humidity of reactant gases) that must be determined based on the applicationW Vst$I (6-1)

PEM Fuel CellsISBN 978-0-12-387710-9,http://dx.doi.org/10.1016/B978-0-12-387710-9.00006-0

2013 Elsevier Inc.All rights reserved. 159jrequirements and constraints.The stack power output is simply a product of stack voltage and current:CHAPTER SIX

Stack Design

As discussed in Chapter 3, the fuel cell electrochemical reactions result intheoretical cell potential of 1.23 V, and the actual potential in operation islower than 1 V. If a single cell were required to generate 1 kW of power, itwould need to generate electrical current higher than 1,000 amperes. Sucha current could be generated only with a large active area (>1000 cm2), andit would require very thick cables between the fuel cell and the load tominimize the resistive losses. A more practical solution would be to havemultiple cells electrically connected in series. The cell active area and thecross-sectional area of the connecting cables would decrease with a numberof cells connected in series. For example, 1 kW power output may beaccomplished with as many as 40 cells connected in series, each cell oper-ating at 0.6 V and 1 A/cm2. Total current would be about 42 amperes at24 volts.

6.1 SIZING A FUEL CELL STACK

The rst step in designing a fuel cell stack is to determine its active areaand number of cells in the stack. When a stack is designed for an application,the design inputs come from the application requirements, such as desiredpower output, desired or preferred stack voltage or voltage range, desiredefciency, and volume and weight limitations. Some of these requirementsmay conict with each other, and the stack sizing and design process oftenresults in a compromise solution that meets the key requirements (such aspower output) and nds an optimum between the conicting requirements.

Another design input is the unit performance, best described by thepolarization curve. The fuel cell polarization curve is the key for sizing anddesigning a fuel cell stack. However, as shown in Chapter 5, the fuel cellperformance is determined by operational conditions (pressure, temperature,

160 PEM Fuel Cellsdemonstrated; more typically, active area is between 50 and 300 cm2The stack potential is simply a sum of individual cell voltages or a product ofaverage individual cell potential and number of cells in the stack:

Vst XNcelli 1

Vi Vcell$Ncell (6-2)

The current is a product of current density and cell active area:

I i$Acell (6-3)Cell potential and current density are related by the polarization curve:

Vcell f i (6-4)The polarization curve may be dened by a set of data (Vcell-i), by anyof the Equations (3-43), (3-46), or (3-52), or by linear approximation(Equation 3-68).

The fuel cell stack efciency may be approximated with a simpleEquation (3-61):

h Vcell=1:482 (6-5)which is not valid only for the potentials close to the open circuit potentials.

The previous section represents a set of ve equations with eight vari-ables. Additional variables or constraints may be stack volume and weight,both being functions of number of cells in the stack and cell active area, inaddition to stack construction and choice of materials. It is therefore a matterof simple arithmetic to calculate the remaining variables if three of them aregivendfor example, power output, stack voltage, and stack efciency.(A little complication is the form of the equation Vcell f(i), which mayrequire some iterative process to calculate current density, i, when cellpotential, Vcell, is given.) If less than three inputs are given, there may be aninnite number of cell active areas and number of cell combinations thatsatisfy the previous equations, with some limitations (Figure 6-1). Bothactive area and number of cells in the stack, as well as their combination,have physical and/or technological limits. For example, a large number ofcells with very small active area would be difcult to align and assemble. Onthe other hand, a small number of cells with a large active area would resultin a high current/low voltage combination and would result in signicantresistive losses in connecting cables.

Very often the number of cells in a stack is limited or determined byrequired stack voltage. Stacks with active area up to 1000 cm2 have been

Stack Design 161depending on application and desired power output. In larger active areas itis more difcult to achieve uniform conditions, which is one of the keyaspects of a successful stack design as it is discussed here. The maximumnumber of cells in a stack is limited by compression forces, structural rigidity,and pressure drop through long manifolds. Stacks with up to 200250 cellshave been demonstrated.

These limits also apply to the case of the determined system, that is, with

0

100

200

300

400

500

600

700

800

900

1000

0 50 100 150 200 250 300number of cells in stack

cell

activ

e ar

ea (c

m)

50 kW

20 kW

5 kW

1 kW

0.4 W/cm2

0.9 W/cm2

Figure 6-1 Fuel cell stack sizing: number of cells and cell active area for different poweroutputs (solid lines are for 0.4 W/cm2 and dashed lines are for 0.9 W/cm2).three variables given. If the solution for number of cells and cell active areafalls outside the limitations, it would be necessary to reconsider and modifythe requirements.

Very often, there is a need to optimize the stack efciency and size.These are two conicting requirements for a given power output anda given polarization curve. Typical fuel cell polarization curves are shown inFigure 6-2. Most of the published fuel cell stack polarization curves fallwithin these two lines.

The nominal operating point (cell voltage and corresponding currentdensity) is the operating point at nominal power output, and it may beselected anywhere on the polarization curve. Selection of this point hasa profound effect on the stack size and efciency. Lower selected cell voltageat nominal power results in higher power density and consequently insmaller stack size for any given power output. Figure 6-3 shows the rela-tionship between stack size (total active area per unit power output) andnominal cell potential for the two polarization curves from Figure 6-2. From

162 PEM Fuel Cells0.2

0.4

0.6

0.8

1

1.2

cell

pote

ntia

l (V)Figure 6-3, it follows that a stack with nominal cell voltage of 0.7 V wouldrequire about 40% larger active area than a stack sized at 0.6 V/cell. Selectionof 0.8 V/cell at nominal power would result in more than twice the size ofa stack sized at 0.7 V/cell. However, higher cell voltage means better ef-ciency and consequently lower fuel consumption. Currently, most fuel cellmanufacturers and developers use between 0.6 V and 0.7 V as voltage atnominal power. However, to reach some system efciency goals, the fuelcells would have to be rated at 0.8 V/cell or even higher. Indeed, inapplications where the efciency (which translates in reactant consumption)

00 200 400 600 800 1000 1200 1400 1600

current density (mA/cm2)Figure 6-2 Typical PEM fuel cell polarization curves.

0

2

4

6

8

10

12

14

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85Nominal cell potential (V)

Activ

e ar

ea (c

m2/W

)

Higher pol. curveLower pol. curve

Figure 6-3 Stack size vs. selected nominal cell potential (corresponding to polarizationcurves in Figure 6-2).

Stack Design 163is critical, such as in space applications in which both reactants must becarried on board, the fuel cells are rated and operated above 0.8 V. The extrafuel cell size is negligible compared with the size (and weight) of hydrogenand oxygen saved.

Optimum cell voltage at nominal power should be determined for eachapplication based on the optimization criteria (such as the lowest cost ofgenerated electricity, the least expensive system, or the lowest size andweight), and it should therefore take into consideration many parameters,

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0 0.2 0.4 0.6 0.8 1power/nominal power

stac

k ef

ficie

ncy

Vnom=0.8 V

Vnom=0.7 V

Vnom=0.6 V

Figure 6-4 Stack efciency (based on LHV) vs. power output for different selectednominal cell potentials (solid lines are for the higher and dashed lines are for the lowerpolarization curves in Figure 6-2).such as the cost of fuel cell, cost of fuel, lifetime, capacity factor, load prole,system efciency, and so on [1]. If the stack is operated at partial load (below20% of nominal power) most of the time, then higher selected nominal cellvoltage does not necessarily mean higher operating efciency. As shown inFigure 6-4, at 20% of nominal power there is no efciency advantage ofhigher selected nominal cell voltage. This is due to operation at very lowcurrent densities where parasitic losses (including gas permeation throughthe polymer membrane) may not be negligible.

6.2 STACK CONFIGURATION

A fuel cell stack consists of a multitude of single cells stacked up so thatthe cathode of one cell is electrically connected to the anode of the adjacentcell. In that way, exactly the same current passes through each of the cells.Note that the electrical circuit is closed, with both electron current passing

164 PEM Fuel CellsA C A C A C A C +

electron pathway

Figure 6-5 Bipolar conguration.through solid parts of the stack (including the external circuit) and ioniccurrent passing through the electrolyte (ionomer), with the electrochemicalreactions at their interfaces (catalyst layers).

The bipolar conguration is best for larger fuel cells because the currentis conducted through relatively thin conductive plates and thus travels a veryshort distance through a large area (Figure 6-5). This causes minimumelectroresistive losses, even with a relatively bad electrical conductor such asgraphite (or graphite polymer mixtures). For small cells it is possible toconnect the edge of one electrode to the opposing electrode of the adjacentcell by some kind of a connector [24]. This is applicable only to very smallactive area cells because current is conducted in a plane of very thin elec-trodes, thus traveling a relatively long distance through a very small cross-sectional area (Figure 6-6).

A A

A A A

C

C CA

C CC

+

+

electron pathway

(a)

(b)

Figure 6-6 Examples of side-by-side stock congurations for smaller fuel cells: (a) zig-zag connections with open air cathode; (b) ip-op conguration.

The main components of a fuel cell stack are the membrane electrodeassemblies, or MEAs (membranes with electrodes on each side with a catalystlayer between them), gaskets at the perimeter of the MEAs, bipolar plates,bus plates (one at each end of the active part of the stack) with electricalconnections, and the end plates (one at each end of the stack) with uidconnections [5]. Cooling of the stack, that is, its active cells, must bearranged in some fashion as discussed next. The whole stack must be kepttogether by tie rods, bolts, shroud, or some other arrangement (Figure 6-7).

In some stack congurations, humidication of one or both reactantgases is included in the stack, either in a separate stack section or betweenthe cells. In both cases water is used for both cooling and humidication, andthe heat generated in each of the active cells is used for humidication.Figure 6-8 shows a stack conguration in which the reactant gases rst passthrough a humidication section and then through the active cells, whereaswater rst passes through the active portion of the stack, gets heated up, andthen passes through the humidication section, where heat andwater transferbetweenwater and the reactant gases occurs through polymermembranes [6].The advantage of this stack conguration is in its compactness of the gas

Stack Design 165humidication system and reduced heat dissipation, but this very advantage isalso its main drawback: lack of versatility in controlling water and heatmanagement and inability to separate heat from water management.

end plate

oxidant in

oxidant + water out

hydrogen out

hydrogen in

bus platebi-polar collector plates

tie rod

membraneanode

cathode

coolant in

coolant out

Figure 6-7 Stack schematic [5].

