冷却表面温差对高温质子交换膜燃料电池性能的影响

doi:10.11949/0438-1157.20231282

摘要/Abstract

摘要：

通过建立高温质子交换膜燃料电池数学模型，模拟了冷却表面存在不同温差时燃料电池内热-电-质的传输特性，分析了温差对电池内温度分布、氧浓度分布、极化曲线、膜质子电导率和电流密度的影响。结果表明：膜内温度和质子电导率随着冷却表面温度的降低而降低；催化层内的局部氧浓度随着冷却表面温差（即温度梯度）的增大而增大，但电流密度受温度及反应物浓度双重因素影响，电流密度及功率密度随着温度梯度的增大而下降。当冷却表面温度梯度从0增加至0.82 K/cm时，峰值功率密度从0.578 W/cm²下降到0.523 W/cm²，下降了9.52%。控制工作电压大于0.5 V、温度梯度小于0.20 K/cm时可获得较好的电流密度均匀性。当工作电压为0.5 V，冷却表面温度梯度为0.20 K/cm时，电流密度均匀性为92.71%。

关键词: 燃料电池, 传热, 传质, 数值模拟, 电流密度均匀性

Abstract:

By establishing a mathematical model of high-temperature proton exchange membrane fuel cells, the heat-electricity-mass transfer characteristics in the fuel cell when there are different temperature differences on the cooling surface are simulated. The effect of temperature difference on the membrane temperature distribution, proton conductivity distribution, current density distribution, and polarization curves are analyzed. The results show that the temperature and proton conductivity in membrane decreases with the decrease of cooling surface temperature difference (temperature gradient). The local oxygen concentration in catalyst layer decreases with decreasing the temperature difference. And the current density is affected by both temperature and gas reactant concentration. A large temperature gradient results a low current density and low power density. The peak power density dropped from 0.578 W/cm² to 0.523 W/cm² with a decrease of 9.52% when the temperature gradient increased from 0 to 0.82 K/cm. The current density uniformity was 92.71% at the operating voltage 0.5 V and the temperature gradient 0.20 K/cm.

Key words: fuel cells, heat transfer, mass transfer, numerical simulation, current density uniformity

中图分类号:

TK 91

王金山, 王世学, 朱禹. 冷却表面温差对高温质子交换膜燃料电池性能的影响[J]. 化工学报, 2024, 75(5): 2026-2035.

Jinshan WANG, Shixue WANG, Yu ZHU. Influence of cooling surface temperature difference on the high temperature proton-exchange membrane fuel cell performance[J]. CIESC Journal, 2024, 75(5): 2026-2035.

图/表 11

表1 HT-PEMFC数学模型及源项表达式［28-29］

Table 1 HT-PEMFC mathematical model and source terms［28-29］

守恒方程	表达式	源项
质量	$\nabla \cdot (ε ρ u) = S_{m}$	$\begin{array}{l} a n o d e C L : S_{m} = - \frac{j_{a}}{2 F} M_{H_{2}} \\ c a t h o d e C L : S_{m} = - \frac{j_{c}}{4 F} M_{O_{2}} + \frac{j_{c}}{2 F} M_{H_{2} O} \end{array}$
物质	$\nabla \cdot (ε ρ u Y_{i}) = ρ D_{i}^{e f f} \nabla Y_{i} + S_{i}$	$\begin{array}{l} a n o d e C L : S_{H_{2}} = - \frac{j_{a}}{2 F} M_{H_{2}} \\ c a t h o d e C L : S_{O_{2}} = - \frac{j_{c}}{4 F} M_{O_{2}}, S_{H_{2} O} = \frac{j_{c}}{2 F} M_{H_{2} O} \end{array}$
动量	$\nabla \cdot (ε ρ u u) = - ε \nabla p + \nabla \cdot τ - ε^{2} \frac{μ}{K} u$
电荷	$电子 : \nabla \cdot (σ_{e l e}^{e f f} \nabla φ_{e l e}) + S_{e l e} = 0$	$a n o d e C L : S_{e l e} = - j_{a}; c a t h o d e C L : S_{e l e} = j_{c}$
	$质子 : \nabla \cdot (σ_{p r o}^{e f f} \nabla φ_{p r o}) + S_{p r o} = 0$	$a n o d e C L : S_{p r o} = j_{c}; c a t h o d e C L : S_{p r o} = - j_{a}$
能量	$\nabla \cdot (ε ρ C_{p} u T) = \nabla \cdot (λ^{e f f} \nabla T) + S_{T}$	$\begin{matrix} a n o d e C L : S_{T} = - \frac{j_{a} T Δ S_{a}}{2 F} + j_{a} \|η_{a c t}\| + {‖\nabla φ_{e l e}‖}^{2} σ_{e l e}^{e f f} + {‖\nabla φ_{p r o}‖}^{2} σ_{p r o}^{e f f} \\ c a t h o d e C L : S_{T} = - \frac{j_{c} T Δ S_{c}}{2 F} + j_{c} \|η_{a c t}\| + {‖\nabla φ_{e l e}‖}^{2} σ_{e l e}^{e f f} + {‖\nabla φ_{p r o}‖}^{2} σ_{p r o}^{e f f} \\ m e m b r a n e : S_{T} = {‖\nabla φ_{p r o}‖}^{2} σ_{p r o}^{e f f}; \\ G D L : S_{T} = {‖\nabla φ_{e l e}‖}^{2} σ_{e l e}^{e f f}; B P : S_{T} = {‖\nabla φ_{e l e}‖}^{2} σ_{e l e}^{} \end{matrix}$

