th
Proceedings of the ASME 2012 10 International Conference on Nanochannels, Microchannels, and Minichannels
ICNNM12
July 8-12, 2012, Rio Grande, Puerto Rico
ICNMM2012-73182
A PRELIMINARY STUDY FOR 3D NUMERICAL SIMULATION OF A THROUGHPLANE TEMPERATURE PROFILE IN A PEMFC INCORPORATING COOLANT
CHANNELS
Mustafa Koz and Satish G. Kandlikar
Mechanical Engineering Department
Rochester Institute of Technology
Rochester, NY, USA
ABSTRACT
In a proton exchange membrane fuel cell (PEMFC), the
water removal from the cathode to reactant flow channels is a
critical aspect of cell operation. This is an active area of
research to understand the transport mechanisms of water. In
the available literature, it has been shown that a significant
portion of the product water is removed in vapor form by the
heat pipe effect through the gas diffusion layer (GDL). The
intensity of the heat pipe effect is dependent on the local mean
temperature and the through-plane temperature gradient across
the GDL. This gradient is spatially affected by the reactant
channel-land patterns of the bipolar plate (BPP) and the coolant
plate operation. Therefore, the heat pipe effect can have spatial
variances depending on the BPP design and cooling method.
In order to show the local temperature and through-plane
temperature gradient distribution in a GDL, a numerical
approach was taken in this work using a commercially available
software package, COMSOL Multiphysics® 4.2a. A repetitive
cathode section of the PEMFC was modeled in 3D with
domains of a GDL and BPP. In-plane thermal conductivity of
the GDL was incorporated by using experimentally obtained
values from the available literature. By changing the design and
operating conditions of the coolant system, the thermal profile
and so, the vapor flux across the GDL were investigated. It was
found that the increasing temperature non-uniformity on
coolant plates leads to less uniform distribution of vapor flux.
This is expected to lead to more condensation of water vapor
under the lands.
1. INTRODUCTION
The coupled nature of heat and water transport in a
PEMFC has a critical importance to engineer its components
for better performance. A PEMFC consumes fuel and oxidant at
the anode and cathode sides respectively. These reactants are
supplied into the cell via convection through the reactant
channels of BPPs. Once they reach to the outer surfaces of
GDLs, they diffuse through each GDL. After reactants diffuse
through GDLs, they are involved in half-cell-reactions at the
catalyst layers (CLs) and as a result, water is produced at the
cathode CL. Water at the cathode CL is distributed to the anode
and cathode BPP directions partially in liquid and vapor forms.
Their relative portions are due to the thermal condition of the
cell, such as the operating temperature and temperature
gradients. It was demonstrated in the available literature that
the liquid water ejection through the GDL can saturate the
pores of the GDL and hinder the reactant transport [1]. This
phenomenon is known as “flooding”.
It is critical to predict what fraction of water is transported
in the vapor form which is favored to decrease the possibility of
flooding of GDL pores. Burlatsky et al. took a theoretical
approach to explain the water vapor transport through a GDL
under a temperature gradient [2]. Even though both sides of the
GDL were at 100% RH, water vapor saturation pressure was a
strong function of temperature and led to a vapor concentration
gradient. The authors showed that the vapor diffusion
coefficient and thermal conductivity of the GDL define the
liquid saturation level and the vapor flux. Moreover, it was
revealed that with the appropriate choice of GDL properties, the
majority of the water can be transported in vapor form.
Therefore, thermal gradients in a GDL were proved to have
critical importance on water management.
As a part of their work, Owejan et al. measured the vapor
diffusion flux under various RH and/or temperature gradients
[3]. With 100% RH on the microporous layer (MPL) side of the
GDL, a vapor flux equivalent to the water generation at 1.5
A/cm2 could be achieved either by keeping the other side of the
GDL at 50% RH irrespective of the temperature gradient or
inducing an 8 oC temperature difference irrespective of the RH
gradient. This work experimentally confirmed the significance
of thermal gradients in the GDL on the relative portion of vapor
water transport.
