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Transcript of Cell and Stack Design - · PDF fileCell and Stack Design Frano Barbir Joint European Summer...
Cell and Stack Design
Frano Barbir
Joint European Summer School for Fuel Cell and Hydrogen Technology
Frano Barbir
Professor, FESB, University of Split, Croatia
FESB = Faculty (School) of electrical engineering,
mechanical engineering and naval architecture
Fuel cell generates current at <1 V
For 1 kW it would have to generate >1000 Ampers
For 100 kW it would have to generate >100000 Ampers
At 1 Amp/cm2 it would need >10 m2
P = V x I
Fuel cells are connected/stacked in series – stack
up to 200 cells in stack
For 100 kW it would need to generate >500 A at <200 V
Each cell in stack would need active area of >500 cm2
In order to get higher voltage fuel cells are stacked in a stack
electrode membrane electrode
oxygen feed
collector
plate
O2
external load
2e-
electrode membrane electrode
oxygen feed
O2
Stack of PEM Fuel Cells - Basic Principle
2H+
H2 →→→→ 2H+ + 2e–
H2
2e-
H2O
hydrogen feed
bi-polar
collector
plate
2H+
H2 H2O
hydrogen feed
2e-
½O2 + 2H+ + 2e– →→→→ H2O
oxidant in
hydrogen out
coolant in
end platebus plate
bi-polar collector plates
In order to get higher voltage fuel cells are stacked in a stack
membrane
anode
cathode
oxidant + water out
hydrogen in
coolant out
tie rod
Stacks with more than 100 cells have been built
Individual stacks may be connected (in series or in parallel)
cathode
energy partners
P R O T O N
300 cm2
25-110 cells
4.5-20 kW
0.6 W/cm2
@0.6 V/cell
pressurized up to 3 bar
liquid cooled
65 cm2
60 cells
1 kW
0.25 W/cm2
@0.7 V/cell
ambient pressure
air cooled
Major stack componentsMajor stack components
Membrane
Catalyst
Catalyst support
Catalyst layer
Gas diffusion layer
Gaskets/frames
MEA
end plate
bus plate
bi-polar collector plates
Gaskets/frames
Flow field
Separator/connector
Bus plates/terminals
End plates
Clamping mechanism
Fluid connections
Manifolds
Cooling plates/arrangements
Humidification section (optional)
Bi-polar
plate
tie rod
Stack design goals
PerformancePower density
Stability
Durability
Size and weight
Manufacturability
>1 W/cm2 peak
0.6-0.7 W/cm2 normal operation (nominal)
0.3-0.4 W/cm2 high efficiency operation
< 1 kg/kW
< 1 l/kWManufacturability
Constraints/inputs
Application requirementsLoad variability
Environmental conditions
Operating conditionsPressure, temperature, flow rates, humidity
W = Vst.I
∑=
cellN
1i
iVcellVVst = = .ncell
W = stack power output
Vst = stack voltage
I = stack current
Vcell = cell voltage
ncell = number of cells
i = current density
Acell = cell active area
w = power density
Stack sizing
I = i.Acell
Vcell = f(i)
η=Vcell/1.482
cell
w = power density
η= stack efficiency
Stack volume
Stack weightw = i V = W/(ncell Acell )
example
Given:
Power output: 20 kW
Vcell = 0.6 V
Find:
Active area
Number of cells
W 20 20 20 20 20 20
Vcell 0,6 0,6 0,6 0,6 0,6 0,6
i 1 1 1 1 1 1
A 100 150 200 300 400 500
I 100 150 200 300 400 500
