Melissa Tweedie May 1, 2014

1. CFD Modeling and Analysis of a Planar Anode Supported Intermediate Temperature Solid Oxide Fuel Cell Melissa Tweedie May 1, 2014

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3. SOFC Stacks Reference 2 http://www.ceramatec.com

4. SOFC Unit Cell Fuel Electrochemistry Anode Interconnect Air Anode FF Anode Electrode BL Anode Electrode ERL Cathode FF Electrolyte Cathode ERL Cathode Interconnect Cathode Electrode BL

5. Objective • To develop a 2-D model of a single cell solid oxide fuel cell. • To include detailed multi-physics: fluid dynamics, heat transfer, mass transfer, chemical and electrochemical reactions. • To utilize the model in analyzing the performance of varying fuel inlet compositions.

6. Model Development • The 2-D CFD model consisted of five physics sub-models as follows: • Fluid flow and Momentum Model • Mass Transfer Model • Heat Transfer Model • Chemical Model • Electrochemical Model

7. Momentum Model Continuity and Navier Stokes Equations • Compressible flow, steady state • Fuel and Air Channels: • Porous Electrode Stokes-Brinkman equations: • Wilke and Herning & Zipperer Method to calculate mixture dynamic viscosity

8. Mass Transfer Model • Maxwell-Stefan Equations • Maxwell-Stefan diffusivity values calculated using Fuller method for flowfields • Effective diffusivity used in porous media combines maxwellstefan binary diffusivity and knudsen diffusivity

9. Heat Transfer Model • Flowfields • Heat capacity and thermal conductivity for individual species assumes ideal gases and is calculated from temperature dependent polynomials. • Mixture heat capacity • Mixture thermal conductivity calculated using method of Wassiljewa with Mason and Saxena modification

10. Heat Transfer Model • Electrodes • Use of effective thermal conductivity and effective heat capacity to account for porosity • Electrolyte and Interconnects • Conduction only

11. Heat Transfer Model • Heat Generation Source Terms • Chemical Reaction • Electrochemical Reaction • Activation Polarization

12. Heat Transfer Model • Heat Generation Source Terms

13. Chemical Model • Water Gas Shift Reaction • Species Balance Equations • Implemented as source term in mass transfer equation • Kinetics

14. Chemical Model • Probability of Carbon Formation • Boudouard Reaction • CO/H2 Reaction • If carbon activity is greater than 1 then carbon will form in the cell

15. Electrochemical Model • Electrochemistry • Anode Oxidation of CO and H2 Fuels • Cathode Reduction of O2 • Species Balance Equations

16. Electrochemical Model • Ion and Charge Transfer

17. Electrochemical Model • Cell Potential (Voltage) • Relationship between potential and current density determined by Butler-Volmer kinetic equation • General Equation for activation polarization Varied BC BC=0V

18. Electrochemical Model • H2 kinetics • CO Kinetics

19. Electrochemical Model • O2 Kinetics • Current Density Relationships

20. Electrochemical Model • Electronic and Ionic Conductivities

21. Cell Properties and Parameters

22. Cell Properties and Parameters

23. Solution Method • 5 Separate Fuel Inlet Cases Examined • Fuel concentrations chosen to represent typical syngas composition ranges.

24. Solution Method • COMSOL Multi-physics FEM Modeling Software • Domain • 34,400 elements-varied distribution horizontally • Segregated Pardiso Solver with parametric voltage steps • Dampening Factor 0.05% applied to electrochemical species and heat generation source terms

25. Comparing Dampening Factor

26. Velocity Profile • Typical Inlet velocity profile (0-0.0065m) • Inlet effects occurring in initial 0.2% of length

27. Pressure Profile • Typical Inlet pressure profile (0-0.0065m) • Inlet effects occurring in initial 0.2% of length

28. Permeability Comparison CO2 H2 • Case 1 Anode: No reactions, κ=2.42x10-14 • Case 1 Anode: No reactions, κ=2.42x10-5

29. Water Gas Shift Reaction • Highest WGS rate observed with greatest amount of H2O in fuel (3) • Increased CO2 in fuel results in negative reaction rate in FF (5) • Increased CO in fuel increases WGS rate (1)

30. Carbon Formation • All carbon activities in this study below 1, case 1 with highest observed activities • Increasing H2 or CO from case 1 or decreasing the current density (incr voltage) will bring the carbon activity closer to or above 1 • Carbon activity in Boudouard reaction (0.925) greater than CO-H2 reaction (0.766) • Higher carbon activity at electrode inlets

31. Temperature • Example Temperature Profile Case 1, 0.4V

32. Characteristic Polarization Curve

33. Characteristic Polarization Curve • Example Polarization Curve with OCV Case 1 • OCV values for all cases ranged between ~0.95 to 1.0V

34. Characteristic Polarization Curves • Case 1 Max Power Density: 720 W/m2

35. Current Density Profiles Example Case 1, 0.7V ERL ranges from 1.58mm to 1.61mm Most of the current generated in initial 1.7% to 3.3% of total ERL thickness

36. Current Density Profiles Example Case 1, 0.7V ERL-Electrolyte Interface Current Density Inlet effects observed in initial 0.2% of total cell length

37. Comparison vs Experiment Data

38. Conclusions • Model agrees reasonably well with experimental data, data at slightly different conditions. • Case 1 best performance with max power density 720W/m2, Case 4 2nd best performance • WGS rate increases with more reactant species, reverses with more product species in fuel • No carbon formation observed under operating conditions with syngas below 0.95V • Proper selection of microstructural parameters (permeability) important • Complexity of model allows for significant future study of parameters, optimization, etc.

39. Questions?

40. References • http://www.fuelcellenergy.com/assets/PID000156_FCE_DFC3000_r3_hires.pdf • S.A. Hajimolana et al., “Mathematical Modeling of Solid Oxide Fuel Cells: A Review,” Renewable and Sustainable Energy Reviews, vol 15, pp.1893-1917, 2011. • M. Tweedie Thesis. CFD Modeling and Analysis of a Planar Anode Supported Intermediate Temperature Solid Oxide Fuel Cell. May, 2014.