laminated direction. Undoubtedly, the surface temperature and temperature difference within battery both would be reduced with the decrease of battery thickness with the same h value as summarized in Table 2 and Table 3. Combining the Table 2 and Table 3, it was found that battery thickness had a more significant effect on temperature difference with battery than outside surface temperature. For example, for 60-cells battery, the thickness only increased by 50% compared with 40-cell battery, but the temperature difference increased to 127.01% with h=150 W/m2 K at the end of discharge process. For the 40-cells battery, both the outside surface temperature and temperature different were in the reasonable range except for the battery which boundary condition was natural convection heat transfer [37]

as showed in Table 2 and Table 3. Therefore, the number of cell should not exceed

40 for the half battery with this electrode thickness and an active battery thermal management was also essential to maintain the battery operating in the optimal

temperature range. Actually, the thickness of the battery can be chosen based on the application. For example, the battery used for lower current device should be fabricated with a larger thickness to simplify the structure of the battery pack. On the contrary, it should be fabricated with a thin thickness for the larger current application and a high-strength battery thermal management is also indispensable to keep the battery operating in the safety temperature range. Table 2 Outside surface temperature of battery with different h value and thickness at 5C discharge rate Surface temperature

h=7.17W/m2K

h=50 W/m2 K

h=100W/m2 K

h=150W/m2 K

Cs=20

320.12K

306.96K

302.79K

301.28K

Cs=40

323.86K

312.98K

306.81K

304.17K

Cs=60

336.31K

318.66K

311.01K

307.41K

Table 3 Temperature difference within the battery with different h value and thickness at 5C discharge rate Temperature difference

h=7.17W/m2K

h=50 W/m2 K

h=100W/m2 K

h=150W/m2 K

Cs=20

0.43K

1.2K

1.25K

1.27K

Cs=40

0.98K

3.97K

4.65K

4.85K

Cs=60

2.12K

8.05K

10.16K

11.01K

As a summary, the non-uniformity distribution of thermal and electrochemical performance in cell level, battery level and pack level must be decreased in the view of improving the performance and prolong the lifespan of battery. The characteristic of active electrode material, structure of battery and cell, configuration of battery pack and thermal management should be considered comprehensively. The cost was another important factors in the manufacture and application.

5. Conclusions In this paper, a one-dimension electrochemical thermal couple model was proposed to simulate several galvanostatic discharge process on one cell and multi-cell under different physical condition. The electrochemical characteristic and thermal characteristic were studied and some conclusions were obtained as below. (1) Discharge rate not only affects the total heat generation rate, but also the proportion of different mechanism heat. At lower discharge rate, reversible dominants the heat generation, but the proportion of irreversible heat gradually increases with the improving of discharge rate especially for polarization heat. (2) Non-uniformity distribution of heat generation and electrochemical reaction rate across the cell increase with the increase of discharge rate, and the capacity fading of cell operating is accelerated at higher discharge rate. (3) Temperature has little effect on average heat generation rate and it mainly influence the distribution uniformity of electrochemical reaction rate and heat generation across the cell. The non-uniformity is aggravated at lower temperature and lead to uneven mechanical stress and thermal response during the discharge process, which will accelerate the aging of electrode layer. (4) The temperature in the battery presents a parabolic distribution in the laminated direction and the temperature gradient significantly increases with the increase of cells number, which is mainly induced from the lower heat conductivity in the laminated direction. This kind of temperature gradient makes the cells in the battery operating at different temperature conditions and increasing electrochemical unbalance for different cells. (5) The bulk temperature will be decreased and safety of battery will be improved with the increase of cooling strength (h), but the temperature difference within the battery will also be significantly increased. The number of cell can’t exceed 40 for a half battery with this electrode thickness and an active battery thermal management system (such as

) is also

indispensable to keep the temperature difference and surface temperature in the reasonable range at 5C discharge rate. At the same time, the thickness of the battery need to be chosen based on the application. Acknowledgement This research was supported by National Natural Science Foundation of China (No. 51776015).

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Proportion of irreversible heat gradually increases with the increase of discharge rate. Non-uniformity of heat generation and electrochemical reaction increase with the discharge rate. The non-uniformity is aggravated at lower temperature and lead to uneven thermal response. The internal temperature and electrochemical characteristic are affected by cooling condition.