Three-dimensional electrochemical-thermal coupling model of a lithium-ion battery module

doi:10.19799/j.cnki.2095-4239.2022.0411

Abstract

Abstract:

Lithium-ion batteries have been widely used in new energy fields, including electric vehicles, among others. Therefore, to facilitate the designing of thermal management schemes for reducing the uneven temperature variation in battery modules and improving battery durability, this study develops a three-dimensional electrochemical-thermal model that can show the heat spatiotemporal production rate and the temperature distribution of battery cells. Besides, the model can predict the electrical characteristics of different parts of electrode pairs and the temperature distribution of battery cells. Specifically, the single-cell thermal model is extended to a thermal model of a battery module comprising three single cells connected in parallel to investigate temperature aggregation phenomenon reduction in the battery modules. The experimental results verify the validity of the proposed electrochemical-thermal model. Specifically, single-cell and three-cell parallel battery strings are placed in an insulation box with a constant temperature of 25 ℃ and discharged at a constant current rate to provide quantitative data on the electrical and thermal behavior. The current model prediction agrees well with the experimental data. The average absolute errors of the cell terminal voltage and temperature are less than 0.016 V and 0.36 ℃, respectively, under the constant discharge current conditions of 0.5 C, 1 C, 2 C, and 3 C. however, the average temperature error of each surface of the three-cell parallel batteries does not exceed 0.4 ℃ under constant discharge current conditions of 0.5 C, 0.75 C, 1 C, 1.25 C, and 1.5 C. Further analyses show that the current density in the cathode material is related to the discharge depth and electrochemical reaction area. In the early and middle stages of discharge, the electrochemical reaction area is mainly at the tab, where the current density is the highest. Conversely, the electrochemical reaction area is mainly at the bottom of the cathode material, where the current density at the bottom is greater than that at the tab in the later stages of discharge. The temperature of a three-cell parallel battery module is not a simple superposition of the temperatures of single cells. Additionally, the temperature of the middle cell is higher than that of the two cells at the sides. In the battery module, when boundary conditions are consistent, the temperature of the two side batteries becomes distributed symmetrically. Furthermore, a temperature aggregation effect caused by air non-circulation among the cells exists. Therefore, the temperature of intermediate cells can be reduced by reducing the gap between monoliths or adding materials with high thermal conductivity to them as heat transfer media.

Key words: electrochemical-thermal model, battery module, lithium-ion battery, thermal properties, experiment

CLC Number:

TM 911

Xueqing WEI, Haipeng DENG, Yu ZHOU, Bingchuan WANG. Three-dimensional electrochemical-thermal coupling model of a lithium-ion battery module[J]. Energy Storage Science and Technology, 2022, 11(12): 3965-3977.

Figures/Tables 19

Table 1

Electrochemical governing equations and energy equations"

方程原理	控制方程	边界条件
固相颗粒中的锂离子扩散	$∂ c s ∂ t = 1 r 2 ∂ ∂ r D s r 2 ∂ c s ∂ r$	$∂ c s ∂ r r = 0 = 0,$ $- F D s ∂ c s ∂ r r = r n = j n, c s t = 0 = c s, 0$
固相电子输运	$i s = - σ s e f f ∇ ϕ s$	$i s x = 0 = i s x = l p + l s + l n = I$ ， $i s x = l p = i s x = l p + l s = 0$
液相锂离子输运	$i l = - σ l e f f ∇ ϕ l + 2 R T σ l e f f F 1 - t 0 1 + ∂ l n f ± ∂ c l ∇ l n c l$	$i l x = 0 = i l x = l p + l s + l n = 0$ ， $i l x = l p = i l x = l p + l s = I$
物质守恒	$ε l ∂ c l ∂ t = ∇ ∙ D l e f f ∇ c l + 1 - t 0 ∇ ∙ i l F$	$i l x = 0 = i l x = l p + l s + l n = 0$ ， $i l x = l p = i l x = l p + l s = I,$ $c l t = 0 = c l, 0$
电荷守恒	$∇ ∙ i l + ∇ ∙ i s = 0$ ， $∇ ∙ i s = - α p j n$	$i l x = 0 = i l x = l p + l s + l n = 0,$ $i l x = l p = i l x = l p + l s = I,$ $c l t = 0 = c l, 0$
界面电化学反应	$j n = j 0 e x p α a F R T η - e x p - α c F R T η$ ， $j 0 = F k i c l c l, r e f α a c s, s u r f α c c s, m a x - c s, s u r f α a$ ， $η = ϕ s - ϕ l - U e$	—
电芯能量传输方程	$ρ c p ∂ T ∂ t - ∇ ∙ k ∇ T = q o h m + q a c t + q r e v + q t a b$ =-i_s· $∇ ϕ s$ i_l - $i l ∙ ∇ ϕ l + α p j n η + α p j n T ∂ U e ∂ T$ + $q t a b$	$k ∂ T ∂ x x = 0 = k ∂ T ∂ x x = l p + l s + l n = - h T - T a$
极耳产热	$q t a b = I 2 R t a b V t a b = I 2 1 σ t a b h t a b A t a b 1 h t a b A t a b = 1 σ t a b I A t a b 2$	—

