差异换热条件下锂离子动力电池内外部关键参数演化研究

doi:10.11949/0438-1157.20250655

化工学报 ›› 2025, Vol. 76 ›› Issue (12): 6644-6657.DOI: 10.11949/0438-1157.20250655

差异换热条件下锂离子动力电池内外部关键参数演化研究

甄箫斐¹^,²(), 黄雷雨¹^,², 孙一铭¹^,², 刘佳¹^,², 曹文炅¹^,², 韩燕³, 董缇¹^,²()

^1.兰州交通大学新能源与动力工程学院，甘肃兰州 730070
^2.甘肃省储能系统与运行控制技术创新中心，甘肃兰州 730070
^3.兰州交通大学经济管理学院，甘肃兰州 730070

收稿日期:2025-06-18 修回日期:2025-08-13 出版日期:2025-12-31 发布日期:2026-01-23
通讯作者: 董缇
作者简介:甄箫斐（1987—），男，博士，教授，zxf283386515@163.com
基金资助:
国家自然科学基金项目(52562050);国家自然科学基金项目(52206255);甘肃省自然科学基金项目(23JRRA903);甘肃省科技专员项目(24CXGA011);甘肃省青年博士基金(2023QB-039);天佑青年托举计划(2023);甘肃省社科规划项目(2024ZD002)

Study on evolution of key internal and external parameters of lithium-ion power battery under different heat transfer conditions

Xiaofei ZHEN¹^,²(), Leiyu HUANG¹^,², Yiming SUN¹^,², Jia LIU¹^,², Wenjiong CAO¹^,², Yan HAN³, Ti DONG¹^,²()

^1.School of New Energy and Power Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
^2.Gansu Provincial Technology Innovation Center for Energy Storage System and Operation Control, Lanzhou 730070, Gansu, China
^3.School of Economics and Management, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Received:2025-06-18 Revised:2025-08-13 Online:2025-12-31 Published:2026-01-23
Contact: Ti DONG

摘要/Abstract

摘要：

锂离子电池的深度应用和大容量高能量的研发趋势促使电池在差异性换热条件下的性能演变备受关注。本研究以20 Ah的软包磷酸铁锂电池为对象，建立了考虑48层并联电芯的单体电池三维电化学-热耦合模型，探讨了单体电池在差异性的换热面积、对流传热系数和温度梯度条件下电池内外部的热行为、电行为以及电化学特征。研究发现，不同换热面积时，在4C放电时，不同换热条件下的温度梯度差异较大，其中某些条件下温差可达8.54℃，10C放电时的温差可达30℃，但三种换热条件之间温差相差不大，受换热面积影响较小。在不同传热系数时，单侧强制对流虽能有效控制整体温升，却加剧了厚度方向的温度不均匀性，10C放电时横截面温差可达5.05℃，为单侧自然对流的1.64倍。不同温度梯度时，10C放电时负极固相锂浓度是1C时的6.1倍，负极过电势峰值增加91%。研究工作揭示了差异性换热条件下电池内部行为的演化规律，为高倍率、大容量电池的热管理与安全设计提供了参考。

关键词: 锂离子电池, 差异性换热条件, 电化学-热模型, 电化学反应不均匀性

Abstract:

The deep application of lithium-ion batteries and the development trend toward high-capacity and high-energy systems have drawn increasing attention to the performance evolution of batteries under non-uniform heat transfer conditions. In this study, a 20 Ah pouch-type lithium iron phosphate battery was investigated by establishing a three-dimensional electrochemical-thermal coupled model of a single cell, considering 48 parallel electrode layers. The model was used to explore the thermal behavior, electrochemical behavior, and electrochemical characteristics of the cell under varying conditions of heat transfer area, convective heat transfer coefficient, and temperature gradient. The study revealed that under different heat transfer areas, at a 4C discharge rate, the temperature gradient varied significantly under different heat dissipation conditions, with a maximum temperature difference reaching 8.54℃ under certain conditions, and under 10C discharge, the temperature difference reached as high as 30℃. However, the temperature differences between the three heat transfer conditions were relatively small and were less affected by the heat transfer area. When varying the convective heat transfer coefficient, single-sided forced convection can effectively controlled overall temperature rise but exacerbated temperature non-uniformity in the thickness direction. At a 10C discharge rate, the cross-sectional temperature difference could reach 5.05℃, which was 1.64 times that under single-sided natural convection. Under different temperature gradients, the solid-phase lithium concentration at the anode during 10C discharge was 6.1 times that at 1C, and the peak anode overpotential increased by 91%. The research work has revealed the evolution law of the internal behavior of batteries under differential heat exchange conditions, providing a reference for the thermal management and safety design of high-rate and large-capacity batteries.

