成组结构对锂离子电池相变热管理性能的影响

doi:10.19799/j.cnki.2095-4239.2020.0124

摘要/Abstract

摘要：

基于相变材料的锂离子电池热管理系统相对于基于风冷、液冷、热管的电池热管理系统，具有无外加能耗、结构简单、温度均匀性好等优势。电池排列方式及间距对模组散热性能影响较大，而通过改进成组结构提升相变热管理系统性能的研究较少。基于有限元方法建立电化学-热耦合模型，通过实验验证模型准确性，采用数值模拟方法，对平行、错列、交叉三种电池排列方式及电池间距对相变热管理系统性能的影响进行研究。结果表明，对于矩形圆柱电池模组，平行排列方式相比于非平行排列方式，对相变材料的利用率更高，整体散热效果更好。放电过程中，电池最高温总体呈上升趋势，并存在减速上升过程，电池间距越小，电池最高温越大，越早出现减速上升；电池最大温差呈上升-下降-上升趋势，上升-下降过程中温差、下降幅度与电池间距成正比，再次上升过程中温差与电池间距成反比；平均相变比例从相变起始时间开始上升，电池间距越小，相变起始时间越早，平均相变比例越大。对于矩形圆柱电池相变热管理系统，电池最优间距为4～5 mm。

关键词: 锂离子电池, 热管理, 成组结构, 相变材料

Abstract:

Phase change material (PCM)-based thermal management systems have the advantages of no extra energy consumption, a simple system structure, and good temperature uniformity compared to air-cooled, liquid-cooled, and heat pipe thermal management systems. The battery arrangement and spacing have a large impact on the heat dissipation performance of the module, and there is little research on improving the performance of PCM-based thermal management systems via improving the module structure. An electrochemical-thermal coupling model was developed based on the finite element method. The accuracy of the model was verified via experiments. The numerical method was used to study the effects of parallel, staggered, and crossed arrangements and the cell spacing on the thermal management performance. For rectangular cylindrical battery modules, compared to non-parallel arrangements, the parallel arrangement can improve the utilization of phase change materials and the heat dissipation effect of a system. During the discharge process, the highest temperature of the battery generally increases and there is a decelerating increase process. The smaller the battery spacing, the higher the maximum temperature of the battery. The maximum temperature difference of the batteries shows a rising-falling-rising trend. The temperature difference and drop during the rising-falling process is positively correlated with the battery spacing, and when the maximum temperature difference rises again, it is inversely proportional to the battery spacing. The average phase change ratio starts to increase from the phase change start time. The smaller the battery spacing, the earlier the phase change occurs and the larger the average phase change ratio. For rectangular phase change material-based cylindrical battery thermal management systems, the optimal battery spacing is between 4 mm and 5 mm.

Key words: Li-ion battery, thermal management, module structure, phase change material

中图分类号:

TM 912

张丹枫, 孙金华, 王青松. 成组结构对锂离子电池相变热管理性能的影响[J]. 储能科学与技术, 2020, 9(5): 1526-1539.

Danfeng ZHANG, Jinhua SUN, Qingsong WANG. Effect of module structure on performance of phase change material based Li-ion battery thermal management system[J]. Energy Storage Science and Technology, 2020, 9(5): 1526-1539.

图/表 17

图1

图2

表1

电化学-热耦合模型中的控制方程和边界条件[20-23]"

项目	控制方程及边界条件	编号
固相电荷守恒	$j = ? σ s e f f ? ? φ s$	(1)
	$- ? σ s e f f ? φ s ? x x = L a l l = i a p p$	(2)
	$- ? σ s e f f ? φ s ? x x = L n e g, ? c c + L n e g, ? x = L s e p + L n e g, ? c c + L n e g = 0$	(3)
液相电荷守恒	$j = - ? σ l e f f ? φ l + 2 R T σ l e f f F 1 - ?? t + 1 + d ? l n ? f ± d ? l n ? c l ?$ $? l n c l$	(4)
液相电荷守恒	$? φ l ? x x = 0, ? x = L a l l = 0$	(5)
固相扩散	$? c s ? t = D s r 2 ? ? r r 2 ? c s ? r$	(6)
	$- ? D s ? c s ? r r = 0 = 0$	(7)
	$- ? D s ? c s ? r r = R s = j S F$	(8)
液相扩散	$ε l ? c l ? t = ? ? D l e f f ? ? c l + 1 - ?? t + F j$	(9)
液相扩散	$? φ l ? x x = 0, ? x = L a l l = 0$	(10)
电化学反应	$j = a v j 0 e x p α a η F R T - ?? e x p α c η F R T$	(11)
	$η =$ $φ s - ?$ $φ l - ? U o c$	(12)
	$j 0 = F K c l α α c s, ? m a x - c s, ? s u r f α α c s, ? s u r f α c$	(13)
电池能量守恒	$ρ b a t t C p, b a t t ? T ? t = ? ? λ b a t t ? ? T + q b a t t$	(14)
电池能量守恒	$q b a t t = q r e v + q o h m + q r x n$	(15)
可逆热	$q r e v = j T$ $? U o c ? T$	(16)
欧姆热	$q o h m = - ??$ i $s ? ? φ s - ??$ i $l ? ? φ l$	(17)
极化热	$q a c t = j η$	(18)
相变材料能量守恒	$ρ P C M C P, ? P C M = ? T ? t = ? ? λ P C M ? T$	(19)
相变过程	$θ = 0, ? T P C M ≤ T 1 T P C M - ?? T 1 T 2 - ?? T 1, ? T 1 < T P C M < T 2 1, ? T P C M ≥ T 2$	(20)
	$ρ P C M = 1 - ?? θ ρ 1 + θ ρ 2$	(21)
	$λ P C M = 1 - ?? θ λ 1 + θ λ 2$	(22)
	$C P, ? P C M = 1 ρ P C M 1 - ?? θ ρ 1 C P, ? 1 + θ ρ 2 C P, ? 2 + l P C M ? α m ? T$	(23)
	$α m = 12 θ ρ 2 - ?? 1 - ?? θ ρ 1 1 - ?? θ ρ 1 + θ ρ 2$	(24)
热边界条件	$- ? λ ? T = h T - ?? T r e f$	(25)