In the 3D two-phase numerical model of Ju, the effect of
anisotropic thermal conductivity of the GDL was investigated
[4]. A GDL with an in-plane thermal conductivity value that
was the same as through-plane value resulted in significant
temperature peaks under reactant channels and cooler regions
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Copyright © 2012 by ASME
under the lands. A GDL with realistic thermal conductivity for
the in-plane direction (10 times the through-plane one)
smoothed out the temperature peaks and resulted in a more
uniform temperature increase. After this modification of
thermal conductivity, a temperature decrease of 1.5 and 2.5 oC
was observed in the membrane under the lands and channels
respectively. These values were comparable to the required
temperature differences across the GDL to remove a significant
portion of water in vapor form [3]. Lower thermal gradients
established by high in-plane thermal conductivity values led to
higher saturation values in the GDL, not only under the lands
but also under the reactant channels. This model showed the
impact of the GDL anisotropy and channel-land pattern of the
BPP on the thermal profile and so, the vapor flux in a fuel cell.
He et al. built a 3D, two phase numerical model of a
complete cell to show the effect of GDL thermal conductivity
anisotropy [5] as in the work of Ju [4]. In addition to
confirming the conclusions of Ju et al., their larger scale model
showed the increased liquid saturation in the membrane closer
to the outlet of the reactant stream. Downstream regions
provided higher current densities but were more prone to
flooding. Similar observations were also reported by Owejan et
al. in their in situ experimental work utilizing neutron
radiography [6]. Both works [5, 6] showed that the two phase
transport of water in the cell along the reactant flow was not
uniform. Thus, additional non-uniformities along the reactant
flow, such as temperature imposed by the cooling system,
should either be eliminated or be engineered in such a way that
they can be used in favor of the cell.
The numerical and experimental observations above [5, 6]
on dry-out at inlets and flooding at the outlets were taken as the
main investigation focus for the 3D, two-phase fuel cell model
by Yang et al. [7]. This model was based on a full length,
straight reactant channel with a repetitive pattern for a cell.
Constant temperature boundary conditions which were applied
on the BPP lands led to a non-uniform water saturation
distribution. Therefore, an increasing temperature boundary
condition was applied from the inlet to outlet. This led to a
more homogenous water distribution in the cell. It was reported
that even though the temperature ramp on the BPP created
highly saturated regions under the lands near the inlet, the
reactant rich flow at the upstream could still provide enough
diffusion to the CLs.
In order to correctly impose temperature boundary
conditions on BPPs, numerical studies have been conducted on
coolant plates in the available literature. The coolant plates are
simulated commonly isolated from the rest of the cell with an
evenly distributed heat flux on their one side. These works aim
to minimize temperature variations on the coolant plate-BPP
interface. The 3D numerical model of Yu et al. presented
different designs and evaluated them with a non-uniformity
index [8]. The performance of each design was reported for
different flow rates and the corresponding pressure drops. Baek
et al. [9] improved the work of Yu et al. [8] by introducing
more complicated designs on larger coolant plates. A deeper
review on the coolant plates was also provided by Zhang and
Kandlikar [10]. However, none of the works mentioned above
[8, 9] incorporated fuel cell components to show if the actual
boundary conditions on the BPPs matched with their
predictions.
Regarding the works mentioned above, there are certain
possibilities of research extension to further refine the thermal
transport models for PEMFCs. The first refinement can be
performed on the constant temperature boundary conditions
imposed on the BPP. On the one hand, numerical models
showed that small temperature variations can lead to different
vapor transport characteristics [4, 5], and on the other, isolated
coolant plates were numerically analyzed to have significant
temperature variations on them [8, 9]. Hence, it is proposed to
question the accuracy of applying a constant temperature
boundary condition on the BPP. The second area is the
anisotropy of the GDL. It was shown in the literature that the
thermal and vapor flux profiles in the cell can be significantly
affected by the anisotropy. However, it was not shown in detail
how the anisotropy in the GDL alters the vapor flux profile in
the cell.
