Pressure drop and flow distribution characteristics of single ...

Journal of Mechanical Science and Technology 26 (9) (2012) 2995~3006

www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-0706-y

Pressure drop and flow distribution characteristics of single and parallel serpentine

flow fields for polymer electrolyte membrane fuel cells†

Seung Man Baek1, Dong Hyup Jeon2, Jin Hyun Nam3,* and Charn-Jung Kim1 1School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, 151-742, Korea

2College of Energy and Environment, Dongguk University, Gyeongju 780-714, Korea 3School of Mechanical and Automotive Engineering, Daegu University, Gyungsan 712-714, Korea

(Manuscript Received November 29, 2011; Revised April 14, 2012; Accepted May 4, 2012)

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Abstract

This study numerically investigates pressure drop and flow distribution characteristics of serpentine flow fields (SFFs) that are de-

signed for polymer electrolyte membrane fuel cells, which consider the Poiseuille flow with secondary pressure drop in the gas channel

(GC) and the Darcy flow in the porous gas diffusion layer (GDL). The numerical results for a conventional SFF agreed well with those

obtained via computational fluid dynamics simulations, thus proving the validity of the present flow network model. This model is em-

ployed to characterize various single and parallel SFFs, including multi-pass serpentine flow fields (MPSFFs). Findings reveal that un-

der-rib convection (convective flow through GDL under an interconnector rib) is an important transport process for conventional SFFs,

with its intensity being significantly enhanced as GDL permeability increases. The results also indicate that under-rib convection can be

significantly improved by employing MPSFFs as the reactant flow field, because of the closely interlaced structure of GC regions that

have different path-lengths from the inlet. However, reactant flow rate through GCs proportionally decreases as under-rib convection

intensity increases, suggesting that proper optimization is required between the flow velocity in GCs and the under-rib convection inten-

sity in GDLs.

Keywords: Polymer electrolyte membrane fuel cell; Serpentine flow field; Under-rib convection; Flow distribution; Pressure drop; Flow network model

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1. Introduction

Fuel cells are promising power sources because of their

numerous advantages, such as high efficiency, clean emission,

and flexible scalability [1, 2]. Extensive research efforts have

been employed to utilize fuel cells as power sources for driv-

ing automobiles or for powering portable electronic devices.

Polymer electrolyte membrane fuel cells (PEMFCs) and direct

methanol fuel cells (DMFCs) are the most suitable fuel cell

technologies for the aforementioned purposes partially be-

cause of their low operating temperature, which contributes to

their satisfactory start-up and ideal transient characteristics.

Studies on PEMFCs are currently focused on enhancing their

operating current density and power density. This goal is pri-

marily achieved by developing new fuel cell materials with

better operating properties. In addition, system-level factors,

including flow-field design, thermal and water management,

and operational control, also require optimization [3-5].

When PEMFCs or DMFCs are operated at high current

densities, cell performance is affected by mass transport limi-

tations, such as reactant deficiency in under-rib regions and

electrode flooding in porous transport layers. Thus, flow-field

design is an important factor for system-level design because

of its influence on mass transport limitations, including reac-

tant distribution and product exhaust, as well as liquid water

removal [6, 7]. Thus, under-rib convection has received con-

siderable attention as a potential method for the performance

enhancement of PEMFCs and DMFCs at transport-limited

operating conditions.

Under-rib convection refers to the flow of reactant gas

through porous gas diffusion layers (GDLs) and under inter-

connector rib structures in PEMFCs and DMFCs. Under-rib

convection is an essential transport mechanism for PEMFCs

based on interdigitated flow fields with dead-end reactant

channel designs [8, 9]. In addition, under-rib convection has

also been recognized as an important transport process for

PEMFCs and DMFCs that employ serpentine flow fields

(SFFs) with long and meandering reactant channel designs

[10-19].

Experimental and numerical studies demonstrated that im-

proved under-rib convection is favorable for the performance

of PEMFCs because of the enhancement of reactant transport

to under-rib regions and the facilitation of liquid water exhaust

*Corresponding author. Tel.: +82 53 850 6675, Fax.: +82 53 850 6689

E-mail address: [email protected] † Recommended by Associate Editor Yong-Tae Kim

© KSME & Springer 2012

2996 S. M. Baek et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2995~3006

out of these regions. Xu and Zhao [20] recently proposed a

novel flow field design called convection-enhanced serpentine

SFF (CESFF) and experimentally demonstrated that better

performance and more stable operation of a DMFC can be

achieved using CESFF as the cathode flow field. They attrib-

uted the observed superior performance to the enhanced un-

der-rib convection intensity in CESFF, which improves mass

transport characteristics [20]. Similar flow field patterns were

independently developed for temperature uniformity in cool-

ing plates for PEMFCs [21, 22]. Uniform temperature is also

believed to be favorable for the operation control and the long-

term durability of PEMFCs.

Inspired by these studies [20-22], Nam et al. [23] proposed

a systematic design method to generate reactant flow fields

with maximized under-rib convection intensity in a given cell

area, which resulted in a new class of flow fields called multi-

pass SFFs (MPSFFs). Geometrical characterization showed

that gas channel (GC) regions with different path lengths

(measured from the inlet) are closely interlaced in MPSFFs,

which can significantly increase under-rib convection intensity

[23]. In addition, numerical studies [24, 25] showed that more

uniform temperatures can be achieved at a fixed coolant flow

rate when MPSFFs are used for the cooling plates of PEMFCs.

This result was also ascribed to the special flow field pattern

formed in MPSFF, the proximally positioned GC regions with

different path lengths. The close placement of flow channels

with different path lengths was proposed and demonstrated by

Kaufman and Terry [26] and Qi and Kaufman [27]. Notably,

under-rib convection intensity is generally negligible in

PEMFCs with parallel flow fields (PFFs) because GC regions

with similar path lengths are located across an interconnected

rib region.

