1. Institute for Chemical Process and Environmental Technology Numerical Studies of the Thermo-electrochemical Performance in Solid-oxide Fuel Cells Steven B. Beale, S.V. Zhubrin, W. Dong steven.beale@nrc.ca International PHOENICS Users Conference Moscow 23-27 September 2002

2. Institute for Chemical Process and Environmental Technology Introduction Fuel cells convert chemical energy into electrical energy and heat. In solid oxide fuel cells (SOFCs) hydrogen, methane or natural gas may used. Reaction is exothermic, at up to 1 000 C. Fuel cells convert chemical energy into electrical energy and heat. In solid oxide fuel cells (SOFCs) hydrogen, methane or natural gas may used. Reaction is exothermic, at up to 1 000 C. Planar fuel cells normally operated in stacks. Interconnects serve to pass the electrical current, and provide a pathway for reactants and products. Cells hydraulically in parallel but electrically series. Planar fuel cells normally operated in stacks. Interconnects serve to pass the electrical current, and provide a pathway for reactants and products. Cells hydraulically in parallel but electrically series. Heat management is a concern: If the cell temperature too low the chemical reaction will shutdown, too high, mechanical failure. Heat management is a concern: If the cell temperature too low the chemical reaction will shutdown, too high, mechanical failure.

3. Institute for Chemical Process and Environmental Technology

4. Introduction If lose one cell, entire stack useless. Therefore important that supply of air and fuel, reaction rates, and temperature are as uniform as possible. If lose one cell, entire stack useless. Therefore important that supply of air and fuel, reaction rates, and temperature are as uniform as possible. Numerical models give insight and provide indispensable tool in dimensioning fuel cells and stacks, minimizing need for expensive test rigs. Numerical models give insight and provide indispensable tool in dimensioning fuel cells and stacks, minimizing need for expensive test rigs. Several models for a single cell, and for entire manifold stack assembly were developed over last 3 years. Several models for a single cell, and for entire manifold stack assembly were developed over last 3 years. Initially considered fluid flow only, then added heat transfer, subsequently chemistry and mass transfer analysis added Initially considered fluid flow only, then added heat transfer, subsequently chemistry and mass transfer analysis added

5. Institute for Chemical Process and Environmental Technology Introduction Two geometries considered: (a) Plane ducts for both air and fuel (b) rectangular ducts on air side. Two geometries considered: (a) Plane ducts for both air and fuel (b) rectangular ducts on air side. Air is composed of N 2 and O 2 Air is composed of N 2 and O 2 Fuel is composed of H 2, H 2 O and N 2 Fuel is composed of H 2, H 2 O and N 2 Flow is laminar Flow is laminar

6. Institute for Chemical Process and Environmental Technology Introduction 3 approaches considered so far: 3 approaches considered so far: (1) Detailed numerical model (DNM) (1) Detailed numerical model (DNM) (2) Distributed resistance analogy (DRA) (2) Distributed resistance analogy (DRA) (3) Presumed flow method (PFM) (3) Presumed flow method (PFM) Low costHigh performance PFM DRA DNM PFM DRA DNM Simple model Complex model Fast convergenceSlow convergence Coarse meshFine mesh

7. Institute for Chemical Process and Environmental Technology Detailed numerical model (DNM) Both single cells and stacks modelled. Compute entire flow field from transport equations general scalar (enthalpy, mass fraction etc.) S is source term.

8. Institute for Chemical Process and Environmental Technology Theory Mass source term (Faradays law) i is current density. The cell voltage, V, may be expressed as, overpotential, R local lumped resistance. Semi-empirical correlation used to compute R. overpotential, R local lumped resistance. Semi-empirical correlation used to compute R.

9. Institute for Chemical Process and Environmental Technology Theory Nernst potential Volumetric heat source,

10. Institute for Chemical Process and Environmental Technology Calculation procedure for prescribed cell voltage Either overall current (density) or voltage may be specified. Originally voltage specified: (1) Initial values assumed for properties, current etc. (2) Source terms computed from Faradays law and transport eqns. solved. (3) Open circuit voltage, internal resistance, and local current density calculated. Steps (2) and (3) repeated until sufficient convergence obtained. Extensive use of GROUND and/or PLANT

11. Institute for Chemical Process and Environmental Technology Cell/stack model based on prescribed current (density) If current (density) specified must do voltage correction. Use a SIMPLE method. Compute where i is difference between value of average current density at current sweep, i*, and desired value, i. This ensures same current for whole stack. NB: R need not to be exact.

