Transcript Numerical Studies of the Thermo-electrochemical Performance in Solid-oxide Fuel Cells Steven B. Beale, S.V.

Numerical Studies of the
Thermo-electrochemical Performance
in Solid-oxide Fuel Cells
Steven B. Beale, S.V. Zhubrin, W. Dong
[email protected]
International PHOENICS Users Conference
Moscow
23-27 September 2002
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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.

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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

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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
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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
Simple model
Fast convergence
Coarse mesh
DRA
DNM
Complex model
Slow convergence
Fine mesh
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Detailed numerical model (DNM)
Both single cells and stacks modelled.
Compute entire flow field from transport equations


 divu   S
t

u 
 

 divu ; u    grad p  div  grad u
t
f 

 divuf  div  grad f  S
t
f general scalar (enthalpy, mass fraction etc.) S is source
term.
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Theory
Mass source term (Faraday’s law)
Mi
S 
1000F
i is current density. The cell voltage, V, may be expressed as,
V  E  iR  ha  hc  E  iR'
h overpotential, R local lumped resistance. Semi-empirical
correlation used to compute R’.
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Theory
Nernst potential
0.5

x
x
RT  H2 O2  RT
0
EE 
ln

ln pa

2 F  xH 2 O  4 F
Volumetric heat source,
iE  V 
S
He
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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
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Cell/stack model based on prescribed
current (density)
If current (density) specified must do “voltage” correction. Use
a “SIMPLE” method.
V i   R
Compute
V '   Ri'
where i’ is difference between value of average current
density at current sweep, i*, and desired value, i.
i  i * i '
This ensures same current for whole stack.
NB: R’ need not to be exact.
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Distributed resistance analogy
(DRA) for fuel cell stacks
In the stack ‘core’ use local volume averaging (porous media
analogy ) so that,
 r k

 divru k  S k
t

  ru k
 

 div  ru ; u k   rk grad pk  Fk rk2 uk
t
 c p rf k
t

 div ruf k  S   lk fl  fk 
In the manifolds solve usual eqns. of motion
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Detailed resistance analogy
Diffusive effects replaced with a rate equation. Inertial effects
still accounted for. Viscous term replaced with a “distributed
resistance”


p   FU
Heat/mass transfer: Diffusion terms supplanted by inter-phase
terms
lk fl  fk 
Constant source term for heat transfer - Detailed
electrochemistry not yet implemented (constant current
implemented)
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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.
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Meshing details
(a) DNM
(b) DRA
ij
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Results: Single cell model
fuel
fuel
a
i
r
(a) Temperature
distribution, CV = 0
a
i
r
(b) Temperature
distribution, CV = 0.65v
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Results: Single cell model
fuel
a
i
r
Nernst voltage, at CV = 0
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Results: Single cell model
fuel
a
i
r
Current density, at CV = 0
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Results: Single cell model
fuel
fuel
a
i
r
(a) Anodic H2 mass
fraction, V = 0
a
i
r
(a) Anodic H20 mass
fraction, V = 0
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Results: Single cell model
fuel
fuel
a
i
r
a
i
r
(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
a
i
r
Fuel utilization, at CV = 0.65v
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yO2
yH2
yH2O
Eo
i
P
t
r
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Single cell: Comparison of methods
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Single cell: Comparison of methods
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10-cell stack
Results: Stack model
Mass fractions
fuel
a
i
r
H2 mass fraction in fuel ducts
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Results: 15-cell stack model
Temperatures
fuel
fuel
a
i
r
Plan
a
i
r
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
(b) DRA
(b) Constant i, R
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10-Cell stack: Comparison of
methods
(a) DNM
(b) Constant i, R
(b) DRA
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10-Cell stack: Adiabatic vs.
Constant-T boundary conditions
(b) Constant i, R
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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 (fuelelectrolyte)
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
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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
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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*YN2
COVAL (O2-OUT ,YN2 ,FIXFLU,GRND)
<SORC21> VAL=-0.0003317*YN2
COVAL (O2-OUT ,YO2 ,FIXFLU,GRND)
Should not need to use PLANT/GROUND here.
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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
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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

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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).

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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).
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