全钒液流电池多孔电极非均匀压缩的数值模拟

doi:10.16085/j.issn.1000-6613.2023-0733

摘要/Abstract

摘要：

电极压缩会导致全钒液流电池的多孔电极侵入流道影响电池性能。本文建立了蛇形流道多孔电极非均匀压缩的三维稳态模型，对比研究了多孔电极非均匀压缩和多孔电极矩形压缩的内部压降、电解质流速和过电位分布的不同，发现多孔电极非均匀压缩与实际情况符合程度高。分析了不同压缩比对电极非均匀压缩多孔电极内部压降、电解质速度、反应物质浓度分布、电解质电位、过电位、局部电流密度和浓差过电位的影响。结果表明：在压缩比增大的情况下，电极非均匀压缩多孔电极内部压降和速度增大程度高于电极矩形压缩，电极非均匀压缩侵入部分与流道接触区域处过电位高于电极矩形压缩。电极非均匀压缩多孔电极内部反应物质浓度分布均匀性增大，电解质电位和过电位降低，阴极区域局部电流密度和浓差过电位上升。

关键词: 全钒液流电池, 电解液, 多孔电极非均匀压缩模型, 数值模拟

Abstract:

Electrode compression can cause the porous electrodes of all vanadium flow batteries to invade the flow channel, affecting battery performance. This article established a three-dimensional steady-state model for non-uniform compression of porous electrodes in a serpentine flow channel, and compared the differences in internal pressure drop, electrolyte flow rate, and overpotential distribution between non-uniform compression of porous electrodes and rectangular compression of porous electrodes. It was found that non-uniform compression of porous electrodes was highly consistent with the actual situation. The effects of different compression ratios on the internal voltage drop, electrolyte velocity, concentration distribution of reactants, electrolyte potential, overpotential, local current density and concentration overpotential of non-uniform compression porous electrode were analyzed.The results showed that with an increase in compression ratio, the increase in internal pressure drop and velocity of the non-uniformly compressed porous electrode was greater than that of the electrode rectangular compression. The overvoltage at the contact area between the electrode non-uniformly compressed invasion part and the flow channel was higher than that of the electrode rectangular compression. The uniformity of the concentration distribution of reactants in the porous electrode with non-uniform compression increased, the electrolyte potential and overvoltage decreased, and the local current density and concentration overvoltage in the cathode area increased.

Key words: vanadium flow battery, electrolyte, non-uniform compression model of porous electrodes, numerical simulation

中图分类号:

TM911

王庆泰, 张赛, 王杰敏. 全钒液流电池多孔电极非均匀压缩的数值模拟[J]. 化工进展, 2024, 43(6): 2940-2949.

WANG Qingtai, ZHANG Sai, WANG Jiemin. Numerical simulation for non-uniform compression of porous electrodes in vanadium flow batteries[J]. Chemical Industry and Engineering Progress, 2024, 43(6): 2940-2949.

图/表 12

图1 全钒液流电池工作原理简图

图2 非均匀压缩多孔电极的几何模型

图3 多孔电极侵入部分等效为等体积的矩形和侵入部分截面形状为抛物线的对比

表1 控制方程和边界条件

名称	控制方程	边界条件
连续性方程 Navier-Stokes方程 Darcy定律	$∇ ν = 0$ $ρ ν ⋅ ∇ ν = - p + μ ∇ ν + ∇ ν T$ $u = d f 2 K c k μ ε 3 1 - ε 2 ∇ p$	$ν$ = $ν$ _inp_out=0
Nernst-Planck方程	$N i = - D i e f f ∇ c i - z i D i e f f F c i ∇ φ l / R T + u c i$	$c V 2 + i n = c 0 ⋅ S O C$ $c V 3 + i n = c 0 ⋅ (1 - S O C)$ $c V 4 + i n = c 0 ⋅ (1 - S O C)$ $c V 5 + i n = c 0 ⋅ S O C$
电荷守恒方程	$∇ ⋅ i s = - ∇ ⋅ i e = - σ s e f f ∇ φ s = k l e f f ∇ φ l = S ϕ$	在电极与集流体界面上： $- σ s e f f ∇ φ s ⋅ n = - I$ 电极与隔膜界面上： $- κ l e f f ∇ φ l ⋅ n = I$
Butler-Volmer定律	$j = A i c 0 c V 3 + s c V 3 + e x p 1 - α c F η c R T - c V 2 + s c V 2 + e x p - α c F η c R T$ $j = A i a 0 c V 4 + s c V 4 + e x p 1 - α a F η a R T - c V 5 + s c V 5 + e x p - α a F η a R T$
交换电流密度	$i c 0 = F k c (c V 2 +) 1 - α c (c V 3 +) α c$ $i a 0 = F k a (c V 5 +) 1 - α a (c V 4 +) α a$
过电位	$η c = φ s - φ e - E c$ $η a = φ s - φ e - E a$
能斯特方程	$E c = E 1 + R T F l n (c V 3 + c V 2 +)$ $E a = E 2 + R T F l n (c V 5 + c V 4 +)$

