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Review
Two-phase flow in GDL and reactant channels of
a proton exchange membrane fuel cell
Satish G. Kandlikar a,b,*, Evan J. See a, Mustafa Koz b, Preethi Gopalan b,
Rupak Banerjee a,b
a
b
Mechanical Engineering, Rochester Institute of Technology, 76 Lomb Memorial Dr., Rochester, NY 14623, USA
Microsystems Engineering, Rochester Institute of Technology, 168 Lomb Memorial Dr., Rochester, NY 14623, USA
article info
abstract
Article history:
Understanding the effect of two-phase flow in the components of proton exchange
Received 30 August 2013
membrane fuel cells (PEMFCs) is crucial to water management and subsequently to their
Received in revised form
performance. The local water saturation in the gas diffusion layer (GDL) and reactant
27 January 2014
channels influences the hydration of the membrane which has a direct effect on the PEMFC
Accepted 7 February 2014
performance. Mass transport resistance includes contributions from both the GDL and
Available online 7 March 2014
reactant channels, as well as the interface between the aforementioned components.
Dropletechannel wall interaction, water area coverage ratio on the GDL, oxygen transport
Keywords:
resistance at the GDLechannel interface, and two-phase pressure drop in the channels are
Two-phase flow
interlinked. This study explores each factor individually and presents a comprehensive
Fuel cells
perspective on our current understanding of the two-phase transport characteristics in the
Mass transport resistance
PEMFC reactant channels.
Pressure drop
Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
Flow patterns
reserved.
Breakthrough pressure
1.
Introduction
Fuel cells are considered as viable contenders as “engines” for
automotive applications with almost all major manufacturers
being close to the commercialization stage. As further improvements in efficiency and durability are considered, water
management remains one of the outstanding areas for
research. The two-phase flow issues are encountered in gas
diffusion layer (GDL) and the reactant channels. The
objectives for an effective water management scheme are: (i)
provide adequate saturation for membrane hydration; (ii)
allow for efficient passage of water and reactants through the
GDL; (iii) remove water efficiently from the reactant channels.
Inadequately addressing these issues may lead to higher mass
transport resistances, local damage to the membrane, degradation of the fuel cell components, and loss of efficiency. This
paper addresses the progress made worldwide, with specific
focus on the work conducted in the authors’ laboratory in the
last seven years.
* Corresponding author. Mechanical Engineering, Rochester Institute of Technology, 76 Lomb Memorial Dr., Rochester, NY 14623, USA.
Tel.: þ1 (585) 475 6728; fax: þ1 (585) 475 6879.
E-mail addresses: [email protected], [email protected] (S.G. Kandlikar), [email protected] (E.J. See), [email protected] (M. Koz),
[email protected] (P. Gopalan), [email protected] (R. Banerjee).
http://dx.doi.org/10.1016/j.ijhydene.2014.02.045
0360-3199/Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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Nomenclature
C
c
DO2 eAir
dh
F
H
hM
i
m
Nu
P
Pr
Ru
r
Re
Sc
Sh
T
t
u
x, y, z
V
W
W
We
the Chisholm parameter
oxygen molar concentration
oxygen diffusivity in the air
hydraulic diameter
Faraday’s constant
channel height
mass transfer coefficient
current density
fraction of product water transported to cathode
side
Nusselt number
pressure
Prandtl number
universal gas constant
droplet radius
Reynolds number
Schmidt number
Sherwood number
temperature
time
superficial velocity
spatial coordinates
voltage
mass flux
channel width
Weber number
CL
DTC
GDL
MPL
PEMFC
RH
USDOE
catalyst layer
down-the-channel
gas diffusion layer
microporous layer
proton exchange membrane fuel cell
relative humidity
The United States Department of Energy
Greek
a
b
m
r
s
q
half of the wedge corner angle
volumetric quality
dynamic viscosity
mass density
surface tension
contact angle
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Subscripts
An
anode
B
base
C
capillary
Ca
cathode
F
film flow regime
FD
fully developed
G
gas
k
element number
L
liquid
S
slug flow regime
TP
two-phase flow
W
channel wall
Abbreviations
Ch
air channel
A description of the PEMFC operation may be found in a
textbook, e.g. Ref. [1]. It consists of a proton exchange membrane which allows hydrogen protons to cross freely across it,
while acting as an insulator for electrons and preventing
reactant cross-over. Hydrogen and air (source of oxygen) are
distributed evenly with a network of reactant channels and
porous GDL over the catalyst layers (CL) on either sides of the
membrane. On the hydrogen side (anode), hydrogen ions and
free electrons are formed at the CL. The hydrogen ions are
transported from the anode CL through the membrane to the
cathode CL where the reaction is completed with oxygen from
the cathode flow field and electrons returning from the
external load. The product water formed at the cathode CL is
the primary topic of interest in the water management
studies.
2.
Water transport and emergence from GDL
2.1.
Transport through the GDLs
The study of liquid water accumulation and two-phase flow in
PEMFC reactant channels have received increased attention in
the recent years [2e7]. Flow in the fuel cell reactant channels
differs from conventional microchannels as the fuel cell
channels are bounded on one side by a porous wall which is
the GDL [8e11]. The GDL typically consists of a macroporous
carbon paper coated with a thin microporous layer (MPL) on
one side. Water generated at the CL travels in liquid and/or
gaseous form through the GDL to the reactant channels,
where it is removed from the cell by the flow of reactants. This
leads to continuous introduction of water along the length of
the reactant flow channels.
2.1.1.
Liquid water transport
Liquid water has been observed to emerge into reactant
channels and its presence in the GDL is well established
[12e14]. A key area of research is the transport of water from
the CL to the reactant channels through the MPL and the GDL.
A number of researchers have proposed different mechanisms for transport from the CL to the reactant channels
[4,15e20]. It has been shown by multiple investigators that the
MPL improves the water management and the fuel cell performance [21,22]. The role of the MPL is still not fully understood, although the cracks appearing on its surface seem to
play an important role in the vapor transport [15,23]. However,
this is not yet conclusively established as the product water in
the vapor form may occur through the MPL, while the
condensed water in the GDL is prevented by the MPL from
going back to the CL.
In 2010, Lu et al. [24] designed and conducted an experimental investigation into the role of the MPL through the use
of breakthrough pressure and visualization of droplet emergence. They sandwiched the GDL between two transparent
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Lexan plates with a design similar to a commercial bipolar
plate [25]. The water was distributed at the MPL surface
through channels providing a more uniform water introduction closely mimicking the water generation at the cathode
catalyst layer. Liquid water flow rate was controlled using a
syringe pump. The rate of water introduction was mapped to
an equivalent current density of 1.2 A cm2.