In this study, the single-phase laminar flow of reactant gas

in a conventional SFF was first calculated using a commercial

computational fluid dynamics (CFD) code called STAR-CD

(CD-Adapco Inc., Korea). Based on CFD results, a flow net-

work model that considers Poiseuille flow in GCs, Darcy flow

in GDLs, and secondary pressure loss in the curved regions of

GCs was developed and validated. Using this flow network

model, the reactant flow in several single and parallel

MPSFFs was calculated, while pressure drop and flow distri-

bution characteristics were investigated.

2. Theory and calculations

2.1 Physical model

Fig. 1(a) presents the schematic diagram of the reactant

flow in an SFF curved region. The reactant flow in the GC is

subjected to the primary pressure drop fp∆ because of the

Poiseuille flow in a straight duct, which is expressed as [28]

2

chf

h2

L up f

d

ρ∆ = (1)

where f is the Darcy friction factor, L is the channel

length, hd is the hydraulic diameter of the duct, ρ is the

fluid density, and chu is the fluid velocity in the channel. The

secondary pressure drop sp∆ also occurs as the reactant gas

flows around the corners of the flow field, which is calculated

as [28]

2

chs L

2

up K

ρ∆ = (2)

where

LK is the secondary loss factor.

The reactant flow through the porous GDL under the inter-

connector rib, which is called under-rib convection, is also

presented in Fig. 1(a). The pressure difference across the rib

structure dp∆ is the driving force for this under-rib convec-

tion. With the geometrical arrangement shown in Fig. 1(a),

under-rib convection velocity ribu can be determined accord-

ing to Darcy’s law as [29]

ribd rib

gdl

wp u

K

µ∆ = (3)

where µ is the dynamic viscosity of the fluid, ribw is the

rib width, and gdlK is the permeability of the GDL.

Aside from frictional drops, the present model also consid-

ered the additional pressure drop in the GC that can be attrib-

uted to under-rib convection (suction/blowing effects). Mo-

mentum conservation predicts that the actual pressure drop in

the GC with blowing should be larger than the frictional pres-

sure drop in order to accelerate the fluid in the GC. Likewise,

(a)

(b)

Fig. 1. Proposed flow network model for calculating the reactant flow

in GCs with under-rib convection effects: (a) definition of GC geome-

tries and explanation of pressure drops; (b) two-dimensional network

of flow resistances.

S. M. Baek et al. / Journal of Mechanical Science and Technology 26 (9) (2012) 2995~3006 2997

the actual pressure drop in the GC with suction is smaller than

the frictional pressure drop because of fluid deceleration. No-

tably, the fluid that leaves the GC by suction has some mo-

mentum in the flow direction, whereas the fluid that enters GC

by blowing has no momentum.

In this study, the additional pressure drop from the momen-

tum balance in the GC is termed as the inertial pressure drop

m,chp∆ . For a given region in the GC, this inertial pressure

drop can be calculated as [30, 31]

m,ch m ch,out ch,out ch,in ch,in ch rib ch,in( )p C m u m u m u→∆ = − +ɺ ɺ ɺ (4)

where ch,inmɺ and ch,outmɺ are respectively the mass flow rates

into and out of the channel region through the channel, while

ch ribm →ɺ denotes the mass flow rate that leaves the channel re-

gion via under-rib convection. As noted above, the mass flow

rate that enters the channel region can be disregarded. In Eq.

(4), mC is the momentum correction factor at 1.44 (for fully

developed laminar flow in square ducts), which is the assumed

value in this study. Notably, m,chp∆ can have a positive value

(pressure drop) or a negative value (pressure compensation).

Fluid properties, channel geometries, and operating condi-

tions are summarized in Table 1. For example, dry air at 70 °C

can be the reactant gas that flows through the GCs.

2.2 Governing equations

An exemplary grid that is used for reactant flow calculation

is shown in Fig. 1(b), where the physical domain is decom-

posed into many two-dimensional square cells with a unit

edge length of unitl . In fact, the grid in Fig. 1(b) corresponds

to the upper corner region of the GC, which is shown in Fig.

1(a). The square cells represent either a channel cell (straight

or corner) or a rib cell according to their location in the flow

field. Calculation nodes (pressure nodes) are located at the

center of the square cells, and each pair of nodes is connected

by a flow resistance. This procedure results in a two-

dimensional network comprising pressure nodes and flow

resistors. The conservation of mass in node i can then be

expressed for incompressible fluid without consumption or

generation of gases as

ewns

0i j

j

Q→

=

=∑ (5)

where i jQ → denotes the steady-state flow rate from node i

to its neighboring node j . A node is connected with four

flow resistances toward the east, west, north, and south direc-

tions that form four neighboring nodes in two-dimensional

grid structures. A similar flow network model was developed

by other researchers for interdigitated flow fields [32].

The constitutive equation for the steady-state flow rate

i jQ → is written as

m,ch, m,ch,ij i j i j i j

i j

ij ij

p p p p pQ

R R

→ →

→

∆ − ∆ − − ∆= = (6)

where ijp∆ is the pressure difference between nodes i and

j , while m,ch,i jp →∆ is the inertial pressure drop calculated by

Eq. (4). m,ch,i jp →∆ has non-zero values when nodes i and

j are from channel cells. If the direction from node i to

node j coincides with the flow direction in the GC,

m,ch,i jp →∆ can be calculated as

m,ch, m,ch,

m,ch,2

i j

i j

p pp →

∆ + ∆∆ = . (7)

In this equation, m,ch,ip∆ and m,ch,jp∆ represent the inertial

pressure drops in channel cells i and j , as calculated by Eq.

(4). The relationship m,ch, m,ch,i j j ip p→ →∆ = −∆ should be used to

ensure the consistency of Eq. (6).

