基于框架设计的液流电池流场优化模拟研究

doi:10.11949/0438-1157.20190558

摘要/Abstract

摘要：

液流电池通常采用对角平推流流场，会形成电解液滞留区，造成电池局部浓差极化大，影响综合性能。鉴于此，提出了一种基于框架设计的流场优化方法，通过设计电极框架，可以得到“蛇形流道”和“平行流道”两类流场。以全钒液流电池为例，通过数学建模，研究了不同流场结构和参数对于多孔电极内电解液流动特性、电化学反应和温度变化特性的影响规律。计算结果与实验结果一致性良好，结果表明：电解液在“平行流场”内的流动均匀性比在“蛇形流场”内好，且不存在滞留区，同时在“平行流场”内浓差极化也较“蛇形流场”低；此外，对于同样的电极面积，在电极内部的“平行流道”越多，电解液的流速分布越均匀，反应特性越好。

关键词: 液流电池, 框架, 流场, 数学模型

Abstract:

The flow battery usually adopts a diagonally pushing flow field, which will form an electrolyte retention zone, which causes a large concentration polarization of the battery, which affects the overall performance. In view of this, a flow field optimization method based on frame design is proposed. By designing the electrode frame, two kinds of flow fields,“serpentine flow path”and“parallel flow path”can be obtained. Taking vanadium redox flow battery as an example, the effects of different flow field structures and parameters on the flow characteristics, electrochemical reaction and temperature change characteristics in porous electrode were studied by mathematical modeling. The calculated results are in good agreement with the experimental results. The results show that the flow uniformity of the electrolyte in the“parallel flow field”is better than that in the“serpentine flow field”, and there is no stagnant zone, and in the“parallel flow field”the concentration polarization is also lower than the“serpentine flow field”; in addition, for the same electrode area, the more“parallel flow channels”inside the electrode, the more uniform the flow velocity distribution of the electrolyte, and the better the reaction characteristics.

Key words: flow battery, frame, flow field, mathematical modeling

中图分类号:

TQ 028.8

尤东江, 魏建云, 李雪菁, 娄景媛. 基于框架设计的液流电池流场优化模拟研究[J]. 化工学报, 2019, 70(11): 4437-4448.

Dongjiang YOU, Jianyun WEI, Xuejing LI, Jingyuan LOU. Simulation study on flow field optimization of flow battery based on flow frame design[J]. CIESC Journal, 2019, 70(11): 4437-4448.

图/表 10

图1 电极框架设计及其结构尺寸

Fig.1 Designing dimension of different electrode flow frames

图2 具有SPF2流场结构的钒电池组装示意图

Fig.2 Schematic contracture of VRFB with SPF2 flow field

表1 模型控制方程和边界条件

Table 1 Governing equations and boundary conditions

名称	控制方程	源项	边界条件
质量守恒方程	$? ε ρ ? t + ? ? (ρ u) = 0$
动量守恒方程	$1 ε ? ρ u ? t + 1 ε (ρ u u) = - ? p + ? ? τ + ρ g + S u$	$S u = - μ K u$	p=p _in p _out =0
物质守恒方程	$? (ε c i) ? t + ? ? (u c i - D i e f f ? c i - z i n F D i e f f c i R T ? ? l) = S i$	V² ⁺ : $S V 2 + = a j N / F$ V³ ⁺ : $S V 3 + = - a j N / F$ V⁴ ⁺ : $S V 4 + = - a j P / F$ V⁵ ⁺ : $S V 5 + = a j P / F$	$c V 2 + i n = c V 0 ? S O C$ $c V 3 + i n = c V 0 ? 1 - S O C$ $c V 5 + i n = c V 0 ? S O C$ $c V 4 + i n = c V 0 ? 1 - S O C$
电荷守恒方程	$? ? i l = - ? ? i s = S ?$	$S ? = a j N$	电极和集流体界面上: $- σ s e f f ? ? s n = - I$ 电极和隔膜界面上: $- κ l e f f ? ? l ? n = I$
能量守恒方程	$? ? t ρ C p ˉ T + ? ? (ρ C p ˉ) l u T - λ ˉ ? 2 T = S T$	$S T = ∑ j Q j$	入口: $T = T i n$ 出口: $- λ ˉ ? T ? n = 0$
Butler-Volmer 定律	$j N = i N 0 e x p - α c F η A R T - e x p α a F η A R T$
浓差过电位	$η C = R T n F l n 1 - j N 1.6 × 10 - 4 n F u 0.4 c V 3 +$
Nernst方程	$U N = U N 0 + R T F l n c V 3 + c V 2 +$

