Electrochemical properties of solid oxide fuel cells under the coupling effect of airflow pattern and airflow velocity

WANG Hao; XIE Jiamiao; HAO Wenqian; LI Jingyang; ZHANG Peng; MA Xiaofan; LIU Fu; WANG Xu

doi:10.7498/aps.74.20250096

Abstract

Under the dual background of deep adjustment of global energy pattern and severe challenges of environmental problems, solid oxide fuel cell (SOFC) has become the focus of research on efficient and clean energy conversion technology due to its many excellent characteristics. The electrochemical performance of SOFC is affected by various factors such as gas flow pattern (co-flow, counter-flow, cross-flow), flow rate (cathode and anode channel gases), and operating voltage. Accurately analysing the variation of electrochemical indexes with each factor is the basis for proposing the design scheme of high efficiency reaction of the cell. Therefore, a three-dimensional multi-field coupling model of SOFC is established in this study, and the model parameters and boundary conditions covering electrochemistry, gas flow, substance diffusion, etc. are set to study the influence of the coupling between factors on the electrochemical performance of the cell. These results show that with the decrease of operating voltage, the electrochemical reaction rate of the cell increases significantly, the gas mole fraction gradient increases, and the inhomogeneity of the electrolyte current density distribution is enhanced. Under low-voltage operating conditions, the cross-flow flow pattern shows better electrochemical performance advantages, and its power density profile takes the lead in different current density intervals. With the increase of the flow rate of the flow channel gas, the output power density curve of the cell shows an overall upward trend, and then the driving effect of the flow rate increase on the power density increase is gradually weakened due to the saturated cathodic reaction. This study reveals the influence of the coupling of flow pattern, flow rate and voltage on the electrochemical performance of SOFC, and provides guidance for the commercial application of SOFC.

Keywords:

Authors and contacts

1.
School of Aeronautics and Astronautics, North University of China, Taiyuan 030051, China
2.
Beijing Tsing Aero Armament Technology Co., Ltd., Beijing 102100, China
3.
School of Mechanical and Electrical Engineering, North University of China, Taiyuan 030051, China

Corresponding author: HAO Wenqian, wqhao@nuc.edu.cn ; LI Jingyang, lijingyang.thu@hotmail.com ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12202407, 12102399) and the Fundamental Research Program of Shanxi Province, China (Grant Nos. 202403021221111, 202103021223198).