Key words: lithium-ion batteries, non-uniform heat transfer conditions, electrochemical-thermal model, non-uniformity of electrochemical reactions

中图分类号:

TM 912

甄箫斐, 黄雷雨, 孙一铭, 刘佳, 曹文炅, 韩燕, 董缇. 差异换热条件下锂离子动力电池内外部关键参数演化研究[J]. 化工学报, 2025, 76(12): 6644-6657.

Xiaofei ZHEN, Leiyu HUANG, Yiming SUN, Jia LIU, Wenjiong CAO, Yan HAN, Ti DONG. Study on evolution of key internal and external parameters of lithium-ion power battery under different heat transfer conditions[J]. CIESC Journal, 2025, 76(12): 6644-6657.

图/表 15

图1 锂离子电池的内外部结构及放电原理示意

Fig.1 Schematic of internal and external structure and discharge principle of lithium-ion battery

表1 电化学控制方程和能量方程

Table 1 Electrochemical control equations and energy equations

方程名称	控制方程	边界条件
固相电荷守恒	$∂ ∂ x κ s e f f ∂ ∂ x φ s + ∂ ∂ y κ s e f f ∂ ∂ y φ s + ∂ ∂ z κ s e f f ∂ ∂ z φ s - a s j L i = 0$ $a s = 3 ε s R s$	$- κ n e g e f f ∂ φ s ∂ z z = 0 = κ p o s e f f ∂ φ s ∂ z z = L = I A$ $- κ n e g e f f ∂ φ s ∂ z z = δ n e g = κ p o s e f f ∂ φ s ∂ z z = δ n e g + δ s e p = 0$
液相电荷守恒	$∂ ∂ x κ l e f f ∂ φ l ∂ x + ∂ ∂ y κ l e f f ∂ φ l ∂ y + ∂ ∂ z κ l e f f ∂ φ l ∂ z + ∂ ∂ x κ D e f f ∂ ∂ x c l + ∂ ∂ y κ D e f f ∂ ∂ y c l + ∂ ∂ z κ D e f f ∂ ∂ z c l + a s j L i = 0$	$∂ φ l ∂ z z = 0 = ∂ φ l ∂ z z = L = 0$
固相质量守恒	$∂ c s ∂ t j L i = 1 r 2 ∂ ∂ r D s r 2 ∂ c s ∂ r$	$∂ c s ∂ r r = 0 = 0, D s ∂ c s ∂ r r = R s = - j L i a s F$
液相质量守恒	$∂ ε l c l ∂ t = ∂ ∂ x D l e f f ∂ c l ∂ x + ∂ ∂ y D l e f f ∂ c l ∂ y + ∂ ∂ z D l e f f ∂ c l ∂ z + a s j L i F 1 - t + 0$	$∂ c l ∂ z z = 0 = ∂ c l ∂ z z = L = 0$
电极动力学	$j L i = i 0 e x p α a F R T η - e x p - α c F R T η η = φ s - φ l - U$ $i 0 = F k c l α a c s, m a x - c s, s u r f a c e α a c s, s u r f a c e α c$