w 0,6 0,6 0,6 0,6 0,6 0,6
Ancell 33333,33 33333,33 33333,33 33333,33 33333,33 33333,33
Ncell 333,33 222,22 166,67 111,11 83,33 66,67
Vstack 200 133,3333 100 66,66667 50 40
0
50
100
150
200
250
300
350
0 100 200 300 400 500 600
Cell active area (cm2)
Nu
mb
er
of
ce
lls
400
500
600
700
800
900
1000
cell
acti
ve a
rea (
cm
²)
50 kW 0.4 W/cm²
Stack sizing
0
100
200
300
400
0 50 100 150 200 250 300
number of cells in stack
cell
acti
ve a
rea (
cm
²)
20 kW
5 kW
1 kW
0.9 W/cm²
0.4
0.5
0.6
0.7
0.8
0.9
1
ce
ll p
ote
ntial (V
)
0 500 1000 1500 2000
current density mA/cm²
300 kPa atm. P
0.4
0.5
0.6
0.7
0.8
0.9
1
ce
ll p
ote
ntial (V
)
0 500 1000 1500 2000
current density mA/cm²
300 kPa atm. P
Single Cell
40
50
60
70
80
90
100
110
0 200 400 600 800 1000 1200 1400
CURRENT DENSITY (mA/cm^2)
ST
AC
K V
OL
TA
GE
@308kPa (EP)
@239kPa (EP)
@170kPa (EP)
Date: 8-26-98 H2/air stoic: 1.5/2.0
Cell #: XXXXXXX Temp. (deg. C): 60
Active area (cm^2): 292 H2/air humid (deg. C): 60
# of cells: 110
110-Cell Stack
1998 1999
current density mA/cm²current density mA/cm² CURRENT DENSITY (mA/cm^2)
0.4
0.6
0.8
1
1.2
cell
pote
ntial (V
)
Typical polarization curves
0
0.2
0.4
0 200 400 600 800 1000 1200 1400 1600
current density (mA/cm²)
cell
pote
ntial (V
)
2
4
6
8
10
12
14
Active
are
a (
cm
²/W
)
Higher pol. curve
Low er pol. curve
Stack size vs. efficiency
0
2
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
Nominal cell potential (V)
0.4 0.45 0.5 0.55
Efficiency (HHV)
0.4 0.45 0.5 0.55
Efficiency (LHV)
0.6 0.65
0.5
0.55
0.6
0.65
0.7
sta
ck e
fficie
ncy
Vnom=0.8 V
Vnom=0.7 V
Vnom=0.6 V
Stack efficiency vs. nominal (selected) cell voltage
0.3
0.35
0.4
0.45
0.5
0 0.2 0.4 0.6 0.8 1
power/nominal power
sta
ck e
fficie
ncy
A C A C A C A C-– +
Bipolar Stack Configuration
electron pathway
-– AA AA AA
CC CCCC
+
Monopolar Stack Configurations
zig-zag configuration
flip-flop configuration
-–AA AACC
CC CCAA
+
electron pathway
flip-flop configuration
Stack design/engineering issuesStack design/engineering issues
Uniform distribution of reactants to each cell
Uniform distribution of reactants inside each cell
Uniform or desired temperature distribution in each cell
Minimal resistive losses
• good electrical contacts
• selection of materials• selection of materials
Account for thermal expansion
No crossover or overboard leaks
Minimum pressure drop (reactant gases and coolant)
No water accumulation pockets
Design for manufacture/design for assembly
Stack design/engineering issuesStack design/engineering issues
Uniform distribution of reactants to each cell
Uniform distribution of reactants inside each cell
Uniform or desired temperature distribution in each cell
Minimal resistive losses
• good electrical contacts
• selection of materials
Un
ifo
rm d
istr
ibu
tio
n
• selection of materials
Account for thermal expansion
No crossover or overboard leaks
Minimum pressure drop (reactant gases and coolant)
No water accumulation pockets
Design for manufacture/design for assembly