166 PEM Fuel CellsIn another conguration (Figure 6-9), water passes between the cells,which are separated by a porous graphite plate from the reactant gases [7].The porous plate allows water transport, effectively facilitating water and

active cellshumidificationsection

oxidant in

oxidant + water out

hydrogen out

hydrogen in

water inwater out

Figure 6-8 Stack conguration with internal humidication.heat management in each cell. Hydrogen, air, and water pressures must becarefully regulated so that water in the porous plate channels is always atslightly negative pressure compared with reactant pressure. Pore size controlsbubble point such that the reactants do not mix. Water recirculation toa radiator provides stack cooling. The main disadvantage of this concept isinability to separate heat from water management, but others are a very tightpressure control requirement and operation at low pressures only.

The following are the key aspects of a fuel cell stack design: Uniform distribution of reactants to each cell Uniform distribution of reactants inside each cell Maintenance of required temperature in each cell Minimum resistive losses (choice of materials, conguration, uniform

contact pressure) No leak of reactant gases (internal between the cells or external) Mechanical sturdiness (internal pressure, including thermal expansion;

external forces during handling and operation, including shocks andvibrations)

These aspects are discussed in the following sections.

Stack Design 167internalwater

passagesMEAs

Figure 6-9 Stack conguration with water management through porous plate.H2Air

H2O

waterfilled

porousplates

H2Air

hydrophobicdiffusionbackings6.3 UNIFORM DISTRIBUTION OF REACTANTSTO EACH CELL

Because fuel cell performance is sensitive to the ow rate of the reactants, itis absolutely necessary that each cell in a stack receive approximately thesame amount of reactant gases. Uneven ow distribution would result inuneven performance between the cells. Uniformity is accomplished byfeeding each cell in the stack in parallel through a manifold that can beeither external or internal. External manifolds can be made much bigger toensure uniformity. They result in a simpler stack design, but they can onlybe used in a cross-ow conguration and are, in general, difcult to seal.Internal manifolds are more often used in PEM fuel cell design, not onlybecause of better sealing but also because they offer more versatility in gasow conguration.

It is important that the manifolds that feed the gases to the cells and themanifolds that collect the unused gases are properly sized. The cross-sectional area of the manifolds determines the velocity of gas ow and thepressure drop. As a rule of thumb, the pressure drop through the manifolds

(Adapted from [7].)

168 PEM Fuel CellsU-shape

Z-shapeshould be an order of magnitude lower than the pressure drop through eachcell in order to ensure uniform ow distribution.

The ow pattern through the stack can be either a U shape, where theinlet and outlet are at the same side of the stack and the ows in inlet andoutlet manifolds are in opposite directions from each other, or a Z shape,where the inlets and outlets are on opposite sides of the stack and the ows ininlet and outlet manifolds are parallel to each other (Figure 6-10). If properlysized, both should result in uniform ow distribution to individual cells.Stacks with more than 100 cells have been successfully built.

The procedure to calculate the pressure drop through the manifolds andthe entire stack, and the resulting ow distribution, involves a ow networkproblem consisting of N-1 loops [8], where N is the number of cells in thestack. The ow in any network must satisfy the basic relations of continuityand energy conservation as follows:1. The ow into any junction must equal the ow out of it.2. The ow in each segment has a pressure drop that is a function of the

ow rate through that segment.3. The algebraic sum of the pressure drops around any closed loop must

be zero.

Figure 6-10 Stack ow congurations.

Stack Design 169decrease along the streamline in the manifold due to velocity loss; the secondterm is the pressure drop due to friction with the walls; and the last term isthe pressure loss due to local disturbances described by the geometriccoefcient.L length of the segment (m)DH hydraulic diameter of the manifold segment (m)Kf local pressure loss coefcient

The rst term on the right side of Equation (6-12) represents the energyQoutN Qin1 for Z conf iguration (6-11)The pressure drop, derived directly from the Bernoulli equation, in eachmanifold segment is [8]:

DPi r ui2 ui 12

2 f r L

DH

ui22

Kfr ui 12

2

(6-12)

where:r density of the gas (kg m3)u velocity (m s1)f friction coefcientThe rst requirement is satised with the following relationships:

Qini Qcelli Qini 1 in inlet manifold (6-6)Qouti Qcelli

Qouti 1 in outlet manifold; U conf iguration(6-7)

Qouti QcelliQouti 1 in outlet manifold; Z conf iguration

(6-8)

Note that by denition of the cells and ows numbering shown inFigure 6-11:

Qout1 Qstack (6-9)For a nonoperating stack, that is, one with no species consumption orgeneration, the ow at the stack outlet is equal to the ow at the inlet:

Qout1 Qin1 for U conf iguration (6-10)

170 PEM Fuel CellsQ in(N)

Q in(N-

1)

Q in(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)

Q cel

l(1)

Q cel

l(2)

Q cel

l(i-1)

Q cel

l(i)

Q cel

l(i+1)

Q cel

l(N-1)

Q cel

l(N)

Pin(N)

Pout(N)

Pin(1)

Pout(1)

Q in(i-1

)

Q out(i-

1)

Q in(N)

Q in(N-

1)

Q in(i)

Q in(i+1

)

Q in(2)Qin(1)

P (N)

Q in(i-1

)The loss of pressure due to local disturbances, such as ow branching outor in (tees) or sudden changes in direction (elbows), should be taken intoaccount in calculating the pressure drop in each segment. Typically in uid-mechanics textbooks, these losses are called minor losses; however, in fuel cellmanifolds they may not be negligible. Koh et al. [8] showed that the owdistribution largely depends on the local pressure loss coefcients. Thoughsome geometrical pressure loss coefcients are available for various pipettings, none t a specic shape of the fuel cell gas ow manifolds. Koh et al.[8] concluded that the geometrical pressure loss coefcients should bedetermined experimentally for each stack design.

For laminar ow (Re < 2000), the friction coefcient f for a circularconduit is:

f 64Re

(6-13)

Qout(N)Q ou

t(N-

1)Q ou

t(i)

Q out(i+

1)

Q out(2

)

Q out(1)

Q cel

l(1)

Q cel

l(2)

Q cel

l(i-1)

Q cel

l(i)

Q cel

l(i+1)

Q cel

l(N-1)

Q cel

l(N)

in

Pout(N)

Pin(1)

Pout(1)

Q out(i-

1)

Figure 6-11 Designation of pressure and ow and ow variables for U (above) and Z(below) stack ow congurations.

Stack Design 171ow distribution than U conguration. It may be shown that for U 0 in Z conf iguration (6-17)For a given ow rate at the stack entrance and a known pressure either at thestack inlet or at the stack outlet, it is possible to calculate the ow ratethrough each of the cells using a method of successive approximations, suchas the Hardy-Cross method commonly used for pipe networks [9] or themethod suggested by Koh et al. [8]. The procedure in either method issimilar:1. It starts with an approximation of the ows in each of the cells Qcell

Qstack /Ncell.2. It calculates the pressure drops in individual manifold segments and cells.3. It checks the sum of pressure drops in each of the loops (it should be

zero).4. It adjusts the ows in each loop by a correction, DQ, proportional to the

error in sum of the pressure drops, and the process is repeated one loop ata time until the error is negligible.

For the same size conduits, Z conguration usually results in more uniform 0 in U conf iguration (6-16)DPini 1 DPcelli 1 DPouti DPcelliFor turbulent ow, the friction coefcient is primarily a function of the wallroughness. The walls of fuel cell manifolds may be considered roughbecause they are not a smooth pipe but instead consist of the bipolar platesclamped together, often with the gasket material protruding into themanifold. The relative roughness, /D, can be as high as 0.1. In that case thefriction coefcient (according to Karman [9]) is:

f 11:14 2 log

D

2 (6-14)The pressure drop through the cell, DPcell, is discussed in Section 6.4.5,Pressure Drop Through the Flow Field. In most cases it is a linear functionof the ow rate through each cell.

The third requirement is that the algebraic sum of the pressure dropsaround any closed loop must be zero:

For i 1 to N 1 (6-15)DPini 1 DPcelli 1 DPouti 1 DPcelli

172 PEM Fuel Cellsconguration, uniform distribution of ows through the individual cellsresults when the pressure drop through the cell is at least an order ofmagnitude higher than the pressure drop through the stack inlet manifold(Figure 6-12). The inlet and outlet manifolds must be sized accordingly.Sometimes it is benecial to have more than one manifold for one reactant,

0.60.70.80.9

11.1

cell # 1 4 7 8 9 10 1165320

flow/

aver

a

Figure 6-12 Flow distribution in individual cells of a 10-cell stack for U and Z cong-urations and for various ratios of pressure drop through individual cells and throughthe inlet manifold (dPcell /dPch).1.21.31.41.51.6

ge fl

owU; dPcell/dPch = 2.5U; dPcell/dPch = 5U; dPcell/dPch = 10Z; dPcell/dPch = 2.5especially for the stacks with larger active area. In that case the pressure dropthrough each manifold must also be balanced to ensure uniform owdistribution to each manifold. Similar methods as depicted previously maybe used for that calculation.

When the stack is in operation, the change in ow rate, gas density,and viscosity due to species consumption and generation must be takeninto account, although it should not signicantly affect the pressure dropresults (

Stack Design 173The ow elds come in different shapes and sizes. The size comes from thepower/voltage requirements as shown in Section 6.1, Sizing a Fuel CellStack. The shape is the result of positioning the inlet and outlet manifolds,ow eld design, heat management, and manufacturing constraints. Themost common shapes of the ow eld are square and rectangular, butcircular, hexagonal, octagonal, or irregular shapes have been used or at leasttried (Figure 6-13).

6.4.2 Flow Field Orientation6.4.1 Shape of the Flow Field

Figure 6-13 Various shapes of the fuel cell active area.The orientation of the ow eld and positions of inlet and outlet manifoldsare important only because of gravitys effect on water that may condenseinside the ow eld (the effect of gravity on the reactant gases is negligible).Condensation may take place either during operation, depending on thechoice of operational conditions, or after shutdown. Numerous combina-tions are possible, some of which are shown in Figure 6-14.