表1 电化学控制方程和能量方程

Table 1 Electrochemical control equations and energy equations

方程名称	控制方程	边界条件
固相电荷守恒	$∂ ∂ x κ s e f f ∂ ∂ x φ s + ∂ ∂ y κ s e f f ∂ ∂ y φ s + ∂ ∂ z κ s e f f ∂ ∂ z φ s - a s j L i = 0$ $a s = 3 ε s R s$	$- κ n e g e f f ∂ φ s ∂ z z = 0 = κ p o s e f f ∂ φ s ∂ z z = L = I A$ $- κ n e g e f f ∂ φ s ∂ z z = δ n e g = κ p o s e f f ∂ φ s ∂ z z = δ n e g + δ s e p = 0$
液相电荷守恒	$∂ ∂ x κ l e f f ∂ φ l ∂ x + ∂ ∂ y κ l e f f ∂ φ l ∂ y + ∂ ∂ z κ l e f f ∂ φ l ∂ z + ∂ ∂ x κ D e f f ∂ ∂ x c l + ∂ ∂ y κ D e f f ∂ ∂ y c l + ∂ ∂ z κ D e f f ∂ ∂ z c l + a s j L i = 0$	$∂ φ l ∂ z z = 0 = ∂ φ l ∂ z z = L = 0$
固相质量守恒	$∂ c s ∂ t j L i = 1 r 2 ∂ ∂ r D s r 2 ∂ c s ∂ r$	$∂ c s ∂ r r = 0 = 0, D s ∂ c s ∂ r r = R s = - j L i a s F$
液相质量守恒	$∂ ε l c l ∂ t = ∂ ∂ x D l e f f ∂ c l ∂ x + ∂ ∂ y D l e f f ∂ c l ∂ y + ∂ ∂ z D l e f f ∂ c l ∂ z + a s j L i F 1 - t + 0$	$∂ c l ∂ z z = 0 = ∂ c l ∂ z z = L = 0$
电极动力学	$j L i = i 0 e x p α a F R T η - e x p - α c F R T η η = φ s - φ l - U$ $i 0 = F k c l α a c s, m a x - c s, s u r f a c e α a c s, s u r f a c e α c$

表2 热模型控制方程

Table 2 Control equations of thermal model

方程名称	控制方程	初始条件与边界条件
能量守衡方程	$ρ c p ∂ T ∂ t = ∂ ∂ x λ x ∂ T ∂ x + ∂ ∂ y λ y ∂ T ∂ y + ∂ ∂ z λ z ∂ T ∂ z + q t o l q t o l = q r e a + q a c t + q o h m$	$λ x ∂ T ∂ x x = a = h x A T a m b - T s u r f a c e λ y ∂ T ∂ y y = b = h y A T a m b - T s u r f a c e λ z ∂ T ∂ z z = c = h z A T a m b - T s u r f a c e$ $t = 0; T (x, y, z, t) = T 0$
反应热	$q r e a = a s j L i T ∂ U ∂ T$
极化热	$q a c t = a s j L i η$
欧姆热	$q o h m = κ s e f f ∂ φ s ∂ x 2 + ∂ φ s ∂ y 2 + ∂ φ s ∂ z 2 + κ l e f f ∂ φ l ∂ x 2 + ∂ φ l ∂ y 2 + ∂ φ l ∂ z 2 + κ D e f f ∂ l n c l ∂ x ∂ φ l ∂ x + ∂ l n c l ∂ y ∂ φ l ∂ y + ∂ l n c l ∂ z ∂ φ l ∂ z$

表2 热模型控制方程

Table 2 Control equations of thermal model

方程名称	控制方程	初始条件与边界条件
能量守衡方程	$ρ c p ∂ T ∂ t = ∂ ∂ x λ x ∂ T ∂ x + ∂ ∂ y λ y ∂ T ∂ y + ∂ ∂ z λ z ∂ T ∂ z + q t o l q t o l = q r e a + q a c t + q o h m$	$λ x ∂ T ∂ x x = a = h x A T a m b - T s u r f a c e λ y ∂ T ∂ y y = b = h y A T a m b - T s u r f a c e λ z ∂ T ∂ z z = c = h z A T a m b - T s u r f a c e$ $t = 0; T (x, y, z, t) = T 0$
反应热	$q r e a = a s j L i T ∂ U ∂ T$
极化热	$q a c t = a s j L i η$
欧姆热	$q o h m = κ s e f f ∂ φ s ∂ x 2 + ∂ φ s ∂ y 2 + ∂ φ s ∂ z 2 + κ l e f f ∂ φ l ∂ x 2 + ∂ φ l ∂ y 2 + ∂ φ l ∂ z 2 + κ D e f f ∂ l n c l ∂ x ∂ φ l ∂ x + ∂ l n c l ∂ y ∂ φ l ∂ y + ∂ l n c l ∂ z ∂ φ l ∂ z$

