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Numerical Studies of the Thermo-electrochemical Performance
in Solid-oxide Fuel Cells
Steven B. Beale, S.V. Zhubrin, W. DongSteven B. Beale, S.V. Zhubrin, W. Dong
[email protected]@nrc.ca
International PHOENICS Users ConferenceInternational PHOENICS Users ConferenceMoscowMoscow
23-27 September 200223-27 September 2002
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Introduction Fuel cells convert chemical energy into electrical energy Fuel cells convert chemical energy into electrical energy and heat. In solid oxide fuel cells (SOFC’s) hydrogen, and heat. In solid oxide fuel cells (SOFC’s) hydrogen, methane or natural gas may used. Reaction is exothermic, at methane or natural gas may used. Reaction is exothermic, at up to 1 000 up to 1 000 C.C.
Planar fuel cells normally operated in stacks. Interconnects Planar fuel cells normally operated in stacks. Interconnects serve to pass the electrical current, and provide a pathway for serve to pass the electrical current, and provide a pathway for reactants and products. Cells hydraulically in parallel but reactants and products. Cells hydraulically in parallel but electrically series. electrically series.
Heat management is a concern: If the cell temperature too Heat management is a concern: If the cell temperature too low the chemical reaction will shutdown, too high, mechanical low the chemical reaction will shutdown, too high, mechanical failure.failure.
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Introduction If lose one cell, entire stack useless. Therefore important If lose one cell, entire stack useless. Therefore important that supply of air and fuel, reaction rates, and temperature are that supply of air and fuel, reaction rates, and temperature are as uniform as possible. as uniform as possible.
Numerical models give insight and provide indispensable Numerical models give insight and provide indispensable tool in dimensioning fuel cells and stacks, minimizing need for tool in dimensioning fuel cells and stacks, minimizing need for expensive test rigs. expensive test rigs.
Several models for a single cell, and for entire manifold Several models for a single cell, and for entire manifold stack assembly were developed over last 3 years.stack assembly were developed over last 3 years.
Initially considered fluid flow only, then added heat Initially considered fluid flow only, then added heat transfer, subsequently chemistry and mass transfer analysis transfer, subsequently chemistry and mass transfer analysis addedadded
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Introduction Two geometries considered: (a) “Plane” ducts for both air Two geometries considered: (a) “Plane” ducts for both air and fuel (b) rectangular ducts on air side.and fuel (b) rectangular ducts on air side.
Air is composed of NAir is composed of N22 and O and O22
Fuel is composed of HFuel is composed of H22, H, H22O and NO and N22
Flow is laminarFlow is laminar
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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 costLow cost High performanceHigh performance
PFMPFM DRA DRA DNM DNM
SimpleSimple model model Complex modelComplex modelFast convergenceFast convergence Slow convergenceSlow convergenceCoarse meshCoarse mesh Fine meshFine mesh
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Detailed numerical model (DNM)
Both single cells and stacks modelled.Both single cells and stacks modelled.
Compute entire flow field from transport equationsCompute entire flow field from transport equations
general scalar (enthalpy, mass fraction etc.) S is source general scalar (enthalpy, mass fraction etc.) S is source term. term.
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Theory
Mass source term (Faraday’s law)Mass source term (Faraday’s law)
ii is current density. The cell voltage, is current density. The cell voltage, VV, may be expressed as,, may be expressed as,
overpotential, overpotential, RR local lumped resistance. local lumped resistance. Semi-empirical Semi-empirical correlationcorrelation used to compute used to compute R’R’. .
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Theory
Nernst potentialNernst potential
Volumetric heat source,Volumetric heat source,
apFRT
x
xx
FRT
EE ln4
ln2 OH
0.5OH0
2
22
eHVEi
S
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Calculation procedure for prescribed cell voltage
Either overall current (density) or voltage may be specified. Either overall current (density) or voltage may be specified. Originally voltage specified: Originally voltage specified:
(1) Initial values assumed for properties, current etc. (1) Initial values assumed for properties, current etc.
(2) Source terms computed from Faraday’s law and transport (2) Source terms computed from Faraday’s law and transport eqns. solved. eqns. solved.
(3) Open circuit voltage, internal resistance, and local current (3) Open circuit voltage, internal resistance, and local current density calculated. density calculated.
Steps (2) and (3) repeated until sufficient convergence Steps (2) and (3) repeated until sufficient convergence obtained.obtained.
Extensive use of GROUND and/or PLANTExtensive use of GROUND and/or PLANT
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Cell/stack model based on prescribed current (density)If current (density) specified must do “voltage” correction. Use If current (density) specified must do “voltage” correction. Use a “SIMPLE” method. a “SIMPLE” method.
