1. Two-Dimensional Mass and Momentum Transport Modeling for PEM Fuel Cells Chunmei Wang Po-Fu Shih Apr 29, 2008 EGEE 520 MATH MODELING

2. Abstract Introduction Mass Modeling –Governing Equations –Solutions Momentum Modeling –Governing Equations –Solutions Validation Parametric Study Conclusions

3. Introduction Since the first oil crisis of 1973 the world energy prospective seeks a sustainable energy source. Proton exchange membrane fuel cells (PEMFCs) are promising with prototype efficiency of up to 64% and with high energy density. Mathematical modeling was constructed to understand empirical relations of parameters such as water diffusion coefficient, electro- osmotic drag coefficient, water adsorption isotherms, and membrane conductivities etc. Liquid water transport or liquid/gas transport is one of major concerns in the fuel cell modeling. One-dimensional models  Verbrugge and Hill (1990)  Bernardi and Verbrugge (1991 & 1992)  Springer et al. (1991) Two-dimensional PEMFC models  Gurau et al. (1998)  Wang et al. (2001)  You and Liu (200) Figure 1.Two dimensional PEMFC model.

4. Mass Modeling Governing Equation: Maxwell-Stefan Mass Transport Solution Initial conditions: Figure 2. Mass distribution in a PEMFC. Where, F i is the driving force on i, at a given T and p, ζ i,j is the friction coefficient between i and j, x j is mole fraction of j. u is velocity.

5. Mass Modeling Solutions Figure 3. Mass distribution of H 2 at the anode.Figure 4. Mass distribution of H 2 O at the anode. Figure 5. Mass distribution of O 2 at the cathode.Figure 6. Mass distribution of H 2 O at the cathode.

6. Momentum Modeling Governing Equation: Darcy’s Law Solution Initial conditions: Figure 7. Momentum modeling result in a PEMFC. p is pressure, u is velocity, μ is dynamic viscosity, ε is permeability, and K is material conductivity.

7. Momentum Modeling Solutions Figure 8. Velocity distribution at the anode.Figure 9. Velocity distribution at the cathode.

8. Validation Comparison to work of Yi and Nguyen & He, Yi, and Nguyen Figure 10. Pressure versus y-orientation (COMSOL Model) Figure 11. Pressure versus y-orientation (Yi and Nguyen)

9. Validation (Continued) Figure 12. Y-direction velocity versus y- orientation (COMSOL Model). Figure 13. Y-direction velocity versus y- orientation (Yi and Nguyen).

10. Parametric Study Figure 14. Without water includedFigure 15. With water included Parameters affect the gas flow and PEM fuel cell performance: Conductivity of the membrane, Operation temperature, Relatively humidity …etc With/without water included in fuel cell

11. Conclusions This model agrees with other authors’ models – Because the electro-osmotic drag of water through the membrane, H 2 mass fraction increased as flux flow toward outlet. – At cathode, oxygen content decreased with flow. – The velocity of gases reached at highest value at the corners of electrochemical reactions. This model can help to determine species’ distributions and flow paths

12. Questions ?