表3 仿真静态参数

Table 3 Static parameters for simulation

参数	负集流体	负极	隔膜	正极	正集流体
厚度δ/μm	10^③	46^③	20^③	59^③	19^③
密度ρ/(kg·m^-3)	900^①	1437.4^①	1978^①	1260.2^①	385^①
颗粒半径r/μm	—	7.5^①	—	0.6^①	—
固相体积分数ε_s	—	0.45^④	—	0.47^④	—
孔隙率ε_l	—	0.525^④	0.54^④	0.354^④	—
最大锂离子浓度c_s,max/(mol·m^-3)	—	31370^①	—	22806^①	—
初始SOC	—	0.8^④	—	0.13^④	—
初始电解质浓度c_l_,0/(mol·m^-3)	—	—	1200^①	—	—
固相电导率σ_s/(S·m^-1)	—	100^①	—	0.5^①	—
Bruggeman因子p	—	1.5^①	1.5^①	1.5^①	—
负/正极转移系数α_a_,α_c	—	0.5^①	—	0.5^①	—
比热容c_p /(J·kg^-1·K^-1)	385^①	1437.4^①	1978^①	1260.2^①	900^①
热导率λ/(W·m^-1·K^-1)	400^①	1.04^①	0.334^①	1.48^①	238^①
自然对流传热系数h/(W·m^-2·K^-1)	—	—	5^②	—	—
参考温度T_ref/K	298.15^①	298.15^①	298.15^①	298.15^①	298.15^①

表4 材料动态参数

Table 4 Material dynamic parameters

描述	参数	正极表达式	负极表达式
固相扩散系数	D_s	$1.18 × 10 - 18 e x p 3.5 × 104 R 1 298.15 - 1 T$	$3.9 × 10 - 15 e x p 3.5 × 104 R 1 298.15 - 1 T$
反应速率常数	k_i	$1.4 × 10 - 12 e x p 3 × 104 R 1 298.15 - 1 T$	$3 × 10 - 11 e x p 2 × 104 R 1 298.15 - 1 T$
平衡电势	U_ref	$3.4323 - 0.4828 e x p - 80.2493 1 - S O C p o s 1.3198 - 3.2474 × 10 - 6 e x p 20.2645 1 - S O C p o s 3.8003 + 3.2482 × 10 - 6 e x p 20.2646 1 - S O C p o s 3.7995$	$0.6379 + 0.5416 e x p (- 305.5309 S O C n e g) + 0.044 t a n h - S O C n e g - 0.1958 0.1088 - 0.1978 t a n h S O C n e g - 1.0571 0.0854 - 0.6875 t a n h S O C n e g - 0.0117 0.0529 - 0.0175 t a n h S O C n e g - 0.5692 0.0875$
熵热系数	$∂ U ∂ T$	$- 0.3537 a 8 + 1.3902 a 7 - 2.2585 a 5 - 0.98716 a 4 + 0.28857 a 3 - 0.046272 a 2 + 0.0032158 a - 1.9186 × 10 - 5$	$344.1347148 e x p (- 32.9633287 b + 8.316711484) 1 + 749.0756003 e x p (- 34.79099646 b + 8.887143624) - 0.8520278805 b + 0.362299229 b 2 + 0.2698001697$
集流体电导率	σ_cc	$- 3.25 T 3 + 3707 T 2 - 1500000 T + 2.408 × 108$	$- 4.889 T 3 + 5465 T 2 - 21800 T + 3.52 × 108$
液相电导率	κ(c_l,T)	$10 - 4 c l × 1.2544 (- 8.2488 + 0.053248 T - 0.00002987 T 2 + 0.26235 × 0.001 c l - 0.0093063 × 0.001 c l T + 0.000008069 × 0.001 c l T 2 + 0.22002 × 10 - 6 c l 2 - 0.0001765 × 10 - 6 c l 2 T) 2$
液相扩散系数	D_l (c_l,T)	$10 - 4.43 - 54 T - 229 - 5 × 0.001 c l - 0.22 × 0.001 c l - 4$
传递系数	$t + 0$	$2.67 × 10 - 4 e x p 833 T C 1000 + 3.09 × 10 - 3 e x p 653 T C 1000 + 0.517 e x p - 49.6 T$