Table 1

Fig. 1

Table 2

Static parameters for simulation"

描述	参数	单位	正极集流体	正极	隔膜	负极	负极集流体	电解液
电解液锂浓度的初始值	$c l, 0$	mol/m³						1000^③
固相锂浓度的初始值	$c s, 0$	mol/m³		273.67^③		25598^③
固体颗粒表面最大锂浓度	$c s, m a x$	mol/m³		22 806^②		31370^②
扩散系数	$D$	m²/s						4.5×10^-11
高度	$H$	m	0.2^①	0.2^①	0.2^①	0.2^①	0.2^①
极耳高度	$H t a b$	m		0.02^②		0.02^②
厚度	$l$	μm	19^③	59^③	20^③	46^③	10^③
活性粒子半径	$r n$	μm		0.2^③		3.5^③
初始温度	$T i n i t$	K	297.7^②	297.7^②	297.7^②	297.7^②	297.7^②	297.7^②
锂离子的迁移数	$t 0$							0.38^③
宽度	$W$	m	0.15^①	0.15^①	0.15^①	0.15^①	0.15^①
极耳宽度	$W t a b$	m		0.045^①		0.045^①
液相体积分数	$ε l$			0.55^③	0.5^③	0.5^③
固相体积分数	ε_s			0.45^③		0.5^③
固相电导率	$σ s$	S/m		6.75^③		2203.8^③
极耳电导率	$σ t a b$	S/m		3.4486×10^7①		5.4645×10^7①

Table 2

Table 3

Material dynamic parameters"

描述	参数	正极表达式	负极表达式
扩散系数	$D s$	$9 × 10 - 16 e x p 3 × 104 R 1 298.15 - 1 T$	$4 × 10 - 13 e x p 2 × 104 R 1 298.15 - 1 T$
反应速率常数	$k i$	$4 × 10 - 9 e x p 3 × 104 R 1 298.15 - 1 T$	$2 × 10 - 10 e x p 3.5 × 104 R 1 298.15 - 1 T$
平衡电势	$U e, r e f$	$3.4277 - 2.0269 × 10 - 2 y + 0.5087 e x p - 81.163 y 1.0138 + 7.6445 × 10 - 8 e x p 25.361 y 3.2983 - 8.4410 × 10 - 8 e x p 25.262 y 3.3111$	$0.6379 + 0.5416 e x p - 305.5309 x + 0.044 t a n h - x - 0.1958 0.1088 - 0.1978 t a n h x - 1.0571 0.0854 - 0.6875 t a n h x - 0.0117 0.0529 - 0.0175 t a n h x - 0.5692 0.0875$
集流体导电率	$σ c c$	$- 3.25 × 102 T 3 + 3.707 × 103 T 2 - 1.5 × 105 T + 2.408 × 108$	$- 4.889 × 102 T 3 + 5.465 × 103 T 2 - 2.18 × 106 T + 3.52 × 108$
液相导电率	$σ l$	$- 8.86 × 10 - 4 T - 4.16 × 10 - 5 T 2 + 0.0562 T - 9.338 2$

Table 3

Table 4

Thermal model parameters"

描述	参数	单位	电芯	正极极耳(铝)	负极极耳(铜)	铝壳
密度	$ρ$	kg/m³	2269	2700	8960	1150
比热容	$c p$	J/(kg·K)	878.92	900	385	1900
XY方向热导率	$k x y$	W/(m·K)	56.15	238	400	0.16
Z方向热导率	$k z$	W/(m·K)	1.2399	238	400	0.16

Table 4

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

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