锂离子电池组的三维电化学-热耦合仿真分析

doi:10.19799/j.cnki.2095-4239.2022.0411

摘要/Abstract

摘要：

锂离子电池广泛用于新能源汽车等领域。为了便于设计高效的电池热管理方案，提高电池耐久性，建立了三维电化学-热耦合模型，该模型能够从时间与空间上反映电芯产热率与电池单体温度分布，用于预测极片不同部分的电特性与电池单体温度分布。3个单体并联的电池组热模型由3个单体尺寸的热模型组成，每一个热模型皆与极片尺寸的三维电化学模型耦合。实验数据验证了该三维电化学-热耦合模型的有效性。其中，电池单体端电压平均绝对误差不超过0.016 V，温度的平均绝对误差不超过0.36 ℃；电池组各表面的温度平均误差不超过0.40 ℃。深入分析表明：正极材料中的电流密度与放电深度和电化学反应区域有关。在放电的前中期，电化学反应区域主要在凸缘处，此时凸缘处电流密度最高；在放电后期，电化学反应区域主要在正极材料的底部，此时底部的电流密度大于凸缘处。此外，电池组的温度不是电池单体温度数值上的简单叠加，中间电池温度比两侧电池温度高，且在电池组边界条件一致时，两侧电池温度成对称分布。电池组之间存在空气不流通而引起的温度聚集效应。减少电池组间的空隙、在其中加入热导率大的材料作为传热介质能有效降低中间电池的温度。

关键词: 电化学-热模型, 电池组, 锂离子电池, 热特性, 仿真实验

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

中图分类号:

TM 911

韦雪晴, 邓海鹏, 周宇, 王冰川. 锂离子电池组的三维电化学-热耦合仿真分析[J]. 储能科学与技术, 2022, 11(12): 3965-3977.

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.

图/表 19

表1

电化学控制方程和能量方程"

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	$q t a b = I 2 R t a b V t a b = I 2 1 σ t a b h t a b A t a b 1 h t a b A t a b = 1 σ t a b I A t a b 2$	—

表1

图1

表2

仿真静态参数"

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

表2

表3

材料动态参数"

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	$σ l$	$- 8.86 × 10 - 4 T - 4.16 × 10 - 5 T 2 + 0.0562 T - 9.338 2$

表3

表4

热模型参数"

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

表4

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

图15

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