In Eq. (6), ijR is the flow resistance between two nodes.

ijR is calculated by summing the flow resistances of nodes i

and j , iR , and jR , which is written as

ij i jR R R= + . (8)

iR is the flow resistance that corresponds to the reactant

flow in the half-length of cell i (flow length of unit / 2l ).

Thus, for a straight channel cell i , flow resistance is

unitf

ch ch unit ch ch

/ 2

2i

lR R

K h l K h

µ µ≡ = = (9)

where chh is the height of the GC (assumed at 1 mm); and

chK is the equivalent permeability of the GC, which is ex-

pressed as

Table 1. Parameters used for the calculations.

Parameters Values

Geometries

Active cell area 3 cm × 3 cm for single SFF

9 cm × 9 cm for parallel SFF

Channel height 1 mm (hch)

Channel and rib width 1 mm (wch = wrib)

GDL thickness 0.25 mm (tgdl)

GDL permeability 1 × 10−12 m2 (Kgdl)

Properties (dry air at 70°C)

Density, ρ 1.029 kg/m3

Viscosity, µ 0.0000203 Pa-s

Operating conditions

Reference pressure 1 bar (xO2 = 0.21)

Reference current density 4 A/cm2 equivalent

Mean inlet fluid velocity a 12.5 m/s (Rein: 691) for single SFF

37.5 m/s (Re: 2074) for 3p parallel SFF

22.5 m/s (Re: 1244) for 5p parallel SFF

a These inlet velocities correspond to the current density of 4 A/cm2 for

dry air supply (xO2 = 0.21) or, equally, 2.7 A/cm2 for fully humidified air

supply (xO2 = 0.144) at 70 °C


2

hch

2

Re

dK

f= (10)

where Re is the Reynolds number. Ref is 64 for laminar

flow in circular ducts and 56.91 for that in square ducts.

Similarly, for rib cell i , flow resistance is calculated as

unitd

gdl gdl unit gdl gdl

/ 2

2i

lR R

K t l K t

µ µ≡ = = (11)

where gdlt is the thickness of the GDL (assumed at 0.25 mm).

For a corner channel cell, flow resistance is expressed as

L chf s

ch ch ch unit2 4

i

K uR R R

K h h l

µ ρ≡ + = + . (12)

Flow resistance for the corner channel cell depends on the

fluid velocity in the channel. Thus, the governing equation of

Eq. (5) becomes nonlinear, which requires an iterative proce-

dure to obtain the solution. The inertial pressure drop in Eq.

(4) also depends on the fluid velocity in the channel and con-

tributes to the nonlinearity of the governing equation.

2.3 Friction factor

GC reactants in PEMFCs generally have rectangular cross-

sectional shapes, while their flow fields have numerous cor-

ners to fit into a given active area, such as the square active

area considered in this study. For a fully developed laminar

flow in a rectangular duct, the product of the friction factor

and the Reynolds number, which is RD( Re)f , can be deter-

mined as [33]

2

RD

3 4 5

( Re) 96(1 1.3553 1.9467

1.7012 0.9564 0.2537 )

f α α

α α α

= − +

− + − (13)

where α is the aspect ratio that is defined as the ratio of the

channel height h to the channel width w ( /h wα ≡ ). Cal-

culation with Eq. (13) derived RD( Re) 56.91f = for a square

channel ( 1α = ).

However, modification is required when the correlation for

RD( Re)f in Eq. (13) is used to calculate the reactant flow in

SFFs of PEMFCs because the reactant flow in GCs of

PEMFCs repeatedly develops after passing through each cor-

ner of the flow fields. The entrance length eL for the laminar

flow inside the duct is estimated as e h/ 0.06ReL d ≈ [28].

Therefore, a fully developed laminar flow is attained when the

flow length x becomes larger than h60d (

h60x d> ) for Re

= 1000 and h120x d> for Re = 2000. That is, the entrance

length is estimated to be approximately 6 cm for Re = 1000

and 12 cm for Re = 2000 for a square channel with 1 mm

length. Prior reaching the entrance length, flow still develops

in the channel, and the apparent friction factor becomes higher

than the fully developed value.

The entrance length of 6 or 12 cm is similar to or longer

than the edge length of the square active area, which is con-

sidered in this study. For the developing flow in a circular duct,

the apparent friction factor CD( Re)f can be determined as

[33]

1/ 2

app CD 1/ 2 2

13.76 5/(4 ) 64 13.76 /( )( Re)

( ) 1 0.00021( )

x xf

x x

+ +

+ + −

+ −= +

+ (14)

where the dimensionless flow length x+ is defined as

hRe

xx

d

+ = . (15)

Note that app CD( Re)f converges to 64 when x+ ap-

proaches infinity.

The above-mentioned Eqs. (14) and (15) indicate that the

apparent friction factor is dependent on the Reynolds number

(hRe /udρ µ= ), unlike the fully developed friction factor that

is constant for the laminar flow. The inlet Reynolds number

inRe , which is based on the inlet fluid velocity inu , is obvi-

ously a good approximation when the channel velocity is rela-

tively constant in SFF with negligible under-rib convection.

However, the pressure drop across SFF can potentially be

over-estimated by using inRe , when the channel velocity

considerably changes along GC due to high under-rib convec-

tion. Thus, in this study, the mean channel velocity chu was

used to determine the Reynolds number required in Eq. (15).

Finally, the apparent friction factor for a rectangular channel

app RD( Re)f was obtained as

app CD

app RD CD RD RD

CD

app CD

RD

( Re)( Re) f ( Re) ( Re)

( Re)

( Re)( Re)

64

ff f f

f

ff

= ⋅ = ⋅

= ⋅

(16)

where app CD( Re)f was derived based on Eqs. (14) and (15).