表1 模型控制方程和边界条件

Table 1 Governing equations and boundary conditions

名称	控制方程	源项	边界条件
质量守恒方程	$? ε ρ ? t + ? ? (ρ u) = 0$
动量守恒方程	$1 ε ? ρ u ? t + 1 ε (ρ u u) = - ? p + ? ? τ + ρ g + S u$	$S u = - μ K u$	p=p _in p _out =0
物质守恒方程	$? (ε c i) ? t + ? ? (u c i - D i e f f ? c i - z i n F D i e f f c i R T ? ? l) = S i$	V² ⁺ : $S V 2 + = a j N / F$ V³ ⁺ : $S V 3 + = - a j N / F$ V⁴ ⁺ : $S V 4 + = - a j P / F$ V⁵ ⁺ : $S V 5 + = a j P / F$	$c V 2 + i n = c V 0 ? S O C$ $c V 3 + i n = c V 0 ? 1 - S O C$ $c V 5 + i n = c V 0 ? S O C$ $c V 4 + i n = c V 0 ? 1 - S O C$
电荷守恒方程	$? ? i l = - ? ? i s = S ?$	$S ? = a j N$	电极和集流体界面上: $- σ s e f f ? ? s n = - I$ 电极和隔膜界面上: $- κ l e f f ? ? l ? n = I$
能量守恒方程	$? ? t ρ C p ˉ T + ? ? (ρ C p ˉ) l u T - λ ˉ ? 2 T = S T$	$S T = ∑ j Q j$	入口: $T = T i n$ 出口: $- λ ˉ ? T ? n = 0$
Butler-Volmer 定律	$j N = i N 0 e x p - α c F η A R T - e x p α a F η A R T$
浓差过电位	$η C = R T n F l n 1 - j N 1.6 × 10 - 4 n F u 0.4 c V 3 +$
Nernst方程	$U N = U N 0 + R T F l n c V 3 + c V 2 +$

表2 物理及操作参数

Table 2 Physical and operational parameters

参数	符号	数值	单位
电极的初始孔隙率	$ε 0$	0.929	—
电极的初始比表面积	$A e$	1.62×10⁴	m²
电极表观尺寸	L×W×H	60×75×5	mm
电极电子电导率	$σ s$	3×10³	S· m^-1
电极纤维直径	d _f	1.76×10^-5	m
Carman-Kozeny常数	K _CK	4.28	—
有效电极表观面积	A	45	cm²
电极表观厚度	d	5	mm
电解液浓度	$ρ$	1290	kg·m^-3
电解液黏度	$μ$	4.928×10^-3	Pa·s
钒离子初始浓度	$c V 0$	1500	mol·m^-3
质子的初始浓度	$c H + 0$	4500	mol·m^-3
质子扩散系数	$D H +$	9.312×10^-9	m²·s^-1
V²⁺扩散系数	$D V 2 +$	2.4×10^-10	m²·s^-1
V³⁺ 扩散系数	$D V 3 +$	2.4×10^-10	m²·s^-1
V⁴⁺扩散系数	$D V 4 +$	3.9×10^-10	m²·s^-1
V⁵⁺扩散系数	$D V 5 +$	3.9×10^-10	m²·s^-1
负极名义反应速率常数	$k N 0$	1.7×10^-7	m·s^-1
正极名义反应速率常数	$k P 0$	6.8×10^-7	m·s^-1
阳极反应传递系数	$α a$	0.45	—
阴极反应传递系数	$α c$	0.55	—
V²⁺/V³⁺平衡电势	$U N 0$	-0.255	V
V⁴⁺/V⁵⁺平衡电势	$U P 0$	1.004	V
电解液的热导率	$λ l$	0.67	W·m^-1·K^-1
电极的热导率	$λ s$	0.15	W·m^-1·K^-1
电解液的热容	$ρ C p l$	4.19×10⁶	J·m^-3·K^-1
电极的热容	$ρ C p s$	3.33×10⁵	J·m^-3·K^-1
负极反应的熵变	- $Δ S N E$	-100	J·mol^-1·K^-1
操作温度	T	298.15	K