In this numerical work, the cathode side of a PEMFC was
modeled three dimensionally under steady-state conditions. It
consisted of two different coolant channel designs, namely:
straight pass and serpentine coolant channels that were parallel
and perpendicular to reactant channels respectively. Normally
coolant channels are integral components of a BPP. In this
work, the coolant system was integrated in a separate coolant
plate. Moreover, only the cathode side was simulated.
Therefore, the BPP will be referred to as a unipolar plate (UPP)
in the following text. The models in this work for the PEMFC
cathode side consisted of a coolant plate, UPP and GDL. The
entire cell was maintained at 100% RH to isolate the effect of
the thermal gradient on the vapor flux across the GDL. As the
input parameters, the operating conditions for the two coolant
plates and the GDL in-plane thermal conductivity were varied.
As a common figure of merit from the literature, the local
temperatures on the heated surface of the GDL were reported.
Moreover, the temperature profile in the GDL was also utilized
to obtain local, through-plane thermal gradients in the GDL.
Local temperatures and thermal gradients were input to the
non-linear vapor saturation pressure formula, and the local
vapor fluxes under the UPP lands and channels were obtained.
Lastly, vapor flux non-uniformities were calculated to predict
areas which may show a different liquid saturation.
NOMENCLATURE
Greek
α
β
Φ
ψ
ρ
2
Coolant channel cross section aspect ratio
Relative vapor flux non-uniformity index
Water vapor flux
Area averaged relative vapor flux non-uniformity
index
Mass density
Copyright © 2012 by ASME
Roman Letters
A
Area
BPP
Bipolar plate
C
Vapor concentration
CL
Catalyst layer
CP
Heat capacity
d
Depth
h
Heat transfer coefficient
k
Thermal conductivity
L
Length
N
Number of coolant channels per module
Nu
Nusselt number
q"
Heat flux
Q
Volumetric flow rate of coolant
RH
Relative humidity
t
Thickness
T
Temperature
UPP
Unipolar plate
W
Width
Subscripts
ac
Active area
av
Surface averaged
cc
Coolant channel
ch
Base area of the reactant channel interfacing GDL
cl
Coolant channel land
cp
Coolant plate
CS
Cooled surface
f
Fluid
GDL
Gas diffusion layer
h
Hydraulic Diameter
HS
Heated Surface
in
Into the domain
in-plane In-plane direction property
land
Reactant channel land
out
Out from the domain
p
Repetitive pattern
rc
Reactant channel
sat
Vapor saturation
T
Constant temperature
w
Heated wall
2. METHODOLGY
2.1 Geometrical Design of the Domains
The numerical models in this work were solved for two
coolant plate designs. Both designs were incorporated with an
electrochemically active cathode area of almost 50 cm2 due to
its dimensions Lac=180.0 mm and Wac=27.3 mm [6]. The first
coolant design was a serpentine channel configuration and its
coolant channels and reactant channels are projected on the cell
active area in Fig. 1. The cathode active area was divided into
three coolant modules that each consists of 15 channels (N=15).
Repetitive Pattern
Tin
N channels
Tout=TN
Reactant Channel
Coolant Channel
Coolant Module
Boundaries
z
CoolantFluid
Temperature
x
Lac=180 mm
mm
Wac=27.3 mm
FIGURE 1: FUEL CELL CATHODE
mmACTIVE AREA
(NUMBER OF CHANNELS AND DIMENSIONS DO NOT
REFLECT THE ACTUAL DESIGN).
A repetitive pattern encapsulating one reactant channel was
chosen from the middle line of the cathode active area. The
black points in the figure above will later be used to impose
coolant fluid temperatures. The 3D projection of the drawing
above for one coolant module is shown in Fig. 2. To better
demonstrate the repetitive pattern, the full cathode geometry is
cut from the left symmetry plane used in the simulations.
Figure 2 shows the serpentine coolant channels crossing the
domain and their flow direction arrows. In simulations,
symmetry planes on both the left and right were used to
simulate only the repetitive pattern. The CL layer was
represented as a heated surface to introduce the dissipated
energy into the domain.
