Two-Dimensional Mass Two-Dimensional Mass and Momentum and Momentum

Transport Modeling for Transport Modeling for PEM Fuel Cells PEM Fuel Cells

Chunmei WangChunmei Wang

Po-Fu ShihPo-Fu Shih

Apr 29, 2008Apr 29, 2008

EGEE 520 MATH MODELING

AbstractAbstract

• Introduction• Mass Modeling

– Governing Equations– Solutions

• Momentum Modeling– Governing Equations– Solutions

• Validation• Parametric Study• Conclusions

IntroductionIntroduction• 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.

H2/H2O Air

H+

MembraneCatalystGDL Catalyst GDL

H2/H2O Air/H2OTwo-Dimensional PEMFC Model

Anode Cathode eaqHgH 2)(2)(2 )(24)(4)( 22 lOHeaqHgO

One-dimensional modelsVerbrugge 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.

Mass ModelingMass Modeling• Governing Equation: Maxwell-Stefan Mass Transport

• Solution

Initial conditions: 1.02 Hx 8.021.02 Ox

Figure 2. Mass distribution in a PEMFC.

)(, jiji

jjii uuxF

Where, Fi is the driving force on i, at a given T and p, dz

dx

x

RTF i

ii

ζi,j is the friction coefficient between i and j, xj is mole fraction of j. u is velocity.

Mass Modeling SolutionsMass Modeling Solutions

Figure 3. Mass distribution of H2 at the anode.Figure 4. Mass distribution of H2O at the anode.

Figure 5. Mass distribution of O2 at the cathode.Figure 6. Mass distribution of H2O at the cathode.

Momentum ModelingMomentum Modeling• Governing Equation: Darcy’s Law

)()()()(

uK

uPuut

u

• Solution

inuxu )0(Initial conditions: inpp

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.

Momentum Modeling SolutionsMomentum Modeling Solutions

Figure 8. Velocity distribution at the anode.Figure 9. Velocity distribution at the cathode.

ValidationValidation• 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)

Validation (Continued)Validation (Continued)

Figure 12. Y-direction velocity versus y-orientation (COMSOL Model) .

Figure 13. Y-direction velocity versus y-orientation (Yi and Nguyen) .

Parametric StudyParametric Study

Figure 14. Without water included Figure 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

ConclusionsConclusions

• This model agrees with other authors’ models– Because the electro-osmotic drag of water

through the membrane, H2 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

QuestionsQuestions??