As the water breakthrough occurs from the GDL into the
channels, large pressure spikes were recorded from the supply
chamber in ex situ experiments. This agrees with previous
observations made in literature [13,26]. Eruptive transport of
liquid water emerging from the GDL into gas channels was
also observed by earlier researchers [12,14]. The pressure
peaks, seen in Fig. 1, correspond to the breakthrough pressures. The GDL samples are identical except for the MPL
coating (SGL 25BC has an MPL while SGL 25BA does not). These
GDLs have randomly distributed 5% PTFE content. When the
GDL samples without MPL were tested, multiple breakthrough
locations were found, corresponding to the different pressure
peaks, which showed that the water emergence location from
the GDL dynamically changed. This contradicted the predictions of pore network models which proposed that water
Fig. 1 e Water breakthrough pressure (Pc) through a) SGL
25BA and b) SGL 25BC samples. Inset images show the
visual observation corresponding to the breakthrough
pressure readings. Adapted from Lu et al. [24].
breakthrough would occur from the same location. Further
research on the PTFE content, its distribution, and MPL on the
breakthrough behavior is warranted.
Lu et al. [24] repeated the experiments for samples with the
MPL. Although multiple breakthrough locations were
observed, the locations did not change once established. This
was contrary to the observations without the MPL and the
stabilization was attributed to the presence of the MPL. The
observations were explained in terms of Haines jumps, a wellestablished phenomenon seen in soil mechanics, as well as
spontaneous redistribution of the water pathways within the
GDL pores.
2.1.2.
Water vapor (gaseous) transport
Owejan et al. [15] stipulated that the majority of the water
transport through the GDL is in the form of vapor, especially at
elevated temperatures. The primary mode of transport is
diffusion. However, the permeability of the GDL has also been
shown to affect the performance of the fuel cell [27], and
therefore deserves to be investigated further.
Different models have been developed for diffusion in
porous media in the past [28e32]. However, experimental results of diffusion in fibrous porous media such as the GDL do
not follow the model predictions [30,33]. Although different
authors have worked at understanding different factors that
affect the effective diffusion coefficient of different gases
through the GDL, none of the current models presents a good
match to the experimental results. A definitive set of the
experimental results as well as a diffusive model were long
warranted.
LaManna and Kandlikar [34] provided an exhaustive
experimental study on the water vapor diffusion through the
GDL materials used in PEM assemblies. Samples from three
different manufacturers were utilized to test for the effects of
the MPL, GDL thickness and PTFE loading. The results showed
that the MPL coatings provided a significantly larger resistance to the diffusion of gases through the GDL which was
attributed to the smaller pores of the MPL and lower overall
porosity. Increased PTFE loading also reduced the effective
diffusion coefficient, an outcome that is also due to the
reduction in porosity and pore diameter. As the GDL is a heterogeneous multilayer structure, it was suggested that variation in the thickness of the GDL with similar manufacturing
methods may have an effect on the effective diffusivity.
However, the thickness showed a negligible effect on the
effective diffusion coefficient.
Permeability of a GDL represents the proportionality between the flow velocity through the GDL and the pressure
drop across this layer. This parameter characterizes the ease
of gas flow though the porous material. The higher the
permeability is, the easier it is for the reactants and product
water vapor to flow through. Numerous authors have studied
the gas permeability of the GDL layers [35e40] both experimentally and numerically. Some of the studies include the
effects due to Knudsen diffusion and convective transport
processes (viscous and inertial transport) on permeability
[41,42].
It has been shown that permeability increases with
porosity and decreases with compression [40,43]. Addition of
PTFE leads to a decrease in the permeability in all directions
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[39,40] and the MPL coating decreases the through-plane
permeability [35] but it does not affect the in-plane permeability [40]. Recently, Sadeghifar et al. reported that the fiber
spacing also affects the transport properties of a GDL [44]. The
fiber spacing has been shown to affect the air permeability
and pressure drop within GDL, and further research in this
area is needed to study its effect on water transport.
2.2.
Channeledroplet interaction
The water emergence into the reactant channel of a PEMFC
can be in the liquid phase. This liquid water from the channel
is removed by the gas flowing in the channel. However, due to
the rough GDL surface structure, the droplets tend to get
pinned on the surface and interact with the channel wall.
Thus, understanding the fundamental problem of droplet
detachment from the GDL surface and its interaction with the
channel sidewall are critical to efficiently remove the liquid
water from the channels.
There have been several approaches used to visualize the
liquid water in the PEMFCs to understand its behavior and
removal pattern from reactant channels [12,25,45e54]. However, these techniques, such as neutron radiography, magnetic resonance imaging, and nuclear magnetic resonance are
quite expensive and further restricted by their inability to
easily resolve single droplets. One of the most efficient
methods for single droplet level resolution is through optically
transparent reactant channel materials.
Bazylak et al. used an optically transparent reactant
channel to visualize the droplet breakthrough and growth [13].
Similar experiments were performed by Yang et al. and they
found that the droplet emerged at preferential pores and grew
to a consistent size before getting detached and removed from
the GDL [55]. Tuber et al. were among the first few groups to
study the effect of GDL wettability using transparent PEMFCs.
They expressed the water accumulation in the channel in
terms of the contact angle [52]. Turhan et al. found that hydrophobic channel walls tend to form discrete droplets on the
GDL surface and remove the droplets more easily [56]. However, in case of a hydrophilic surface, the liquid tends to form a
film on the channel walls, a case that leads to a difficulty in
water removal. Lu et al. also performed similar experiments
and found that the hydrophilic channels help in uniform
water distribution along the GDL surface and reduce the
pressure drop in the channels [58].
Cheah et al. performed an experimental study on the effect
of channel wettability, geometry and orientation on slug
removal [59]. They showed that a hydrophilic square channel
produced large slugs. These slugs required lower energy to be
removed but they created large mass transport resistances for
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the reactant gases to diffuse to the catalyst layer. On the other
hand, hydrophobic square channel produced smaller slugs
which required higher energy for their removal but minimized
the reactant transport resistance. Therefore, the reactant
channel needs to be configured by taking all the studied factors into account.
Extensive work has been performed by Kandlikar et al. to
understand the basis for water accumulation in reactant
channels using a visually accessible fuel cell [2,24,25,57,58].
They brought out the importance of superficial air velocity and
water generation rate on the water hold up in the reactant
channels. Apart from these and other experimental studies,
there have been several papers in the literature from the
recent past addressing the droplet behavior in the reactant
channels numerically.
Theodorakakos et al. analyzed the droplet behavior in a
high aspect ratio channel geometry to avoid dropletewall
interaction [60]. They correlated the critical diameter of the
droplet at detachment with the superficial air velocity in the
reactant channel. Similarly, Zhu et al. performed a 3D
simulation of a reactant channel with different surface
wettability conditions [61]. They found that a hydrophilic
surface leads to the spreading of the liquid near the channel
wall, forming a film and resulting in the blockage of the
reactant channel. They also performed simulations to understand the droplet growth and detachment process as a
function of channel geometry [62]. The droplet removal time
was lower for triangular and trapezoidal channels compared
to those in rectangular and upside-down trapezoidal channels. Likewise, Cai et al. numerically investigated the effect
of surface wettability of the GDL on the behavior of a droplet
and film [63]. They concluded that using the combination of
a hydrophobic GDL and hydrophilic side channel walls leads
to an efficient water removal from the channels. On the
same note, Quan et al. also reported that a hydrophilic
channel tends to push the water along the channel edges
and facilitates the reactant gas transport to the catalyst
layer [64]. The electric double layer interactions and their
effect on the contact angles of droplets has been reported by
Das and Mitra [66].
