Modeling and Simulation For A 3D Nonisothermal, Anisotropic, Multiphase Transport of PEM Fuel Cell

1. Modeling and Simulation For A 3D Nonisothermal, Anisotropic, Multiphase Transport of PEM Fuel Cell Pengtao Sun Department of Mathematical Sciences University of Nevada, Las Vegas 3/1/2010 1 IMA PI Workshop

2. Outline Model Multi-phases Nonisothermality Anisotropy Simulation Kirchhoff Transformation & DD method Newton-Krylov method Combined finite element-upwind finite volume method 3/1/2010 2 IMA PI Workshop

3. New Numerical Techniques for a Liquid-feed 3D Full Direct Methanol Fuel Cell Model, Pengtao Sun, G. Xue, C.Y. Wang and J. Xu, SIAM J. Applied Mathematics, 70 (2009), 600-620. A Domain Decomposition Method for Two-phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell, Pengtao Sun, G. Xue, C.Y. Wang and J. Xu, J. Comput. Phys. 228 (2009), 6016-6036. Fast Numerical Simulation of Two-Phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell, Pengtao Sun, G. Xue, C.Y. Wang and J. Xu, Commun. Comput. Phys., 6 (2009), 49-71 A Combined Finite Element-Upwind Finite Volume Method for Liquid-Feed Direct Methanol Fuel Cell Simulations, Pengtao Sun, C.Y. Wang and J. Xu, J. Fuel Cell Science and Technology, 2010 (in press) Numerical Studies of Heat Transport For Polymer Electrolyte Fuel Cell Stack In Sub-freezing Environment, Pengtao Sun, Su Zhou, J. Fuel Cell Science and Technology, 2010 (in press) Relevant work 3/1/2010 3 IMA PI Workshop

4. Part I A New Formulation Based on Multiphase Mixture Model for PEM Fuel Cell 3/1/2010 4 Multiphase flow and heat transfer in porous media, C. Y. Wang and P. Cheng, Adv. Heat Transfer, 30 (1997), 93�196. Two-phase flow and transport in the air cathode of PEMFCs, Z. Wang, C. Y. Wang, and K. S. Chen, J. Power Sources, 94 (2001), 40�50. Fundamental models for fuel cell engineering, Chem. Rev., C. Y. Wang, 104 (2004), 4727�4766. IMA PI Workshop

5. Proton Exchange Membrane Fuel Cell (PEMFC) 3/1/2010 5 IMA PI Workshop

6. Principles of Conservation in PEMFC Mass Momentum Species Charge Thermal energy 3/1/2010 6 IMA PI Workshop

7. Single-/Two-Phase Regions coexisting Fig. 1 Snapshorts showing water droplet dynamics from GDL surface (C. Y. Wang, Chem. Rev., 104 (2004), 4727�4766) 3/1/2010 7 IMA PI Workshop

8. Two-phase Relations 3/1/2010 8 Liquid saturation Density Velocity Effective viscosity Kinematic viscosity Relative permeability Concentration Diffusivity IMA PI Workshop

9. Nonisothermality Liquid Saturation where Water saturated concentration 3/1/2010 9 IMA PI Workshop

10. Anisotropy of GDL Structure Species diffusion and capillary transport of liquid water Protonic conducivity Electronic conductivity Thermal conductivity 3/1/2010 10 IMA PI Workshop

11. Flow Brinkman Model (Navier- Stokes equations) Mass Momentum Single Domain Approach 3/1/2010 11 IMA PI Workshop

12. Species General species transport equation where 3/1/2010 12 IMA PI Workshop

13. Capillary-Diffusional Flux jl . Capillary pressure . 3/1/2010 13 IMA PI Workshop

14. where Water Transport 3/1/2010 14 IMA PI Workshop

15. Discontinuous and Degenerate Diffusivity Capillary Diffusivity in Liquid Phase 3/1/2010 15 IMA PI Workshop

16. Water Diffusivity In Membrane . where Water content Water activity 3/1/2010 16 IMA PI Workshop

17. Water Diffusivity In Membrane 3/1/2010 17 Discontinuous Diffusivity IMA PI Workshop

18. Hydrogen Transport 3/1/2010 18 where IMA PI Workshop

19. where 3/1/2010 19 Oxygen Transport IMA PI Workshop

20. 3/1/2010 20 Sources of Species Transport IMA PI Workshop

21. Potential Equations Proton Transport Electron Transport Source term Charge 3/1/2010 21 IMA PI Workshop

22. Thermal Energy . where Conductive heat flux in GDL: 3/1/2010 22 IMA PI Workshop

23. Source of Energy Transport Irreversible heat Entropic heat Joule heating , Heat release/absorption , 3/1/2010 23 IMA PI Workshop

24. Transfer Current Density j Anode Side (Tafel, Bulter-Volmer) Cathode Side Surface overpotential Equilibrium potential 3/1/2010 24 IMA PI Workshop

25. Dirichlet BCs @Inlet No-flux BCs @Outlet No-slip Velocity and No-flux BCs @Walls Fixed temperature @Walls Electron Potential: Domain & Boundary Condition 3/1/2010 25 IMA PI Workshop

26. Unknowns @ Subregions Total 10 unknowns in PEM fuel cell model 3/1/2010 26 IMA PI Workshop

27. Part IIEfficient Numerical methods for PEM Fuel Cell 3/1/2010 27 IMA PI Workshop

28. Challenges in Numerical Simulation Strongly Nonlinear Coupling Newton�s method Discontinuous and Degenerate Diffusivity Kirchhoff transformation & Domain Decomposition method Dominant Convection in Channel Upwind finite volume scheme-finite element method 3D Large-scale Computation ~ MegaDOFs Krylov iterative solver & parallel computing 3/1/2010 28 IMA PI Workshop

29. Newton�s Method with Negative Derivatives of Sources . . . . . 3/1/2010 29 IMA PI Workshop

30. Kirchhoff Transformation Introduce Kirchhoff Transformation in membrane 3/1/2010 30 IMA PI Workshop

31. Kirchhoff Transformation Original water transport ? 3/1/2010 31 IMA PI Workshop

32. In single phase region and gas channel In two-phase region (Newton�s method) In membrane (Newton�s method) Inverse Kirchhoff Transformation 3/1/2010 32 IMA PI Workshop

33. Convergence Performance Converge in 130 Iteration Steps VERSUS Nonconvergence if no new numerical technique is employed 3/1/2010 33 IMA PI Workshop

34. Hydrogen Concentration 3/1/2010 34 IMA PI Workshop

35. Oxygen Concentration 3/1/2010 35 IMA PI Workshop

36. Water Concentration 3/1/2010 36 IMA PI Workshop

37. Temperature 3/1/2010 37 IMA PI Workshop

38. Proton Potential 3/1/2010 38 IMA PI Workshop

39. Electron Potential 3/1/2010 39 IMA PI Workshop

40. Pressure 3/1/2010 40 IMA PI Workshop

41. Velocity Field 3/1/2010 41 IMA PI Workshop

42. Acknowledgement This work is supported by NSF DMS-0913757 3/1/2010 42 IMA PI Workshop