Anode and cathode may be oriented in the same direction, in oppositedirections, or in cross-conguration. The position of the anode vs. thecathode may have some effect on fuel cell performance because of variedconcentration of reactant gases and water. In some cases the ow elds areoriented so that the cathode outlet is next to the anode inlet, and vice versa,allowing water exchange through the membrane due to the waterconcentration gradient (i.e., the exiting gas has much higher temperatureand water content).

174 PEM Fuel Cellssame side inlets and outlets adial (outwards) radial (inwards)top to bottom bottom to top side to sideThe stack orientation, and so the ow eld orientation, may be eithervertical or horizontal. In the latter case, either anode or cathode may befacing up (Figure 6-15). Again, this may have some effect on liquid waterremoval, particularly after shutdown and cooling.

6.4.3 Conguration of ChannelsThere are many congurations of channels that have been tried in PEM fuelcells, all with the same goal: to ensure uniform reactant gases distribution andproduct water removal (see Figure 6-16). Some most common designs are asfollows: Straight channels with large manifolds. Although this appears to ensure

uniform distribution, it actually does not work in PEM fuel cells.Distribution is indeed uniform but only under ideal conditions. Any

Figure 6-14 Possible ow eld orientations.

anode facing up cathode facing up

horizontal stack-up vertical stack-up

ac

c

a

a c

Figure 6-15 Stack and cell orientation options.

Stack Design 175straight criss-cross

single-channelserpentine

multichannelserpentine mixed serpentine

straightwater droplet that develops in a channel would effectively block theentire channel, and the velocity would not be sufcient to push thewater out.

Straight channels with small manifolds. This design has the same short-comings and, in addition, has inherent maldistribution of reactant gasesbecause the channels immediately below or above the manifold receivemost of the ow. The early fuel cells built with such a ow eldexhibited low and unstable cell voltages.

subsequentserpentine mirror serpentine

interdigitated fractal

biomimetic screen/mesh porous

Figure 6-16 Various ow eld congurations.

176 PEM Fuel Cells Criss-cross conguration. This ow eld attempts to eliminate the short-comings of the straight channel ow eld by introducing traversalchannels allowing the gas to bypass any trouble spot, that is, coalescingwater droplets. The problems of low velocities and uneven ow distri-bution due to positioning of the inlet and outlet manifolds are notreduced with this design.

Single-channel serpentine. As described by Watkins et al. [10], this is themost common ow eld for small active areas. It ensures that the entirearea is covered, although the concentration of reactants decreases alongthe channel. There is a pressure drop along the channel due to friction onthe walls and due to turns. The velocity is typically high enough to pushany water condensing in the channel. Attention must be paid to pressuredifferentials between the adjacent channels, which may cause signicantbypassing of channel portions.

Multichannel serpentine. A single-channel serpentine conguration wouldnot work for the large ow eld areas because of a large pressure drop.Although a pressure drop is useful in removing the water, excessivepressure drop may generate larger parasitic energy losses. Watkins et al.[11] proposed a ow eld that has a multitude of parallel channelsmeandering through the entire area in a serpentine fashion. Except for thelower pressure drop, this ow eld has the same features, advantages, andshortcomings of the single-channel serpentine. The fact that there areparallel channels means that there is always a possibility that one of thechannels may get blocked, as discussed previously with straight channels.

Multichannel serpentine with mixing. As suggested by Cavalca et al. [12], thisow eld design allows gases to mix at every turn in order to minimizethe effect of channel blocking. This does not reduce the chance ofchannel blockage, but it limits its effect to only a portion of the channelbecause the ow eld is divided in smaller segments, each with its ownconnecting channel to both the inlet and the outlet.

Subsequent serially linked serpentine. This ow eld also divides the oweld into segments in an attempt to avoid the long, straight channels andrelatively large pressure differentials between the adjacent sections, thusminimizing the bypassing effect [13].

Mirror serpentine. This is another design to avoid large pressure differen-tials in adjacent channels, particularly suited for a larger ow elds withmultiple inlets and outlets. These are arranged so that the resultingserpentine patterns in adjacent segments are mirror images of each other,

Stack Design 177which results in balanced pressures in adjacent channels, again mini-mizing the bypassing effect [14].

Interdigitated. First described by Ledjeff [15], advocated by Nguyen [16],and successfully employed by Energy Partners in its NG-2000 stack series[17,18], this ow eld differs from all of the previously described eldsbecause the channels are discontinued, that is, they do not connect theinlet to the outlet manifolds. This way the gas is forced from the inletchannels to the outlet channels through the porous back-diffusion layer.Wilson et al. [19] suggested a variation of interdigitated ow eld inwhich the channels are made by cutting out the strips of the gas diffusionlayer. Convection through the porous layer shortens the diffusion pathand helps remove any liquid water that otherwise may accumulate in thegas diffusion layer, resulting in better performance, particularly at highercurrent densities. However, depending on the properties of the gasdiffusion layer, this ow eld may result in higher pressure drops. Due tothe fact that the most of the pressure drop occurs in the porous media,the uniformity of ow distribution between individual channels andbetween individual cells strongly depends on uniformity of gas diffusionlayer thickness and effective porosity (after being squeezed). One of theproblems with this ow eld is inability to remove liquid water fromthe inlet channels. Issacci and Rehg [20] suggested the porous blocks atthe end of the inlet channels, allowing water to be removed.

Biomimetics. Suggested by Morgan Carbon [21], this is a further rene-ment of the interdigitated concept. Larger channels branch to smallerside channels, further branching to really tiny channels interweavingwith outlet channels that are arranged in the same fashiondtiny channelsleading to larger side channels leading to the large channels. This type ofbranching occurs in nature (leaves or lungs), hence the name biomimetic.

Fractal. This ow eld suggested by the Fraunhoffer Institute [22] isessentially the interdigitated ow eld concept, but the channels are notstraight and they have branches.

Mesh. Metallic meshes and screens of various sizes are successfully beingused in electrolyzers. The uniformity may greatly be affected by posi-tioning of the inlet manifolds. The researchers at Los Alamos NationalLaboratory successfully incorporated metal meshes in fuel cell design[23]. The problems with this design are introduction of anothercomponent with tight tolerances, corrosion, and interfacial contactresistance.

tapered channels would be very difcult to obtain by machining, but they

178 PEM Fuel Cellsare essential if the bipolar plate is manufactured by molding. Channelgeometry may have an effect on water accumulation. In the round-bottomed channel, condensed water forms a lm of water at the bottom,whereas in the channel with tapered walls, condensed water forms smalldroplets (Figure 6-17). The sharp corners at the bottom of the channel helpbreak the surface tension of the water lm, resisting lm formation [25].

The shape and size of the water droplets in the channels also depend onhydrophobicity of the porous media and the channel walls. Figure 6-18 Porous media ow eld [24]. This is similar to the mesh ow eld; thedifference is in pore sizes and material. The gas distribution layer mustbe sufciently thick and have enough pores sufciently large to permita substantially free ow of reactant gas both perpendicular to andparallel to the catalyst layer. Although metallic porous materials (foams)are brittle, carbon-based ones may be quite exible. This type of oweld may only be applicable for smaller fuel cells because of the highpressure drop.

6.4.4 Channel Shape, Dimensions, and SpacingThe ow eld channels may have different shapes, often resulting from themanufacturing process rather than functionality. For example, slightly

Figure 6-17 The shape of the channel cross-section affects the form of liquid waterformation.shows the possible combinations of hydrophobicity and hydrophilicity ofthe porous gas diffusion layer and the channel walls and their effect on waterdroplet shape and size [26].

Typical channel dimensions are around 1 mm but may vary from 0.4 mmto 4 mm. The spacing between the channels is similar. With todaysadvances in micromanufacturing techniques (MEMS, photolithography) it ispossible to produce channels of 0.1 mm and even smaller. The dimensions ofthe channels and their spacing affect the reactant gas access to the gasdiffusion layer and pressure drop as well as electrical current and heat

Stack Design 179Figure 6-18 Possible combinations of hydrophobicity and hydrophilicity of the porousconduction. Wider channels allow more direct contact of the reactants gasto the gas diffusion layer and also provide wider area for water removal fromthe gas diffusion layer. Figure 6-19 shows O2 concentration in a cross-section of an H2/air fuel cell with serpentine or straight channels [27].Oxygen concentration, and therefore current density, is higher in the areadirectly above the channel, and it is signicantly lower in the area above theland between the channels.

However, if the channels are too wide there will be no support for theMEA, which will deect into the channel. Wider spacing enhances

gas diffusion layer and the channel walls and their effect on droplet size and shape.

Figure 6-19 Oxygen concentration distribution in and above the channel. (Adaptedfrom [27].)

180 PEM Fuel Cellsconduction of electrical current and heat; however, it reduces the areadirectly exposed to the reactants and promotes the accumulation of water inthe gas diffusion layer adjacent to these regions. For a geometry shown inFigure 6-20, and with simplication of the current path in the control area(one half channel and one half spacing between the channels), the voltageloss through the control area is [28]:

DV DVBP DVGDL DVCR (6-18)where:

DVBP is the voltage drop through the bipolar plate:" #

wC wL

(wC + wL)/2 C/4W

GDL

CL

BP

dBP/2

dC

dGDL

Figure 6-20 Current path through bipolar plate and gas diffusion layer (left, actual;right, approximation).DVBP wL wCwL dC dBP2

rBP;z wL wCwC

4dBPrBP;xy i (6-19)

DVGDL is the voltage drop through the gas diffusion layer:

DVGDL dGDLrGDL;z

wL wCwC8dGDL

rGDL;xy

i (6-20)

and DVCR is the voltage drop due to interfacial contacts:

DVCR RCRwL wCwC i (6-21)

Stack Design 181channel may be approximated by the equation for incompressible ow inNote that the voltage loss through the entire bipolar plate, two gasdiffusion layers, and two interfaces is twice as much as what is calculatedby Equation (6-18).

In general, as landing width wL narrows, the fuel cell performanceimproves until there is either MEA deection into the channel or the gasdiffusion layer crashes because of excessive force applied. The optimumchannel size and spacing are therefore a balance between maximizing theopen area for the reactant gas access to the gas diffusion layer and providingsufcient mechanical support to the MEA and sufcient conduction pathsfor electrical current and heat.