Liquid water flow in PEMFC reactant channels leads to
different flow patterns depending on the gas and water flow
rates. The flow patterns identified in the PEMFC channels are
water droplet, film and slug flow as shown in Fig. 2 and discussed further in Section 4.1. The analysis of water droplet
emergence, growth, interaction with the channel wall, formation of films or slugs, and removal of the water features
from the channel as a function of gas flow velocity are
important to understand the two-phase flow mechanism in
the PEMFC channels.
Fig. 2 e Flow patterns observed from the PEMFC gas channel cross section: a) Droplet, b) Slug, c) Film. Image credit [65].
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2.2.1.
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Fundamental study on dropletewall interaction
There has been very little work done in the literature to understand the droplet detachment from a reactant channel
from a fundamental perspective. Chang et al. studied the
wetting phenomenon of a droplet in the vicinity of the corner
boundary [67]. They found that the droplet follows the
Young’s equation when the contact line of the droplet is away
from the edge. Once the contact line reaches the edge, the
droplet pinning occurs until the apparent contact angle reaches the critical angle which extends the droplet over to the
new surface.
Rath and Kandlikar studied the droplet formation and its
accumulation that takes place in the corner of a channel with
a microscopic visualization [68]. They varied the angle between the base and the sidewall (2a) to observe the droplet
interaction with the wall. The effect of surface tension forces
on the dropletechannel wall interaction was the main focus of
this parametric study. The ConcuseFinn condition [69,70] was
used to explain the behavior of the droplet near the channel
corner.
The ConcuseFinn condition dictates that the rise height of
a fluid in a wedge shaped domain is predictable if the
following condition is true: a þ q > p/2. Rath and Kandlikar
Fig. 3 e a) Contact angles made by the droplet near the
channel corner; b) Graphical representation of the
condition for corner filling of a droplet in a channel corner.
Adapted from Gopalan and Kandlikar [67].
used this formulation to predict the water filling the channel
corner where the GDL and the channel wall meet [68]. Using
the graphical representation in Fig. 3, they reported that the
channel corner will be filled only if the contact angle data
point falls inside the shaded region. They also found that the
use of contact angles instantaneously measured during the
water movement is the key in understanding the droplet
behavior in the reactant channel as opposed to the static
contact angle measurements. These instantaneously
measured advancing and receding contact angles are called
“instantaneous dynamic contact angles”. They showed that
2a has a transitional value at which the dropletecorner
interaction switches from non-filling to filling for a given
material pair.
Rath and Kandlikar had studied the droplet behavior in a
channel without air flow. Gopalan and Kandlikar extended the
previous work to understand the droplet interaction with
reactant channel walls in the presence of air flow [72]. They
showed that the ConcuseFinn condition is not valid in the 2a
range close to the transition angle for corner filling in presence
of the air flow. It was shown that the air flow in the channel
causes oscillations in the droplet which changes the dynamic
contact angle and affects the droplet filling behavior near the
transition angle as shown in Fig. 4. Polverino et al. also showed
that the oscillations in the droplet due to the air flow affect the
droplet detachment from the GDL [73].
Gopalan and Kandlikar also investigated the effect of
droplet emergence location on the droplet dynamics. It was
found that the droplet would fill the channel corner irrespective of any channel open angle when the droplet emerges
from under the land area [71]. Gopalan and Kandlikar proposed to use grooves that are in the channel sidewall and
directed towards the top channel wall to avoid the water
clogging near the channel corners. Grooves strengthen the
capillary forces on liquid water. Hence, the water at the corner
fills in and moves to the top of the channel where the liquid
water could be removed easily by the air flow [74]. However,
the water accumulation near the corners is one of the issues
that is still persistent in the fuel cells and needs to be
addressed further.
Gopalan and Kandlikar also highlighted in one of their
studies that the droplet dynamics inside the gas channel is
dependent on the material properties that are used for the
reactant channels [75,76]. They concluded that the contact
angle hysteresis (defined as the difference between the
advancing and receding contact angles) of the channel wall
material plays a major role in the channel corner filling
behavior. Higher contact angle hysteresis of the channel wall
material leads to a stronger pinning of the droplet. This
consequently can allow larger oscillations to occur in the
droplet without being de-pinned from the sidewall. This can
prevent the contact line of the droplet from moving towards
the channel corner to fill it. However, the droplet removal
from the channel required a higher drag force from the air
flow due to the stronger pinning of the droplet. They also
found that the different GDL materials they used did not have
any significant impact on the droplet dynamics inside the
reactant channel.
Gopalan and Kandlikar also performed similar experiments to analyze the effect of GDL deterioration due to
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extended PEMFC operation [76]. MRC-105 GDL samples that
had run for 40 and 125 h were utilized for further droplet
emergence studies. The authors reported that the wettability
of the GDL material decreases with the duration of operation
and hence, the transition point for the corner filling of that
material also decreases. Hence, the water droplet fills the
channel corner at a lower open angle, 2a.
3.
Oxygen interfacial transport from the air
channel to GDL
For accurate performance prediction of PEMFCs at high current densities, the oxygen (O2) transport resistance at the
cathode side needs to be characterized. Interfacial O2 transport resistance at the GDLeair channel interface is a nonnegligible component of the total transport resistance. The
two-phase flow in the channel complicates the prediction of
the interfacial O2 transport resistance in two ways:
1) The GDLechannel interface is blocked by water features,
such as droplets, films, and slugs. This blockage varies with
location and time.
2) Water features disrupt the fully developed (FD) air velocity
and O2 concentration profiles. The developing velocity and
O2 concentration profiles in the wake of the water features
lead to an interfacial resistance different than the fully
developed value in the channel.
The understanding of liquid water coverage on the
GDLechannel interface enables more accurate prediction of
the interfacial O2 resistance. By using the experimentally obtained water feature geometries and positions in the channel,
the interfacial O2 resistance can be numerically simulated
downstream of a particular water feature or set of features.
3.1.
Liquid water coverage of the GDL interface
As liquid water is produced and enters into air channels, the
water blocks the area available for the oxygen to diffuse
through the GDL to reaction sites at the catalyst layer. The
ability to accurately visualize and quantify this coverage is the
key to understanding the interfacial transport.