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References

[1]	Minh N Q, Takahashi T 1995 Science and Technology of Ceramic Fuel Cells (Amsterdam: Elsevier Science) p147
[2]	Singhal S C, Kendall K 2002 Mater. Today 5 55
[3]	申双林, 张小坤, 万兴文, 郑克晴, 凌意瀚, 王绍荣 2022 物理学报 71 164401 Google Scholar Shen S L, Zhang X K, Wan X W, Zheng K Q, Ling Y H, Wang S R 2022 Acta Phys. Sin. 71 164401 Google Scholar
[4]	徐晗, 张璐, 党政 2020 物理学报 69 098801 Google Scholar Xu H, Zhang L, Dang Z 2020 Acta Phys. Sin. 69 098801 Google Scholar
[5]	李凯, 李霄, 李箭, 谢佳苗 2019 无机材料学报 34 611 Google Scholar Li K, Li X, Li J, Xie J M 2019 J. Inorg. Mater. 34 611 Google Scholar
[6]	Su Y, Zhu D Y, Zhang T T, Zhang Y R, Han W P, Zhang J, Ramakrishna S, Long Y Z 2022 Chin. Phys. B 31 057305 Google Scholar
[7]	Al-Masri A, Peksen M, Blum L, Stolten D 2014 Appl. Energy 135 539 Google Scholar
[8]	Razbani O, Assadi M, Andersson M 2013 Int. J. Hydrogen Energy 38 10068 Google Scholar
[9]	Schluckner C, Subotic’ V, Lawlor V, Hochenauer C 2014 Int. J. Hydrogen Energy 39 19102 Google Scholar
[10]	Schluckner C, Subotic ́ V, Lawlor V, Hochenauer C 2015 Int. J. Hydrogen Energy 40 10943 Google Scholar
[11]	Danilov V A, Tade M O 2009 Int. J. Hydrogen Energy 34 8998 Google Scholar
[12]	Haberman B A, Young J B 2004 Int. J. Heat Mass Transfer. 47 3617 Google Scholar
[13]	Lu P Z, Wei S L, Du Z H, Ma W D, Ni S D 2024 Int. J. Heat Mass Transfer. 229 125708 Google Scholar
[14]	Zhang Z G, Yue D T, Yang G G, Chen J F, Zheng Y F, Miao H, Wang W G, Yuan J L, Huang N B 2015 Int. J. Heat Mass Transfer. 84 942 Google Scholar
[15]	Andersson M, Paradis H, Yuan J L, Sunde’n B 2013 Electrochim. Acta 109 881 Google Scholar
[16]	Sohn S, Baek S. M, Nam J. H, Kim C-J 2016 Int. J. Hydrogen Energy 41 5582 Google Scholar
[17]	Wang G L, Yang Y Z, Zhang H O, Xia W S 2007 J. Power Sources 167 398 Google Scholar
[18]	Choudhary T, Sanjay 2016 Int. J. Hydrogen Energy 41 10212 Google Scholar
[19]	Tan W C, Iwai H, Kishimoto M, Yoshida H 2018 J. Power Sources 400 135 Google Scholar
[20]	William J, Sembler, Kumar S 2011 J. Fuel Cell Sci. Technol. 2 021007
[21]	Park J M, Kim D Y, Baek J D, Yoon Y J, Su P C, Lee S H 2018 Energies 11 473 Google Scholar
[22]	Li Z, Yang G G, Cui D A, Li S, Shen Q W, Zhang G L, Zhang H P 2022 J. Power Sources. 522 230981 Google Scholar
[23]	Zhan R B, Wang Y, Ni M, Zhang G B, Du Q, Jiao K 2020 Int. J. Hydrogen Energy 45 6897 Google Scholar
[24]	Sawangtong W, Dunnimit P, Wiwatanapataphee B, Sawangtong P 2024 Part. Diff. Eq. Appl. Math. 11 100890
[25]	Li J S, Zhang J C, Zhang R 2025 J. Comput. Appl. Math. 460 116411 Google Scholar
[26]	Shirsat V R, Vaidya P D, Dalvi V H, Singhal R. S, Kelkar A K, Joshi J B 2025 Sep. Purif. Technol. 354 129215 Google Scholar
[27]	刘艺辉 2023 硕士学位论文(大连: 大连海事大学) Liu Y H 2023 M. S. Thesis (Dalian: Dalian Maritime University
[28]	Shanma S M, Dutta A 2025 J. Alloys Compd. 1010 177931
[29]	Nerat M, Juric ̌ic ́ D 2016 Int. J. Hydrogen Energy 41 3613 Google Scholar
[30]	Chaudhary T N, Saleem U, Chen B 2019 Int. J. Hydrogen Energy 44 8425 Google Scholar
[31]	Wang Y, Zhan R B, Qin Y Z, Zhang G B, Du Q, Jiao K 2018 Int. J. Hydrogen Energy 43 20059 Google Scholar

Cited By

图 1 SOFC几何结构和有限元模型　(a) 顺流/逆流形式的几何结构; (b) 交叉流形式的几何结构; (c) 顺流/逆流形式的有限元模型; (d) 交叉流形式的有限元模型

Figure 1. Geometry structure and finite element model of SOFC: (a) Geometry structure of co-flow/counter-flow patterns; (b) geometry structure of cross-flow pattern; (c) finite element model of co-flow/counter-flow patterns; (d) finite element model of cross-flow pattern.