Wilkinson and Vanderleeden [25] suggested the use of the followingequation to calculate the maximum deection of the MEA in the channel,dmax (mm):

dmax 0:032

1 v2

t3

1

b4 1L4

pE

(6-22)

where:n Poissons ratiot MEA thickness, (mm)b unsupported channel width, (mm)L channel length, (mm)p pressure, (kPa)E Youngs modulus, (kPa)

6.4.5 Pressure Drop Through the Flow FieldMost of the ow elds are arranged as a number of parallel channels(Figure 6-17). In that case the pressure drop along a channel is also thepressure drop in the entire ow eld. The pressure drop along a ow eldwhere dimensions wL, wC, dGDL, dC, and dBP are dened in Figure 6-20, and

r resistivity of either bipolar plate (BP) or gas diffusion layer (GDL) ineither z-direction (through-plane) or xy-direction (in-plane), UcmRCR contact resistance between the gas diffusion layer and bipolarplate, Ucm2

i current density at the GDLcatalyst layer interface, A cm2

182 PEM Fuel Cellspipes and conduits with sufcient accuracy as long as the pressure drop is lessthan 30% of the inlet pressure:

L v2 X v2

1

1.5

2

2.5

3

3.5

4

1.5 2 2.5 3 3.5 4Flow Rate (LPM)

Pres

sure

Dro

p (kP

a)Cold air

60C & 100% RH air

Cold air with current

60C & 100% RH airwith current

Figure 6-21 Pressure drop of a three-cell, 65-cm2 stack as a function of ow rate [33].DP fDH

r2 KLr

2(6-23)

where:f friction factorL channel length, mDH hydraulic diameter, mr uid density, kg m3v average velocity, m s1KL local resistance (for example, in sharp turns)

Hydraulic diameter is dened as four times the channel cross-sectional areadivided by its perimeter. For a typical rectangular channel with wc as widthand dc as depth (Figure 6-21):

DH 2wCdCwC dC (6-24)

Channel length is:

L AcellNchwC wL (6-25)

Stack Design 183v 4F rO2 wCdC P 4Psat (6-28)where:Acell cell active area, m2Nch number of parallel channelswC channel width, mwL space between the channels, m

The velocity in a fuel cell channel at the entrance of the cell is:

v QstackNcellNchAch

(6-26)

where:v velocity in the channel, m s1Qstack air ow rate at the stack entrance, m3 s1Ncell number of cells in the stackNch number of parallel channels in each cellAch cross-sectional area of the channel, for a rectangular channel Ach

bd, as dened previouslyThe total ow rate at the stack entrance is (combining Equations 5-42 and5-47, and dividing by density of humid air):

Qstack I4F

SrO2

RTinPin 4PsatTin

Ncell (6-27)

where:Q volumetric ow rate, m3 s1I stack current, A, I iAcellF Faraday constant 96, 485, As mol1S oxygen stoichiometric ratiorO2 oxygen content in air, by volume 0.2095R universal gas constant 8.314 J mol1 K1Tin temperature at stack inlet, KPin pressure at stack inlet, Pa4 relative humidityPsat saturation pressure at given inlet temperature (Equation 5-25)Ncell number of cells in stack

By combining the previous Equations (6-24 through 6-27), the velocity atthe stack inlet is:

i S wC wLL RT

184 PEM Fuel Cells0 0

cient, C, is also listed in Table 6-1.The Reynolds number is important to determine whether the ow in thechannel is laminar or turbulent. The Reynolds number at the channelentrance is:

Re rvDHm

1m

i2F

SrO2

wC wLLwC dC

MAir MH2O

4PsatTinPin 4PsatTin

!

(6-29)

The ow rate at the stack outlet is somewhat different than the ow at theinlet. It can be lower, equal, or higher, depending on the conditions at theinlet and outlet (ow rate, temperature, pressure, and humidity). Assumingthat the outlet ow is saturated with water vapor, the ow rate at the stackoutlet is:

Qoutstack I4F

SrO2

1

RToutPin DP PsatTout

Ncell (6-30)

where:DP pressure drop through the stack

The ratio between the outlet and inlet ow rate, thus velocity, is:

QoutstackQinstack

S rO2inS

ToutTin

Pin 4PvsTinPin DP PsatTout

(6-31)

The rst factor is always lower than 1, the second factor is either higher thanor equal to 1 (depending on the inlet temperature being lower than or equalto outlet temperature), and the third factor also depends on the inlettemperature and humidity (if the gas at the inlet is saturated at the stacktemperature, then this factor is higher than 1). For all practical purposes, thedifference between the inlet and outlet ow rates varies within 5%.

The values for viscosity of common fuel cell gases are shown in Table 6-1.The variation of viscosity with pressure is small for most gases, but viscosityvaries with temperature [29]:

m m0T0 CT C

TT0

32

(6-32)

where m is known viscosity at temperature T , from Table 6-1; the coef-

Stack Design 185M1, M2 are the molecular weights of components 1 and 2For steady laminar ow in a channel, the product of the friction factor andthe Reynolds number is a constant [31]:

Re f constant (6-36)For a circular channel, Re f 64. For rectangular channels, the value of Re fdepends on the channel aspect ratio, wC/dC:

Re fz55 41:5 exp 3:4wC=dC

(6-37)

For a square channel, Re fz 56.Viscosity of gas mixtures, such as humidied air or humidied hydrogen,can be calculated from the following equation [30]:

mmix m1

1J1 M2M1 m2

1J2 M1M2(6-33)

where:

J1 2

p

4

1

m1m2

0:5r2r1

0:25!21 r1

r2

0:5(6-34)

J2 2

p

4

1

m2m1

0:5r1r2

0:25!21 r2

r1

0:5(6-35)

andm1, m2 are the viscosities of components 1 and 2r1, r2 are the volume fractions of components 1 and 2 in the mixture

TABLE 6-1 Viscosity of Fuel Cell Gases (at 25C)Viscosity kgm1 s1 Coefcient C

Hydrogen 0.92 105 72Air 1.81 105 120Water vapor 1.02 105 660Though some geometrical pressure-loss coefcients, KL, are available forvarious bends or elbows, none ts a specic shape of gas ow channels in fuelcells. Values as high as 30 f have been suggested for 90-degree bends and ashigh as 50 f for close pattern return bends [29].

For fully turbulent ow, the friction coefcient f is independent of theReynolds number and may be approximated by the Karmans equation

186 PEM Fuel Cells(Equation 6-14). Note that the three walls of the channel are smooth, butthe fourth one is the porous gas diffusion layer.

For the porous ow elds, the pressure drop may be determined byDarcys law [32]:

DP mQcellkA

L (6-38)

where:m viscosity of the uid, kg m1 s1Qcell volumetric ow rate through a cell, m3 s1k permeability, m2A cross-sectional area of the ow eld, m2L length of the ow eld, m

The same equation may be used to approximate the pressure drop throughany ow eld as long as the ow is laminar. The permeability factor, k, thenrefers to the entire ow eld and must be determined experimentally.

In most cases the ow through the fuel cell ow eld is laminar, whichmeans that the pressure drop is linearly proportional to velocity, that is, toow rate. However, in a fuel cell channel there are some deviations from theuniform pipe ow: Roughness of the GDL is different than that of the channel walls. The reactant gas participates in the chemical reaction and the ow rate

varies along the channel, although not signicantly. Temperature may not be uniform along the channel. Typically the channel is not straight, but there are numerous sharp turns

(90 or 180 degrees). Liquid water may be present inside the channel, either in the form of

little droplets or as a lm, in both cases effectively reducing the channelcross-sectional area.

Figure 6-21 shows a linear relationship between the ow rate and thepressure drop through the cathode side of a three-cell, 65-cm2 stack whendry air at room temperature is run through the stack and no current, and thusno water, is being generated [33]. The Reynolds number at the entrance ofthe cathode channels was

isline hepro wrate enmo heinc nolon llywit assho

Nch wC wL 6 0:08 0:08

Stack Design 187The ow rate at the stack entrance is (Equation 6-27):

Qstack I4F

SrO2

RTinPin 4PsatTin

Ncell

0:4 654 96; 485

3

0:21

8:314 273:15 60125; 000 19; 944 60

0:00152 m3 s1 1520 cm3 s1

where 19,944 Pa is the saturation pressure at 60C.L Acell 65 67:7 cmChannel length is (Equation 6-25):Hydraulic diameter is (Equation 6-24):

DH 2wc dcwc dc 2 0:08 0:08=0:08 0:08 0:08 cmDP f LDH

rv2 KL r v

2cathode ow eld consists of six parallel serpentine channels 0.8 mm wide,0.8 mm deep, and 0.8 mm apart, with four 90-degree bends.

SolutionThe pressure drop is (Equation 6-23):

2 X 2Calculate the pressure drop through a cathode ow eld of a 60-cell stackwith 65-cm2 cell area. The stack operates at 125 kPa (inlet), 60C, withsaturated air. The ow rate is kept proportional to current at three timesstoichiometry. Nominal operating point is 0.4 A cm2 at 0.7 V. Thewn in Figure 6-21.