A variety of imaging techniques have been experimentally
used over the years to obtain a spatial distribution of water
within reactant channels. Although the difficulty of gaining
6625
access to a neutron source discourages its widespread application, neutron imaging has been an effective choice
[25,47,77e79]. Several groups experimented with X-rays to
observe the liquid water distribution within the reactant
channels [12,80e82]. X-rays have been used to obtain either a
high spatial resolution or a high temporal resolution, but not
both simultaneously.
Direct optical imaging technique is the most advanced
option in terms of spatial and temporal resolution. However,
as traditional fuel cell materials are opaque in the visible
spectrum, a fuel cell needs modification to allow optical
visualization [78,82]. This technique is well suited to observe
liquid water in the reactant channels after the modifications.
Tuber et al. [52] was the first to use optical visualization in
2003 by modifying an operating PEMFC to visualize two-phase
flow in the channels. Other researchers have also utilized this
diagnostic technique to understand the behavior of liquid
water in the channels [2,24,25,58,83e85].
Sergi and Kandlikar [86] developed a dual visualization
setup to visualize the anode and cathode sides of an operating
PEMFC simultaneously. A temporal resolution of 60 frames per
second (higher resolution was possible, but was not warranted) was recorded along with a spatial resolution of
approximately 34 mm per pixel. They defined the term area
coverage ratio (ACR) which is defined as the fraction of
interfacial area covered by liquid water present in the reactant
channels to the total area available for gas transport in dry
reactant channels.
Sergi and Kandlikar [86] also developed and implemented
an algorithm using MATLAB to process the image sequences
captured during testing. A flow chart of the algorithm is
shown in Fig. 5. The algorithm processes the test videos on a
frame-by-frame basis. The test frame is first converted to
grayscale and subtracted from the dry reference frame void of
any water features. This subtraction highlights the water regions within the test frame. A mask is then applied to isolate
the channel regions only for further processing. A threshold is
applied to detect the water features based on the pixel intensities and reduces the optical noise. In the final step,
morphological processing is utilized to remove the noise and
smooth the detection of the water features. The morphological processes check for connected pixels and apply closing
operations in order to fine tune the water feature detection.
For visual inspection and spatial context of the water features,
the final processed frame is added to the original video frame
to create a superimposed detection area over the test frame.
Fig. 4 e Droplet behavior near the transition angle (Open angle: 2a [ 50 ) for MRC-105 GDL base and polycarbonate sidewall
for the superficial air velocities: a) 0.4 m sL1 e corner filling, b) 1.6 m sL1 e no corner filling [71].
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Additionally, a second algorithm was developed to distinguish the water features present, in terms of slug and film flow
regions. This provided supplementary information regarding
different flow structures dominant within reactant channels
at different current densities and stoichiometric ratios. The
data reported in their work focused on a specific operating
condition: cell temperature of 35 C and 100% inlet RH for both
gas streams.
3.2.
Interfacial oxygen transport resistance
Interfacial oxygen transport resistance is the proportionality
between the O2 molar flux and the required O2 concentration
drop at the GDLechannel interface. By minimizing the concentration drop across the interface, a higher O2 concentration can be supplied through the GDL to the reaction sites,
thus the performance of a PEMFC can be enhanced. The proportionality between the concentration drop and molar flux is
expressed by the mass transfer coefficient (hM). This coefficient is non-dimensionalized by the channel hydraulic
diameter (dh) and O2 diffusivity in the air ðDO2 eAir Þ, and the
Sherwood number ðSh ¼ hM dh =DO2 eAir Þ is obtained. The
interfacial resistance is reported by the Sherwood number
which is specific to a flow and boundary condition, and
channel aspect ratio.
In the literature, simplified PEMFC models utilize the
Sherwood number as a constant input to save computational
resources from the simulation of forced convection in the air
channels [87e98]. The constant input of Sherwood number is
a valid assumption if the flow is fully developed in the reactant channels, such as the absence of liquid water features in
high temperature PEMFCs [97]. However, the constant Sherwood number assumption is not always applicable. Kim et al.
shared a similar anticipation that the Sherwood number
might depend on specific fuel cell operating conditions and
configurations [90].
Since the research on the Sherwood number in PEMFC
reactant channels has not yet been very well established, 2D
approaches (parallel plates) in the available literature still
provided insight for the direction of the 3D studies. The results
by the 2D models do not reflect realistic conditions due to fact
that PEMFC reactant channels typically have an aspect ratio
close to unity. However, these earlier numerical studies in 2D
domains provided the following knowledge: The porous
GDLechannel interface is not necessarily subjected to zero air
velocity in the normal direction to the interface. The cell
consumes and produces known amounts of oxygen and water
respectively at a given current density. Depending on the
thermal conditions of the cell, water leaves the cell in the form
of liquid and vapor with a varying fraction. If the entire water
flow is in the liquid form, the GDLechannel interface is subjected to air suction into the GDL. In case water is completely
in the vapor phase, air injection into the channel takes place.
Depending on the intensity of suction or injection, the flow
may remain developing. Under developing flow conditions,
the Sherwood number can vary and hence, has been a subject
of investigation.
2D numerical studies by Wang et al. [99], Jeng et al. [100]
and Hassanzadeh et al. [101] showed that air injection and
suction have a weak or negligible effect on the Sherwood
number. The aforementioned authors obtained the fully
developed Sherwood number values as 5.274 (readjusted Sh
with dh instead of the channel height) [99], 6.0 [100] and 5.411
[101]. These findings allow the simulations to neglect any injection or suction at the GDLechannel interface. However,
these results cannot reflect the Sherwood number in 3D
channels due to their 2D assumption. Moreover, they neglected the effect of liquid water present in the channel on the
Sherwood number. Casalegno et al. also underlined the need
for Sherwood number in two-phase flow conditions [95].
The first attempt to simulate the Sherwood number in a 3D
channel which incorporated a water droplet was performed
by Koz and Kandlikar [102]. The simulation domain was
formed by placing a droplet-shaped obstruction into the
channel. With this approach, the two-phase flow in the
channel was simulated as single-phase flow. The channel
cross section dimensions (W H ¼ 0.70 mm 0.40 mm) were
taken from the design that meets the USDOE performance
Fig. 5 e Graphical flow chart representation of the image processing algorithm developed by Sergi et al. [86].
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 6 6 2 0 e6 6 3 6
targets for automotive applications [25]. The droplet obstruction radius (r) varied between 0.10 and 0.20 mm. The superficial air flow velocity (uG) equivalent to the range of current
density 0.1e1.5 A cm2 (at T ¼ 80 C and RH ¼ 100%) varied
from 1.59 to 15.89 m s1.
The fully developed Sherwood number was obtained to be
3.36 which was shown to significantly differ from the values
provided by the 2D numerical studies: 5.274 [99], 6.0 [100] and
5.411 [101]. By placing a droplet in the fully developed region,
the Sherwood number in the droplet wake was investigated.
Fig. 6 shows the effect of superficial air velocity on the Sherwood number while the droplet radius was 0.15 mm. It was
shown that there is a threshold value of air velocity to obtain
an overshoot of Sherwood number in the droplet wake. The
threshold air velocity was found to be dependent on the
droplet size.