Stack design/engineering issuesStack design/engineering issues
Uniform distribution of reactants to each cell
a) “U”-shape b) “Z”-shape
Ce
ll #
1
Ce
ll #
2
Ce
ll #
3
Ce
ll #
4
Ce
ll #
5
Ce
ll #
6
Ce
ll #
n
Ce
ll #
(n-1
)
Un
ifo
rm d
istr
ibu
tio
n
c) Combined parallel-serial
Ce
ll #
1
Ce
ll #
2
Ce
ll #
3
Ce
ll #
4
Ce
ll #
5
Ce
ll #
6
Ce
ll #
n
Ce
ll #
(n
Pressure dropPressure drop
feeder
∆∆∆∆Pfeeder << ∆∆∆∆Pcell
Un
ifo
rm d
istr
ibu
tio
n
exit
Pressure dropPressure drop
2
v
D
LfP
2
ρ∆ ====
vD
L32P
2µ∆ ====
νDv
====ReRe
Re64
f2000for ====<<<<For laminar flow
For non-compressible flow
also for compressible as long as ∆∆∆∆P<0.1P
D
hR4D ====m
hP
AR ====
A
mv
ρ
&==== m
A
LP2P
3
2m &ν∆ ====
For non-circular conduits
++++====−−−−
2
12
222
21
P
P2
D
Lf
A
RTmPP ln&For compressible flow
The flow in any network must satisfy
the basic relations of continuity and
energy conservation:
1) The flow into any junction must
equal the flow out of it
2) The flow in each segment has a
pressure drop that is a function of
Piping Network Problem
Q in(N
)
Q in(N
-1)
Qin(i)
Q in(i+
1)
Q in(2
)
Qin(1)
Q out(
N)
Q out(
N-1
)
Q out(i)
Q out(i+
1)
Q out(2)Qout(1)
Qce
ll(1)
Qce
ll(2)
Qcell(
i-1)
Qce
ll(i)
Qce
ll(i+
1)
Qce
ll(N
-1)
Qce
ll(N
)
Pin(N)
Pout(N)
Pin(1)
Pout(1)
Q in(i-
1)
Q out(i-
1)
pressure drop that is a function of
the flow rate through that segment
3) The algebraic sum of the pressure
drops around any closed loop must
be zero
Q in(N
)
Q in(N
-1)
Qin
(i)
Q in(i+
1)
Q in(2
)
Qin(1)
Qout(N)
Q out(N-1
)
Q out(i)
Q out(i+
1)
Q out(2)
Q out(1)
Qce
ll(1)
Qce
ll(2)
Qce
ll(i-1)
Qce
ll(i)
Qce
ll(i+
1)
Qcell(
N-1
)
Qcell(
N)
Pin(N)
Pout(N)
Pin(1)
Pout(1)
Q in(i-
1)
Q out(i-1
)
1) The flow into any junction must equal the flow out of it
Q in(N
)
Q in(N
-1)
Qin(i)
Q in(i+
1)
Q in(2
)
Qin(1)
Q out(
N)
Q out(
N-1
)
Q out(i)
Q out(i+
1)
Q out(2)Qout(1)
Qce
ll(1)
Qce
ll(2)
Qcell(
i-1)
Qce
ll(i)
Qce
ll(i+
1)
Qce
ll(N
-1)
Qce
ll(N
)
Pin(N)
Pout(N)
Pin(1)
Pout(1)
Q in(i-
1)
Q out(i-
1)
in inlet manifold:
Qin(i) = Qcell(i) + Qin(i+1)
in outlet manifold, “U”
configuration
Qout(i) = Qcell(i) + Qout(i+1)
in outlet manifold, “Z”
configuration
Qout(i) = Qcell(i) + Qout(i-1) Q
Q out
Q out
Q
Q in(N
)
Q in(N
-1)
Qin
(i)
Q in(i+
1)
Q in(2
)
Qin(1)
Qout(N)
Q out(N-1
)
Q out(i)
Q out(i+
1)
Q out(2)
Q out(1)
Qce
ll(1)
Qce
ll(2)
Qce
ll(i-1)
Qce
ll(i)
Qce
ll(i+
1)
Qcell(
N-1
)
Qcell(
N)
Pin(N)
Pout(N)
Pin(1)
Pout(1)
Q in(i-
1)
Q out(i-1
)
Qout(i) = Qcell(i) + Qout(i-1)
Qin(1) = Qstack
For a non-operating stack, i.e.,
no species consumption nor
generation, the flow at the stack
outlet is equal to the flow at inlet:
for “U” configuration
Qout(1) = Qin(1)
for “Z” configuration
Qout(N) = Qin(1)
2) The flow in each segment has a pressure drop that is a function of the flow
rate through that segment
( ) ( )[ ] ( )[ ]+
−−ρ−=∆
2
1iuiuiP
22
f( )[ ] ( )[ ]
2
1iuK
2
iu
D
L2
f
2
H
−ρ+ρ
Bernoulli equation (without gravity forces):
f =64
For laminar flow: f =Re
For laminar flow:
f = 2
D2141
1
ε− log.