ExampleWhen the stack is operational and generates water, the pressure droparly proportional to the ow rate if the incoming air is dry because all tduct water gets evaporated in the ow of air. Note that the molar oat the exit is higher than the ow rate at the inlet because each oxyglecule consumed is replaced by two water vapor molecules. When toming air is fully humidied, evaporation of the product water isger possible; as a result the pressure drop starts to increase exponentiah the air ow rate (and with current, that is, water generation rate),

3188 PEM Fuel Cells5300 Pa).The inlet and outlet manifolds of this 60-cell stack should be sizedso that the pressure drop through a manifold is at least an order ofmagnitude lower than the pressure drop through individual cells, that is,less than 445 Pa (the total stack pressure drop would then be aboutvelocity at the outlet is somewhat lower, so the average velocity throughoutthe channel would be lower and, consequently, the pressure drop would besomewhat lower. The exact solution may be obtained through an iterativeprocess.DP fDH

r2 KLr

2 0:172

0:00081:23

2

4 30 0:172 1:23 6:62

2 DP 4452 Pa Answer

This pressure drop has been calculated based on inlet conditions. Thef 56=Re 56=324:7 0:172And nally, the pressure drop is:

L v2 X v2 0:677 6:62Re fz55 41:5 expb=d

56

Friction factor:Re Hm

0:00123 660 0:08=0:0002 324:73:4m 2 105 kg m1 s1 0:0002 g cm1 s1

rvDRT

125; 000 19; 944 29 19; 944 188314 273:15 60 1:23 kg m

3 0:00123 g cm

Viscosity of humidied air is (from Table 6-1 and Equations 6-32through 6-35):6-26):

v QstackNcell Nch Ach

152060 6 0:08 0:08 660 cm s

1

The Reynolds number at the channel entrance is (Equation 6-29):

Re rvDHm

r density of humidified air P PsatMair PsatMH2OThe velocity in a fuel cell channel at the entrance of the cell is (Equation

6.5 HEAT REMOVAL FROM A FUEL CELL STACK

To maintain the desired temperature inside the cells, the heatgenerated as a byproduct of the electrochemical reactions must be takenaway from the cells and from the stack. Different heat management schemes(Figure 6-22) may be applied, such as:1. Cooling with coolant owing between the cells. Coolant may be deionized

water, antifreeze coolant, or air. Cooling may be arranged between eachcell, between each pair of cells (in such a conguration, one cell has thecathode and the other cell has the anode next to the cooling arrange-ment), or between a group of cells (this is feasible only for low-powerdensities because it results in higher temperatures in the center cells).

Stack Design 189Equal distribution of coolant may be accomplished by the manifoldingarrangement similar to that of reactant gases. If air is used as a coolant,equal distribution may be accomplished by a plenum.

2. Cooling with coolant at the edge of the active area (with or without ns). The heatis conducted through the bipolar plate and then transferred to thecooling uid, typically air. To achieve relatively uniform temperaturedistribution within the active area, the bipolar plate must be a very goodthermal conductor. In addition, the edge surface may not be sufcientfor heat transfer and ns may need to be employed. This method resultsin a much simpler fuel cell stack and fewer parts, but it has heat transferlimitations and is typically used for low-power outputs.

3. Cooling with phase change. Coolant may be water or another phase-changemedium. Use of water simplies the stack design because water is alreadyused in both anode and cathode compartments.

Figure 6-22 Different cell/stack cooling options.

190 PEM Fuel Cells6.5.1 Stack Heat BalanceThere are several ways to set the fuel cell stack energy balance. In general,energy of fuel (higher heating value) is converted into either electricity orheat, or:

I2F

HHHVncell Qgen IVcellncell (6-39)

Heat generated in a fuel cell stack is then:

Qgen 1:482 VcellIncell (6-40)

The previous equation assumes that all the product water leaves the stack asliquid at 25C, which may be the case if the inlet is fully saturated at the stackoperating temperature. If all of the product water leaves the stack as vapor,then the following equation is more appropriate:

Qgen 1:254 VcellIncell (6-41)

The previous Equations (6-39 through 6-41) are just approximations.A complete stack energy balance (such as shown in Equations 5-62 through5-67) should take into account the heat (enthalpy) brought into the stackwith reactant gases as well as the heat of the unused reactant gases leaving thestack, including both latent and sensible heat of water at the stack inlet andstack outlet:

Enthalpy of reactant gases in Electricity generated Enthalpy ofunused reactant gases including heat of product water Heat dissipated tothe surrounding Heat taken away from the stack by active coolingor X

Qin Wel X

Qout Qdis Qc (6-42)

On closer examination of this energy balance, it is clear that some ofthe heat generated in the stack is carried away by reactant gases andproduct water, some is lost to the surroundings by natural convection andradiation, and the rest must be taken away from the stack by activecooling.

Because heat generation is associated with the (voltage) losses in a fuelcell, most heat is generated in the catalyst layers, predominantly on the

Radiation/convection to the surrounding

Stack Design 191cathode side, then in the membrane due to ohmic losses and in the elec-trically conductive solid parts of the fuel cell (also due to ohmic losses). Thisheat is rst carried by heat conduction through solid parts of the fuel cell,namely porous electrode structures, including the gas diffusion layer and

Leaving the stackwith coolant

Leaving the stackwith unused reactant gas(both sensible and latent)

Figure 6-23 Heat paths in a fuel cell segment.Conduction through solidConvection with fluids

Conduction/convectionthrough porous mediabipolar plates (Figure 6-23). Some heat is transferred to the reactant gases(depending on their temperature), some is transferred to the coolingmedium through convection, and some is conducted to the edge of thestack, where it is transferred to the surrounding air through radiation andnatural convection (or, in some cases, forced convection when this is theprimary way of stack temperature control).

6.5.2 Heat ConductionThe rate of heat transferred by conduction in the x-direction througha nite cross-sectional area A is, according to the Fourier law of conduction,proportional to the temperature difference:

Qx kAdTdx

(6-43)

where k is the thermal conductivity, W m1 k1.

192 PEM Fuel CellsThe values of thermal conductivity, k, for some typical fuel cell materialsare given in Table 6-2.

TABLE 6-2 Thermal Conductivity of Some Fuel Cell Materials

Material Thermal Conductivitya Wm1 K1

Aluminum 237Copper 401Nickel 91Nickel alloys (Inconel, Hasteloy) 12Titanium 22Stainless steel 316 13Platinum 71Graphite 98Graphite/polymer mix ~20b

Carbon ber paper 1.7b

Teon 0.35Liquid water 0.611Water vapor 0.0198Air 0.0267Hydrogen 0.198aAt 300 K; bthrough-plane.More generally, the steady-state heat conduction is governed by theequation (easily obtained by differentiating Equation 6-43):

d2Tdx2

0 (6-44)

which can also easily be extended to three-dimensional steady-state heatconduction:

V$VT 0 (6-45)To solve this equation, two boundary conditions (for each direction) mustbe given that describe the behavior of T at the system boundaries (constant Tor prescribed ux).

When the heat is conducted through two adjacent materials withdifferent thermal conductivities, the third boundary condition comesfrom a requirement that the temperature at the interface is the same forboth materials (in cases when the contact resistance may be neglected) orthere is a discontinuity in temperature distribution at the interface

des htc,de

6)

7)

For ce,Equ

8)

where:

Stack Design 193removed by a cooling uid at 60C, with heat transfer coefcient h 1600Wm2 K1. Electrical resistivity of the gas diffusion layer andbipolar plate is 0.08 Ohm-cm and 0.06 Ohm-cm, respectively. There isa contact resistance of 0.005 Ohm-cm2 between the gas diffusion layer andqint rate of heat generation per unit volume

In the fuel cell, internal heat generation results from electrical and ionicresistance:

qint i2rs (6-49)

In porous media, an effective thermal conductivity is used that takes intoaccount porosity of the media, :

keff 2ks

2ks k1 3ks

1(6-50)

ExampleA fuel cell operates at 0.6 V and 1 A cm2. Calculate the temperaturedistribution through a gas diffusion layer/bipolar plate sandwich on thecathode side. Assume a constant heat ux at the gas diffusion/catalyst layerinterface equal to all the fuel cell losses except those due to ionic andelectrical resistance. Assume that half of the resistive losses apply to theanode side and half to the cathode. Ionic resistance through the membraneis 0.1 Ohm-cm2. At the outer edge of the bipolar plate, assume that heat isdx2 kcribed by either contact resistance Rtc or thermal contact coefcientned by:

Q htcADT (6-4

Rtc 1htcA (6-4

the case involving internal heat generation due to electrical resistanation (6-44) becomes:

d2T qint 0 (6-4

194 PEM Fuel CellsQ2 0:594 0:00198 0:592 W cmHeat ux at the bipolar plateegas diffusion layer interface (on the GDLside):

Q3 0:592 0:005 0:587 W cm2plate side):2Voltage loss due to contact resistance 1 0.005 0.005 VTotal electrical resistance (one side) 0.00304 0.00198 0.005 0.01 VTotal electrical resistance (both sides) 0.01 2 0.02 VVoltage loss due to ionic resistance 1 0.1 0.1 VTotal resistive losses 0.12 VFuel cell voltage corrected for resistance 0.6 0.12 0.72 VHeat generation in fuel cell (except resistance) (1.254 0.72) 12 0.534W cm2

Heat ux at the catalystegas diffusion layer interface (including 1/2 of theionic resistance):

Q4 0:534 12 0:1=2 0:584 W cm2

Heat generation due to resistance in GDL i DV 1 0.00304 0.00304W cm2

Heat generation due to resistance in bipolar plate 1 0.00198 0.00198W cm2

Heat generation due to contact resistance 1 0.005 0.005W cm2Heat ux at the bipolar plateecooling uid interface:

Q1 0:584 0:00304 0:00198 0:005 0:594 W cm2

Heat ux at the bipolar plateegas diffusion layer interface (on the bipolarAssume one-dimensional steady-state conduction.Let T1 be the temperature at the bipolar plateecooling uid interface,

T2 be the temperature of the bipolar plate facing the gas diffusion layer, T3 bethe temperature of the gas diffusion layer facing the bipolar plate, and T4 bethe temperature of the gas diffusion layer facing the catalyst layer.

Voltage loss through GDL is: V IR i rGDLdGDL 1 0.08 0.038 0.00304 VVoltage loss through bipolar plate i rBPdBP 1 0.06 0.33 0.00198 Vcontact resistance between these two layers equal to 1C/W thickness ofGDL and the bipolar plate is 0.38 mm and 3.3 mm, respectively.