Repetitive
Pattern
Coolant
Plate
Water in
Tin
UPP
Water in
Tin
GDL
GDL
Heated
surface
z
y
Water
out
Left
Symmetry
x Plane Tout=TN
Heated
surface
Water
out
UPP
FIGURE 2: 3D MODEL FOR THE CATHODE SIDE.
(CHANNEL NUMBER IS REDUCED)
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Copyright © 2012 by ASME
The dimensions for the repetitive block are given in Fig. 3.
Its length is consistent with the active area length, Lac=180.0
mm. The BPP design meeting the United States Department of
Energy transportation targets [6] was used to the define reactant
channel width and depth
(Wrc, drc), and the repetitive UPP
pattern width and thickness (Wp, tUPP).
Symmetry
Planes
Coolant
Plate
tUPP
tcp
Repetitive
Block
Serpentine
Straight
dcc
(mm)
1
0.6
Wcc
(mm)
2
0.5
Wcl
(mm)
2
0.7
tcp
(mm)
2
1
TABLE 1: DIMENSIONS FOR COOLANT PLATE.
Table 2 below presents the geometrical parameters shared
by the both designs. The GDL thickness, tGDL was assumed to
be 200 µm.
Wp
drc
dcc
Wrc
drc
(mm)
0.4
UPP
Lands
Coolant
Channels
UPP
Channels
Wcc
Wcl
Wrc
(mm)
0.7
Wp
(mm)
1.2
Wac
(mm)
27.3
Lac
(mm)
180
tGDL
(mm)
0.2
tUPP
(mm)
0.7
TABLE 2: DIMENSIONS FOR UPP AND GDL.
2.2 Governing Equations and Boundary Conditions
In the 3D geometrical domain presented above, the steadystate heat conduction equation was solved with no heat sources
or sinks.
z
y
x
(1)
FIGURE 3: DIMENSIONS FOR SERPENTINE COOLANT
PLATE DESIGN.
The second coolant plate design was a straight pass coolant
channel configuration. The coolant channel depth was taken
from the same design paper by Owejan et al. [6]. This design
had straight coolant channels that were parallel to the reactant
channels. The active area was consistent with the last one. The
cross sectional drawing for this design is presented in Fig. 4.
Symmetry Planes
Wcc/2
tcp
Coolant
Channels
dcc
Wcl
y
tUPP
x
Wp
UPP Channel drc
Wrc
Heated Surface
UPP
The UPP and coolant plate had the same thermal
conductivities (k) to mimic the heat transfer characteristic of a
BPP. In order to accentuate the imposed in-plane temperature
variances due to the coolant plate design, the thermal
conductivity of the UPP and coolant plate was chosen as the
lowest as found in the literature. As in the numerical models
cited previously [6, 7], k is chosen to be 20 W/(m.K).
The GDL thermal conductivity is anisotropic unlike the
UPP and coolant plates. Therefore, the scalar k in the heat
conduction equation was replaced with a matrix, kGDL. As seen
below, the in-plane thermal conductivity was left as a
parametric value to analyze its effect. The experimentally
obtained 0.55 W/(m.K) value for Spectra Carb GDL with 11%
PTFE content and under 1.4 MPa compression was used as the
through-plane conductivity in all simulations [11]. In
simulations of comparison, kin-plane was either assumed to be
equal to 0.55 W/(m.K) or set to its experimentally derived value
(Spectra Carb GDL with 12% PTFE) of 9.73 W/(m.K) [12].
These two cases are referred to as isotropic and anisotropic
GDLs.
GDL
FIGURE 4: DIMENSIONS FOR THE CROSS SECTION OF
STRAIGHT PASS COOLANT PLATE DESIGN.
(2)
The dimensional differences for the coolant plate designs
are presented in Table 1. Smaller coolant channels and narrower
coolant lands were utilized for the straight pass design. The
total flow was divided into three inlets in the serpentine design
whereas it was divided into 22 in the straight pass design.
