Institute for Chemical Process and Environmental Technology Numerical Studies of the Thermo-electrochemical Performance in Solid-oxide Fuel Cells Steven.

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. 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


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.



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


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


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


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.

Sut

div

upuutu

graddivgrad;div

Sut

graddivdiv


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’. .

FMi

S

1000

'iREiREV ca


Theory

Nernst potentialNernst potential

Volumetric heat source,Volumetric heat source,

apFRT

x

xx

FRT

EE ln4

ln2 OH

0.5OH0

2

22

eHVEi

S


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


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


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

kkk Sur

tr

div

kllkkkp Sur

t

rc

div

kkkkkkk urFpruur

tur

2grad;div


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

UFp

kllk


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.



Meshing details

(a)(a) DNMDNM

(b) DRA(b) DRA

ijij


Results: Single cell model

fuel

air

fuel

air

(a) Temperature distribution, CV = 0

(b) Temperature distribution, CV = 0.65v



fuel

air

Nernst voltage, at CV = 0



fuel

air

Current density, at CV = 0



fuel

air

fuel

air

(a) Anodic H2 mass fraction, V = 0

(a) Anodic H20 mass fraction, V = 0



fuel

air

fuel

air

(b) Anodic H2O mass fraction, V = 0.65V

(b) Cathodic O2 mass fraction, V = 0.65V



fuel

air

Fuel utilization, at CV = 0.65v


Eo

yH2yO2

P

r

yH2O

t

i


Single cell: Comparison of methods


Single cell: Comparison of methods

10-cell stack10-cell stack


Results: Stack modelMass fractions

fuel

air

H2 mass fraction in fuel ducts


Results: 15-cell stack modelTemperatures

fuel

air

fuel

air

Plan Elevation


10-Cell stack: Comparison of DNM and DRA methods


10-Cell stack: Comparison of methods


(a) DNM(a) DNM

(b) DRA(b) DRA

(b) Constant (b) Constant ii, , RR


10-Cell stack: Comparison of methods

(a) DNM(a) DNM (b) DRA(b) DRA



10-Cell stack: Adiabatic vs. Constant-T boundary conditions




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


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


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.


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


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


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).


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).

Institute for Chemical Process and Environmental Technology Numerical Studies of the Thermo-electrochemical Performance in Solid-oxide Fuel Cells Steven.

Documents

chemical process

environmental technology

chemical reaction

dimensioning fuel cells

planar fuel cells

chemical energy

single cells

electrical current