The overshoot of Sherwood number in the droplet wake
can be increased with superficial air velocity and droplet size.
However, the air velocity and droplet size are limited by the
droplet adhesion to the GDLechannel interface since the drag
on the droplet increases with the aforementioned two parameters. The numerically obtained drag force on the dropletshaped obstruction was compared against the experimentally
obtained force to initiate droplet sliding on an inclined surface
by Das et al. [104]. Certain sets of the air velocity and droplet
radius were removed from the results as their drag force
exceeded the adhesion force.
The distance between two droplets adhered to the
GDLechannel interface can be as low as 1.00 mm which was
visualized in an operative PEMFC by Yang et al. [55] and Zhang
et al. [105]. The overshoot of Sherwood number in the droplet
wake was shown to affect lengths which can easily cover
the distance between two droplets (up to w18 mm). Hence,
Koz and Kandlikar posed the possibility that droplets in a row
along the flow direction may lead to an increase of Sherwood
number. Moreover, this increase can be intensified in multiple
stages since the visualizations by Yang et al. and Zhang et al.
showed that number of droplets in a row can exceed two
[55,105].
Fig. 6 e The effect of superficial air velocity (uG) on the
Sherwood number (Sh) for the droplet radius r [ 0.15 mm.
Adapted from Koz and Kandlikar [103].
6627
Koz and Kandlikar extended their earlier work to multiple
droplets in a row [103]. The higher resolution simulations in
this recent study updated their previous fully developed
Sherwood number from 3.36 [102] to 3.349. They also provided
an additional aspect of validity for the use of droplet-shaped
obstructions by considering the droplet deformation due to
the air flow. They predicted the deformation by incorporating
a correlation by Cho et al. [106,107] at a given superficial air
velocity and droplet size. The calculated droplet deformations
and air drag values led to sets of air velocity and droplet size
that would allow the droplets to adhere to the GDLechannel
interface and remain spherical.
The results in Fig. 7 show eleven droplet obstructions with
uniform droplet spacing of 2.00 mm, variable superficial air
velocity and droplet radius. The case uG ¼ 10.59 m s1 and
r ¼ 0.15 mm led to the highest average Sherwood number in
the flow direction out of four sets of the aforementioned parameters. Multiple droplet obstructions were shown to have a
significant effect on the Sherwood number in the channel.
After the seventh obstruction, the Sherwood number follows
the same pattern and the maximum average Sherwood
number in between two consequent droplets is 7.466
(2.229 ShFD).
The authors estimated the impact of Sherwood number
increase on the PEMFC performance. They used the following
equation to calculate the difference in cell voltage for a
change in oxygen concentration at the catalyst layer: DV1e2 ¼
Ru TF1
c lnðc2 =c1 Þ [1]. The oxygen concentration values were
calculated for the current density of 1.0 A cm2. The results
showed that the exclusion of fully developed flow interfacial
O2 transport resistance from a performance model would lead
to a voltage prediction that is 4.8 mV higher than the case with
the inclusion of the interfacial resistance. The 122.9% increase
in Sherwood number can reduce this loss of voltage from 4.8
to 2.0 mV. This shows that droplets in a channel can increase
the cell performance when the superficial air velocity and
Fig. 7 e The effect of eleven droplets on the Sherwood
number (Sh). Variable superficial air velocity (uG) and
droplet radius (r). Position of the first droplet, x [ 3.00 mm
and uniform droplet spacing: 2.00 mm. Adapted from Koz
and Kandlikar [103].
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droplet size are high enough. Similar to the effect multiple
droplets, Heidary and Kermani proposed to increase the
performance of direct methanol and proton exchange membrane fuel cells by placing indentations into the reactant
channels [108].
Koz and Kandlikar also investigated the link between the
heat and mass transfer analogy in a PEMFC air channel with
droplets. In the literature, researchers pointed out the
possible utilization of this analogy to use Nusselt number
(Nu) values for Sherwood number [93e97,108]. However,
there had not been any work published on how the Nusselt
and Sherwood numbers are related to each other in the
PEMFC air channel. Although the Sherwood and Nusselt
numbers are the same in fully developed laminar flow conditions, they may differ under developing flow conditions. If
the Schmidt number (Sc) is not equal to the Prandtl number
(Pr), the Sherwood number differs from the Nusselt number
in the developing flow regions. As the Sc Pr difference
grows, so does the Sh Nu difference. Hence, for the condition Sc ¼ Pr, the Nusselt number can be mapped to the
Sherwood number directly in both fully developed and
developing flow conditions.
In typical PEMFC operating conditions, the Schmidt and
Prandtl numbers differ. Hence, the Sherwood number in the
vicinity of droplets would not be same as the Nusselt number
in the equivalent heat transfer problem. By numerically
obtaining the difference between Sherwood-Nusselt numbers
with the largest possible Sc Pr difference in PEMFC operating
conditions, researchers can use the Nusselt number data to
predict the Sherwood number in PEMFC air channels with a
known maximum error. The same knowledge can also serve
as the extent of validity for the Sherwood number data obtained for a single Sc and used in conditions at different Sc
than the original.
Koz and Kandlikar numerically solved for the equivalent
heat transfer problem to the convective mass transport in an
air channel in the presence of multiple droplets in a row [103].
The Schmidt and Prandtl numbers were 0.633 and 0.824,
respectively at 80 C and fully humidified air. The numerically
calculated Nusselt number was compared locally to the
Sherwood number. These two values started to differ from
each other with the flow disruption induced by the first
droplet. The Nusselt number was always found to be larger
than the Sherwood number. The difference increased in the
flow direction and reached an asymptotic value. The lowest
Sh/Nu ratio 0.876 was found to be at the superficial air velocity
10.59 m s1, droplet radius 0.12 mm, and uniform droplet
spacing 2.00 mm.
4.
Down-the-channel (DTC) transport
Traditionally, DTC transport resistance is characterized
through channel pressure drop. Additionally, flow maldistribution and two-phase flow maps allow for additional
characterization of two-phase flow conditions and the
resulting DTC transport resistance. These DTC studies fall
into
two
primary
categories:
single-channel
and
multichannel.
4.1.
Single channel transport
For the study of DTC transport in a PEMFC reactant channel,
single channel experiments provide a fundamental perspective that is advantageous for investigating the underlining
phenomena within the channel. Through the use of a single
channel the experimentation can be significantly simplified,
cross-channel effects can be removed, and fewer assumptions
are required.
4.1.1.
Flow regimes
DTC water transport in PEMFCs presents an issue due to the
additional mass transport losses associated with two-phase
flow: the combination of reactant gas, evaporated water,
and liquid water. There are three main two-phase flow regimes which are considered in this work: slug flow, film flow,
and mist flow. The key differences between these flow regimes are characterized by the frequency of their pressure
drop fluctuations and their two-phase multiplier, which
scales the single-phase pressure drop based on flow
conditions.