A natural choice for the flow length x in Eq. (15) is the edge

length of the square active area. That is, 3x = cm for a 3 cm

× 3 cm active cell area and 9x = cm for a 9 cm × 9 cm ac-

tive cell area. In Eq. (16), CDf is used to convert the fully

developed friction factor RD( Re)f into the apparent friction

factor with the entrance effect app RD( Re)f .

3. Results and discussion

3.1 Model validation

The proposed flow network model was first validated to en-

sure the reliability of subsequent calculations for single and

parallel SFFs. For the validation of this model, laminar flow in

a conventional SFF, as shown in Fig. 2(a), was calculated

using the present network model. The results were then com-

pared with those obtained via CFD simulation. The conven-

tional SFF was designed to cover a small active cell area of 9


cm2 (3 cm × 3 cm) with 15 straight GC regions and 28 mitered

elbows (90° bend). In the flow network calculation, the unit

cell size of unit 1 mml = was used to decompose the domain,

resulting in a two-dimensional network of 961 square cells or

pressure nodes.

In the CFD simulation, the grid for the conventional SFF

was generated for two regions. First, the grid for the GC re-

gion was constructed by allocating a total of 100 finite volume

cells (10 × 10 cells) at the cross-sectional area (1 mm width

and 1 mm height). Second, the grid for the GDL region (0.25

mm thickness) was constructed with five layers of finite vol-

ume cells. In summary, 322,000 finite volume cells were used

in the CFD model, where 161,500 cells were in the GC region,

and 160,500 cells were in the GDL region. This grid density

sufficiently ensured reliable flow calculation inside the SFFs

of PEMFCs [24, 25]. The geometrical and operating parame-

ters employed in both calculations are detailed in Table 1,

along with the fluid properties (dry air at 70 °C). A commer-

cial CFD solver, STAR-CD (CD-Adapco Inc., USA), was

used to solve the laminar and incompressible flow in the GC

with an isotropic GDL permeability of 1×10−12

m2.

Fig. 2 compares the pressure drop characteristics of conven-

tional SFF, which were obtained using the present flow net-

work model and by CFD simulation. In Fig. 2(a), the secon-

dary loss factor LK required in Eq. (2) was determined as

L

Re1.2 0.19

1000K = − (17)

which resulted in a relatively satisfactory agreement between

the network calculation results and the CFD results, except for

the fact that the flow network model slightly overestimated the

pressure for low and high inlet velocities. Based on the above

correlation of Eq. (17), LK has a value between 0.8 and 1.2

for the laminar flow (Re < 2100), which is similar to the re-

ported values for 90° mitered bends in the literature [28]. Fig.

2(a) shows that the present flow network calculation can prop-

erly replicate the nonlinear dependence of the pressure drop

across the flow field chp∆ on inlet fluid velocity

inu , as pre-

dicted by CFD simulation in laminar flow regimes.

Fig. 2(b) demonstrates the variation of pressure in the GC of

the conventional SFF (with respect to the path length px ) for

inlet velocities of 20 and 40 m/s. The path -length px denotes

the distance traveled by the reactant gas along the GC from an

inlet. Thus, px spans as long as 45 cm for conventional SFF

(15 pass × 3 cm length). The pressure distribution along the

GC exhibited staircase-shaped decreasing profiles, combined

with longer and less steep gradient lines that correspond to

straight regions. In contrast, shorter and steep gradient lines

correspond to the bend regions of GC. A relatively good

agreement is also observed in Fig. 2(b) between the pressure

distribution from the flow network model and that from the

CFD simulation, which verifies the validity of the present

network model. Thus, the flow network model is believed to

properly account for the primary pressure drop in straight

regions of the GC and the secondary pressure drop in the 90°

bend regions in the conventional SFF.

The present network model was employed to investigate the

effects of the GDL permeability gdlK on the pressure drop

and flow distribution characteristics in the conventional SFF.

The inlet velocity of dry air (oxygen mole fraction 2Ox is

0.21) was set to 12.5 m/s based on the current density of 4

A/cm2 for the active cell area of 9 cm

2. The inlet velocity of

12.5 m/s also corresponds to the current density of 2.7 A/cm2,

which is supplied to the cathode, for fully humidified air at 70°C

(2O 0.144x = ). The pressure drop results from the flow net-

work calculation and the CFD calculation are compared in Fig.

3(a) for different GDL permeabilities. From the slight over-

estimation of pressure drop in Fig. 2, the flow network model

is believed to predict the pressure drop across conventional

SFF properly for GDL permeability of less than 1 × 10−11

m2.

As GDL permeability is further increased to 1 × 10−10

m2, the

difference in pressure drop results also increases by approxi-

mately 10%. However, general trends are well-predicted by

the flow network model.

Fig. 3(a) clearly shows that higher GDL permeability results

in lower pressure drop across the conventional SFF. That is,

(a)

(b)

Fig. 2. Comparison of pressure drop characteristics for a conventional

SFF with an active cell area of 9 cm2 (3 cm × 3 cm): (a) pressure drop

across the flow field (chp∆ ) with respect to the inlet gas velocity

inu ;

(b) pressure distribution along GC for inu = 20 and 40 m/s.


chp∆ is reduced from 6.9, 6.8, and 6.0 kPa to 2.7 kPa as GDL

permeability increases from 1 × 10−13

, 1 × 10−12

, and 1 × 10−11

m2 to 1 × 10

−10 m

2. This result can be understood by inspecting

the variation in the relative channel velocity ch in/u u along

the GC, as shown in Fig. 3(b). Note that ch in/u u = 1 corre-

sponds to a situation in which all reactant flows are carried

through the GC with negligible flow through the GDL (negli-

gible under-rib convection). In Fig. 3(b), channel velocity in

the conventional SFF shows a periodically increasing and

decreasing trend. The peaks are observed at the corners of the

GC where the minimum under-rib convection is observed,

whereas the valleys are observed at the center of the straight

GC region where the maximum under-rib convection is ap-

parent.