ComputeCompute
where where ii’ is difference between value of average current ’ is difference between value of average current density at current sweep, density at current sweep, ii*, and desired value, *, and desired value, ii. .
This ensures same current for whole stack.This ensures same current for whole stack.
NB: R’ NB: R’ need not to be exact.need not to be exact.
RiV
'' RiV
'* iii
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In the stack ‘core’ use local volume averaging (porous media In the stack ‘core’ use local volume averaging (porous media analogy ) so that,analogy ) so that,
In the manifolds solve usual eqns. of motionIn the manifolds solve usual eqns. of motion
Distributed resistance analogy (DRA) for fuel cell stacks
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Diffusive effects replaced with a rate equation. Inertial effects Diffusive effects replaced with a rate equation. Inertial effects still accounted for. Viscous term replaced with a “distributed still accounted for. Viscous term replaced with a “distributed resistance” resistance”
Heat/mass transfer: Diffusion terms supplanted by inter-phase Heat/mass transfer: Diffusion terms supplanted by inter-phase terms terms
Constant source term for heat transfer - Detailed Constant source term for heat transfer - Detailed electrochemistry not yet implemented (constant current electrochemistry not yet implemented (constant current implemented)implemented)
Detailed resistance analogy
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Two sets of velocities, pressures, Two sets of velocities, pressures, mass fractions (air and fuel), plus mass fractions (air and fuel), plus temperatures in fluid and solid temperatures in fluid and solid regions requiredregions required
Use multiply-shared space MUSES Use multiply-shared space MUSES method. Provide several blocks of method. Provide several blocks of grid to cover same volume of space grid to cover same volume of space for different variables: (1) air; (2) fuel; for different variables: (1) air; (2) fuel; (3) electrolyte (including electrolyes) (3) electrolyte (including electrolyes) (4) interconnect.(4) interconnect.
Detailed resistance analogy
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Meshing details
(a)(a) DNMDNM
(b) DRA(b) DRA
ijij
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Results: Single cell model
fuel
air
fuel
air
(a) Temperature distribution, CV = 0
(b) Temperature distribution, CV = 0.65v
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Results: Single cell model
fuel
air
Nernst voltage, at CV = 0
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Results: Single cell model
fuel
air
Current density, at CV = 0
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Results: Single cell model
fuel
air
fuel
air
(a) Anodic H2 mass fraction, V = 0
(a) Anodic H20 mass fraction, V = 0
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Results: Single cell model
fuel
air
fuel
air
(b) Anodic H2O mass fraction, V = 0.65V
(b) Cathodic O2 mass fraction, V = 0.65V
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Results: Single cell model
fuel
air
Fuel utilization, at CV = 0.65v
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Eo
yH2yO2
P
r
yH2O
t
i
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Single cell: Comparison of methods
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Single cell: Comparison of methods
10-cell stack10-cell stack
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Results: Stack modelMass fractions
fuel
air
H2 mass fraction in fuel ducts
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Results: 15-cell stack modelTemperatures
fuel
air
fuel
air
Plan Elevation
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10-Cell stack: Comparison of DNM and DRA methods
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10-Cell stack: Comparison of methods
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(a) DNM(a) DNM
(b) DRA(b) DRA
(b) Constant (b) Constant ii, , RR
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10-Cell stack: Comparison of methods
(a) DNM(a) DNM (b) DRA(b) DRA
(b) Constant (b) Constant ii, , RR
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10-Cell stack: Adiabatic vs. Constant-T boundary conditions
(b) Constant (b) Constant ii, , RR
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Detailed resistance analogy
Original form (Patankar-Spalding) of DRA did not work Original form (Patankar-Spalding) of DRA did not work because volume-averaging eliminated important secondary because volume-averaging eliminated important secondary heat transfer effectsheat transfer effects
Had to be modified to account by replacing in-cell values Had to be modified to account by replacing in-cell values with linkages from N-S neighbours for one pair of values (fuel-with linkages from N-S neighbours for one pair of values (fuel-electrolyte)electrolyte)Replace<SORC03> VAL=TEM1[,,-32]Replace<SORC03> VAL=TEM1[,,-32]COVAL(el2fu,TEM1,HFE,GRND) with COVAL(el2fu,TEM1,HFE,GRND) with <SORC03> VAL=TEM1[,+1,-32]<SORC03> VAL=TEM1[,+1,-32]COVAL(el2fu,TEM1,HFE,GRND)COVAL(el2fu,TEM1,HFE,GRND)