For turbulent flow:
3) The algebraic sum of the pressure drops around any closed loop must be zero
For i = 1 to (N – 1)
in “U” configuration
∆Pin(i+1) + ∆Pcell(i+1) +
∆Pout(i+1) –
∆Pcell(i) = 0
Q in(N
)
Q in(N
-1)
Qin
(i)
Q in(i+
1)
Q in(2
)
Qin(1)
Q out(
N)
(N-1
)
Q out(i)
out(i+
1)
Q out(
2)Qout(1)
Qce
ll(1)
Qce
ll(2)
Qce
ll(i-1)
Qcell(
i)
Qcell(
i+1)
Qce
ll(N
-1)
Qce
ll(N
)
Pin(N)
Pout(N)
Pin(1)
Pout(1)
Qin(i-
1)
out(i-1
)
in “Z” configuration
∆Pin(i+1) + ∆Pcell(i+1) –
∆Pout(i) –
∆Pcell(i) = 0
Q out
Q out(
NQ out
Q out(i+
1)
Q out
Q out(i
Q in(N
)
Q in(N
-1)
Qin
(i)
Q in(i+
1)
Q in(2
)
Qin(1)
Qout(N)
Q out(N-1
)
Q out(i)
Q out(i+
1)
Q out(
2)
Q out(1)
Qce
ll(1)
Qce
ll(2)
Qce
ll(i-1)
Qcell(
i)
Qcell(
i+1)
Qce
ll(N
-1)
Qce
ll(N
)
Pin(N)
Pout(N)
Pin(1)
Pout(1)
Qin
(i-1)
Q out(i-1
)
The problem must be solved
by iteration a loop at a time
Flow Distribution through Individual Cells
Un
ifo
rm d
istr
ibu
tio
n
1.2
1.3
1.4
1.5
1.6flow
/avera
ge f
low
U; dPcell/dPch = 2.5
U; dPcell/dPch = 5
U; dPcell/dPch = 10
Z; dPcell/dPch = 2.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7 8 9 10 11
cell #
flow
/avera
ge f
low
Example of cell voltages in a 40Example of cell voltages in a 40--cell stackcell stack
Un
ifo
rm d
istr
ibu
tio
n
0.85
0.9
0.95
1
ce
ll v
olt
ag
e (
V)
172 mA/cm²
515 mA/cm²
858 mA/cm²
1200 mA/cm²
1540 mA/cm²
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0 5 10 15 20 25 30 35 40
cell position
ce
ll v
olt
ag
e (
V)
1.6
1.8
2-C
EL
L P
AC
K V
OL
TA
GE
280mA/cm 2 480mA/cm 2 680mA/cm 2
Date: 8-29-98 H2/air stoic: 1.5/2.5
Stack type: NG2000 Temp. (deg. C): 60
Active area (cm 2): 292 H2/air humid (deg. C): 60
# of cells: 110 Cells/pack: 2
Pressure (kPa): 170
Example of cell voltages in a 110Example of cell voltages in a 110--cell stackcell stackU
nif
orm
dis
trib
uti
on
In the lab
1
1.2
1.4
0 10 20 30 40 50
2-CELL PACK POSITION
2-C
EL
L P
AC
K V
OL
TA
GE
Source:Fuel Cell Power for Transportation, SAE SP-1505, pp. 63-69, 2000
3.5
4
4.54
-CE
LL
PA
CK
VO
LT
AG
E
280mA/cm 2 480mA/cm 2 680mA/cm 2
Date: 5-19-99 H2/air stoic: 1.6-2.8/3.5-10
Stack type: NG2000 Temp. (deg. C): 60
Active area (cm 2): 292 H2/air humid (deg. C): 60
# of cells: 110 Cells/pack: 4
Pressure (kPa): 170
Example of cell voltages in a 110Example of cell voltages in a 110--cell stackcell stackU
nif
orm
dis
trib
uti
on
In the vehicle
1.5
2
2.5
3
0 5 10 15 20 25 30
4-CELL PACK POSITION
4-C
EL
L P
AC
K V
OL
TA
GE
Source:Fuel Cell Power for Transportation, SAE SP-1505, pp. 63-69, 2000
Stack design/engineering issuesStack design/engineering issues
Uniform distribution of reactants to each cell
Uniform distribution of reactants inside each cell
Flow field needed to ensure uniform reactant distribution
Flo
w f
ield
Flow field needed to ensure uniform reactant distribution
Flow field design variablesFlow field design variables
Shape
Orientation (position of inlet and outlet manifolds)
Orientation (horizontal or vertical)
Configuration of channels
Flo
w f
ield
Configuration of channels
Dimensions of channels and spacing
Anode vs. cathode orientation
Geometry of channels
square rectangularcircular
Flow field shapeFlow field shape
Flo
w f
ield
hexagonal irregular
anode facing up cathode facing up
horizontal stack-up vertical stack-up
Flow field orientationFlow field orientation
a cFlo
w f
ield
a
c a
c
top to bottom bottom to top side to side
Flow field orientationFlow field orientation
Flo
w f
ield
same side inlets and outlets
radial (outwards) radial (inwards)
Flow field configurationsFlow field configurations
straight criss-crosssingle channel
serpentine
multi-channel
serpentine
Flo
w f
ield
mixed serpentine mirror serpentine
subsequent