Slug flow is defined as large liquid plugs separated by
relatively large gas pockets. These slugs completely fill the
channel geometry. Slug flow typically results in a higher twophase pressure drop multiplier and low frequency fluctuations in the pressure drop of a system.
Film flow is defined as liquid film on channel wall with
significant gas pockets. These films are typically annular in
round channels or cover only one channel wall in rectangular
geometries. Film flow typically causes a relatively low twophase multiplier compared to slug flow, but induces higher
frequency pressure drop fluctuations.
Mist flow is defined as both phases being equally distributed throughout the channel cross section. Usually the liquid
is entrained as very small droplets in the gas flow. Mist flow
regularly has a two-phase multiplier close to 1 in PEMFC applications, and produces with minimal fluctuation in the
pressure drop.
4.1.2.
Pressure drop in single channels
A primary consideration in characterizing two-pressure
drop in simulated reactant channels is the method of liquid
introduction into the channel. Primarily experiments utilize
air and water as working fluids at near atmospheric conditions, which mimic that of a PEMFC cathode. However, it
should be noted that these studies are typically adiabatic and
do not consider continuous introduction of liquid throughout
the channel [109]. Scaling of large tube correlations for pressure drop does not yield accurate results due to the dissimilar
comparative magnitude of the gravitational, viscous, and
surface tension forces between the large scale tubes and the
microchannels [109].
In a separated flow model, the superficial velocity of each
phase is calculated separately. A two-phase multiplier is
utilized based on the flow conditions to scale the singlephase pressure drop to two-phase. Most notably, this form
of modeling is based on the model by Lockhart and Martinelli [110] which suggested the two-phase multiplier as a
function of the ratios of each phases fluid properties and gas
fraction.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 6 6 2 0 e6 6 3 6
Chisholm [111] later provided a basis for predicting the
Chisholm parameter (C) based on the liquid and gas Reynolds
numbers. This parameter has become the primary basis for
two-phase pressure drop correlations.
In 1996, Mishima and Hibiki [112] conducted experiments
with 1e4 mm hydraulic diameter channels with both circular
and rectangular cross-sections. Flow was forced in a vertical
upwards direction through both glass and aluminum tubes.
Over a wide range of superficial velocities, turbulent flow was
observed in both the liquid and gaseous phases. It was noted
that the hydraulic diameter affected the two-phase multiplier.
The Chisholm parameter was then correlated to hydraulic
diameter.
In 2006, English and Kandlikar [113] observed two-phase
flow in horizontal channels while studying the effects of
surfactants. Rectangular channels in Lexan with a hydraulic
diameter of 1.018 mm were used. Over the range of superficial velocities studied, laminar flow conditions were
observed. It was concluded that in laminar conditions the
Chisholm parameter was similarly correlated to the hydraulic diameter. The correlation by Mishima and Hibiki
[112] was modified to revise the two-phase multiplier for
laminarelaminar flow.
In 2001, Lee and Lee [114] conducted experiments while
varying aspect ratio with channels of hydraulic diameter from
0.78 to 6.67 mm. The width of the channel was held constant
at 20 mm while the height of the channel was varied. The
effect of aspect ratio, as well as the effect of hydraulic diameter, was highlighted and a further correlation was proposed.
They proposed the Chisholm parameter as a function of three
non-dimensional parameters which describe the fluid properties of the liquid phase.
These single channel experiments provide a fundamental
basis for two-phase pressure drop prediction in PEMFCs.
While most fundamental work in two-phase pressure drop
focuses primarily on simultaneous air and water introduction
at the inlet of the channel, this is not representative of PEMFC
reactant channels. Continuous water introduction through
the gas diffusion layer and condensation of water vapor from
the flow stream play a primary role in changing the quality
along the flow channel length. The continuous water introduction creates a variable liquid mass flow rate, which creates
the potential for flow regime changes along the channel.
Furthermore, mass consumption of reactant gases is neglected in most studies. These factors are more aptly examined
through multichannel experiments.
4.1.3.
Instantaneous flow rate
Single channel experimentation as a simplified method to
mimic parallel channel arrangements implies that channels
will experience uniform flow distribution. However, flow
maldistribution can be inherently caused by many factors. In
2009, Kandlikar et al. [57] identified two main causes of maldistribution in parallel channels:
1) Manifold design and local pressure distribution across
inlet/exit; and
2) Uneven flow resistance (due to changes in channel geometry, flow length, and fluid properties or presence of twophase flow).
6629
Kandlikar et al. [57] proposed a technique for the experimental measurement of flow maldistribution in each of parallel channels to quantify flow maldistribution through a
minimally invasive measurement. Through the use of the
non-linear pressure drop within the entrance region, the
Hornbeck equation was used to correlate the flow rate to the
pressure drop. Pressure taps were located within entrance
region of each channel, and known flow rates were supplied to
calibrate individual flow channels. This method was then
tested using 4 circular stainless steel tubes of various lengths.
The measured flow rates averaged an error of 3.3% when
validated against established theoretical predictions. This
methodology presented by Kandlikar et al. [57] has been
employed in ex situ and in situ PEMFC flow channel studies as
well as flow distributor design [2,25,58,115].
4.2.
Parallel multichannel transport
In order to study multichannel effects on water management,
Owejan et al. [25] designed a standardized geometry 50 cm2
fuel cell that could meet the needs for in situ and ex situ
experimentation. In order to ensure the robustness of the
studies, the design was specified in accordance with the
United States Department of Energy (USDOE) performance
targets.
A channel width of 0.7 mm was selected for both anode and
cathode sides. A land width of 0.5 mm was selected for the
cathode in order to obtain a land-to-channel ratio of 1.4.
However, the anode land width was selected to be 1.5 mm for
three reasons. Firstly, reducing channels would increase the
hydrogen volumetric flow rate in each channel. Secondly, it
would increase the contact area greatly, thus reducing the
ohmic losses. Finally, it would minimize any pinching effect
between cathode and anode channels. A channel depth of
0.4 mm was selected to allow for a reasonable repeat distance
to meet the USDOE energy density targets. A channel length
(183 mm) was back calculated from peak power density predictions. The channels were arranged as parallel straight
channels, with a 15 switchback angle to prevent shearing of
the GDL and the MEA. This design was employed in various
water management studies through in situ [57,86] and ex situ
[2,58,71] experiments.
4.2.1.
Flow maldistribution
The flow maldistribution seen by Kandlikar et al. [57] led to an
investigation into how the GDL is compressed under channels
and lands of a flow field. In a following study, Kandlikar et al.
[115] investigated the GDL intrusion into the gas channel and
its effect on flow. A flow field made of Lexan with the channel
geometry suggested by Owejan et al. [25] was developed for
visualization from two sides of the channel to measure
intrusion. A confocal digital microscope (Keyence VHX-500)
was used to optically image the cross-section of the channel,
as well as to create 3-D scans of the GDL perpendicular to the
flow direction. Additionally, flow rate was measured to
quantify the effect of intrusion on the flow within the channel.