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图 2 当前有限元模型的极化曲线与文献[27]得到的结果对比图

Figure 2. Comparison of the polarization curves between the results of current finite element model and the results obtained in Ref. [27].

DownLoad: Full-Size Img PowerPoint

图 3 当前有限元模型的气体组分分布与文献[27]得到的结果对比图　(a) 氢气摩尔分数; (b)氧气摩尔分数; (c) 水蒸气摩尔分数

Figure 3. Comparison of the gas components distribution between the results of current finite element model and the results obtained by Ref. [27]: (a) Hydrogen mole fraction; (b) oxygen mole fraction; (c) water vapor mole fraction.

DownLoad: Full-Size Img PowerPoint

图 4 顺流情况下SOFC电解质电流密度分布　(a)不同电压下电解质电流密度最大值与最小值曲线图; (b)电压为0.9 V时电解质电流密度云图; (c)电压为0.6 V时电解质电流密度云图; (d)电压为0.3 V时电解质电流密度云图

Figure 4. SOFC electrolyte current density distribution in the case of downstream: (a) Plot of maximum and minimum electrolyte current density at different voltages; (b) electrolyte current density cloud at voltage of 0.9 V; (c) electrolyte current density cloud at voltage of 0.6 V; (d) electrolyte current density cloud at voltage of 0.3 V.

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图 5 不同电压下氢气摩尔分数、氧气摩尔分数的极差

Figure 5. The extremes of the molar fraction of hydrogen, oxygen at different voltages.

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图 6 不同流型下SOFC的极化曲线和功率密度曲线　(a) 极化曲线; (b) 功率密度曲线

Figure 6. Polarization curves and power density curves of SOFC under different flow modes: (a) Polarization curves; (b) power density curves.

DownLoad: Full-Size Img PowerPoint

图 7 不同电压下不同流道内氢气分布情况　(a) 氢气摩尔分数极差直方图; (b) 氢气摩尔分数分布云图

Figure 7. Distribution of hydrogen in different flow channels under different voltages: (a) Histogram of the range of hydrogen mole fraction; (b) hydrogen molarity fraction distribution.

DownLoad: Full-Size Img PowerPoint

图 8 不同电压下不同流道内氧气分布情况　(a) 氧气摩尔分数极差直方图; (b) 氧气摩尔分数分布云图

Figure 8. Distribution of oxygen in different flow channels under different voltages: (a) Histogram of the variation range of oxygen mole fraction; (b) contour map of oxygen mole fraction distribution.

DownLoad: Full-Size Img PowerPoint

图 9 电池电压为0.9 V时流道内速度分布　(a) 阳极流道内速度分布; (b) 阴极流道内速度分布

Figure 9. Velocity distribution in the flow channel when the cell voltage is 0.9 V: (a) Velocity distribution in the anode flow channel; (b) velocity distribution in the cathode flow channel.

DownLoad: Full-Size Img PowerPoint

图 10 电池电压为0.5 V时流道内速度分布　(a) 阳极流道内速度分布; (b) 阴极流道内速度分布

Figure 10. Velocity distribution in the flow channel when the cell voltage is 0.5 V: (a) Velocity distribution in the anode flow channel; (b) velocity distribution in the cathode flow channel.

DownLoad: Full-Size Img PowerPoint

图 11 阳极流道气体不同流速下电池极化曲线　(a) 顺流; (b) 逆流; (c) 交叉流

Figure 11. SOFC polarization curves under different airflow velocities of anode channel gas: (a) Co-flow; (b) counter-flow; (c) cross-flow.

DownLoad: Full-Size Img PowerPoint

图 12 阳极流道气体不同流速下电池功率密度曲线　(a) 顺流; (b) 逆流; (c) 交叉流

Figure 12. SOFC power density curves at different airflow velocities of anode channel gases: (a) Co-flow; (b) counter-flow; (c) cross-flow.