serpentine
spiral
biomimeticinterdigitated fractal
Flow field configurations (cont.)Flow field configurations (cont.)F
low
fie
ld
screen/mesh porous
unveils flow field design
FCX Clarity
Improved flow field design
reactant gases distribution coolant distribution
FCX Clarity
Improved flow field design – better performance
FCX Clarity
Improved water drainage
FCX Clarity
Velocity Vector Plot i = 1.0 A/cm2 (Qair = 1813 sccm)
CFD can be a powerful tool for flow field designCFD can be a powerful tool for flow field design
Velocity distribution in flow field channels
inletFlow field “A” inletFlow field “B”
Flo
w f
ield
outlet outlet
Velocity distribution in flow field channels
inletFlow field “A” inletFlow field “B”
Flo
w f
ield
outlet outlet
Oxygen molar fractionconventional flow field vs. interdigitated flow field
0
500
1000
Y(X
10
-3mm
)
1
0
100
200
300
0.1680
0.1428
0.1176
0.0924
0.0672
0.0420
Oxygen mole fraction
-1
-0.5
0
0.5
1
Z (mm)
400
500
600
700
800
X (x10- 2 cm)
0
0.5
1
Y(m
m)
0
0.5
1
1.5
2
Z (mm)
0
1
2
3
4
X (cm)
0.1680
0.1260
0.0840
0.0420
In
H. Liu, T. Zhou and L. You, NSF Workshop on Engineering Fundamentals of Low-
Temperature PEM Fuel Cells, Arlington, VA, November 14-15, 2001
Channel shapeChannel shape
rectangular
ovalrounded corners
triangletrapezoid
corrugated
Flo
w f
ield
ovalrounded corners
• Shape dictated not only by design, but also by
the manufacturing process (machining, molding, stamping, R)
corrugated
Effect of Channel Shape on Water FormEffect of Channel Shape on Water Form
Flo
w f
ield
droplets film
Issues:
Hydrophobicity/hydrophilicity
Velocities required for water removal
Droplet coalescing
Droplet movement in bends and turns
hydrophobic
hydrophobic
hydrophobic
hydrophilic
Interaction between flow field and GDL
Flo
w f
ield
hydrophilic
hydrophilic
hydrophobic
hydrophilic
hydrophilic
S. Kandlikar et al., (2009)
S. Kandlikar et al., (2009)
S. Kandlikar et al., (2009)
S. Kandlikar et al., (2009)
S. Kandlikar et al., (2009)
k = l/(l+c) k = (l-o)/(l+c) k = (l-c)/(l+c)
Parallel
Anode vs. cathode orientationAnode vs. cathode orientation
Flo
w f
ield
k = l/(l+c) k = (l-o)/(l+c) k = (l-c)/(l+c)
Cross
k = [l/(l+c)]2
Effect on electrical resistance
Anode vs. cathode flow directionAnode vs. cathode flow direction
CoCo--flowflow
CounterCounter--flowflow
Cross flowCross flow
Current density (A/cm2) distributions
Co-flow Counter flow
Stationary operating
conditions:
H2 80 C
Air 70 C dew point
at 40%
1.2/2.0 Stoich with
101 kPa pressure 70
C cell temperature
S. Shimpalee, J.W. Van Zee, Numerical studies on rib & channel dimension of flow-field on PEMFC
performance, Int. J. of Hydrogen Energy, Volume 32, Issue 7, 2007, Pages 842-856
Automotive operating
conditions:
H2 75% RH at 80 C/
Air: DRY dew point at
100%
1.3/2.0 Stoich
274 kPa pressure
80 C cell temperature
channel = land channel > land channel < land
Channel dimensions and spacingChannel dimensions and spacingF
low
fie
ld
• Dimensions dictated by flow rates and desired velocities
Current density (A/cm2) distributions at Iavg = 1.2 A/cm2; stationary conditions
Current density (A/cm2) distributions at Iavg = 0.8 A/cm2; automotive conditions
Temperature (K) distributions at the cross flow plan (x–y plane)
located in the middle of flow-field
Base case
Wide channels
Narrow channels
S. Shimpalee, J.W. Van Zee, Numerical studies on rib & channel dimension of flow-field on PEMFC
performance, Int. J. of Hydrogen Energy, Volume 32, Issue 7, 2007, Pages 842-856
Conclusions: The effect of channel/rib width on PEMFC performance
• The performance is slightly higher for the narrower channel with
wider rib spacing for stationary condition.
