Effect of module structure on performance of phase change material based Li-ion battery thermal management system

doi:10.19799/j.cnki.2095-4239.2020.0124

Abstract

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

CLC Number:

TM 912

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.

Figures/Tables 17

Fig.1

Fig.2

Table 1

Governing equations and boundary conditions in the electrochemical-thermal coupling model [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)

Table 1

Table 2

Table 3

Table 4

Temperature-dependent parameters of battery[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)

Table 4

Table 5

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.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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