Fig. 3(b) clearly indicates that under-rib convection be-

comes important when gdlK is larger than 1 × 10−13

m2. This

finding is consistent with previously reported results [12, 14]

that under-rib convection cannot be ignored when GDL per-

meability exceeds 1 × 10−13

m2. The average relative channel

velocity ch in/u u is found to be 0.98 for gdlK = 1 × 10

−12 m

2,

0.86 for gdlK = 1 × 10−11

m2, and 0.40 for gdlK = 1 × 10

−10 m

2.

In other words, the reactant gas that is transported through the

GDL amounts to as high as 2% for gdlK = 1 × 10−12

m2, 14%

for gdlK = 1 × 10−11

m2, and 60% for gdlK = 1 × 10

−10 m

2.

Higher GDL permeability is generally desirable, because un-

der-rib convection facilitates reactant transport toward and

liquid water exhaust out of the reaction sites under intercon-

nected ribs. However, higher GDL permeability also reduces

reactant gas velocity in the GC because of cross-leakage or

by-pass flow [34]. Thus, liquid water transport inside the GC

may be hindered.

As a summary of the flow distribution characteristics of the

conventional SFF, Fig. 4 presents the mean channel velocity

chu and the mean under-rib velocity ribu , as well as the

minimum channel velocity min

chu . These mean velocities were

obtained by averaging the velocities of all channel cells and all

rib cells in the flow field. Fig. 4 clearly shows an inverse rela-

tionship between chu and

ribu , indicating that higher under-

rib convection accompanies lower flow rate through the GC.

Fig. 4 also reveals that chu decreases from 12.5 m/s to 5.0

m/s with GDL permeability during gdlK increases from 1 ×

10−13

m2 to 1 × 10

−10 m

2. In contrast,

ribu increases from 0.24

cm/s to 89.3 cm/s (an increase in magnitude of approximately

370 times) along with the increase in gdlK . Thus, Fig. 4

clearly indicates that under-rib convection intensity in conven-

tional SFFs can be significantly enhanced by GDLs with

higher permeabilities.

The minimum channel velocity min

chu is also an important

parameter that should be carefully examined in designing flow

fields for PEMFCs because the two-phase flow or the liquid

droplet motion in GCs is closely related to channel velocity.

Thus, fluid velocity in the GC should be maintained suffi-

ciently high to ensure fast exhaustion of liquid water through

the GC. In Fig. 4, min

chu is higher than 2.8 m/s for all perme-

ability values considered in this study, indicating fast liquid

water exhaustion in the GC.

3.2 Single SFFs

Various SFFs were designed for a small square cell area of

9 cm2 (3 cm × 3 cm), as shown in Fig. 5, and their pressure

drop and flow distribution characteristics were investigated

using the flow network model. Using the unit cell size of 1

mm, the two-dimensional flow network was made to have

8,281 square cells or pressure nodes. The flow field in Fig.

0

4

8

12

16

0

25

50

75

100

(m/s)

chu

Mea

nChan

nel V

elocity

(cm/s)

rib

uM

ean U

nder-rib V

elocity

Channel Under-ribMinimum

chu ribuchumin

12.5

10.8

20.5

2.35

12.3

0.24

89.3

5.0

12.5

10.4

12.3

2.8

213gdl m10−=K 1210− 1110− 1010−

Fig. 4. Mean channel velocity, chu , and under-rib velocity,

ribu , for a

conventional SFF with different GDL permeabilities.

(a)

(b)

Fig. 3. Effects of GDL permeability on the pressure drop and flow

distribution characteristics of a conventional SFF: (a) pressure distribu-

tion along the GC; (b) relative channel flow velocity ch in/u u along

the GC.


5(a) is the conventional SFF employed for model validation,

whereas that in Fig. 5(f) is the conventional spiral flow field.

The flow fields in Fig. 5(b)-5(e) are MPSFFs based on various

patterns. Nam et al. [23] proposed a systematic method to

generate cooling performance as a MPSFFs, and their superior

coolant flow field was numerically demonstrated by Yu et al.

[24] and Baek et al. [25]. In fact, the MPSFF with a two-pass

pattern (single-b) is similar to one of the coolant flow fields

considered by Chen et al. [21] and Choi et al. [22]. The

MPSFF with a three-pass pattern (single-c) is the same as the

cathode flow field for a DMFC that was considered by Xu and

Zhao [20]. Meanwhile, the spiral flow field (single-f) has

geometrical similarity with the MPSFF with a two-pass pat-

tern (single-b).

Fig. 6 shows pressure drop and flow distribution character-

istics of the single SFFs in this study. In the calculation, inlet

fluid velocity was set to 12.5 m/s, and GDL permeability was

fixed at 1 × 10−12

m2, as listed in Table 1. This permeability

value was selected based on the measured values for Toray

carbon papers that range from 2 × 10−12

m2 to 9 × 10

−12 m

2

[35−37]. GDL permeability of 1 × 10−12

m2 is assumed to be

reasonable, considering the reduction of pore volume due to

hydrophobic coating and compression during fabrication, as

well as liquid water accumulation in GDL during operation

[23]. Fig. 6(a) shows that the conventional SFF (single-a) has

the largest pressure drop (approximately 6.8 kPa), followed by

the MPSFF with a five-path pattern (single-d) and the MPSFF

with a three-path pattern (single-c). On the contrary, the spiral

flow field (single-f) exhibits the smallest pressure drop (ap-

proximately 3.8 kPa), which indicates the largest under-rib

convection intensity. MPSFF with a five-pass spiral pattern

(single-e) and that with a two-pass pattern (single-b) show

similarly small pressure drop characteristics. This trend is

consistent with the prediction by Nam et al. [23] based on the

geometrical characterization of MPSFFs, which showed that

the spiral flow field and MPSFFs with a two-pass or spiral

pattern induce the largest under-rib convection intensity.