The intrusion was measured at compressions ranging from
1.03 MPa to 10.34 MPa. A minimum intrusion of 0.2 mm was
observed, while a maximum of 111.0 mm was observed at the
highest compressive pressure. At typical operating ranges, the
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observed intrusion varied between 30 and 70 mm which can
significantly constrict the flow channel. Significant variance in
the intrusion between the channels was also seen to create
significant flow maldistribution.
Lee and Lee [114]. Grimm et al. provided transition criteria
from slug to film and film to mist. For the transition from slug
to film flow, the ratio between gas inertial force and surface
tension is compared.
4.2.2.
1=0:594 ReL mG
uG ¼ 2:808We0:216
L
rG dh
Multichannel effects investigation
In order to investigate the combined result of the multichannel effects, Lu et al. [2] developed an ex situ PEMFC test
section made of Lexan with a set of 8 parallel channels, 4
water introduction chambers, and 12 water inlet holes representing an active area. The apparatus allowed for the measurement of pressure drop and individual channel flow rates,
and direct optical visualization of the flow field. The flow
conditions were tested over a range of stoichiometric ratios
from 1 to 50 for the equivalent current densities from 0 to
2.0 A cm2. Significant amounts of water holdup were noted at
the outlet manifold. Sharp spikes in the airflow rate of an individual channel were observed. These spikes were seen to be
caused by the periodic water drainage at the channel outlet.
Additionally, it was found that slug residence time in the
channel generally decreased with increase in the superficial
air velocity. At a superficial air velocity of 4 m s1 the residence
time was no longer decreased and above 7.4 m s1 the flow
maldistribution and slug flow were significantly reduced.
Using the pressure drop from various flow conditions, Lu et al.
[2] identified pressure drop signatures indicative of slug, film
and mist flow.
In 2011, Lu et al. [58] investigated the effect of surface
wettability, channel geometry, and orientation. Three surface
wettability conditions were tested including a baseline (85 ),
hydrophobic (116 ), and hydrophilic coating (11 ). The hydrophilic coating was observed to provide a more uniform water
distribution with less flow maldistribution, while hydrophobic
and baseline channels acted very comparable to one another.
Channel geometry was varied from a rectangular shape
(meant to represent laboratory studies), to sinusoidal geometry (meant to represent stamped plates), and trapezoidal
shapes (meant to represent molded plates) while the hydraulic diameter was held similar to allow for comparison.
The sinusoidal channels showed a predilection to forming
film flow due to their small corner angles with the GDL surface. Both the rectangular and trapezoidal channels acted
comparably, and formed slugs more regularly than the sinusoidal channels.
4.2.3.
(1)
For the transition from film to mist flow, the ratio between
viscous and inertial forces is compared.
("
0:64 #1=1:116 )1=1:726
rG mL
s
1:283
mG
rL mG UL
uG ¼
(2)
Grimm et al. [9] provided a flow regime differentiated correlation for the Chisholm parameter based on the model
proposed by Lee and Lee [114] for each the slug and the film
flow regimes. This parameter is a function of l ¼ u2L/(rL s dh)
and j ¼ mL (uG þ uL)/s. For the slug flow conditions, the Chisholm parameter was given by:
l0:134 j0:421
CS ¼ 1:9087Re0:405
L
0:107
1x
x
(3)
For flow conditions in the film flow regime, the Chisholm
parameter was given by:
l0:016 j1:716
CF ¼ 0:772Re0:051
L
0:034
1x
x
(4)
For the mist flow conditions, two-phase pressure drop was
given by a traditional homogeneous model where two-phase
properties are given by the correlation proposed by Dukler
[116].
mTP ¼ bmG þ ð1 bÞmL
(5)
rTP ¼
1
1 1x
þ
rG
rL
(6)
The results of these correlations are shown in Fig. 8. In the
slug flow regime, the mean error of the new pressure drop
Pressure drop modeling
The aforementioned multichannel effects can have a significant effect on the superficial velocity within a PEMFC reactant
channel. These effects must be incorporated into the twophase pressure drop models. Continuous water introduction
from the GDL into the channel must be simulated experimentally to provide the changing mass quality DTC seen in
operating PEMFCs. Due to the change in mass quality DTC in
PEMFCs, specialized pressure drop modeling techniques must
be developed.
In 2012, Grimm et al. [9] utilized a test section that provided
continuous water introduction in lieu of introduction at the
entrance. The study provided modifications to English and
Kandlikar [113] model to incorporate mass quality, as well as a
three part flow regime separated model based on the work of
Fig. 8 e Pressure drop during slug, film, and mist flow with
variable air superficial velocity and constant water flow
rate of 0.04 mL minL1. Adapted from Grimm et al. [9].
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 6 6 2 0 e6 6 3 6
model was 14%. Film flow showed a mean error of 4%. The use
of a homogeneous model yielded a mean error of 6% for the
mist flow regime. Averaged across all flow regimes the mean
error was reported as 9%.
Grimm et al. [9] also provide a single model based on the
update of the English and Kandlikar [113] correlation which
incorporates the changing mass quality into the modified
Chisholm parameter.
b
1x
C¼A
x
(7)
A ¼ 0:0856ðuL Þ1:202
(8)
b ¼ 0:004ðuL Þ0:526
(9)
Over the tested conditions, the mean error from experimental data was 14% for slug and film flow regimes. In the
mist flow regime, a homogeneous flow model was recommended. This correlation provides a balance between the
simplicity of a single correlation for all flow regimes and
compromised accuracy in very low superficial velocity ranges.
While the correlations proposed by Grimm et al. [9] predict the
two-phase pressure drop reasonably well on the cathode side,
they cannot be applied to the anode without modification to
incorporate consumption of reactants.
In 2012, See and Kandlikar [8] reviewed down-the-channel
(DTC) two-phase pressure drop modeling within the PEMFC
field. Both Grimm et al. [9] and See and Kandlikar [8] noted a
lack of a comprehensive methodology and correlation to
predict the two-phase pressure drop in the PEMFC field. See
and Kandlikar [8] proposed three key differences between
PEMFC channels and adiabatic two-phase flow literature.
Firstly, the evaporation and condensation within the flow
channel was reviewed. For most studies including evaporation and condensation, limit of thermal equilibrium is used.
This assumption can be omitted in order to capture the effect
of air flow. It was shown that with a dry inlet stream all
product water could be removed at typical operating temperature (80 C), as seen in Fig. 9.
Additionally, it was noted that in most studies that account
for water uptake, thermal equilibrium was used. This
assumption needs to be critically evaluated. Secondly, the
Fig. 9 e Cathode reactant stream’s ability to remove
product water. Adapted from See and Kandlikar [8].