12. Institute for Chemical Process and Environmental Technology In the stack core use local volume averaging (porous media analogy ) so that, In the manifolds solve usual eqns. of motion Distributed resistance analogy (DRA) for fuel cell stacks

13. Institute for Chemical Process and Environmental Technology Diffusive effects replaced with a rate equation. Inertial effects still accounted for. Viscous term replaced with a distributed resistance Heat/mass transfer: Diffusion terms supplanted by inter-phase terms Constant source term for heat transfer - Detailed electrochemistry not yet implemented (constant current implemented) Detailed resistance analogy

14. Institute for Chemical Process and Environmental Technology Two sets of velocities, pressures, mass fractions (air and fuel), plus temperatures in fluid and solid regions required Use multiply-shared space MUSES method. Provide several blocks of grid to cover same volume of space for different variables: (1) air; (2) fuel; (3) electrolyte (including electrolyes) (4) interconnect. Detailed resistance analogy

15. Institute for Chemical Process and Environmental Technology Meshing details (a)DNM (b) DRA ij ij

16. Institute for Chemical Process and Environmental Technology Results: Single cell model fuel airair airair (a) Temperature distribution, CV = 0 (b) Temperature distribution, CV = 0.65v

17. Institute for Chemical Process and Environmental Technology Results: Single cell model fuel airair Nernst voltage, at CV = 0

18. Institute for Chemical Process and Environmental Technology Results: Single cell model fuel airair Current density, at CV = 0

19. Institute for Chemical Process and Environmental Technology Results: Single cell model fuel airair airair (a) Anodic H2 mass fraction, V = 0 (a) Anodic H20 mass fraction, V = 0

20. Institute for Chemical Process and Environmental Technology Results: Single cell model fuel airair airair (b) Anodic H2O mass fraction, V = 0.65V (b) Cathodic O2 mass fraction, V = 0.65V

21. Institute for Chemical Process and Environmental Technology Results: Single cell model fuel airair Fuel utilization, at CV = 0.65v

22. Institute for Chemical Process and Environmental Technology EoEo yH 2 yO 2 P r yH 2 O t i

23. Institute for Chemical Process and Environmental Technology Single cell: Comparison of methods

24. Institute for Chemical Process and Environmental Technology Single cell: Comparison of methods

25. 10-cell stack

26. Institute for Chemical Process and Environmental Technology Results: Stack model Mass fractions fuel airair H2 mass fraction in fuel ducts

27. Institute for Chemical Process and Environmental Technology Results: 15-cell stack model Temperatures fuel airair airair PlanElevation

28. Institute for Chemical Process and Environmental Technology 10-Cell stack: Comparison of DNM and DRA methods

29. Institute for Chemical Process and Environmental Technology 10-Cell stack: Comparison of methods

30. Institute for Chemical Process and Environmental Technology (a) DNM (b) DRA (b) Constant i, R

31. Institute for Chemical Process and Environmental Technology 10-Cell stack: Comparison of methods (a) DNM (b) DRA (b) Constant i, R

32. Institute for Chemical Process and Environmental Technology 10-Cell stack: Adiabatic vs. Constant-T boundary conditions (b) Constant i, R

33. Institute for Chemical Process and Environmental Technology Detailed resistance analogy Original form (Patankar-Spalding) of DRA did not work because volume-averaging eliminated important secondary heat transfer effects Original form (Patankar-Spalding) of DRA did not work because volume-averaging eliminated important secondary heat transfer effects Had to be modified to account by replacing in-cell values with linkages from N-S neighbours for one pair of values (fuel- electrolyte) Replace VAL=TEM1[,,-32] COVAL(el2fu,TEM1,HFE,GRND) with VAL=TEM1[,+1,-32] COVAL(el2fu,TEM1,HFE,GRND) Had to be modified to account by replacing in-cell values with linkages from N-S neighbours for one pair of values (fuel- electrolyte) Replace VAL=TEM1[,,-32] COVAL(el2fu,TEM1,HFE,GRND) with VAL=TEM1[,+1,-32] COVAL(el2fu,TEM1,HFE,GRND) Means cells must correspond to SOFC geometry Means cells must correspond to SOFC geometry