Solutionbipolar plate. Effective thermal conductivity of GDL and bipolar plateis 1.7 Wm1 K1 and 20Wm1 K1, respectively. There is a thermal

Stack Design 195plate interface due to contact resistance. Temperature T3 is then:

T3 T2 Rtc Q3 64:74 1 0:587 65:33C 64:74CThere is a discontinuity in temperature at the gas diffusion layer/bipolarThe temperature T2 (at x dBP) is:

T2 T1 Q2kBP dBP qint;BPkBP

dBP2

2 63:71 0:592

0:190:33 0:006

0:19

0:332

2Temperature distribution in the bipolar plate is:

T T1 Q2kBP xqint;BPkBP

dBPx x

2

2

where:

qint;BP 0:00198=0:33 0:006 W cm3C2 T1and

C1 Q2k qintk

dBPboundary conditions:

At x 0 T T1At x dBP k dTdx Q2

therefore:T k 2

C1x C2

The integration constants, C1 and C2, can be determined from theAfter two integrations, it becomes:

qint x26-48):

d2T

dx2 qint

k 0Q1 hTF T1

The temperature T1 is then:

T1 TF Q1=h 60 :594=0:16 63:71

The governing equation for heat ux inside the bipolar plate is (EquationConvection heat ux from the bipolar plate surface to the cooling uid(Equation 6-52):

6.5Froa hcooconhea

64

pera

Figu yersan

196 PEM Fuel CellsThe temperature distribution inside the GDL is (applying the same equationas for the bipolar plate):

T T3 Q4kGDL xqint;GDLkGDL

dGDLx x

2

2

where:

qint;GDL 0:00304=0:038 0:080 W cm3re 6-24 Temperature distribution across the bipolar plate/gas diffusion ladwich.60

61

0 0.1 0.2 0.3 0.4 0.5distance, cm

TF6263

tem65

66

67

68tu

re,

Cbipolar plate GDLcooling

channel

T1T2

T3T4

CLThe temperature T4 (at x dGDL) is:T4 T3 Q4kGDL dGDL

qint;GDLkGDL

dGDL2

265:33 0:584

0:0170:038 0:08

0:017

0:0382

2

T4 66:6 64C

The resulting temperature distribution across the bipolar plate/gas diffusionlayer sandwich is shown in Figure 6-24.

.3 Active Heat Removalm the heat removal point of view, a fuel cell stack may be consideredeat exchanger with internal heat generation. The walls of the fuel cellling channels may be neither at constant temperature nor have thestant heat ux, but these two cases are often used as boundary cases fort transfer analyses.

Stack Design 197The heat to be removed by active cooling (Equation 6-42) is:

Qc X

Qin Wel X

Qout Qdis (6-51)The same heat, Qc, has to be transferred to the cooling uid:

dQcdAc

hTS TC (6-52)

or integrated over the entire heat exchange surface, Ac, just as in a heatexchanger:

Qc UAcLMTD (6-53)where:

h local heat transfer coefcient, Wm2CU overall heat transfer coefcient, Wm2CAc heat exchange area surface area of the cooling channels, m2

LMTD logarithmic mean temperature difference, C, dened as

LMTD TS TCin TS TCoutln

TS TCinTS TCout

(6-54)

The temperature difference between the stack body, TS, and the coolinguid, TC, may be constant (constant thermal ux case), or it may vary fromone side of the stack to the other, depending on the position of coolant inletsand outlets vs. reactant inlets and outlets, internal coolant and reactantpassages conguration, and current density conguration.

The same heat,Qc, has to be absorbed by the cooling uid and carriedout of the fuel cell stack:

Qc _mcpTc;out Tc;in (6-55)The temperature difference DTc (Tc,out Tc,in) is a design variable that hasto be selected in conjunction with the coolant ow rate. As usual in fuel celldesign, in selecting the temperature difference between coolant outlet andinlet there are conicting requirements. To achieve uniform temperaturedistribution through the stack, DTc should be selected as small as practicallypossible, unless larger temperature gradients are required by stack design (forexample, to facilitate water management). However, small DTcwould resultin large coolant ow rate, which would increase parasitic power and reducesystem efciency. On the other side, larger DTc would result in lowertemperature to which the coolant must be cooled, and there may be

practical limits imposed by the ambient temperature and by the character-istics and performance of the heat rejection device.

The coefcient of convection heat transfer, h, depends on the Nusseltnumber, that is, properties of the coolant, geometry of the passages, and owcharacteristics:

h Nu kDH

or h NuL kL or h NuLkL

(6-56)

The Nusselt number represents the ratio of convection heat transfer for uidin motion to conduction heat transfer for a motionless layer of uid [34].Common expressions for the Nusselt number and for various ow char-acteristics (i.e., developed/undeveloped, laminar/turbulent) are summarizedin Table 6-3 [34], and the thermal properties of some uids commonlyfound in fuel cells are given in Table 6-4.

TABLE 6-3 Nusselt Number for Various Internal Flow Conditions (Adapted from [34])

Condition Equation

Laminar owHydraulically fully developed,x/D > 0.05 Re PrThermally fully developedx/D > 0.05 Re PrUniform wall temperatureSquare tube Nu 2.98Circular tube Nu 3.66Thermal entryUniform wall temperature

198 PEM Fuel CellsUniform wall temperaturex/D < 0.01 Re PrUniform wall heat ux x/D < 0.01 Re PrHydraulic and thermal entry x/D< 0.01 Re Pr

Turbulent owHydraulically fully developedThermally fully developed

where f 4/(1.58 ln Re 3.28)2Thermal entry x/D < 60Hydraulic and thermal entry x/D < 60Transitional turbulent ow Nu CtrNuL2 + (1 Ctr)NuT8

NuL2 Nu for Re 2000NuT8 Nu for Re 8000Ctr 1.33 Re/6000

TAB r Isat 2

Gas 1

Wa

Ethg

Prog

Air

Hy

Stack Design 199Coolant (50% water and 50% ethylene glycol) ows with the velocity of1 m/s through a 1-mm-square channel at 80C. Calculate the heat transferExampledrogen 0.0841 8.8 10 0.178 14.20.0741 9.6 106 0.198 14.4lycol1010 0.0075 2.721.21 18 106 0.0257 1.0051.06 20 106 0.0287 1.008

6Densitykgm3

Viscositykgm1 s1

ConductivityWm1 K1

SpecicHeat kJ kg1 K

ter 998 0.001 0.602 4.18984 0.000466 0.654 4.18

ylenelycol

1116 0.0214 0.249 2.38

1088 0.0052 0.260 2.56pylene 1036 0.054 0.200 2.47LE 6-4 Properties of Some Fuel Cell Gases and Coolant Mediums (Upper Numbe0C and Lower Is at 60C)

Thermalcoefcient for hydraulically and thermally fully developed ow underuniform wall heat ux conditions. If the heat ux is 1W cm2, calculate therequired temperature difference between the wall and the uid.

SolutionThe heat transfer coefcient is:

h Nu kDH

Nu 3.61DH 4 A/Pm 4 0.0012/4 0.001 0.001 mk for water at 80C 0.671Wm1 K1k for ethylene glycol at 80C 0.261k for 50/50 mixture of water and ethylene glycol 0.466Wm1 K1

h 3:61 0:466=0:001 1682Wm2 K1

The average temperature difference between the wall of the cooling channeland coolant required for transfer of 1W cm2 (or 10,000Wm2) is:

Ts TC QAK 10000 Wm2

1682 Wm2 K 6C

6.5anMarad

92

Figu(Ada

200 PEM Fuel Cells0 0.5 1 1.5 28082

84

86

88

Tem

pera

ture

(C

Near inletMiddle of channelNear exit

Cathode gas channel Anode gas channel

Diffuser

Diffuser90) Membrane94CatalystEquation (6-45) may be solved numerically for a variety of boundaryconditions, such as constant TS at the walls or constant or prescribed heatux. Because of complicated three-dimensional heat transfer pathways(shown in Figure 6-23), calculation of heat uxes and temperature prolesin a fuel cell stack requires 3-D numerical simulation. Figure 6-25 showstemperature distribution in a representative cross-section of a fuel cellobtained by 3-D numerical simulation [28]. From Figure 6-25, it is obviousthat there are signicant temperature variations inside a fuel cell stack.Because most heat in a fuel cell stack is produced in the cathode catalystlayer, that layer expectedly has the highest temperature.

.4 Heat Dissipation from the Stack by Natural Convectiond Radiationximum heat that the stack may lose through natural convection andiation to the surroundings is:

Qdis TS T0Rth

(6-57)

Y (mm)

re 6-25 Temperature distribution through a fuel cell characteristic cross-section.pted from [28].)

Stack Design 2011Pr

>: >;

NuL 0:825 0:387Ra

1=6L"

0:59=16#8=27

>>>>>>>>

>>>>>=>>>>

(6-62)h kLNuL (6-61)

For vertical plates and natural convection, the Nusselt number is someempirical function of Prandtl and Rayleigh numbers,NuL f(Pr, RaL), suchas, for example: 8 92to obtain the desired operating temperature.The heat transfer coefcient, h, in Equation (6-59) is a function of the

Nusselt number, Nu:the rate of heat generation. This is often the case with single cells used inlaboratories that must use heat pads (or other means of temperature control)where:TS stack surface temperatureT0 temperature of the surrounding wallsRth thermal resistance, dened as

Rth 11RC

1RR

(6-58)

where:

RC convective thermal resistance, dened asRC 1hAS (6-59)

andRR radiative thermal resistance dened as

RR 1sFASTS T0

T2S T20

(6-60)where:

s StefanBoltzman constant 5.67 108Wm2 K4F shape factor; for the rst approximation it may be assumed as F 1AS stack exposed surface area, m2

For short stacks, the ratio of exposed (external) surface area and the (internal)active area, AS/Aact, may be too large and the stack cannot reach theoperating temperature at all because the rate of heat dissipation is higher than

2 1 6 6

202 PEM Fuel CellsFor horizontal plate:1/4where:

RaL gbTS T0L3

na(6-63)

and

Pr na

(6-64)

where:g gravity acceleration (9.81 m s2)b thermal expansion coefcient; for gases b 1/TL characteristic length or length of travel of the uid in the boundarylayer, that is, the height of the stack, mn kinematic viscosity, m2 s1a thermal diffusivity, m2 s1

Fluid properties may be evaluated at the free stream or lm (wall)temperature.

NuL 0.54 RaL

Kinematic viscosity, n, m s 15.68 10 20.76 10Prandtl number, Pr 0.708 0.697TABLE 6-5 Air Thermal Properties

Property @300K @350K

Density, r, kg m3 1.1774 0.998Specic heat, cp, kJ kg

1C1 1.0057 1.0090Thermal conductivity, k, Wm1C1 0.02624 0.03003Thermal diffusivity, a, m2 s1 0.2216 104 0.2983 104Thermal expansion, b, C1 0.00333 0.00286Viscosity, m, kg m1 s1 1.846 105 2.075 105L A/Pm (area/perimeter)Some air properties at 300 and 350 K are listed in Table 6-5.

