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Numerical Studies of the Thermo-electrochemical Performance in Solid-oxide Fuel Cells

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. Introduction.

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Numerical Studies of the Thermo-electrochemical Performance in Solid-oxide Fuel Cells

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  1. 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 Institute for Chemical Process and Environmental Technology

  2. Introduction • Fuel cells convert chemical energy into electrical energy and heat. In solid oxide fuel cells (SOFC’s) 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. • Heat management is a concern: If the cell temperature too low the chemical reaction will shutdown, too high, mechanical failure. Institute for Chemical Process and Environmental Technology

  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. • 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. • Initially considered fluid flow only, then added heat transfer, subsequently chemistry and mass transfer analysis added Institute for Chemical Process and Environmental Technology

  5. Introduction • Two geometries considered: (a) “Plane” ducts for both air and fuel (b) rectangular ducts on air side. • Air is composed of N2 and O2 • Fuel is composed of H2, H2O and N2 • Flow is laminar Institute for Chemical Process and Environmental Technology

  6. Introduction • 3 approaches considered so far: (1) Detailed numerical model (DNM) (2) Distributed resistance analogy (DRA) (3) Presumed flow method (PFM) Low cost High performance PFM DRA DNM Simple model Complex modelFast convergence Slow convergenceCoarse mesh Fine mesh Institute for Chemical Process and Environmental Technology

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

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

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

  10. 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 Faraday’s 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 Institute for Chemical Process and Environmental Technology

  11. 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. Institute for Chemical Process and Environmental Technology

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

  13. Detailed resistance analogy 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) Institute for Chemical Process and Environmental Technology

  14. Detailed resistance analogy 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. Institute for Chemical Process and Environmental Technology

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

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

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

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

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

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

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

  22. yO2 yH2 yH2O Eo i P r t Institute for Chemical Process and Environmental Technology

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

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

  25. 10-cell stack

  26. Results: Stack modelMass fractions fuel air H2 mass fraction in fuel ducts Institute for Chemical Process and Environmental Technology

  27. Results: 15-cell stack modelTemperatures fuel fuel air air Plan Elevation Institute for Chemical Process and Environmental Technology

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

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

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

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

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

  33. Detailed resistance analogy • 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<SORC03> VAL=TEM1[,,-32]COVAL(el2fu,TEM1,HFE,GRND) with <SORC03> VAL=TEM1[,+1,-32]COVAL(el2fu,TEM1,HFE,GRND) • Means cells must correspond to SOFC geometry Institute for Chemical Process and Environmental Technology

  34. Discussion: • 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 • 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 • Interior stack temperatures are independent of wall bc’s Institute for Chemical Process and Environmental Technology

  35. Discussion: • Mass transfer calculation is clumsy: Have to “put back in” species which are not convected out by sink terms e.g. for O2 sink on air side we have put N2 back in: PATCH (O2-OUT ,HIGH,1,NX,1,NY,11,11,1,1)COVAL (O2-OUT,P1,FIXFLU ,-3.317E-04) <SORC20> VAL=0.0003317*YN2COVAL (O2-OUT ,YN2 ,FIXFLU,GRND) <SORC21> VAL=-0.0003317*YN2COVAL (O2-OUT ,YO2 ,FIXFLU,GRND) Should not need to use PLANT/GROUND here. Institute for Chemical Process and Environmental Technology

  36. Discussion: Detailed numerical simulations • Flow is laminar so very precise results possible • 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. • VR front end is very useful for making stacks • Multiple diffusion coefficients via PROPS file would be useful Institute for Chemical Process and Environmental Technology

  37. Discussion: Distributed resistance analogy • Reasonably accurate though fine details of simulations lost • Separation of “phases” into “meshes” useful feature • 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) • Perhaps best solution to couple presumed flow solution in the stack core with CFD code in manifolds Institute for Chemical Process and Environmental Technology

  38. 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) • 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). Institute for Chemical Process and Environmental Technology

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

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