• Larger rib area gives better heat transfer from MEA toward collector.
• The global uniformity of distributions is similar for all channel/rib
width.
• Wider channel with narrower rib shows more local nonuniformity
distributions between channel and rib.
• Pressure drop increases when the channel area is reduced.
Effect on local current densityEffect on local current density
0.0680.0
87
0.106
0.106
0.124
0.124
0.143
0.1
0.161
0.1
0.180
0.1
0.7
0.8
0.9
1 catalyst
gasdiffuser
½ channel½ land
Oxygen concentration contours
0.1240.180
Z(mm)
Y(m
m)
0 0.25 0.5 0.75 10
0.1
0.2
0.3
0.4
0.5
0.6
Collector plate gaschannel
collector plate
Source: University of Miami presentation at Annual National Laboratory R&D Meeting
DOE Fuel Cells for Transportation Program, Oak Ridge, June 6 - 8, 2001
The motivation of this study was to understand
the implication of L:C ratio and channel–DM
interface on the liquid water content stored in
the diffusion media and flow channels during
steady-state operation
Neutron imaging at the Penn State Breazeale
Nuclear Reactor Fuel Cell Imaging Laboratory was
used to quantify liquid water content and
distribution in 50 cm2 fuel cells with L:C ratios
from 1:3 to 2:1.
Results indicate: (1) for L:C ratios of one, the liquid water tends to preferentially
accumulate under landings rather than in, or under the channels,
(2) water storage is not only a function of diffusion media but also
dependent on the flow-field geometry and the number of interfaces
for a hydrophilic channel wall,
(3) it is possible to obtain similar cell performance at low to
moderate current density with vastly different amounts of stored
water by tailoring the flow-field geometry, water by tailoring the flow-field geometry,
(4) as the L:C ratio is reduced, the liquid stored in the cell
decreases, with an optimal condition for L:C ratios smaller than 2:3,
(5) the number of channel–DM interface for the same L:C ratio has
an important influence on water accumulation. Corners are
preferred water storage sites and a reduced number of channel–DM
interface corresponds to less corners and turns for a serpentine
design which results in low water mass in the cell,
(6) at dry operation, a high L:C ratio can be helpful, while at high
humidity ratio, a low L:C is preferred.
∆P = f ∑ ρ+ρ2
vK
2
v
D
L 22
H
A
wch
dch
wLPressure drop in channel
f = friction factor
L = channel length, m
DH = hydraulic diameter, m
ρ = fluid density, kg m-3
v = average velocity, m s-1
K = local resistance (for example in sharp turns)
chch
chchH
dw
dw2D
+=
( )Lchch
cell
wwN
AL
+=
Velocity in channel - example wch
dch
wL
Air
S = 2
i = 1 A/cm2
T = 60ºC
P = 101.3 kPa
chLSiRTv ==== air 1IM
Sm ====& chL1SiRTv ====
Lch = 10 cm
wch = 0.1 cm
wL = 0.1 cm
dch = 0.1 cm
chL
chch
dr
L
nF
Si
P
RTv ====
2O
airch
cF4Sm ====&
chL
ch
2Och
dr
L
c
1
nF
Si
P
RTv ====
sm351001050
10
210
1
485964
000102
300101
3333148vch /.
..
.
.,
,
,
.====
⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
====
νDv
====Re hR4D ==== m00025000104
0010
P
AR
2
mh .
.
.====
⋅⋅⋅⋅========
7210871
35100025045
====⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅==== −−−−.
..Re
©2002 by Frano Barbir.