表1 控制方程和边界条件

名称	控制方程	边界条件
连续性方程 Navier-Stokes方程 Darcy定律	$∇ ν = 0$ $ρ ν ⋅ ∇ ν = - p + μ ∇ ν + ∇ ν T$ $u = d f 2 K c k μ ε 3 1 - ε 2 ∇ p$	$ν$ = $ν$ _inp_out=0
Nernst-Planck方程	$N i = - D i e f f ∇ c i - z i D i e f f F c i ∇ φ l / R T + u c i$	$c V 2 + i n = c 0 ⋅ S O C$ $c V 3 + i n = c 0 ⋅ (1 - S O C)$ $c V 4 + i n = c 0 ⋅ (1 - S O C)$ $c V 5 + i n = c 0 ⋅ S O C$
电荷守恒方程	$∇ ⋅ i s = - ∇ ⋅ i e = - σ s e f f ∇ φ s = k l e f f ∇ φ l = S ϕ$	在电极与集流体界面上： $- σ s e f f ∇ φ s ⋅ n = - I$ 电极与隔膜界面上： $- κ l e f f ∇ φ l ⋅ n = I$
Butler-Volmer定律	$j = A i c 0 c V 3 + s c V 3 + e x p 1 - α c F η c R T - c V 2 + s c V 2 + e x p - α c F η c R T$ $j = A i a 0 c V 4 + s c V 4 + e x p 1 - α a F η a R T - c V 5 + s c V 5 + e x p - α a F η a R T$
交换电流密度	$i c 0 = F k c (c V 2 +) 1 - α c (c V 3 +) α c$ $i a 0 = F k a (c V 5 +) 1 - α a (c V 4 +) α a$
过电位	$η c = φ s - φ e - E c$ $η a = φ s - φ e - E a$
能斯特方程	$E c = E 1 + R T F l n (c V 3 + c V 2 +)$ $E a = E 2 + R T F l n (c V 5 + c V 4 +)$

表2 全钒液流电池性能参数

参数	数值
碳纤维直径（d_f）/μm	17.9
电导率（σ_s）/S·m^-1	66.7
钒离子初始浓度（c₀）/mol·m³	1500
阴极传递系数（α_c）	0.5
阳极传递系数（α_a）	0.5
黏度（μ）/Pa·s	4.928×10^-3
阴极标准反应速率常数（k_c）/m·s^-1	6.8×10^-7
阳极标准反应速率常数（k_a）/m·s^-1	1.7×10^-7
阴极标准电位（E₁）/V	-0.225
阳极标准电位（E₂）/V	1.004
荷电状态（SOC）	0.8
操作温度（T）/K	293

图4 不同SOC下电池电压模拟值和实验值[19]的对比

图5 进口流量对CR=10%和CR=50%下电极矩形压缩和电极非均匀压缩多孔电极内部压降的影响

图6 CR=10%和CR=50%下电极矩形压缩和电极非均匀压缩在不同进口流量时负极处电解质速度变化（沿X轴方向的线2计算多孔电极中电解质速度）

图7 非均匀多孔电极在CR =10%和CR=50%下V2+/V5+离子分布、电解质电位和过电位分布

图8 电极非均匀压缩和电极矩形压缩阴极中部在不同CR下过电位的分布（沿X轴方向的红色线计算多孔电极中过电位）

图9 CR=10%和CR=50%阴极区域局部电流密度分布的对比

图10 CR=10%和CR=50%阴极区域浓差过电位分布的对比

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