As shown in Fig. 2 and 4, on the heated surface of the GDL
(facing catalyst layer), a uniform heat flux boundary condition
of 6600 W/m2 was imposed to represent the heat generation at
1.5 A/cm2 and 0.6 V at 70 oC with an anode-cathode
distribution assumption of 50%. The heat flux distribution is
non-uniform in the real cell operation, especially at high current
densities. However, this work omitted the thermal non-
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Copyright © 2012 by ASME
uniformities due to electrochemical reactions for isolating the
effects of reactant channel-BPP land pattern, and the coolant
plate. Moreover, the obtained non-uniformities in this work are
the minimum values due to the aforementioned and inevitable
design constraints. Non-uniform current density will have an
additional contribution on non-uniformities.
(3)
The system was designed to be cooled by water through
the coolant channels. The convective cooling effect of the
reactant channels was neglected in this model. Heat was
removed only by the surfaces of coolant channels. To reduce
the computational cost of the model, instead of solving for
coolant transport equations, a heat transfer coefficient (h)
boundary condition was imposed on the channel walls along
with varying coolant fluid temperature (Tf) in the direction of
reactant flow. The local heat flux leaving the coolant channels
surfaces was given as:
dependent on the total volumetric flow rate, Q: 0.3, 0.6, 1.2, 1.8
x 10-6 m3/s. The Q values were chosen according to the work of
Baek et al. [9] by scaling their Q values according to the active
area ratio between this work and theirs.
(9)
where water properties are, ρ: 971.80 kg/m3 and Cp: 4198
J/(kg.K).
In this numerical model, 70 oC coolant temperature was
targeted at each coolant outlet. Therefore, the cell could operate
around 80 oC which was an optimum value. In order to achieve
this, each calculated ΔT for a coolant flow rate was subtracted
from the limit of Tout=70 oC and the resulting temperature was
assigned as the Tin. Tf along the reactant channel was
interpolated between Tout and Tin as a continuous expression in
the straight pass design.
(10)
(4)
The coolant channels were assumed to be at constant
temperature which leads to the use of constant temperature
boundary condition Nusselt number (NuT) which is a function
of channel cross section aspect ratio (α).
(5)
Dh is the hydraulic diameter of the coolant channel:
(6)
whereas Tf was calculated discretely for the serpentine coolant
channel design:
(11)
while 1 ≤ n ≤ N and n is the order of a coolant pass in a
serpentine coolant module from inlet to outlet.
2.3 Post Processing
After the distribution of temperature in the domain was
obtained as a result of the simulation, the thermal gradient
between the heated and cooled surfaces of the GDL was
calculated:
The water thermal conductivity, kf is 0.62 W/(m.K) and
NuT is as given by Kakac et al. [13]:
(7)
(8)
The coolant fluid temperature increases as it accumulates
heat. The change of fluid temperature was assumed to take
place only along the reactant channel. Therefore, straight pass
coolant channels kept accumulating heat across the domain in a
continuous manner. Contrarily, serpentine coolant channels
formed three modules which were designed to share the total
heat dissipation along the reactant channels. Therefore, at the
transition between each coolant module, a relatively cooler
fluid was introduced into the system. This disrupted the
temperature rise along the reactant channels at two different
interfaces.
The coolant temperature rise in one serpentine coolant
channel module and in a straight pass coolant channel (ΔT) was
(12)
Both sides of the GDL were assumed to have 100% RH
without any condensation in between. At this equilibrium, the
partial pressure of the water vapor in the air (Psat) was
equivalent to the saturation pressure of vapor (Pvap).
(13)
The saturation pressure of the water vapor is given by the
correlation [14] where T is in Kelvin:
(14)
5
Copyright © 2012 by ASME
The water vapor concentration (C) in the air corresponding
to a partial pressure was obtained with the following equation:
(15)
where Pvap and T are in Pascal and Kelvin respectively.
The through-plane vapor flux (Φ) was calculated as below
by using the vapor concentration at both sides of the GDL and
neglecting the in-plane vapor diffusion:
(16)
The effective diffusivity of water vapor through a Grafil U105 GDL (Deff) was obtained experimentally as 0.104x10-4 m2/s
by LaManna and Kandlikar [15]. This value was incorporated
into this model to calculate the through-plane vapor flux.