表1 HT-PEMFC数学模型及源项表达式［28-29］

Table 1 HT-PEMFC mathematical model and source terms［28-29］

守恒方程	表达式	源项
质量	$\nabla \cdot (ε ρ u) = S_{m}$	$\begin{array}{l} a n o d e C L : S_{m} = - \frac{j_{a}}{2 F} M_{H_{2}} \\ c a t h o d e C L : S_{m} = - \frac{j_{c}}{4 F} M_{O_{2}} + \frac{j_{c}}{2 F} M_{H_{2} O} \end{array}$
物质	$\nabla \cdot (ε ρ u Y_{i}) = ρ D_{i}^{e f f} \nabla Y_{i} + S_{i}$	$\begin{array}{l} a n o d e C L : S_{H_{2}} = - \frac{j_{a}}{2 F} M_{H_{2}} \\ c a t h o d e C L : S_{O_{2}} = - \frac{j_{c}}{4 F} M_{O_{2}}, S_{H_{2} O} = \frac{j_{c}}{2 F} M_{H_{2} O} \end{array}$
动量	$\nabla \cdot (ε ρ u u) = - ε \nabla p + \nabla \cdot τ - ε^{2} \frac{μ}{K} u$
电荷	$电子 : \nabla \cdot (σ_{e l e}^{e f f} \nabla φ_{e l e}) + S_{e l e} = 0$	$a n o d e C L : S_{e l e} = - j_{a}; c a t h o d e C L : S_{e l e} = j_{c}$
	$质子 : \nabla \cdot (σ_{p r o}^{e f f} \nabla φ_{p r o}) + S_{p r o} = 0$	$a n o d e C L : S_{p r o} = j_{c}; c a t h o d e C L : S_{p r o} = - j_{a}$
能量	$\nabla \cdot (ε ρ C_{p} u T) = \nabla \cdot (λ^{e f f} \nabla T) + S_{T}$	$\begin{matrix} a n o d e C L : S_{T} = - \frac{j_{a} T Δ S_{a}}{2 F} + j_{a} \|η_{a c t}\| + {‖\nabla φ_{e l e}‖}^{2} σ_{e l e}^{e f f} + {‖\nabla φ_{p r o}‖}^{2} σ_{p r o}^{e f f} \\ c a t h o d e C L : S_{T} = - \frac{j_{c} T Δ S_{c}}{2 F} + j_{c} \|η_{a c t}\| + {‖\nabla φ_{e l e}‖}^{2} σ_{e l e}^{e f f} + {‖\nabla φ_{p r o}‖}^{2} σ_{p r o}^{e f f} \\ m e m b r a n e : S_{T} = {‖\nabla φ_{p r o}‖}^{2} σ_{p r o}^{e f f}; \\ G D L : S_{T} = {‖\nabla φ_{e l e}‖}^{2} σ_{e l e}^{e f f}; B P : S_{T} = {‖\nabla φ_{e l e}‖}^{2} σ_{e l e}^{} \end{matrix}$