DownLoad: Full-Size Img PowerPoint

图 13 阴极流道气体不同流速下电池极化曲线　(a) 顺流; (b) 逆流; (c) 交叉流

Figure 13. SOFC polarization curves under different airflow velocities of cathode flow channel gases: (a) Co-flow; (b) counter-flow; (c) cross-flow.

DownLoad: Full-Size Img PowerPoint

图 14 阴极流道气体不同流速下电池功率密度曲线　(a) 顺流; (b) 逆流; (c) 交叉流

Figure 14. SOFC power density curves at different airflow velocities of cathode channel gases: (a) Co-flow; (b) counter-flow; (c) cross-flow.

DownLoad: Full-Size Img PowerPoint

表 1 SOFC单电池模型几何参数^[27]

Table 1. Geometric parameters of SOFC single-cell model^[27].

几何参数	数值
电池长度/mm	20.000
电池宽度/mm	20.000
流道高度/mm	1.000
流道宽度/mm	1.500
肋宽/mm	1.000
阳极和阴极连接体厚度/mm	2.000
阳极扩散层厚度/mm	0.015
阳极厚度/mm	0.400
阴极扩散层厚度/mm	0.020
阴极厚度/mm	0.050
电解质厚度/mm	0.010

DownLoad: CSV

表 2 电化学模型参数^[29,30]

Table 2. Electrochemical model parameters^[29,30].

参数	数值
阳极平衡电位/V	0
电池工作电压/V	0.5
阳极交换电流密度/(A·cm^–2)	5
阴极交换电流密度/(A·cm^–2)	2
阳极活性比表面积/m^–1	1×10⁵
阴极活性比表面积/m^-1	1×10⁵
电解质电导率/(S·m^–1)	5
阳极电导率/(S·m^–1)	1000
阴极电导率/(S·m^–1)	1000
阳极扩散层电导率/(S·m^–1)	8.5×10⁵
阴极扩散层电导率/(S·m^–1)	7700
集流体电导率/(S·m^–1)	1.4×10⁶

DownLoad: CSV

表 4 物质扩散模型参数^[29,30]

Table 4. Material diffusion model parameters^[29,30].

参数	数值
参考扩散率/(m²·s^–1)	3.16×10^–8
燃料气孔隙体积分数/%	40
氧化气孔隙体积分数/%	40
氢气摩尔质量/(g·mol^–1)	2
氧气摩尔质量/(g·mol^–1)	32
水蒸气摩尔质量/(g·mol^–1)	18
氮气摩尔质量/(g·mol^–1)	28

DownLoad: CSV

表 3 气体流动模型参数^[23,31]

Table 3. Gas flow model parameters^[23,31].

参数	数值
大气压强/atm	1
阳极渗透率/m²	1×10^–12
阴极渗透率/m²	1×10^–12
阳极孔隙率	0.3
阴极孔隙率	0.3
阳极流道气体入口速度/(m·s^–1)	0.1—0.5
阴极流道气体入口速度/(m·s^–1)	0.5—2.5