表1

表2

表3

表4

温度相关的电化学参数[23-24]"

参数名称	方程	公式编号
液相电导率	$σ l = 10 - ? 4 c l × 1.2544 × - 8.2488 + 0.053248 T - 0.00002987 T 2 + 2.26235 ×$ $0.001 c l - 0.0093063 × 0.001 c l T + 0.000008069 × 0.001 c l T + 0.22002 × 10 - 6 c l 2$ $- ? 0.0001765 × 10 - 6 c l 2 T 2$	(26)
液相扩散系数	$D l = 10 - ?? 4.43 - ?? 54 T - ?? 229 - ?? 0.005 c l - ?? 0.22 × 0.001 c l - ? 4$	(27)
负极扩散系数	$D s, n e g = 1.4523 × 10 - ? 13 × e x p 68025.7 8.314 1 T r e f - ? 1 T$	(28)
负极开路电压	$U r e f, n e g = 0.1493 - ? 0.0313 a r c t a n (25.59 S O C - ? 4.099)$ $+ 0.8493 e x p (- ? 61.79 S O C) + 0.3824 e x p (- ? 665.8 S O C)$ $- ? 0.009434 a r c t a n (32.49 S O C - ? 15.74)$ $- ? e x p (39.42 S O C - ? 41.92)$ $U O C, n e g = U r e f, n e g e x p E a, n e g R 1 T r e f - ?? 1 T$	(29)
正极开路电压	$U r e f, p o s = - ? 10.27 S O C 4 + 23.88 S O C 3 - ? 16.77 S O C 2$ $+ 2.595 S O C + 4.563$ $U O C, p o s = U r e f, p o s e x p E a, p o s R 1 T r e f - ?? 1 T$	(30)

表4

表5

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

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参数名称	参数值
电池容量/ A·h	2.5
电池半径/ mm	9
电池高度/ mm	65
初始电压/V	4.2
截止电压/V	2.75

参数名称	符号及单位	正极	负极	隔膜
电极活性材料颗粒半径	R_s /μm	10.5	10.5	—
电极活性材料体积分数	ε_s	0.52	0.49	—
Bruggeman系数	B	2.98	2.98	3.15
电解液体积分数	ε_l	0.31	0.33	0.37
反应速率系数	k_i /m·s^-1	11×10^-12	11×10^-12	—
初始锂离子浓度	c_s,0 /mol·m^-3	2500	30876	—
固相电导率	σ_s /S·m^-1	100	100	—
液相电导率	σ_l /S·m^-1	—	—	式(26)
液相扩散系数	D_l /m²·s^-1	—	—	式(27)
电荷转移系数	α	0.5	0.5	—
锂离子迁移数	t₊	—	—	0.36
固相扩散系数	D_s /m²·s^-1	5e-13	式(28)	—
一维模型长度	L /μm	60	65	25
活化能	E_a /kJ·mol^-1	30	20	—
环境温度	T_ref /K	293.15	—	—

项目	热导率/W·m^-1·K^-1	密度 /kg·m^-3	比热容 /J·kg^-1·K^-1	潜热/J·kg^-1
正极	1.58	2328.5	1269.21	—
负极	1.04	1347	1437.4	—
正极集流体	170	2770	875	—
负极集流体	398	8933	385	—
隔膜	0.34	1008.98	1978.16	—
相变材料(固)	3.99	721	2340	176460
相变材料(液)	3.6	652	2052	—

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