表2 物理及操作参数

Table 2 Physical and operational parameters

参数	符号	数值	单位
电极的初始孔隙率	$ε 0$	0.929	—
电极的初始比表面积	$A e$	1.62×10⁴	m²
电极表观尺寸	L×W×H	60×75×5	mm
电极电子电导率	$σ s$	3×10³	S· m^-1
电极纤维直径	d _f	1.76×10^-5	m
Carman-Kozeny常数	K _CK	4.28	—
有效电极表观面积	A	45	cm²
电极表观厚度	d	5	mm
电解液浓度	$ρ$	1290	kg·m^-3
电解液黏度	$μ$	4.928×10^-3	Pa·s
钒离子初始浓度	$c V 0$	1500	mol·m^-3
质子的初始浓度	$c H + 0$	4500	mol·m^-3
质子扩散系数	$D H +$	9.312×10^-9	m²·s^-1
V²⁺扩散系数	$D V 2 +$	2.4×10^-10	m²·s^-1
V³⁺ 扩散系数	$D V 3 +$	2.4×10^-10	m²·s^-1
V⁴⁺扩散系数	$D V 4 +$	3.9×10^-10	m²·s^-1
V⁵⁺扩散系数	$D V 5 +$	3.9×10^-10	m²·s^-1
负极名义反应速率常数	$k N 0$	1.7×10^-7	m·s^-1
正极名义反应速率常数	$k P 0$	6.8×10^-7	m·s^-1
阳极反应传递系数	$α a$	0.45	—
阴极反应传递系数	$α c$	0.55	—
V²⁺/V³⁺平衡电势	$U N 0$	-0.255	V
V⁴⁺/V⁵⁺平衡电势	$U P 0$	1.004	V
电解液的热导率	$λ l$	0.67	W·m^-1·K^-1
电极的热导率	$λ s$	0.15	W·m^-1·K^-1
电解液的热容	$ρ C p l$	4.19×10⁶	J·m^-3·K^-1
电极的热容	$ρ C p s$	3.33×10⁵	J·m^-3·K^-1
负极反应的熵变	- $Δ S N E$	-100	J·mol^-1·K^-1
操作温度	T	298.15	K

图3 四种流场物理区域网格划分示意图

Fig.3 Schematic diagram of four flow field physical area meshes

图4 具有SPF1型流场的VRFB半电池照片(a)及实验数据与模拟结果的对比曲线(b)

Fig.4 Photography of half VRFB with SPF1 flow field (a) and model validation with experimental data (b)

图5 电解液在不同流道内的流动特性

Fig.5 Flow characteristics of electrolyte in different channels

图6 电极几何中心线方向上不同流道内反应电流密度的分布情况

Fig.6 Local current density distribution of geometric center line of electrode in different channels

图7 不同流道内反应物V3+浓度[(a)~(d)]和浓差过电位[(e)~(h)]在XY平面（Z=2.5 mm）上的分布

Fig.7 Distribution of electrolyte concentration of V3+ [(a)~(d)] and concentration over-potential [(e)—(h)] on Z=2.5 mm XY plane in different flow channels

图8 不同流道内热效应对比

Fig.8 Thermal effects of different flow fields

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