6.5.5 Alternative Stack Cooling OptionsAir CoolingAir is already passing through the cathode compartment in excess of oxygenexact stoichiometry. Can the same air be used as a coolant? Theoretically,yes, although the ow rate would have to be much higher. How high? Thiscan be found from a simple heat balance: Heat generated by a fuel cell mustbe equal to heat taken away by the ow of air.

The heat generated, assuming that the product water evaporates andleaves the stack as vapor, which actually should be the case for this coolingscheme, is (Equation 6-41):

Q 1:254 VcellIncell (6-65)The heat transferred to air is:

Q _mcpTAir;out TAir;in (6-66)The mass ow rate at the stack exit is given by Equation (5-56):

_mAirout SO2 1MO2 SO2 1 rO2inrO2in MN2

i$ncell4F

(6-67)

By combining the previous equations, an expression for required stoichio-metric ratio is obtained:

Stack Design 203SO2 MO2 4F1:254 VcellcpDTMO2 1 rO2inrO2in MN2

(6-68)

The only variables in the previous equation are the cell potential, Vcell, andtemperature difference between air at the stack inlet and outlet,DT. The cellpotential determines the cell efciency, and at a lower efciency more heatis generated (which follows directly from Equation 6-65). The airtemperature difference is determined by the ambient temperature and thestack operating temperature. Figure 6-26 shows the resulting cathode

0102030405060708090

100

10 20 30 40 50 60 70Air dT (C)

stoi

chio

met

ry

'@ 0.6V'@0.7 V'@0.7 V*

Figure 6-26 Required air stoichiometry for stack cooling. (*This curve takes intoaccount heat dissipation from the stack surface.)

ow rate requirement, because cooling would be achieved by evaporation

204 PEM Fuel Cellsof injected water. Using the mass and energy balance equation (Chapter5), it is possible to calculate the exact amount of water and air ow rateneeded to achieve saturation conditions at the outlet and provide suf-cient cooling of the stack. The example in Chapter 5 shows the calcu-lation for one set of operational conditions. Figure 6-27 shows theresulting water and air ow rate requirements for evaporative coolingover a range of operating conditions (cell potential and temperature) foran atmospheric pressure fuel cell (outlet pressure is atmospheric, and air atthe inlet is at 20C and 70% relative humidity). In addition, the condi-tions in Figure 6-27 assume no net water ux across the membrane,that is, electroosmotic drag is equal to back diffusion. In case that elec-troosmotic drag is higher than back diffusion, the water injectionrequirement would be reduced. Indeed, Wilson et al. [35] suggestedadiabatic cooling of an atmospheric stack with water introduced on theanode side and then relying on wicking through the gas diffusion layer(using hydrophilic thread) and electroosmotic drag to saturate the ambientair on the cathode side.stoichiometric ratio as a function of two typical operating cell potentials(0.6 V and 0.7 V) and as a function of air temperature difference. The twoupper curves were calculated by Equation (6-68), and the lower curve tookinto account the heat dissipation from the stack surface (for a 1 kW stackwith the ratio of surface area to active area As/Aact 0.27). Very large airow rates are required, with a stoichiometric ratio higher than 20. Productwater is not sufcient to saturate these large amounts of air, and therefore thiscooling scheme would cause severe drying of the anode and would not bepractical. Relative humidity at the outlet may be calculated from thefollowing equation:

4 2rO2;inSO2 rO2;in

PPvs

(6-69)

For a normal operating range of temperatures (from 40C to 80C) and forstoichiometric ratios above 20, relative humidity at the outlet would bebelow 10%, and the cell would experience severe drying.

Evaporative CoolingIf additional liquid water is injected at the stack cathode inlet, it would bepossible to prevent drying and at the same time dramatically reduce the air

Stack Design 205Edge CoolingIf a fuel cell ow eld is made narrow enough, the heat generated may beremoved on the sides of the cells instead of the more conventional waybetween the cells. In this case, heat is conducted in the plane of the bipolarplate rather than through it. Active cooling may still be needed at the edge of

0

5

10

15

20

25

30 40 50 60 70 80 90operating temperature C

O2

stoi

chio

met

ric ra

tio

0.15

0.2

0.25

0.3

0.35

0.4

0.45

wate

r inje

ction

rate

(g/s

per k

W)

@0.6 V

@0.7 V

@0.6 V

@0.7 V

stoich

water

Figure 6-27 Air and water injection rates required for stack cooling and air saturationat the outlet.the bipolar plates. To enhance heat transfer, ns may be added and/or highthermal conductivity material may be used.

Obviously, in this case the maximum temperature will be achieved in thecenter of the ow eld. In a narrow and long ow eld, the heat transfermay be approximated as one-dimensional (i.e., heat removed through thelong sides is signicantly larger than the heat removed at the narrow sides).

The equation that describes one-dimensional heat transfer (conduction)in a at plane with internal heat generation is:

d2Tdx2

QkAdeffBP

0 (6-70)

where:Q heat generated in the cell (either given by Equation 6-65 or bya detailed energy balance analysis), Wk bipolar plate in-plane thermal conductivity (in some cases, in-planeconductivity may be signicantly different from through-plane thermalconductivity), Wm1 K1

206 PEM Fuel CellsA cell active area, m2deffBP effective (or average) thickness of the bipolar plate in the activearea, m

Although the heat is not actually generated inside the plate but rather ina thin catalyst layer above the plate, Equation (6-70) may be used withsufcient accuracy because the thickness of the plates is very small comparedwith the width (i.e., a few millimeters vs. a few centimeters). In that case, thesolution of Equation (6-70) for symmetrical cooling on both sides with T(0) T(L) T0 is:

T T0 QkAdeffBP

L2

2

"xLxL

2#(6-71)

where:T0 the temperature at the edge of the active areaL width of the active area

The maximum temperature difference is between the edge (x 0 or x L)and the center (x L/2):

DTmax QkAdeffBP

L2

8(6-72)

In addition, the heat must be conducted from the edge of the ow eld tothe edge of the plate or to the n over the ow eld border with width b.The thickness of the plate at the border is dBP. For this reason, thetemperature will further decrease, according to Fouriers law:

T0 Tb Q2kA

Ldb

b (6-73)

where Tb is the temperature at the edge of the bipolar plate.Therefore, the total temperature difference between the center of the

plate and the edge of the plate, or the base of a n, is:

DTmax QkAL

L

8deffBP b

2dBP

!(6-74)

Figure 6-28 shows the geometry of the narrow at plate, and Figure 6-29shows the maximum temperature difference in the active area (tempera-ture in the center temperature at the edge of the active area) as a functionof ow eld width and plate thermal conductivity (Q 0.279W/cm2,

Stack Design 207L bdBPeff 1.8 mm). The maximum temperature difference in the active areashould be limited to

208 PEM Fuel Cells6.6 STACK CLAMPING

The individual components of a fuel cell stack, namely MEAs, gasdiffusion layers, and bipolar plates, must be somehow held together withsufcient contact pressure to (1) prevent leaking of the reactants between thelayers and (2) minimize the contact resistance between those layers. This is

Tie-rodnut

Clamping force

Figure 6-30 Compression of fuel cell components with tie rods.typically accomplished by sandwiching the stacked components betweenthe two end plates connected with several tie rods around the perimeter(Figure 6-30) or in some cases through the middle. Other compression andfastening mechanisms may be employed too, such as snap-in shrouds orstraps.

The clamping force is equal to the force required to compress the gasketplus the force required to compress the gas diffusion layer, plus internal force(for example, the internal operating pressure).

The pressure required to prevent the leak between the layers depends onthe gasket material and design. Various materials, ranging from rubber toproprietary polymer congurations, are used for fuel cell gaskets. Thedesigns also vary from manufacturer to manufacturer, including at orprole gaskets or gaskets as individual components or molded on bipolarplates or on or around the gas diffusion layer. A so-called seven-layer MEAincludes the catalyzed membrane, two gas diffusion layersdone on eachsidedand the gasket that keeps the entire MEA together.

The torque on the bolts necessary to achieve the required force may becalculated from the following equation:

T FKbDbNb

(6-75)

where:T tightening torque, NmF clamping force, NKb friction coefcient (0.20 for dry and 0.17 for lubricated bolts)Db bolt nominal diameter, mNb number of bolts

Too much force on the perimeters may cause bending of the end plates (asshown in Figure 6-31), which has an adverse effect on the compression overthe active area. Compression distribution inside the cell may be monitored

Stack Design 209by pressure-sensitive lms (which register only the highest force applied) orby pressure-sensitive electronic pads, which, connected to a monitor, allowinspection of compression force distribution in real time throughout theassembly process. Because of the possibility of bending, the end plates mustbe designed with sufcient stiffness. Alternatively, end plates witha hydraulic or pneumatic piston that applies a uniform force throughout theactive area may be used. Another alternative is to put the tie rods through thecenter of the plate and then design the ow eld around it.

Figure 6-32 shows the compressive force distribution in a cell usinga pressure-sensitive lm with two different end plate designs: one withinadequate stiffness that resulted in insufcient force (i.e., very bad contacts)

Figure 6-31 Bending of the end plates if too much force is applied on tie rods aroundthe perimeter.

inside the active area and one with a hydraulic piston that resulted in very

Figure 6-32 Compressive force distribution in a cell with inadequate stiffness of theend plates (left) and in a cell with a hydraulic piston in one of the end plates(right).[36]

210 PEM Fuel Cellsuniform compressive force distribution inside the active area [36].As discussed in Chapter 4 (Figure 4-22), a pressure of 1.5 to 2.0 MPa is

required to minimize the contact resistance between a gas diffusion layer anda bipolar plate. The gas diffusion layer is compressible (Figure 4-17), and therequired squeeze may be determined by the cell design, that is, by care-fully matching the thicknesses of the gas diffusion layer, gaskets, and hard-stops or recesses on the bipolar plate. If the gas diffusion layer is compressedtoo much, it will collapse and will lose its main functiondgas and waterpermeability, as is very graphically illustrated in Figure 6-33. As the0.4

0.5

0.6

0.7

0.8

0.9

1

cell

pote

ntia

l (V)

0 200 400 600 800 1000 1200 current density (mA/cm)

16 24 30 39Compression (%):

Figure 6-33 Effect of too much compression of the gas diffusion media on cellperformance.

