This document discusses modeling and simulations of proton exchange membrane (PEM) fuel cells. It describes modeling PEMFCs using macroscale, mesoscale, and microscale approaches. It also discusses using commercial software like ANSYS Fluent to model PEMFC performance, temperature distribution, current density, and other factors. Several case studies are presented modeling different PEMFC geometries and conditions.

1. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Modeling and Simulations of Multiphysics
Phenomena and Performance in Proton
Exchange Membrane Fuel Cells-DEMO
2020 | MVKF25 Hydrogen, Batteries and Fuel Cells
See also Chapter 10 in course book

2. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Outline
(1) Modeling of PEMFCs
(2) Examples

3. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Modeling of PEMFCs
(1) Macroscale
Based on the continuum assumption: FVM, FEM etc.
❖ Numerical methods at three levels?
(2) Mesoscale
Lattice-Boltzmann method (LBM)
(3) Microscale
Molecular dynamics simulation (MDS)

4. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Modeling of PEMFCs
❑ In-house codes
❑ Commercial softwares
❖ Macroscale modeling approaches
• ANSYS-FLUENT
• COMSOL Multiphysics
• OPEN FOAM (open source code)
• ...

5. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Modeling of PEMFCs
ANSYS Fluent is a commercial software for modeling
fluid flow and several other related physical
phenomena.
❖ What is ANSYS Fluent?
❖ ANSYS Fluent applications
Aerodynamics, heat transfer, combustion, reacting
flows, mixtures of liquids/solids/gas, particle
dispersions, hydrodynamics, and much more.

6. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Modeling of PEMFCs
❖ Numerical simulation procedure

7. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Modeling of PEMFCs
❖ How to model PEMFCs in Fluent
❑ Add-on modules
❑ Models developed using UDFs
• General CFD code
• Additional submodels

8. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Modeling of PEMFCs
❖ ANSYS Fluent fuel cell add-on module

9. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Introduction
❖ How do PEM fuel cells work?
http://www.intelligent-energy.com/technology/technology-faq/ (Animation)
𝑨𝒏𝒐𝒅𝒆: 𝐻2 → 2𝐻+ + 2𝑒−
Τ
𝑪𝒂𝒕𝒉𝒐𝒅𝒆: 1 2 𝑂2 + 2𝐻+ + 2𝑒− → 𝐻2𝑂
𝑶𝒗𝒆𝒓𝒂𝒍𝒍: 𝐻2 +
𝟏
𝟐
𝑂2 → 𝐻2𝑂

10. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Introduction
❖ Why do we need PEM fuel cells?
• Fuel efficient energy conversion
• High power density
• Environmental friendliness
❖ PEM fuel cell applications

11. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Introduction
❖ PEM fuel cell components?
Gas diffusion layer
Catalyst layer
Membrane
Catalyst layer
Gas diffusion layer
Zamel, N., & Li, X. (2013). Progress in Energy and Combustion Science, 39(1), 111-146 (GDL SEM image).
Siddique, N. A., & Liu, F. (2010). Acta, 55(19), 5357-5366 (CL SEM image).
Current collector
Current collector

12. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Mathematical Model
❖ Governing equations
• Mass conservation equation
𝛻 ⋅ (𝜌𝑢) = 𝑆𝑚𝑎𝑠𝑠
• Momentum conservation equation
𝛻 ⋅ 𝜌𝑢𝑢 = 𝛻 ∙ 𝜇𝛻𝑢 − 𝛻𝑃 + 𝑆𝑚𝑜𝑚
• Species conservation equation
𝛻 ⋅ 𝜌𝑢𝑌𝑖 = 𝛻 ∙ 𝜌𝐷𝑒𝑓𝑓,𝑖𝛻𝑌𝑖 + 𝑆𝑖
• Energy conservation equation
𝛻 ⋅ 𝜌𝑐𝑝𝑢𝑇 = 𝛻 ∙ 𝑘𝑒𝑓𝑓𝛻T + 𝑆𝑇
• Charge conservation equation
𝛻 ⋅ 𝜎𝑒𝑓𝑓,𝑠𝛻𝜙𝑠 + 𝑆𝑠 = 0
𝛻 ⋅ 𝜎𝑒𝑓𝑓,𝑚𝛻𝜙𝑚 + 𝑆𝑚 = 0

13. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Mathematical Model
❖ Governing equations
• Liquid water transport equation
𝛻 ⋅ 𝜌𝑙
𝐾𝑟𝑙𝜇𝑔
𝐾𝑟𝑔𝜇𝑙
𝑢 = 𝛻 ∙ 𝜌𝑙𝐷𝑠𝛻𝑠 + 𝑆𝑙
• Dissolved water transport equation
−𝛻 ⋅
𝑛𝑑
𝐹
𝜎𝑚𝛻𝜙𝑚 = 𝛻 ∙
𝜌𝑚
𝑀𝑚
𝐷𝜆𝛻𝜆 + 𝑆𝜆

14. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 1
❖ Geometry description

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Results – Case 1
❖ Cell performance

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❖ Pressure
Results - Case 1

17. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 1
❖ Oxygen mass fraction

18. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 1
❖ Liquid water saturation

19. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 1
❖ Local current density

20. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
❖ Effect of GDL deformation
1. Zhou, P., Wu, C. W., & Ma, G. J. (2007). Journal of Power Sources, 163(2), 874-881.
2. Nitta, I., Karvonen, S., Himanen, O., & Mikkola, M. (2008). Fuel Cells, 8(6), 410-421.
Results - Case 2

21. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 2
❖ Local thickness and porosity

22. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 2
❖ Cell performance

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Results - Case 2
❖ Oxygen concentration

24. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 2
❖ Temperature distribution

25. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 2
❖ Liquid water saturation

26. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 2
❖ Local current density

27. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 3
Case A Case B
❖ Schematic of the HT-PEMFCs

28. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 3
❖ Cell performance

29. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 3
❖ Temperature distribution
443 443.2 443.4 443.6 443.8 444 444.2 444.4
443 443.2 443.4 443.6 443.8 444 444.2 444.4
444.4
444.2
444
443.8
443.6
443.4
443.2
443
Case A Case B

30. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 3
❖ Oxygen mass fraction

31. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 3
❖ Local current density

32. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 4
❖ Geometry description

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Results - Case 4
❖ Cell performance

34. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 4
❖ Oxygen mass fraction

35. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 4
❖ Temperature distribution

36. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Results - Case 4
❖ Local current density

37. DIVISION OF HEAT TRANSFER | DEPARTMENT OF ENERGY SCIENCES
Summary
❖ The PEM fuel cell working
http://www.intelligent-energy.com/technology/technology-faq/ (Animation)
𝑨𝒏𝒐𝒅𝒆: 𝐻2 → 2𝐻+ + 2𝑒−
Τ
𝑪𝒂𝒕𝒉𝒐𝒅𝒆: 1 2 𝑂2 + 2𝐻+ + 2𝑒− → 𝐻2𝑂
𝑶𝒗𝒆𝒓𝒂𝒍𝒍: 𝐻2 +
𝟏
𝟐
𝑂2 → 𝐻2𝑂