34. Institute for Chemical Process and Environmental Technology Discussion: If fuel cell designed properly, pressure and flow are uniform If fuel cell designed properly, pressure and flow are uniform There is bound to be a temperature rise across the cell due to Ohmic heating regardless of how uniform the flow is There is bound to be a temperature rise across the cell due to Ohmic heating regardless of how uniform the flow is Main factor for minimising temperature gradient is conductivity of interconnect Main factor for minimising temperature gradient is conductivity of interconnect There are secondary heat transfer phenomena in SOFC stacks even if fluid flow, current density, and resistance are entirely constant There are secondary heat transfer phenomena in SOFC stacks even if fluid flow, current density, and resistance are entirely constant Interior stack temperatures are independent of wall bcs Interior stack temperatures are independent of wall bcs

35. Institute for Chemical Process and Environmental Technology Discussion: Mass transfer calculation is clumsy: Have to put back in species which are not convected out by sink terms e.g. for O 2 sink on air side we have put N 2 back in: Mass transfer calculation is clumsy: Have to put back in species which are not convected out by sink terms e.g. for O 2 sink on air side we have put N 2 back in: PATCH (O2-OUT,HIGH,1,NX,1,NY,11,11,1,1) COVAL (O2-OUT,P1,FIXFLU,-3.317E-04) VAL=0.0003317*YN2 COVAL (O2-OUT,YN2,FIXFLU,GRND) VAL=-0.0003317*YN2 COVAL (O2-OUT,YO2,FIXFLU,GRND) Should not need to use PLANT/GROUND here.

36. Institute for Chemical Process and Environmental Technology Discussion: Detailed numerical simulations Flow is laminar so very precise results possible Flow is laminar so very precise results possible Useful numerical benchmark for simpler models (since little experimental data available at present time) Useful numerical benchmark for simpler models (since little experimental data available at present time) But extremely fine meshes (5 million cells so far) and extremely long compute times (24 hours on ICPET beowulf) required. But extremely fine meshes (5 million cells so far) and extremely long compute times (24 hours on ICPET beowulf) required. VR front end is very useful for making stacks VR front end is very useful for making stacks Multiple diffusion coefficients via PROPS file would be useful Multiple diffusion coefficients via PROPS file would be useful

37. Institute for Chemical Process and Environmental Technology Discussion: Distributed resistance analogy Reasonably accurate though fine details of simulations lost Reasonably accurate though fine details of simulations lost Separation of phases into meshes useful feature Separation of phases into meshes useful feature But grid cells must be oriented to coincide with fuel cells. But grid cells must be oriented to coincide with fuel cells. Difficult to optimize so simulations still take excessive amounts of time. Due to (i) direction of flow solver (ii) segregated scheme (PEA of little use) Difficult to optimize so simulations still take excessive amounts of time. Due to (i) direction of flow solver (ii) segregated scheme (PEA of little use) Perhaps best solution to couple presumed flow solution in the stack core with CFD code in manifolds Perhaps best solution to couple presumed flow solution in the stack core with CFD code in manifolds

38. Institute for Chemical Process and Environmental Technology Conclusions DNS is a viable option for cell performance but not (as yet) for day-to-day stack design due to large computational requirements (most fuel cell manufacturers cannot afford) DNS is a viable option for cell performance but not (as yet) for day-to-day stack design due to large computational requirements (most fuel cell manufacturers cannot afford) DRA vs DNS validation for fluid flow and heat transfer shows good agreement. Validation for mass transfer and surface/volume chemistry in progress. DRA vs DNS validation for fluid flow and heat transfer shows good agreement. Validation for mass transfer and surface/volume chemistry in progress. Modifying DRA to include partial elimination algorithm will not improve convergence (due to segregated solver). Modifying DRA to include partial elimination algorithm will not improve convergence (due to segregated solver).

39. Institute for Chemical Process and Environmental Technology Future Work Non-dilute binary-species diffusion (Stefan-Maxwell eqns.) Non-dilute binary-species diffusion (Stefan-Maxwell eqns.) Thermal radiation Thermal radiation Poisson equation for potential + porous media diffusion/catalysis Poisson equation for potential + porous media diffusion/catalysis Internal reforming of methane to hydrogen Internal reforming of methane to hydrogen Arbitrary mesh geometry for DRA Arbitrary mesh geometry for DRA Validation of models with data (V-i curve). Validation of models with data (V-i curve).