表2 HT-PEMFC数学模型及几何结构参数

Table 2 Parameters in the mathematical model and structure of HT-PEMFC

参数	数值	文献
流道宽度、高度、脊宽度/m	1×10^-3、1×10^-3、1×10^-3	[31]
膜、催化层、扩散层厚度/m	5×10^-5、1×10^-5、2.25×10^-4	[29]
催化层中电解液分数	0.21	[29]
催化层和扩散层孔隙率	0.4、0.6	[29]
PEM、CL、GDL和BP密度/(kg/m³)	1300、2145、1800、2266	[29]
PEM、CL、GDL和BP比热容/(J/(kg·K))	1650、3300、568、2930	[29]
PEM、CL、GDL和BP热导率/(W/(m·K))	0.95、1.5、1.2、20	[29]
CL、GDL和BP材料的电导率/(S/m)	500、1000、20000	[29]
氢气热导率/(W/(m·K))	$0.03591 + 4.5918 \times 10^{- 4} T - 6.4933 \times 10^{- 8} T^{2}$	[31]
氧气热导率/(W/(m·K))	$0.00121 + 8.6157 \times 10^{- 5} T - 1.3346 \times 10^{- 8} T^{2}$	[31]
水蒸气热导率/(W/(m·K))	$0.00053 + 4.7093 \times 10^{- 5} T - 4.95518 \times 10^{- 8} T^{2}$	[31]
氮气热导率/(W/(m·K))	$0.00309 + 7.5930 \times 10^{- 5} T - 1.1014 \times 10^{- 8} T^{2}$	[31]
氢气动力黏度/(Pa·s)	$3.205 \times 10^{- 3} {(T / 293.85)}^{1.5} {(T + 72)}^{- 1.0}$	[28]
氧气动力黏度/(Pa·s)	$8.46 \times 10^{- 3} {(T / 292.25)}^{1.5} {(T + 127)}^{- 1.0}$	[28]
水蒸气动力黏度/(Pa·s)	$7.512 \times 10^{- 3} {(T / 291.15)}^{1.5} {(T + 120)}^{- 1.0}$	[28]
氢气扩散系数/(m²/s)	$1.055 \times 10^{- 4} {(T / 333.15)}^{1.5} (101325 / p)$	[28]
氧气扩散系数/(m²/s)	$2.652 \times 10^{- 5} {(T / 333.15)}^{1.5} (101325 / p)$	[28]
水蒸气扩散系数/(m²/s)	$2.982 \times 10^{- 5} {(T / 333.15)}^{1.5} (101325 / p)$	[28]
磷酸掺杂水平	10	[28]
阳极、阴极传递系数	0.5、0.45	[28]
氢气、氧气参考浓度/(mol/m³)	40.88、40.88	[28]

表2 HT-PEMFC数学模型及几何结构参数

Table 2 Parameters in the mathematical model and structure of HT-PEMFC

参数	数值	文献
流道宽度、高度、脊宽度/m	1×10^-3、1×10^-3、1×10^-3	[31]
膜、催化层、扩散层厚度/m	5×10^-5、1×10^-5、2.25×10^-4	[29]
催化层中电解液分数	0.21	[29]
催化层和扩散层孔隙率	0.4、0.6	[29]
PEM、CL、GDL和BP密度/(kg/m³)	1300、2145、1800、2266	[29]
PEM、CL、GDL和BP比热容/(J/(kg·K))	1650、3300、568、2930	[29]
PEM、CL、GDL和BP热导率/(W/(m·K))	0.95、1.5、1.2、20	[29]
CL、GDL和BP材料的电导率/(S/m)	500、1000、20000	[29]
氢气热导率/(W/(m·K))	$0.03591 + 4.5918 \times 10^{- 4} T - 6.4933 \times 10^{- 8} T^{2}$	[31]
氧气热导率/(W/(m·K))	$0.00121 + 8.6157 \times 10^{- 5} T - 1.3346 \times 10^{- 8} T^{2}$	[31]
水蒸气热导率/(W/(m·K))	$0.00053 + 4.7093 \times 10^{- 5} T - 4.95518 \times 10^{- 8} T^{2}$	[31]
氮气热导率/(W/(m·K))	$0.00309 + 7.5930 \times 10^{- 5} T - 1.1014 \times 10^{- 8} T^{2}$	[31]
氢气动力黏度/(Pa·s)	$3.205 \times 10^{- 3} {(T / 293.85)}^{1.5} {(T + 72)}^{- 1.0}$	[28]
氧气动力黏度/(Pa·s)	$8.46 \times 10^{- 3} {(T / 292.25)}^{1.5} {(T + 127)}^{- 1.0}$	[28]
水蒸气动力黏度/(Pa·s)	$7.512 \times 10^{- 3} {(T / 291.15)}^{1.5} {(T + 120)}^{- 1.0}$	[28]
氢气扩散系数/(m²/s)	$1.055 \times 10^{- 4} {(T / 333.15)}^{1.5} (101325 / p)$	[28]
氧气扩散系数/(m²/s)	$2.652 \times 10^{- 5} {(T / 333.15)}^{1.5} (101325 / p)$	[28]
水蒸气扩散系数/(m²/s)	$2.982 \times 10^{- 5} {(T / 333.15)}^{1.5} (101325 / p)$	[28]
磷酸掺杂水平	10	[28]
阳极、阴极传递系数	0.5、0.45	[28]
氢气、氧气参考浓度/(mol/m³)	40.88、40.88	[28]