The concentration variation from the heated to the cooled
side of the GDL was assumed to be linear since the variation of
Psat around 70 oC for temperature changes less than 4 oC was
found to be linear [2].
The area averaged vapor flux (Φav) was defined for two
GDL subdomains which were regions under the reactant
channel (Φav,ch) and lands (Φav,land). They were encapsulated by
the repetitive pattern.
(17)
In addition to area averaged vapor fluxes, it was important
to quantify the non-uniformity of vapor fluxes under the
channel and lands separately. In the work of Baek et al. [9], a
temperature non-uniformity index was already defined to show
the intensity of temperature variations on the heated surface of
a coolant plate. This parameter was adopted for vapor flux, Φ
by dividing the non-uniformity index by Φav to obtain the area
averaged relative non-uniformity index, ψ:
between the mesh nodes. With the settings mentioned, the
straight and serpentine coolant channel designs led to 2 and 4.7
million degrees of freedom. The models were solved with 10-3
relative tolerance by generalized minimal residual method
which utilizes geometric multigrid solver.
3. RESULTS & DISCUSSION
3.1 Introduction of Figure of Merits
The straight pass channel design was first analyzed by
linking its temperature map and temperature gradients in the
GDL to vapor flux variations. A fundamental understanding
was aimed to be achieved on the dependency of the
aforementioned parameters on the GDL anisotropy and coolant
flow rate. This understanding would later be utilized to explain
the dependency of the vapor flux and its non-uniformity of both
coolant designs on the coolant flow rate and GDL anisotropy.
It was important to analyze the local temperature variations
at the heated surface of the GDL because they would lead to
locally different water carriage capacities. The temperature
mappings for the heated surface of the isotropic GDL are
shown in Fig. 5. The cases with the minimum and maximum Q
values are compared against each other in an isotropic GDL.
The results show that at both flow rates, the temperature
variation normal to the reactant channel remained constant,
around 4 oC. The temperature variation along the reactant
channel was reduced significantly with the increased coolant
flow rate. However, even at the highest flow rate it was not
possible to call the heated surface isothermal.
In addition to the isotropic GDL, the anisotropic GDL was
also analyzed without presenting a figure here. The temperature
variations normal to the reactant channels were eliminated.
Only the temperature variation along the reactant channel
remained. Therefore, the anisotropy of the GDL heat
conductivity is very useful to eliminate the temperature
variation at the heated surface due to the high thermal
resistance that reactant channels introduce.
a
Land & Reactant Ch.
Boundaries
Coolant & Reactant
Flow
(18)
(oC)
Land & Reactant Ch.
Boundaries
b
(19)
x
2.4 Numerical Implementation
The 3D numerical model explained above was solved with
COMSOL Multiphysics® 4.2a. In order to refine the thinness of
the GDL, it was meshed with 4 elements in the through-plane
direction. By exploiting the regularity of the straight coolant
pass geometry, a surface mapped mesh was extruded in the
coolant channel flow direction. However, the serpentine coolant
channel design was meshed with free tetrahedrals. Quadratic
elements were used to interpolate the temperature values
Coolant & Reactant
Flow
(oC)
z
FIGURE 5: T DISTRIBUTION AT y=yGDL,HS AND FOR THE
ISOTROPIC GDL WITH STRAIGHT PASS COOLANT
CHANNELS: (a) Q=0.3x10-6 m3/s, (b) Q=1.8x10-6 m3/s.
Another parameter that affected the water flux through the
GDL (Φ) was the ΔT between the heated and cooled surface of
the GDL. A higher magnitude of the ΔT would lead to a larger
difference of vapor concentration and so, higher Φ. Hence, the
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Copyright © 2012 by ASME
distribution of ΔT provided an insight about the high Φ areas.