6631
linkage between anode and cathode water balance through
electro-osmotic drag, thermo-osmosis, hydraulic permeation,
and back diffusion was reviewed. As noted by Dai et al. [117]
these parameters are difficult to measure individually and a
lumped coefficient, such as net water drag, was suggested. See
and Kandlikar [8] suggested that the fraction of product water
to the cathode can be used as a representative parameter for
this linkage. Lu et al. [118] reported the net water drag coefficients as a function of distance along the channel in lieu of
a constant. They introduced a spatially resolved modeling
approach around 10 discrete differential volumes within the
PEMFC. This spatially resolved modeling approach can be
extended to analyze other aspects of two-phase flow within
PEMFCs.
Finally, consumption of reactants in the channel was
evaluated by See and Kandlikar [8]. While most studies neglect
this factor, it can lead to approximately a 10% reduction in gas
superficial velocity on the cathode, and a 66% reduction in gas
superficial velocity on the anode as shown in Fig. 10. It was
noted that a simple mass balance approach adequately accounts for the mass consumption. The stoichiometric ratio
plays a critical role in the effect of consumption. As the stoichiometric ratio decreases, the rate of change in the superficial gas velocity increases significantly.
Many studies have focused on the effect of material and
consequently surface energy of the channel on flow pattern
transitions. PEMFC reactant channels are typically formed
from stainless steel, graphite, or plated alloys [119,120].
However, See and Kandlikar [8] noted that most two-phase
pressure drop studies have used alternative materials such
as Lexan channels, fused silica tubes, glass tubes, and
aluminum channels. It was also noted that the effect of
elevated temperatures has not been well investigated in the
field of two-phase flow in microchannels. It has been consistently reported that PEMFCs typically have enhanced performance at higher temperature [1]; however, the majority of
studies have been conducted at room temperature.
A new modeling was proposed using the 1D analysis with
element division in the DTC direction [8]. A step-wise
marching technique allows for the identification of flow
pattern transitions along the length of the channel. The use of
this elemental approach was selected for the identification of
Fig. 10 e Superficial gas velocity along the anode flow
channel. Adapted from See and Kandlikar [8].
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Fig. 11 e Schematic of element division. Adapted from See and Kandlikar [8].
changing flow regimes along the length of the channel. As
shown in Fig. 11, fourteen elements were utilized to represent
a typical PEMFC reactant channel. The authors highlighted
several factors, such as the length of reactant channels, stoichiometry, and operating range that affect the number/sizing
of the elements.
At each element, a control volume (shown in Fig. 12) is
evaluated for the mass balance using the steps summarized
below:
1. Mass flux of liquid water, vapor, and reactants from the
previous element, or initial condition, is evaluated.
2. Consumption of reactants is calculated using local current
density and Faraday’s Law.
3. Water production is divided between anode and cathode
using m (fraction of product water attributed to the cathode
side flow).
4. Local saturation pressure is evaluated and water uptake is
used to determine the two-phase mass quality.
5. The two-phase multiplier and pressure drop is calculated
from the correlations by Grimm et al. [9], Eqs. (7)e(9).
6. The pressure drop in each element is summed and steps
1e5 are repeated for the next element.
In Step 5, many of the widely available correlations for the
Chisholm parameter (C) can be used in the pressure drop
multiplier. However, correlations proposed by Grimm et al. [9]
have been developed specifically for the PEMFC conditions.
This proposed methodology fully incorporates the key
considerations and operating parameters that differentiate
PEMFCs from traditional adiabatic two-phase flow research.
Fig. 12 e Control volume for mass flux balance. Adapted
from See and Kandlikar [8].
This is accomplished through the use of an iterative control
volume and step-wise marching approach. Good agreement
between the model and both ex situ and in situ pressure drop
data was noted [8].
5.
Concluding remarks
As PEMFCs approach production in transportation sector,
water management remains one of the unresolved areas for
research. Understanding the effects and mechanisms of twophase flow throughout the components of PEMFCs is crucial to
the water management. An in-depth review of the current
status in this field is presented in this paper.
Gas and liquid flow through the GDL have been investigated individually by a number of researchers. The role of the
MPL in water management is probed. It has been proposed
that the cracks in the MPL stabilized the flow of liquid water
produced at the CL, although this interpretation requires
further evaluation.
Droplets which fill the corner of a channel act as a
pinning site for other droplets, which are difficult to be
removed and also aid in slug/film formation. Air flow in the
channel causes oscillations in the droplet, which determines the dynamic contact angle the droplet makes with
the channel and hence the channel corner filling condition.
Channel wall material with larger contact angle hysteresis
can accommodate larger oscillations due to air flow in the
gas channel without de-pinning from the wall surface and
fill the channel corners to form slug/film flow. A new
parameter for the blockage of the reactant paths, area
coverage ratio (ACR) was defined for defining the effect of
liquid water on fuel cell performance.
Water features on the surface of the GDL block the area
available for reactant diffusion into the GDL. This adds to the
interfacial resistance of reactant transport. ACR defines the
ratio of area blocked for reactant transport. The interfacial O2
transport resistance in PEMFC air channels was expressed
with the Sherwood Number and investigated numerically in a
3D channel. Although the fully developed Sherwood number
in the channel can be predicted through the use of reported
Nusselt number values in the literature, the impact of water
features on the Sherwood number required the use of a numerical approach. It was demonstrated that even a single
droplet can significantly affect Sh in the wake region if superficial air velocity in the channel is high enough. Droplets in
a row were shown to increase Sh with a significantly higher
intensity which can exceed a 100% increase. This shows the
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importance of characterizing the Sherwood number for
channels with droplets in a row to better predict PEMFC
performance.
Key experimental techniques, such as individual channel
flow rate measurement, optically visible test apparatuses, and
segmented PEMFCs, allowed for significant advancement of
understanding two-phase issues within PEMFC flow channels.
Significant flow maldistribution was identified through a variety of causes including manifold geometry, variation in
channel dimensions, water accumulation, and intrusion of
the GDL into the channel.
A fundamental two-phase pressure drop model has been
applied to PEMFCs and a new scheme for pressure drop predictions with constant water production and species consumption down-the-channel (DTC) has been provided. This
enhanced our understanding of DTC transport and subsequently led to the development of an elemental technique
which accurately represents the two-phase flow conditions in
a fuel cell.
Although the two-phase flow understanding of PEMFC researchers has significantly improved over the past few years,
continued research in two-phase flow is needed to elevate the
state of the art in PEMFC performance, longevity, and
durability.
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
Acknowledgments
This work was conducted in the Thermal Analysis, Microfluidics, and Fuel Cell Laboratory in the Mechanical Engineering Department at the Rochester Institute of Technology
and was supported by the US Department of Energy contract
No. DE-EE0000470. The authors gratefully acknowledge the
valuable input and material support from Wenbin Gu and
Jeffrey Gagliardo at General Motors Electrochemical Laboratory at Pontiac, MI.
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