Influence of cooling surface temperature difference on the high temperature proton-exchange membrane fuel cell performance

doi:10.11949/0438-1157.20231282

Abstract

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

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

CLC Number:

TK 91

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.

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.

Figures/Tables 11

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

守恒方程	表达式	源项
质量	$∇ ⋅ ε ρ u = S m$	$a n o d e C L : S m = - j a 2 F M H 2 c a t h o d e C L : S m = - j c 4 F M O 2 + j c 2 F M H 2 O$
物质	$∇ ⋅ ε ρ u Y i = ρ D i e f f ∇ Y i + S i$	$a n o d e C L : S H 2 = - j a 2 F M H 2 c a t h o d e C L : S O 2 = - j c 4 F M O 2, S H 2 O = j c 2 F M H 2 O$
动量	$∇ ⋅ ε ρ u u = - ε ∇ p + ∇ ⋅ τ - ε 2 μ K u$
电荷	$电子 : ∇ ⋅ σ e l e e f f ∇ φ e l e + S e l e = 0$	$a n o d e C L : S e l e = - j a; c a t h o d e C L : S e l e = j c$
	$质子 : ∇ ⋅ σ p r o e f f ∇ φ p r o + S p r o = 0$	$a n o d e C L : S p r o = j c; c a t h o d e C L : S p r o = - j a$
能量	$∇ ⋅ ε ρ C p u T = ∇ ⋅ λ e f f ∇ T + S T$	$a n o d e C L : S T = - j a T Δ S a 2 F + j a η a c t + ∇ φ e l e 2 σ e l e e f f + ∇ φ p r o 2 σ p r o e f f c a t h o d e C L : S T = - j c T Δ S c 2 F + j c η a c t + ∇ φ e l e 2 σ e l e e f f + ∇ φ p r o 2 σ p r o e f f m e m b r a n e : S T = ∇ φ p r o 2 σ p r o e f f; G D L : S T = ∇ φ e l e 2 σ e l e e f f; B P : S T = ∇ φ e l e 2 σ e l e$

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

守恒方程	表达式	源项
质量	$∇ ⋅ ε ρ u = S m$	$a n o d e C L : S m = - j a 2 F M H 2 c a t h o d e C L : S m = - j c 4 F M O 2 + j c 2 F M H 2 O$
物质	$∇ ⋅ ε ρ u Y i = ρ D i e f f ∇ Y i + S i$	$a n o d e C L : S H 2 = - j a 2 F M H 2 c a t h o d e C L : S O 2 = - j c 4 F M O 2, S H 2 O = j c 2 F M H 2 O$
动量	$∇ ⋅ ε ρ u u = - ε ∇ p + ∇ ⋅ τ - ε 2 μ K u$
电荷	$电子 : ∇ ⋅ σ e l e e f f ∇ φ e l e + S e l e = 0$	$a n o d e C L : S e l e = - j a; c a t h o d e C L : S e l e = j c$
	$质子 : ∇ ⋅ σ p r o e f f ∇ φ p r o + S p r o = 0$	$a n o d e C L : S p r o = j c; c a t h o d e C L : S p r o = - j a$
能量	$∇ ⋅ ε ρ C p u T = ∇ ⋅ λ e f f ∇ T + S T$	$a n o d e C L : S T = - j a T Δ S a 2 F + j a η a c t + ∇ φ e l e 2 σ e l e e f f + ∇ φ p r o 2 σ p r o e f f c a t h o d e C L : S T = - j c T Δ S c 2 F + j c η a c t + ∇ φ e l e 2 σ e l e e f f + ∇ φ p r o 2 σ p r o e f f m e m b r a n e : S T = ∇ φ p r o 2 σ p r o e f f; G D L : S T = ∇ φ e l e 2 σ e l e e f f; B P : S T = ∇ φ e l e 2 σ e l e$

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))	$0.03591 + 4.5918 × 10 - 4 T - 6.4933 × 10 - 8 T 2$	[31]
氧气热导率/(W/(m·K))	$0.00121 + 8.6157 × 10 - 5 T - 1.3346 × 10 - 8 T 2$	[31]
水蒸气热导率/(W/(m·K))	$0.00053 + 4.7093 × 10 - 5 T - 4.95518 × 10 - 8 T 2$	[31]
氮气热导率/(W/(m·K))	$0.00309 + 7.5930 × 10 - 5 T - 1.1014 × 10 - 8 T 2$	[31]
氢气动力黏度/(Pa·s)	$3.205 × 10 - 3 T / 293.85 1.5 T + 72 - 1.0$	[28]
氧气动力黏度/(Pa·s)	$8.46 × 10 - 3 T / 292.25 1.5 T + 127 - 1.0$	[28]
水蒸气动力黏度/(Pa·s)	$7.512 × 10 - 3 T / 291.15 1.5 T + 120 - 1.0$	[28]
氢气扩散系数/(m²/s)	$1.055 × 10 - 4 T / 333.15 1.5 101325 / p$	[28]
氧气扩散系数/(m²/s)	$2.652 × 10 - 5 T / 333.15 1.5 101325 / p$	[28]
水蒸气扩散系数/(m²/s)	$2.982 × 10 - 5 T / 333.15 1.5 101325 / p$	[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]

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))	$0.03591 + 4.5918 × 10 - 4 T - 6.4933 × 10 - 8 T 2$	[31]
氧气热导率/(W/(m·K))	$0.00121 + 8.6157 × 10 - 5 T - 1.3346 × 10 - 8 T 2$	[31]
水蒸气热导率/(W/(m·K))	$0.00053 + 4.7093 × 10 - 5 T - 4.95518 × 10 - 8 T 2$	[31]
氮气热导率/(W/(m·K))	$0.00309 + 7.5930 × 10 - 5 T - 1.1014 × 10 - 8 T 2$	[31]
氢气动力黏度/(Pa·s)	$3.205 × 10 - 3 T / 293.85 1.5 T + 72 - 1.0$	[28]
氧气动力黏度/(Pa·s)	$8.46 × 10 - 3 T / 292.25 1.5 T + 127 - 1.0$	[28]
水蒸气动力黏度/(Pa·s)	$7.512 × 10 - 3 T / 291.15 1.5 T + 120 - 1.0$	[28]
氢气扩散系数/(m²/s)	$1.055 × 10 - 4 T / 333.15 1.5 101325 / p$	[28]
氧气扩散系数/(m²/s)	$2.652 × 10 - 5 T / 333.15 1.5 101325 / p$	[28]
水蒸气扩散系数/(m²/s)	$2.982 × 10 - 5 T / 333.15 1.5 101325 / p$	[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]

Fig.1 HT-PEMFC structure and mesh grid

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

Fig.2 Comparison of the experimental data and simulation data

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

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

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

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

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

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

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