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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




Uniform or desired temperature distribution in each cell



• selection of materials

Un

ifo

rm d

istr

ibu

tio

n

• selection of materials








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




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

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)

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


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




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


Ce

ll c

om

pre

ss

ion




Uniform temperature distribution in each cell



• selection of materials• selection of materials






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


for residential

cogeneration


for motive power--------------------------------------

Material handling:

forklift trucks


for motive power--------------------------------------

Bus and Heavy duty

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