Means cells must correspond to SOFC geometryMeans cells must correspond to SOFC geometry
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Discussion:
If fuel cell designed properly, pressure and flow are uniformIf fuel cell designed properly, pressure and flow are uniform
There is bound to be a temperature rise across the cell due There is bound to be a temperature rise across the cell due to Ohmic heating regardless of how uniform the flow isto Ohmic heating regardless of how uniform the flow is
Main factor for minimising temperature gradient is Main factor for minimising temperature gradient is conductivity of interconnectconductivity of interconnect
There are secondary heat transfer phenomena in SOFC There are secondary heat transfer phenomena in SOFC stacks even if fluid flow, current density, and resistance are stacks even if fluid flow, current density, and resistance are entirely constantentirely constant
Interior stack temperatures are independent of wall bc’sInterior stack temperatures are independent of wall bc’s
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Discussion:
Mass transfer calculation is clumsy: Have to “put back in” Mass transfer calculation is clumsy: Have to “put back in” species which are species which are notnot convected out by sink terms e.g. for O convected out by sink terms e.g. for O22
sink on air side we have put Nsink on air side we have put N22 back in: back in:
PATCH (O2-OUT ,HIGH,1,NX,1,NY,11,11,1,1)PATCH (O2-OUT ,HIGH,1,NX,1,NY,11,11,1,1)COVAL (O2-OUT,P1,FIXFLU ,-3.317E-04)COVAL (O2-OUT,P1,FIXFLU ,-3.317E-04) <SORC20> VAL=0.0003317*YN2 <SORC20> VAL=0.0003317*YN2COVAL (O2-OUT ,YN2 ,FIXFLU,GRND)COVAL (O2-OUT ,YN2 ,FIXFLU,GRND) <SORC21> VAL=-0.0003317*YN2 <SORC21> VAL=-0.0003317*YN2COVAL (O2-OUT ,YO2 ,FIXFLU,GRND)COVAL (O2-OUT ,YO2 ,FIXFLU,GRND)
Should not need to use PLANT/GROUND here.Should not need to use PLANT/GROUND here.
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Discussion: Detailed numerical simulations
Flow is laminar so very precise results possibleFlow is laminar so very precise results possible
Useful numerical benchmark for simpler models (since little Useful numerical benchmark for simpler models (since little experimental data available at present time)experimental data available at present time)
ButBut extremely fine meshes (5 million cells so far) and extremely fine meshes (5 million cells so far) and extremely long compute times (24 hours on ICPET beowulf) extremely long compute times (24 hours on ICPET beowulf) required.required.
VR front end is very useful for making stacksVR front end is very useful for making stacks
Multiple diffusion coefficients via PROPS file would be usefulMultiple diffusion coefficients via PROPS file would be useful
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Discussion: Distributed resistance analogy
Reasonably accurate though fine details of simulations lostReasonably accurate though fine details of simulations lost
Separation of “phases” into “meshes” useful featureSeparation of “phases” into “meshes” useful feature
ButBut grid cells must be oriented to coincide with fuel cells. grid cells must be oriented to coincide with fuel cells.
Difficult to optimize so simulations still take excessive Difficult to optimize so simulations still take excessive amounts of time. Due to (i) direction of flow solver (ii) amounts of time. Due to (i) direction of flow solver (ii) segregated scheme (PEA of little use)segregated scheme (PEA of little use)
Perhaps best solution to couple presumed flow solution in Perhaps best solution to couple presumed flow solution in the stack core with CFD code in manifoldsthe stack core with CFD code in manifolds
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Conclusions
DNS is a viable option for cell performance but not (as yet) DNS is a viable option for cell performance but not (as yet) for day-to-day stack design due to large computational for day-to-day stack design due to large computational requirements (most fuel cell manufacturers cannot afford)requirements (most fuel cell manufacturers cannot afford)
DRA vs DNS validation for fluid flow and heat transfer DRA vs DNS validation for fluid flow and heat transfer shows good agreement. Validation for mass transfer and shows good agreement. Validation for mass transfer and surface/volume chemistry in progress.surface/volume chemistry in progress.
Modifying DRA to include partial elimination algorithm will Modifying DRA to include partial elimination algorithm will not improve convergence (due to segregated solver).not improve convergence (due to segregated solver).
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Future Work Non-dilute binary-species diffusion (Stefan-Maxwell eqns.)Non-dilute binary-species diffusion (Stefan-Maxwell eqns.)
Thermal radiationThermal radiation
Poisson equation for potential + porous media Poisson equation for potential + porous media diffusion/catalysisdiffusion/catalysis
Internal reforming of methane to hydrogenInternal reforming of methane to hydrogen
Arbitrary mesh geometry for DRAArbitrary mesh geometry for DRA
Validation of models with data (Validation of models with data (VV--ii curve). curve).