µρ
= HvDRe
2
3
00
T
T
CT
CT
++
µ=µ
Viscosity of fuel cell gases (at 25°C)
Viscosity
kg m-1 s-1
Coefficient C
Hydrogen 0.92×10-5 72
Air 1.81×10-5 120
Water vapor 1.02×10-5 6600
0TCT
+ Water vapor 1.02×10 660
2
12
2
1
21
1mix
M
M1
M
M1 Ψ+
µ+
Ψ+
µ=µ
50
2
1
2250
1
2
50
2
11
r
r1
r
r1
4
2... −
+
µµ
+=Ψ
50
1
2
2250
2
1
50
1
22
r
r1
r
r1
4
2... −
+
µ
µ+=Ψ
Velocity in channel
ch
chch
A
Qv =
chchch dwA ====
PM
RTmmQ chch
ch
&&=
ρ=
wch
dch
wL
Volumetric flow rate:
Mass flow rate:
in2Och
c
1
nF
MISm =& iAI ==== (((( ))))Lchch wwLA ++++====
( )Lch
chL
ww
wr
+=
L
chch
r
wLA ====
chL
ch
in2O
chdr
L
c
S
nF
i
P
RTv =
Mass flow rate:
Velocity in channel
©2002 by Frano Barbir.
chL
ch
in2Ovsat
chdr
L
c
S
nF
i
PP
RTv
ϕ−=
For dry air:
For humid air:
Re f = constantFor laminar flow
Re f = 64
∆P = f ∑ ρ+ρ2
vK
2
v
D
L 22
H
For circular channels (pipes):
Re f
−+≈db
4354155
/
.exp.
Re f = 64
For rectangular channels:
For circular channels (pipes):
Re f ≈ 56For square channels:
∆P = f ∑ ρ+ρ2
vK
2
v
D
L 22
HK = 30 f
K = 50 f
For sharp turns (90°):
For return bends (180°):
x
z
y
x
z
y
cellsat2O
stack NPP
RT
r
S
F4
IQ
ϕ−=
( )sat2O PP
RT
bd
Lwb
r
S
F4
iv
ϕ−+
=
cellsatin
out
2O
outstack N
PPP
RT1
r
S
F4
IQ
−∆−
−=
∆P = f ∑ ρ+ρ2
vK
2
v
D
L 22
H
Pressure drop
Cathode side
pressure drop
measured
Stack at room
temperature
Current drawn
Un
ifo
rm d
istr
ibu
tio
n
Current drawn
proportional to flow rate
1.75 LPM every 10 A
Pressure drop as a function of flow rate and stack inlet
conditions for both operating and non-operating stack
Stack design/engineering issuesStack design/engineering issues
Uniform distribution of reactants to each cell
Uniform distribution of reactants inside each cell
Uniform temperature distribution in each cell
Te
mp
era
ture
dis
trib
uti
on
Cooling is required to ensure uniform temperature distribution
Te
mp
era
ture
dis
trib
uti
on
Fuel cell cooling schemesFuel cell cooling schemes
cooling with coolant air cooling edge cooling evaporative
cooling
Te
mp
era
ture
dis
trib
uti
on
Te
mp
era
ture
dis
trib
uti
on
Heat Transfer Paths in Fuel CellHeat Transfer Paths in Fuel Cell
Radiation/convection to the surrounding
Conduction through solid
Convection with fluids
Electrochemical reactions
Enthropic
Irreversible losses
Ohmic
Ionic
Electronic
Interface contacts
Condensation/evaporation
Sources of Heat in Fuel CellSources of Heat in Fuel Cell
Te
mp
era
ture
dis
trib
uti
on
With coolant
With unused reactant gas
(both sensible and latent)
Conduction/convection
through porous media
Condensation/evaporation
Te
mp
era
ture
dis
trib
uti
on
Effect of cooling cell distribution
0.65
0.6
0.7
Te
mp
era
ture
dis
trib
uti
on
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
0.5
0.55
0.6
Cell position in the stack
Te
mp
era
ture
dis
trib
uti
on
Gas diffuser MEA
Y
Z
X
CFD simulation of temperature distribution
in a portion of a flow field
Te
mp
era
ture
dis
trib
uti
on
Inlet channel Outlet channel
Gas diffuser MEA
Te
mp
era
ture
dis
trib
uti
on
Edge CoolingTe
mp
era
ture
dis
trib
uti
on
Te
mp
era
ture
dis
trib
uti
on
L bL b
12
Limitation of Edge Cooling: Conductivity of MaterialLimitation of Edge Cooling: Conductivity of Material
Te
mp
era
ture
dis
trib
uti
on
dd
0
2
4
6
8
10
-0.25 0 0.25 0.5 0.75 1 1.25
active area width (inches)
tem
pe
ratu
re d
iffe
ren
ce
(°C
)
20 W/mK
40 W/mK
60 W/mK
Te
mp
era
ture
dis
trib
uti
on
Effect on electrical resistanceEffect on electrical resistance