Stack Design 211compression (expressed as a percentage of gas diffusion media squeeze) isincreased, the cell performance improves because of the reduced interfacialresistance. If the compression is too much, the polarization curve exhibitssevere mass transport problems. Optimum compression must be experi-mentally determined for any gas diffusion media. The test cells may bespecially designed to allow change of compression, even during cell oper-ation [37,38].

The stack design must also ensure that adequate clamping force ismaintained during cell operation. As a result of different coefcients ofthermal expansion for different materials used in a fuel cell stack, thecompression force may increase or decrease when the stack reaches itsoperating temperature. This must be compensated for by the use of coil,disc, or polyurethane springs.

PROBLEMS

1. Determine the required number of cells and cell active area for a fuel cellstack that has to generate 50 kW at 120 volts. The polarization curve maybe approximated by:

Vcell 0:85 0:2i where i is in A cm2The stack should have efciency of 0.5.

2. For an H2/O2 fuel cell polarization curve determined by the followingparameters: T 60C, P 101.3 kPa, i0 0.002 A cm2, R 0.21 Ohm-cm2, iL 2 A cm2, iloss 1.2 m A cm2, determine theefciency at 0.6 V and 0.7 V. Also determine the efciency at 20% ofnominal power for both Vnom 0.6 V and Vnom 0.7 V.

3. A fuel cell has 100-cm2 active area covered by six parallel channels on thecathode. Each channel is 0.8 mm wide and 0.8 mm deep, withequal spacing between the channels of 0.8 mm. The fuel cell generates0.8 A/cm2. Air at the inlet is fully saturated at 60C. Pressure at the inletis 200 kPa, and there is a 15-kPa pressure drop through the ow eld.Oxygen stoichiometric ratio is 2.5. Calculate the velocity and Reynoldsnumber at the air inlet and outlet (neglect liquid water at the outlet).

4. For a fuel cell from Problem 3, calculate the heat generated at 0.65 V and1 A cm2 using Equation (6-41) and by doing a detailed mass and heatbalance analysis (assume that hydrogen is supplied in dead-end mode

212 PEM Fuel Cellssaturated at 60C and that net water transport through the membrane issuch that there is no water accumulation on the anode side). Explain thedifference in results.

5. Calculate the amount of liquid water produced in the cell from Problem3. This liquid is probably dispersed in numerous droplets. However,assuming that a liquid water lm is formed at the bottom of the channeland that water in the lm is moving with a velocity that is 1/3 of the airvelocity, calculate the depth of the lm at the fuel cell exit, or thepercentage of the channels cross-sectional area lled with liquid water.

6. Calculate the temperature at a center of the long, narrow ow eld(2.2 cm) of a fuel cell operating at 0.75 V and 0.33 A cm2. Cooling isobtained at the edge of the cell byowing air at 25C (h 50Wm2K1).The bipolar plate is made out of graphite/polymer mixture with k 19 W m1 K1, and it is 2 mm thick in the active area and 3 mm thick atthe border. The border around the active area is 8 mm wide.

QUIZ

1. A ow eld is:a. Flow channels that feed each cell in the fuel cell stackb. A maze of channels on the surface of the bipolar platec. A plane in which the fuel cell electrochemical reaction takes place

2. The velocity in the ow eld channel does not depend on:a. Channel lengthb. Channel depthc. Channel width

3. One of the most important features of the ow eld is:a. It allows the ow of the reactant gases through each cell with

minimum pressure dropb. It has a uniform supply of reactants over the entire active areac. It allows signicant heat removal by circulating excess air

4. Nonuniform distribution of gases over the active area results in:a. Starving regionsb. High pressure dropc. Hiccups

5. The ow in the fuel cell channels is typically:a. Laminar

2Stack Design 213a. Linearly decreasesb. Decreases faster near the entrancec. Decreases faster near the exit

9. Removal of heat from the fuel cell stack is intended to:a. Keep the stack at a desired temperatureb. Maintain a desired efciencyc. Maintain some liquid water in the membrane

10. Squeezing the gas diffusion layer:a. Always improves the fuel cell performance because it reduces the

interfacial resistanceb. Improves the performance only up to a certain squeeze; if the

squeeze is excessive, it has an adverse effectc. It has nothing to do with performancedit only prevents overboard

leaks

REFERENCES[1] Barbir F. PEM Fuel Cell Stack Design Considerations. In: Proc. Fuel Cell Technology:

Opportunities and Challenges. New Orleans, LA: AIChE Spring National Meeting;March; 2002. p. 52030.

[2] Barbir F. Development of an Air-Open PEM Fuel Cell, SBIR Phase I Final TechnicalReport. A report by Energy Partners, Inc. to U.S. Army Research Laboratory; 1995.contract DAAL01-95-C-3511.

[3] Ledjeff K, Nolte R. New SPFC-Technology with Plastics. In: Savadogo O,Roberge PR, Veziroglu TN, editors. New Materials for Fuel Cell Systems. Montreal:Editions de lEcole Politechnique de Montreal; 1995. p. 12834.

[4] Cisar A, Weng D, Murphy OJ. Monopolar Fuel Cells for Nearly Passive Operation. In:Proc. 1998 Fuel Cell Seminar. CA: Palm Springs; November 1998. p. 3768.

[5] Barbir F. Progress in PEM Fuel Cell Systems Development, in Hydrogen Energy System.In: Yurum Y, editor. Utilization of Hydrogen and Future Aspects, NATO ASI SeriesE-295. Dordrecht, The Netherlands: Kluwer Academic Publishers; 1995. p. 20314.b. Turbulentc. Mixed/transient

6. A characteristic of laminar ow is:a. Pressure drop is minimalb. Pressure drop is higher than in turbulent owc. Pressure drop is directly proportional to the ow rate

7. If all the product water in a fuel cell is in liquid form, its volumecompared with the volume of air exiting the fuel cell would be:a. An order of magnitude lessb. About the samec. Several orders of magnitude less

8. As oxygen is consumed along the channel, O content in air:

[6] Chow CY, Wozniczka BM. Electrochemical Fuel Cell Stack with Humidication

214 PEM Fuel CellsSection Located Upstream from the Electrochemically Active Section; 1995. U.S. Patent5,382,478.

[7] Reiser CA, Sawyer RD. Solid Polymer Electrolyte Fuel Cell Stack Water Manage-ment System; 1988. U.S. Patent 4,769,297.

[8] Koh J-H, Seo HK, Lee CG, Yoo Y-S, Lim HC. Pressure and Flow Distribution inInternal Gas Manifolds of a Fuel Cell Stack. Journal of Power Sources 2003;115:5465.

[9] Daugherty RL, Franzini JB. Fluid Mechanics with Engineering Applications. 7th ed.New York: McGraw-Hill; 1977.

[10] Watkins DS, Dircks KW, Epp DG. Novel Fuel Cell Fluid Flow Field Plate; 1991. U.S.Patent 4,988,583.

[11] Watkins DS, Dircks KW, Epp DG. Fuel Cell Fluid Flow Field Plate; 1992. U.S. Patent5,108,849.

[12] Cavalca C, Homeyer ST, Walsworth E. Flow Field Plate for Use in a Proton ExchangeMembrane Fuel Cell; 1997. U.S. Patent 5,686,199.

[13] Rock JA. Serially Linked Serpentine Flow Channels for PEM Fuel Cell; 2001. U.S.Patent 6,309,773.

[14] Rock JA.Mirrored Serpentine FlowChannels for Fuel Cell; 2000. U.S. Patent 6,099,984.[15] Ledjeff K, Heinzel A, Mahlendorf F, Peinecke V. Die Reversible Membran-

Brennstoffzelle. In: Elektrochemische Energiegewinnung, Dechema Monographien,128; 1993. 103.

[16] Nguyen TV. Gas Distributor Design for Proton-Exchange-Membrane Fuel Cells.Journal of the Electrochemical Society 1996;143(5):L1035.

[17] Barbir F, Neutzler J, Pierce W, Wynne B. Development and Testing of High-Performing PEM Fuel Cell Stack. In: Proc. 1998 Fuel Cell Seminar. CA: Palm Springs;1998. p. 71821.

[18] Barbir F, Fuchs M, Husar A, Neutzler J. Design and Operational Characteristics ofAutomotive PEM Fuel Cell Stacks, Fuel Cell Power for Transportation. Warrendale,PA: SAE; 2000. SAE SP-15056369.

[19] Wilson MS, Springer TE, Davey JR, Gottesfeld S. Alternative Flow Field and BackingConcepts for Polymer Electrolyte Fuel Cells. In: S. Gottesfeld, G. Halpert, A. Lan-grebe, editors. Proton Conducting Membrane Fuel Cells I. The ElectrochemicalSociety Proceedings Series, PV 95-23; 1995. p. 115. Pennington, NJ.

[20] Issacci F, Rehg TJ. Gas Block Mechanism for Water Removal in Fuel Cells; 2004.U.S. Patent 6,686,084.

[21] Chapman AR, Mellor IM. Development of BioMimetic Flow-Field Plates for PEMFuel Cells. In: Proc. 8th Grove Fuel Cell Symposium; September 2003. London.

[22] Tuber K, Oedegaard A, Hermann M, Hebling C. Investigation of Fractal Flow Fieldsin Portable PEMFC and DMFC. In: Proc. 8th Grove Fuel Cell Symposium; September2003. London.

[23] Zawodzinski C, Wilson MS, Gottesfeld S. Metal Screen and Foil Hardware forPolymer Electrolyte Fuel Cells. In: Gottesfeld S, Fuller TF, editors. Proton Con-ducting Membrane Fuel Cells II, Electrochemical Society Proceedings, 9827; 1999.p. 44656.

[24] Damiano PJ. Fuel Cell Structure; 1978. U.S. Patent 4,129,685.[25] Wilkinson DP, Vanderleeden O. Serpentine Flow Field Design. In: Vielstich W,

Lamm A, Gasteiger H, editors. Handbook of Fuel Cell Technology: Fun