The variation in relative channel velocity ch in/u u along the

GC is shown in Fig. 6(b), where ch in/u u remains unchanged

at 0.98 for the conventional SFF (single-a). However, the

MPSFFs exhibited lower relative channel velocities. The

minimum value for ch in/u u is 0.84 for the MPSFF with a

five-pass pattern (single-d), 0.66 for the MPSFF with a three-

pass pattern (single-c), 0.59 for the MPSFF with a two-pass

pattern (single-b), and 0.52 for the MPSFF with a five-pass

spiral pattern (single-e). The spiral flow field (single-f) pro-

duced the lowest channel velocity with a minimum value of

0.45. With the previous assumption that under-rib convection

intensity is inversely proportional to channel velocity, spiral

flow fields and MPSFFs can significantly enhance under-rib

convection intensity, regardless of the small active cell area.

In summary, under-rib convection intensities in single

MPSFFs, as predicted by the present flow network model, are

Fig. 5. Single SFFs that are designed for a small active cell area of 9

cm2 (3 cm × 3 cm): (a) conventional SFF; (b) single MPSFF with two-

pass pattern; (c) single MPSFF with three-pass pattern; (d) single

MPSFF with five-pass pattern; (e) single MPSFF with five-pass spiral

pattern; (f) spiral flow field. These flow fields are denoted as single-a, -

b, -c, -d, -e, and -f, respectively.

(a)

(b)

Fig. 6. Pressure drop and flow distribution characteristics of single

SFFs for a small active cell area of 9 cm2: (a) pressure distribution in

the GC; (b) relative channel velocity ch in/u u in the GC.

(a)

(c)

(e)

(b)

(d)

(f)


smaller than those predicted by a previous geometrical charac-

terization study [23]. This discrepancy is mainly attributed to

the reduction of the pressure drop in MPSFFs, as shown in Fig.

6(a). Since under-rib convection is primarily driven by the

pressure difference between two GC regions across an inter-

connected rib, the reduction of total pressure drop potentially

decreases under-rib convection intensity.

Fig. 7 presents the mean channel velocity chu and the

mean under-rib velocity ribu of single SFFs as a summary for

the flow distribution characteristics. The conventional SFF

(single-a) exhibited the highest chu of 12.3 m/s, similar to

inlet velocity (inu = 12.5 m/s), but the smallest

ribu of 2.4

cm/s. In contrast, the spiral flow field (single-f) revealed the

smallest chu of 8.4 m/s, but the largest

ribu of 7.1 cm/s, thus

registering the highest under-rib convection intensity among

the single SFFs considered in this study. The MPSFFs (single-

b, c, d, and e) had chu that ranged from 9.1 m/s to 11.1 m/s

and ribu from 5.5 cm/s to 6.8 cm/s, which ensured relatively

high under-rib convection in single MPSFFs. Thus, Fig. 7

illustrates that under-rib convection intensity can be enhanced

by approximately two to three times when single MPSFFs

(single-b, c, d, and e) are used instead of the conventional SFF

(single-a). The minimum channel velocity min

chu is also pre-

sented in Fig. 7, where min

chu is higher than 5 m/s for all single

SFFs. This result suggests that liquid water accumulation in

these flow fields is insignificant.

3.3 Parallel SFFs

For PEMFCs with a large active cell area, parallel SFFs are

preferred because single SFFs require extremely high pump

power for the reactant flow in GCs. If a conventional SFF

similar to Fig. 5(a) is formed in a large cell area of 81 cm2 (9

cm × 9 cm), the channel path length px readily exceeds 405

cm (45 pass × 9 cm length). In addition, the inlet fluid velocity

inu must be higher than 100 m/s to supply a sufficient

amount of dry air for a 4 A/cm2 current density in a large ac-

tive cell area. Fig. 8 shows the parallel SFFs that were de-

signed for a large square cell area of 81 cm2 (9 cm × 9 cm).

The flow fields in Figs. 8(a) and 8(c) are conventional SFFs

that have three or five parallel paths. Note that conventional

SFFs have been widely used in numerical and experimental

research, as well as in the actual fabrication of PEMFCs. The

flow field in Fig. 8(b) is the three-path parallel MPSFF based

on a five-pass pattern, whereas that in Fig. 8(d) is the five-path

parallel MPSFF based on a three-pass pattern. The method for

constructing parallel MPSFFs in a given cell area is also ex-

plained by Nam et al. [23]. Subsequently, the maximum chan-

nel path-length px is 135 cm for SFFs with three parallel

paths (parallel-a and parallel-b) and 81 cm for SFFs with five

parallel paths (parallel-c and parallel-d).

The pressure drop and flow distribution characteristics of

parallel SFFs were investigated, as shown in Fig. 9. In the

calculation, an inlet fluid pressure that can produce the reac-

tant flow rate corresponding to the reference current density of

4 A/cm2 was imposed on all parallel paths in the parallel SFFs.

Notably, these velocities result in laminar flow in a square

channel of a 1 mm × 1 mm cross-sectional area, as indicated

in Table 1. Figs. 9(a) and 9(b) present the predicted pressure

distribution along each path of the GC in the three-path paral-

lel SFFs and in the five-path parallel SFFs, respectively. The

pressure drop across the GC chp∆ is predicted as 55.6 kPa

for the conventional three-path SFF (parallel-a) and 16.5 kPa

for the three-path MPSFF (parallel-b). Similarly, chp∆ is

predicted as 16.8 kPa for the conventional five-path SFF (par-

allel-c) and 7.2 kPa for the five-path MPSFF (parallel-d). Figs.