图1 HT-PEMFC几何结构及网格划分

Fig.1 HT-PEMFC structure and mesh grid

表3 冷却表面温度分布函数参数

Table 3 Temperature distribution function parameters in cooling surface

温差/K	温度梯度/(K/cm)	a	b
0	0	0	433.15
5	0.10	102.04	428.10
10	0.20	204.08	423.05
20	0.41	408.16	412.95
30	0.61	612.24	402.84
40	0.82	816.33	392.74

图2 模拟结果与实验结果对比

Fig.2 Comparison of the experimental data and simulation data

图3 膜中心面温度和质子电导率分布、催化层中心面氧浓度及电流密度分布

Fig.3 Temperature and proton conductivity distribution at the membrane center plane, oxygen concentration and current density distribution at the CL center plane

图4 不同冷却表面温差时膜中心线处的质子电导率

Fig.4 Proton conductivity at the center line of PEM under different cooling surface temperature difference

图5 不同冷却表面温差时催化层中心线处的电流密度

Fig.5 Current density at the center line of CL under different cooling surface temperature difference

图6 不同冷却表面温差时催化层中心线处的氧浓度

Fig.6 Oxygen concentration at the center line of CL under different cooling surface temperature difference

图7 不同冷却表面温差时的极化曲线和功率密度曲线及电流密度变化率

Fig.7 Polarization curves and power density curves and current density change rate under different cooling surface temperature difference

图8 不同温差时膜质子电导率均匀性和电流密度均匀性

Fig.8 Membrane proton conductivity uniformity and current density uniformity under different cooling surface temperature difference

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次数	27	104
比例	21%	79%

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[4]	关朝阳, 黄国庆, 张一喃, 陈宏霞, 杜小泽. 泡沫铜导离气泡强化流动沸腾换热实验研究[J]. 化工学报, 2024, 75(5): 1765-1776.
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[7]	刘帆, 张芫通, 陶成, 胡成玉, 杨小平, 魏进家. 歧管式射流微通道液冷散热性能[J]. 化工学报, 2024, 75(5): 1777-1786.
[8]	冯彬彬, 卢明佳, 黄志宏, 常译文, 崔志明. 碳载体在质子交换膜燃料电池中的应用及优化[J]. 化工学报, 2024, 75(4): 1469-1484.
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[10]	蒋方涛, 钱刚, 周兴贵, 段学志, 张晶. 基于［bmim］［BF₄］相转移催化的氟代碳酸乙烯酯高效合成[J]. 化工学报, 2024, 75(4): 1543-1551.
[11]	张劲, 郭志斌, 罗来明, 卢善富, 相艳. 5 kW重整甲醇高温质子交换膜燃料电池系统设计与性能[J]. 化工学报, 2024, 75(4): 1697-1704.
[12]	孙铭泽, 黄鹤来, 牛志强. 铂基氧还原催化剂：从单晶电极到拓展表面纳米材料[J]. 化工学报, 2024, 75(4): 1256-1269.
[13]	赵金鹏, 张永民, 兰斌, 罗节文, 赵碧丹, 王军武. 气固鼓泡床结构双流体传热模型及其模拟验证[J]. 化工学报, 2024, 75(4): 1497-1507.
[14]	董霄, 白志山, 杨晓勇, 殷伟, 刘宁普, 于启凡. CHPPO工艺氧化液耦合除杂技术的研究与工业应用[J]. 化工学报, 2024, 75(4): 1630-1641.
[15]	吉笑盈, 郑园, 李晓鹏, 杨振, 张维, 邱诗蕊, 张倩颖, 罗沧海, 孙东鹏, 陈东, 李东亮. 微流控可控制备液滴、颗粒和胶囊及其应用[J]. 化工学报, 2024, 75(4): 1455-1468.