1. Modelling of miniature PEM fuel cells Modelling of miniature proton exchange membrane fuel cells for portable applications J.O. Schumacher 1, E. Fontes 3, D. Gerteisen 1, F. Goldsmith 1, R. Klöfkorn 2, A. Hakenjos 1, K. Kühn 1, M. Ohlberger 2, A.Schmitz 1, K. Tüber 1, C. Ziegler 1 1. Fraunhofer Institute for Solar Energy Systems, Heidenhofstr. 2, 79110 Freiburg, schum@ise.fhg.de, Germany 2. Institute of Applied Mathematics, University of Freiburg, Herrmann-Herder-Str. 10, 79104 Freiburg, Germany 3. COMSOL AB, Tegnergatan 23, SE-111 40 Stockholm, Sweden

2. Modelling of miniature PEM fuel cells Overview Examples of portable fuel cell systems Model based analysis of impedance spectra Modelling of self-breathing fuel cells Characterisation of an along-the-channel fuel cell Dynamic simulation of two-phase flow Conclusion and outlook

3. Modelling of miniature PEM fuel cells Fuel cell system for a 50 W max laptop

4. Modelling of miniature PEM fuel cells Completely integrated system with 4 fuel cell stacks 40 W average system power 2 Metal Hydride Storages (100 Nl H 2 or 150 Wh el ) Integrated DC/DC- Converter Miniature fans for air supply Fuel cell system for a professional broadcast camera

5. Modelling of miniature PEM fuel cells Portable power supply Power: max. 100 W average 50 W Metal Hydride Storage Control based on micro processor 12 V voltage supply with DC/DC- Converter Mobile power box

6. Modelling of miniature PEM fuel cells Electrode agglomerate model Electrode is assumed to be made of porous spherical catalyst grains Oxygen is dissolved at the outer surface of the agglomerate Diffusion of dissolved oxygen in the grain and the film in radial direction Local current density is given by the Tafel-equation Graph: Jaouen et al., 2002

7. Modelling of miniature PEM fuel cells Cathode agglomerate model Mass balance Charge balance Oxygen flux in agglomerate

8. Modelling of miniature PEM fuel cells Cathode agglomerate model Charge balance Ohm`s law

9. Modelling of miniature PEM fuel cells cell potential / [V] current density / [A/m 2 ] Comparision of measured and simulated polarisation curves Small current density: change of Tafel-slope Influence of surface-to-volume ratio  of agglomerates  = 6 10 5 m -1  = 9 10 4 m -1

10. Modelling of miniature PEM fuel cells Resistance [  m 2 ] Simulation of impedance spectra Perturbation of solution variables of PDEs Small perturbations: linearise and Laplace-transform PDEs Calculate impedance:

11. Modelling of miniature PEM fuel cells current density [A/m 2 ] meas sim Minimum value of the radius of the impedance arc is reached at a current density of 260mA/cm 2. Mass transport limitation is observed for higher current density: increase of radius of impedance arc. Comparision of measured and simulated impedance spectra

12. Modelling of miniature PEM fuel cells Influence of double layer capacitance on impedance spectra GDL Influence of electrode current density [A/m 2 ] current density [A/m 2 ] Double layer capacitance C DL = 3 10 7 F m -3 Small double layer capacitance: Two seperate semicircles appear

13. Modelling of miniature PEM fuel cells Planar and self-breathing fuel cells based on printed circuit board technology Benefits of technology: Small cell thickness High mechanical strength Low cost components Well known printed circuit board production technology Integration of electronic circuits

14. Modelling of miniature PEM fuel cells Modelling domain and assumptions Two dimensional model Plug flow conditions in anodic gas channel Convective flux of species through membrane and on cathode side neglected No phase transition accounted for

15. Modelling of miniature PEM fuel cells Multicomponent diffusion of gas species: Stefan-Maxwell equation Electronic and protonic potential: Poisson equation Transport of water across membrane: modified Stefan-Maxwell equation Temperature distribution: heat equation l Discretisation mesh and governing equations