9(a) and 9(b) clearly indicate that pressure drop can be signifi-

cantly reduced by using parallel MPSFFs instead of conven-

tional parallel SFFs. In addition, pressure drop decreases as

the number of parallel paths chn increases, as can be ob-

(a) (b) a b

(c) (d) c d

Fig. 8. Parallel SFFs designed for a large active cell area of 81 cm2 (9

cm × 9 cm): (a) conventional three-path SFF; (b) three-path MPSFF

with a five-pass pattern; (c) conventional five-path SFF; (d) five-path

MPSFF with a three-pass pattern. These flow fields are denoted as

parallels-a, -b, -c, and -d, respectively.

single-a b c d e f0

4

8

12

16

0

4

8

12

16

Channel

Under-rib

(m/s)

chu

Mea

nChan

nel V

elocity

(cm/s)

rib

uM

ean U

nder-rib V

elocity

12.3

10.0

6.46.2

9.4

2.4

5.5

11.1

8.4

6.8

9.1

7.1

12.3

8.2

7.4

10.5

5.7

6.5

Minimum

chu

ribu

chumin

Fig. 7. Mean channel velocity chu and under-rib velocity

ribu of

single SFFs for a small active cell area of 9 cm2.


served from the comparison in Figs. 9(a) and 9(b).

Figs. 9(c) and 9(d) present the relative flow rate in the

channel (ch in/q q ) along each path of the GC in parallel SFFs.

Unlike single SFFs, fluid velocity at each inlet of the parallel

SFFs varies. Thus, only the mean inlet fluid velocity can be

defined. As described in Table 1, the average inlet fluid veloc-

ity amounts to 37.5 m/s for parallel SFFs with three paths

(parallel-a and parallel-b) and 22.5 m/s for those with five

paths (parallel-c and d). Figs. 9(c) and 9(d) show that conven-

tional parallel SFFs have a relatively similar channel flow rate

chq at an average flow rate of in ch/q n : mean

ch in/ 3q q= for

conventional three-path SFFs (parallel-a) and mean

ch in/ 5q q=

for conventional three-path SFFs (parallel-c). ch in/q q = 1/3 in

Fig. 9(c) corresponds to chu = 37.5 m/s, whereas

ch in/q q = 1/5 in Fig. 9(d) corresponds to chu = 22.5 m/s. The

relatively small variation of chq in conventional parallel

SFFs (parallel-a and parallel-c) indicates that under-rib con-

vection intensity is not large.

Meanwhile, the relative channel flow rate ch in/q q reveals

significant variation along the GC of parallel MPSFFs, start-

ing from high values of approximately ch1/n , decreasing to

lower values, and then increasing back to high values of ap-

proximately ch1/n . In Figs. 9(c) and 9(d), the flow rates differ

among parallel inlets of MPSFFs, which can be attributed to

different flow resistances among the parallel paths of MPSFFs.

chq is generally lower than the mean channel flow rate mean

chq ,

especially in the middle GC region of parallel MPSFFs. The

minimum ch in/q q is estimated to be 0.03 for the three-path

MPSFF (parallel-b) and 0.03 for the five-path MPSFF (paral-

lel-d). Since the difference between mean

chq and

chq is closely

related to the reactant flow rate through the GDL, under-rib

convection in parallel MPSFFs is expected to be considerably

higher than that in conventional parallel SFFs.

Fig. 10 summarizes the flow distribution characteristics of

parallel SFFs in terms of the mean channel velocity chu and

(a) (b)

(c) (d)

Fig. 9. Pressure drop and flow distribution characteristics of parallel SFFs for a large active cell area of 81 cm2: pressure distribution along the GC

for (a) three-path parallel SFFs; (b) the five-path parallel SFFs. The relative channel flow rate ch in/q q , along the GC for (c) three-path parallel

SFFs; (d) five-path parallel SFFs.

0

10

20

30

40

0

5

10

15

20

parellel-a b c d

(m/s)

chu

Mea

nChan

nel Velocity

(cm

/s)

rib

uM

ean U

nder

-rib V

elo

city

Channel

Under-rib

Minimum

chu

ribu

chumin36.1

22.1

1.8

16.1

13.76.2

10.9

11.1

34.0

21.1

3.5 3.4

Fig. 10. Mean channel velocity chu and under-rib velocity

ribu for

parallel SFF for a large active cell area of 81 cm2.


the mean under-rib velocity ribu , as well as the minimum

channel velocity min

chu . Conventional parallel SFFs generally

exhibit high chu , such as 36.1 m/s for the three-path SFF

(parallel-a) and 22.1 m/s for the five-path SFF (parallel-c).

However, ribu in conventional parallel SFFs is relatively

small, such as 6.2 cm/s for the three-path SFF (parallel-a) and

1.8 cm/s for the five-path SFF (parallel-c). In contrast, parallel

MPSFFs show an opposite tendency of reduced chu with

enhanced ribu . In Fig. 10, the three-path MPSFF (parallel-b)

has chu of 13.7 m/s and

ribu of 16.1 cm/s, whereas the five-

path MPSFF (parallel-d) has chu of 11.1 m/s and

ribu of

10.9 cm/s. Thus, under-rib convection intensity can be en-

hanced by approximately three to six times when parallel

MPSFFs (parallel-b and parallel-d) are used instead of con-

ventional SFFs (parallel-a and parallel-c). As indicated in Fig.

10, the minimum channel velocity min

chu is very high for con-

ventional SFFs (parallel-a and parallel-c), indicating fast liq-

uid water removal in these flow fields. min

chu in parallel

MPSFFs (parallel-b and parallel-d) is relatively small com-

pared with conventional SFFs, but still larger than 3.4 m/s.

Thus, liquid water accumulation in parallel MPSFFs is ex-

pected to be insignificant.

3.4 Limitations of the model

The flow network model in this study has some limitations.