DownLoad: CSV

[1]	Minh N Q, Takahashi T 1995 Science and Technology of Ceramic Fuel Cells (Amsterdam: Elsevier Science) p147
[2]	Singhal S C, Kendall K 2002 Mater. Today 5 55
[3]	申双林, 张小坤, 万兴文, 郑克晴, 凌意瀚, 王绍荣 2022 物理学报 71 164401 Google Scholar Shen S L, Zhang X K, Wan X W, Zheng K Q, Ling Y H, Wang S R 2022 Acta Phys. Sin. 71 164401 Google Scholar
[4]	徐晗, 张璐, 党政 2020 物理学报 69 098801 Google Scholar Xu H, Zhang L, Dang Z 2020 Acta Phys. Sin. 69 098801 Google Scholar
[5]	李凯, 李霄, 李箭, 谢佳苗 2019 无机材料学报 34 611 Google Scholar Li K, Li X, Li J, Xie J M 2019 J. Inorg. Mater. 34 611 Google Scholar
[6]	Su Y, Zhu D Y, Zhang T T, Zhang Y R, Han W P, Zhang J, Ramakrishna S, Long Y Z 2022 Chin. Phys. B 31 057305 Google Scholar
[7]	Al-Masri A, Peksen M, Blum L, Stolten D 2014 Appl. Energy 135 539 Google Scholar
[8]	Razbani O, Assadi M, Andersson M 2013 Int. J. Hydrogen Energy 38 10068 Google Scholar
[9]	Schluckner C, Subotic’ V, Lawlor V, Hochenauer C 2014 Int. J. Hydrogen Energy 39 19102 Google Scholar
[10]	Schluckner C, Subotic ́ V, Lawlor V, Hochenauer C 2015 Int. J. Hydrogen Energy 40 10943 Google Scholar
[11]	Danilov V A, Tade M O 2009 Int. J. Hydrogen Energy 34 8998 Google Scholar
[12]	Haberman B A, Young J B 2004 Int. J. Heat Mass Transfer. 47 3617 Google Scholar
[13]	Lu P Z, Wei S L, Du Z H, Ma W D, Ni S D 2024 Int. J. Heat Mass Transfer. 229 125708 Google Scholar
[14]	Zhang Z G, Yue D T, Yang G G, Chen J F, Zheng Y F, Miao H, Wang W G, Yuan J L, Huang N B 2015 Int. J. Heat Mass Transfer. 84 942 Google Scholar
[15]	Andersson M, Paradis H, Yuan J L, Sunde’n B 2013 Electrochim. Acta 109 881 Google Scholar
[16]	Sohn S, Baek S. M, Nam J. H, Kim C-J 2016 Int. J. Hydrogen Energy 41 5582 Google Scholar
[17]	Wang G L, Yang Y Z, Zhang H O, Xia W S 2007 J. Power Sources 167 398 Google Scholar
[18]	Choudhary T, Sanjay 2016 Int. J. Hydrogen Energy 41 10212 Google Scholar
[19]	Tan W C, Iwai H, Kishimoto M, Yoshida H 2018 J. Power Sources 400 135 Google Scholar
[20]	William J, Sembler, Kumar S 2011 J. Fuel Cell Sci. Technol. 2 021007
[21]	Park J M, Kim D Y, Baek J D, Yoon Y J, Su P C, Lee S H 2018 Energies 11 473 Google Scholar
[22]	Li Z, Yang G G, Cui D A, Li S, Shen Q W, Zhang G L, Zhang H P 2022 J. Power Sources. 522 230981 Google Scholar
[23]	Zhan R B, Wang Y, Ni M, Zhang G B, Du Q, Jiao K 2020 Int. J. Hydrogen Energy 45 6897 Google Scholar
[24]	Sawangtong W, Dunnimit P, Wiwatanapataphee B, Sawangtong P 2024 Part. Diff. Eq. Appl. Math. 11 100890
[25]	Li J S, Zhang J C, Zhang R 2025 J. Comput. Appl. Math. 460 116411 Google Scholar
[26]	Shirsat V R, Vaidya P D, Dalvi V H, Singhal R. S, Kelkar A K, Joshi J B 2025 Sep. Purif. Technol. 354 129215 Google Scholar
[27]	刘艺辉 2023 硕士学位论文(大连: 大连海事大学) Liu Y H 2023 M. S. Thesis (Dalian: Dalian Maritime University
[28]	Shanma S M, Dutta A 2025 J. Alloys Compd. 1010 177931
[29]	Nerat M, Juric ̌ic ́ D 2016 Int. J. Hydrogen Energy 41 3613 Google Scholar
[30]	Chaudhary T N, Saleem U, Chen B 2019 Int. J. Hydrogen Energy 44 8425 Google Scholar
[31]	Wang Y, Zhan R B, Qin Y Z, Zhang G B, Du Q, Jiao K 2018 Int. J. Hydrogen Energy 43 20059 Google Scholar

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