16. Modelling of miniature PEM fuel cells Hydrogen and oxygen distribution H 2 molar fractionO 2 molar fraction Arrows: total flux of hydrogen and oxygen. V cell = 0.4 V anodecathode

17. Modelling of miniature PEM fuel cells Water distribution and flux H 2 O molar fraction x 10 -3 H 2 O molar fraction Arrows: total flux of water. V cell = 0.4 V anodecathode

18. Modelling of miniature PEM fuel cells Heat flux and temperature anodecathode T [K] Arrows: total flux of heat. Cooling effect of ribs. V cell = 0.4 V

19. Modelling of miniature PEM fuel cells Electronic and protonic potential, current direction Electronic potential Protonic potential  e [V]  p [V] Arrows indicate the technical current direction.

20. Modelling of miniature PEM fuel cells Comparison of Experiment and Simulation ExperimentSimulation Opening ratio = cathode opening width / current collector rib width. Limiting current is determined by oxygen supply through cathode opening.

21. Modelling of miniature PEM fuel cells membrane GDL cathode electrode Normalised y-coordinateNormalised x-coordinate Current distribution in cathode gas diffusion layer (e) cut line (e) (e)

22. Modelling of miniature PEM fuel cells PEM fuel cell model based on FLUENT CFD-software Submodels: The electrochemical submodel predicts the local current-to- voltage relation in the MEA. The electrical submodel accounts for electron flow and ohmic heat generation. The MEA submodel describes transport of water and ions through a Nafion membrane.

23. Modelling of miniature PEM fuel cells Segmented fuel cell ‚Along - the - Channel‘ Flow-field geometry: Parallel channels Determination of spatially resolved current density Measured values: temperature, gas flow-rates, relative humidity

24. Modelling of miniature PEM fuel cells Current distribution along the channel Comparison of measurement (dots) and simulation (lines) Variation of air flow rate on the cathode side All model parameters are kept constant except air flow and average current gas flow direction:

25. Modelling of miniature PEM fuel cells Analysis Relative humidity of air in the channel Temperature of air in the channel Relative humidity of air at MEA Membrane protonic resistivity

26. Modelling of miniature PEM fuel cells Profiles of flow velocity and temperature including inlet region velocity profiletemperature profile

27. Modelling of miniature PEM fuel cells Dynamic simulation of two phase flow Solution of the PDEs for: Adaptive grid generation in space / time Problem: Determination of material parameters Two phase flow in porous media Species transport in the gas phase Energy balance in the porous media Potential flow of electrons and protons Colours: pressure distribution for counter-flow case. Modelling concept by Mario Ohlberger (Institute for Applied Mathematics, Freiburg).

28. Modelling of miniature PEM fuel cells Two-phase flow in porous gas diffusion layer and electrodes Mass balance Darcy-law Water and gas saturation Capillary pressure phase-transition

29. Modelling of miniature PEM fuel cells Model geometry and discretization mesh

30. Modelling of miniature PEM fuel cells Simulation examples O2O2 H2H2 Wasser- dampf Mass fraction of gas components and saturation of liquid water Colors: Red: 1, Blue: 0 flüssiges Wasser

31. Modelling of miniature PEM fuel cells Conclusion The agglomerate model reproduces both, measured polarisation curves and impedance spectra. Change of active agglomerate surface-to-volume ratio depending on the operation point? Agglomerate model Planar fuel cells Our two-dimensional one-phase model includes all relevant processes of planar fuel cells: gas transport, heat transport, electrochemical reaction. The model serves as a design tool for self- breathing planar fuel cells.

32. Modelling of miniature PEM fuel cells Conclusion Current distribution We validated the CDF model with locally distributed current measurements. The CFD model agrees to measurement results if the cell is operated in the one-phase regime. We are working on a dynamic two-phase flow model taking into account liquid water transport in porous media. The model is extended to 3D. Parallel computing and adaptive grid generation is utilised. Two-phase flow