resis
tan
ce
contact resistanceexample of pressure
distribution
forc
e
force
resis
tan
ce
forc
e
Ele
ctr
ica
l re
sis
tan
ce
Resistance is a function of clamping forceResistance is a function of clamping force
Conta
ct R
esis
tance,
RD
/Gr[mΩ
-cm
2] 7
6
5
4
3
Conta
ct R
esis
tance,
R
Clamping Pressure, P [MPa]
3
2
1
00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Carbon Fiber Paper
Carbon Cloth
V. Mishra, F. Yang and R. Pitchumani, Electrical contact resistance between gas diffusion layers and bi-polar plates
in a PEM fuel cell, Proc. 2nd Int. Conf. Fuel Cell Science, Engineering and Technology. Rochester, NY, 2004
Ele
ctr
ica
l re
sis
tan
ce
0.14
0.16
0.18
0.2
iR (
Oh
m-c
m²)
series 6000 series 5000
Contact Pressure Investigation
0.1
0.12
0.14
iR (
Oh
m-c
m²)
4 6 8 10 12 14 16 18
compression (mils)
Compression = difference in MEA thickness before and after installation in the cell
Ele
ctr
ica
l re
sis
tan
ce
Contact Pressure Investigation
0.7
0.8
0.9
1 cell
pote
ntial (V
)7.2 10.6 13.2 17compression:
(150 cm2, hydrogen/air, 60°C, 3 bar, H2 stoich 1.5, air stoich. 3.5, air humidification at 60°C)
0.4
0.5
0.6
0.7
cell
pote
ntial (V
)
0 200 400 600 800 1000 1200
current density (mA/cm²)
Ele
ctr
ica
l re
sis
tan
ce
Cell compressionCell compression
Clamping Force =
Force required to compress the GDL
+ Force required to compress the gasket
+ Internal force(s)Tie-rod
nut
GDL
gasket
Issues:
Contact resistance
Sealing
Pressure distribution
End plate bowing
Internal pressure
Thermal expansionCe
ll c
om
pre
ss
ion
Cell/stack compressionCell/stack compression
Non-uniform Uniform
Hydraulic or pneumatic piston
Ce
ll c
om
pre
ss
ion
Avoiding loss of stack compression
Bellville washers on tie-rods
Endplate
Tie Rods
Spring Washers
Positive Terminal
Negat ive Terminal
Reversible Cells
Fluid Manifold
A Novel Approach: springs (coil or polyurethane) – central compression
©2002 by Frano Barbir.
Ce
ll c
om
pre
ss
ion
Stack design/engineering issuesStack design/engineering issues
Uniform distribution of reactants to each cell
Uniform distribution of reactants inside each cell
Uniform temperature distribution in each cell
Minimal resistive losses
• good electrical contacts
• selection of materials• selection of materials
Account for thermal expansion
No crossover or overboard leaks
Minimum pressure drop (reactant gases and coolant)
No water accumulation pockets
Design for manufacture/design for assembly
Oth
er
ConclusionsConclusions
A fuel cell stack is a simple, yet complex device
Uniformity of local conditions is essential for good design
Understanding of operating conditions is important
Information may be gathered through modeling/numerical Information may be gathered through modeling/numerical
simulations and experimentally
Selection of key parameters and conditions must be made
from the system perspective
Good stack design with commercially available MEAs
should yield close to 1 W/cm2
300 W – 3 kW
PEM Fuel Cell Stacks
for back-up power
PEM Fuel Cell Stacks
for residential
cogeneration
PEM Fuel Cell Stacks
for motive power--------------------------------------
Material handling:
forklift trucks
PEM Fuel Cell Stacks
for motive power--------------------------------------
Bus and Heavy duty
Copyright © 2007 NedStack fuel cell technology BV.
Copyright © 2007 NedStack fuel cell technology BV.
Copyright © 2007 NedStack fuel cell technology BV.