First, the flow network model cannot provide detailed flow

characteristics that CFD calculations can provide. However,

CFD calculations generally require longer pre-processing time

in handling complex flow-field designs, and their computa-

tional cost is very high. Meanwhile, the flow network model

can quickly evaluate pressure drop and flow distribution char-

acteristics along the flow channel, which are most important in

designing flow fields.

Second, the flow network model is generally focused on

cathode flow-field designs. Thus, it may not be useful for an-

ode flow-field designs. This is because hydrogen consumption

at the anode significantly decreases the flow rate along the

flow channel, especially at low stoichiometry. The present

model did not consider consumption or generation of gases,

thus it is not relevant for anode flow calculation. However, the

flow rate change at the cathode is not significant in ordinary

fuel cell operations.

Finally, the flow network model did not consider two-phase

flow due to formation, accumulation, and motion of liquid

water in GC. These two-phase flow effects were found to

significantly influence pressure drop and flow distribution in

GC of PEMFC [38]. However, the single-phase flow calcula-

tion is still applicable when investigating the overall pressure

drop and flow distribution characteristics of a given flow-field

design or when comparing such characteristics in different

flow-field designs. In fact, Hsieh et al. [39] showed that two-

phase flow pressure drop in GC can be correlated with the

single-phase pressure drop using the amplification factor,

which is defined as the ratio of the two-phase friction factor to

the single-phase friction factor. The measured amplification

factor was in the range of 1.0 to1.3 for the normal operation of

PEMFC, depending on the amount of water accumulation [39].

In addition, Adroher and Wang [40] also reported that the

pressure amplifier for the two-phase channel flow reaches 1.0

at sufficient high channel velocity. By carefully using these

amplification factors, the single-phase results from the present

flow network model can be extrapolated to two-phase results.

4. Conclusion

In this study, the pressure drop and flow distribution charac-

teristics of several single and parallel SFFs, including conven-

tional SFFs and MPSFFs, were investigated. Thus, a flow

network model that considers Poiseuille flow in the GC and

Darcy flow in the porous GDL was developed. Based on CFD

results, the loss factor for the secondary pressure drop at the

curved GC regions was determined as a function of the Rey-

nolds number in the channel. In addition, the inertial pressure

drop in the GC due to the suction/blowing effects of under-rib

convection was also accounted for. The good agreement be-

tween the flow network results and the CFD results indicated

the validity of the present network model. After the validation

study, the flow network model was used to investigate the

effects of GDL permeability on the pressure drop and flow

distribution characteristics in a conventional SFF. The results

showed that pressure drop decreases as GDL permeability

increases. In addition, channel flow rate decreases with in-

creasing GDL permeability, which indicates that higher under-

rib convection can be obtained by increasing GDL permeabil-

ity.

The pressure drop and flow distribution characteristics of

various single and parallel SFFs were then investigated using

the flow network model. The results revealed that MPSFFs

have larger variation in the channel flow rate along the GC,

which proves the enhanced under-rib convection intensity.

This result can be attributed to the flow field structure that

allows the close contact of GC regions with widely different

path lengths. Under high under-rib convection intensity, pres-

sure drop across MPSFFs was also significantly reduced. This

lower pressure drop is generally favorable for reducing the

pump power required to supply reactant gas to the flow fields.

The minimum channel velocity in MPSFFs was found to be

approximately 3 m/s to 10 m/s, which is believed to be suffi-

ciently large for the fast removal of liquid water droplets in-

side the GC.

In summary, MPSFFs have several advantages over con-

ventional SFFs, including higher under-rib convection inten-

sity, lower pressure drop, and sufficiently large minimum

channel velocity. In addition, more uniform distribution of

temperature and density of reactant gas concentration are

achieved with MPSFFs, as predicted by previous studies [24,

25]. Further studies are currently under way to investigate

experimentally the advantages of MPSFFs in actual operations

of PEMFCs.


Acknowledgment

This work was supported by the second stage of Brain Ko-

rea 21 (BK21) Project and also by Daegu University Research

Fund.

Nomenclature------------------------------------------------------------------------

dh : Hydraulic diameter, m

f : Darcy friction factor

h,l,w,t : Height, length, width, thickness, m

K : Flow permeability, m2

KL : Secondary loss factor

mɺ : Mass flow rate, kg/s

n : Number of parallel channels

p : Pressure, Pa

Q : Flow rate, m3/s

R : Flow resistance, Pa-s/m3

Re : Reynolds number

u : Velocity, m/s

xp : Channel path length, m

Greek letters

µ : Fluid viscosity, Pa-s

ρ : Fluid density, kg/m3

Subscripts

ch : Channel region

gdl : Gas diffusion layer (GDL)

in : Inlet or inflow

min : Minimum

out : Outflow

rib : Under-rib region

unit : Unit cell

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Seung Man Baek received his Bache-

lor of Science degree in Mechanical

Engineering from Seoul National Uni-

versity of Technology, Korea in 2005.

He then received his Master of Science

degree in Mechanical Engineering from

Seoul National University, Korea in

2007. Currently, he is a Doctor of Phi-

losophy candidate in the School of Mechanical and Aerospace

Engineering at Seoul National University. His research is fo-

cused on the thermal modeling of Li-ion battery systems, fuel

cell systems, and solar thermal systems.

Jin Hyun Nam received his Bachelor of

Science, Master of Science, and Doctor

of Philosophy degrees in Mechanical

Engineering from Seoul National Uni-

versity, Korea in 1996, 1998, and 2003,

respectively. Dr. Nam currently works

as an Assistant Professor in the School

of Mechanical and Automotive Engi-

neering at Daegu University in Gyungsan, Korea. His research

interests include fuel cell and battery systems, heat and mass

transfer, and thermo-fluid process modeling.

Pressure drop and flow distribution characteristics of single ...

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