表4 材料动态参数

Table 4 Material dynamic parameters

描述	参数	正极表达式	负极表达式
固相扩散系数	D_s	$1.18 × 10 - 18 e x p 3.5 × 104 R 1 298.15 - 1 T$	$3.9 × 10 - 15 e x p 3.5 × 104 R 1 298.15 - 1 T$
反应速率常数	k_i	$1.4 × 10 - 12 e x p 3 × 104 R 1 298.15 - 1 T$	$3 × 10 - 11 e x p 2 × 104 R 1 298.15 - 1 T$
平衡电势	U_ref	$3.4323 - 0.4828 e x p - 80.2493 1 - S O C p o s 1.3198 - 3.2474 × 10 - 6 e x p 20.2645 1 - S O C p o s 3.8003 + 3.2482 × 10 - 6 e x p 20.2646 1 - S O C p o s 3.7995$	$0.6379 + 0.5416 e x p (- 305.5309 S O C n e g) + 0.044 t a n h - S O C n e g - 0.1958 0.1088 - 0.1978 t a n h S O C n e g - 1.0571 0.0854 - 0.6875 t a n h S O C n e g - 0.0117 0.0529 - 0.0175 t a n h S O C n e g - 0.5692 0.0875$
熵热系数	$∂ U ∂ T$	$- 0.3537 a 8 + 1.3902 a 7 - 2.2585 a 5 - 0.98716 a 4 + 0.28857 a 3 - 0.046272 a 2 + 0.0032158 a - 1.9186 × 10 - 5$	$344.1347148 e x p (- 32.9633287 b + 8.316711484) 1 + 749.0756003 e x p (- 34.79099646 b + 8.887143624) - 0.8520278805 b + 0.362299229 b 2 + 0.2698001697$
集流体电导率	σ_cc	$- 3.25 T 3 + 3707 T 2 - 1500000 T + 2.408 × 108$	$- 4.889 T 3 + 5465 T 2 - 21800 T + 3.52 × 108$
液相电导率	κ(c_l,T)	$10 - 4 c l × 1.2544 (- 8.2488 + 0.053248 T - 0.00002987 T 2 + 0.26235 × 0.001 c l - 0.0093063 × 0.001 c l T + 0.000008069 × 0.001 c l T 2 + 0.22002 × 10 - 6 c l 2 - 0.0001765 × 10 - 6 c l 2 T) 2$
液相扩散系数	D_l (c_l,T)	$10 - 4.43 - 54 T - 229 - 5 × 0.001 c l - 0.22 × 0.001 c l - 4$
传递系数	$t + 0$	$2.67 × 10 - 4 e x p 833 T C 1000 + 3.09 × 10 - 3 e x p 653 T C 1000 + 0.517 e x p - 49.6 T$

表5 磷酸铁锂电池的基本参数

Table 5 Basic parameters of LiFePO4 battery

参数	数值
标称容量/Ah	20
标称电压/V	3.3
充电截止电压/V	3.6
放电截止电压/V	2.0
外形尺寸/(mm×mm×mm)	227×160×7.5
质量/g	496

图2 电池充放电测试平台

Fig.2 Battery charge-discharge testing platform

图3 模型电压与温度验证结果

Fig.3 Validation results of model voltage and temperature

图4 电池内部状态及工况设置示意图

Fig.4 Schematic diagram of the internal state and operating conditions of the battery

图5 不同换热面积工况下电池平均温度变化情况

Fig.5 Variation of average temperature of the battery under different heat transfer area conditions

图6 三维体温度分布：(a)~(c) Case1工况; (d)~(f) Case2工况; (g)~(i) Case3工况

Fig.6 Three-dimensional temperature distribution: (a)—(c) Case1 condition; (d)—(f) Case2 condition; (g)—(i) Case3 condition

图7 放电结束时刻的温度最大值、温度最小值及温差分布

Fig.7 Distribution of maximum temperature, minimum temperature, and temperature difference at the end of discharge

图8 放电结束时刻y方向中间截面二维温度分布：(a)~(c) Case3工况；(d)~(f) Case4工况；(g)~(i) Case5工况

Fig.8 Two-dimensional temperature distribution at the middle cross-section in the y-direction at the end of discharge: (a)—(c) Case3 condition; (d)—(f) Case4 condition; (g)—(i) Case5 condition

图9 放电结束时刻固相锂浓度分布：(a)~(c) Case6工况；(d)~(f) Case7工况；(g)~(i) Case8工况(正负极初始值分别为:2971.8、25096 mol·m-³)

Fig.9 Solid-phase lithium concentration distribution at the end of discharge: (a)—(c) Case 6 condition; (d)—(f) Case 7 condition; (g)—(i) Case 8 condition (initial values for anode and cathode: 2971.8 and 25096 mol·m-³, respectively)

图10 放电结束时刻负极过电势分布：(a)~(c) Case6工况；(d)~(f) Case7工况；(g)~(i) Case8工况

Fig.10 Anode overpotential distribution at the end of discharge: (a)—(c) Case6 condition; (d)—(f) Case7 condition; (g)—(i) Case8 condition

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差异换热条件下锂离子动力电池内外部关键参数演化研究

Study on evolution of key internal and external parameters of lithium-ion power battery under different heat transfer conditions

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