The ΔT profile chosen from the mid-height of the active area
(z=Lac/2) is shown in Fig. 6. However, this ΔT profile does not
show any variation at different heights (z) or at different flow
rates (Q). In Fig. 6, variations of ΔT for isotropic and
anisotropic GDLs are shown. The most significant difference
between two profiles is the overshoot of ΔT at the land-reactant
channel boundaries in the isotropic GDL. This is mainly due to
the poor in-plane conduction in the isotropic GDL. Both GDLs
utilized land areas to remove all the heat accumulated under the
reactant channel. However, the isotropic GDL did not have the
same capacity to distribute the heat flux on the x axis as the
anisotropic GDL had. Therefore, the through-plane heat
conduction was concentrated at the land-reactant channel
boundaries in the isotropic case whereas the through-plane
conduction was much more uniform for the anisotropic case.
When profiles were compared, the anisotropic GDL provided a
ΔT which was lower under the lands and higher under the
reactant channel. ΔT peaks in case of the isotropic GDL were
expected to introduce highly concentrated vapor flux areas at
the boundary between the reactant channel and lands.
Moreover, the uniformity of the ΔT profile was much higher for
the anisotropic case.
significantly closer to the outlet. Moreover, even though the ΔT
does not differ along the reactant channel direction, the same
ΔT corresponds to higher concentration differences at higher
local temperatures due to the non-linear nature of vapor
saturation pressure, as presented in Eq. 14.
Figure 7b shows the scenario with the highest Q. Due to
high Q, the heated surface of the GDL had a much lower
temperature variation and the regions in the upstream areas
were warmer, as presented in Fig. 5b. This led to a nonuniformity distribution that varied much less along the reactant
channel direction. Moreover, the intensity of the variations
decreased with the increased Q. Another detail that is not
presented in Fig. 7 is the effect of the anisotropic GDL on the β
profile. When the GDL property in Fig. 7 is switched to
anisotropic, the main trend in each subfigure remains the same
but the intensity of the non-uniformities is observed to
decrease. This can be correlated to the observations presented
for Fig. 6 which showed that the anisotropic GDL reduces the
ΔT overshoot at the channel-land boundary.
a
Land & Reactant Ch.
Boundaries
Coolant & Reactant
Flow
(%)
Land & Reactant Ch.
Boundaries
b
Land-Reactant
Boundaries
Coolant & Reactant
Flow
x
(%)
z
FIGURE 7: β IN THE STRAIGHT PASS COOLANT CHANNEL
DESIGN, ISOTROPIC GDL:
(a)Q=0.3x10-6 m3/s, (b) Q=1.8x10-6 m3/s.
FIGURE 6: ΔT ACROSS THE GDL WITH STRAIGHT PASS
COOLANT CHANNELS, z=Lac/2, Q=0.3x10-6 m3/s.
By using the observations from Figs. 5 and 6, the relative
vapor flux non-uniformity (β) distribution for the isotropic
GDL can be analyzed with respect to the varying Q. In Fig. 7,
as introduced in Eq. 18, each vapor flux variation is presented
relative to the average vapor flux of subdomains, such as the
land or channel areas. Therefore, the same β values on different
subdomains corresponded to different Φ values. The subdomain
specific Φav values will be presented in detail later.
In Fig. 7, β values are presented for the isotropic GDL at
the lowest and highest coolant flow rates. The black areas in the
figures represent the transition between Φ values that are higher
or lower than the subdomain average, Φav. Figure 7a presents
the case with minimum Q. The non-uniformity increased closer
to the downstream due to the increased temperature of the
coolant. As previously shown in Fig. 5a, there is a temperature
increase around 16 oC from the inlet to outlet on the heated
surface of the GDL. This increased the water carriage capacities
3.2 Parametric Dependence of Figure of Merits
Figure 8 demonstrates the area averaged water flux values
(Φav) in subdomains under the lands and reactant channel of the
straight pass design with respect to the coolant flow rate, Q.
Regardless of the subdomain or GDL type, Q had a positive
effect on the Φav. This increasing trend became less significant
as Q rised and can be considered negligible for Q higher than
1.2x10-6 m3/s. As shown in Fig. 5, the GDL heated surface
temperature approaches to a higher average value and becomes
more uniform as Q increases. This led to higher vapor
concentration differences across the GDL as it was explained
by the non-linear nature of the vapor saturation pressure. In
addition to the parameter Q, the type of GDL has a significant
effect on the Φav because the GDL type affects the ΔT profile
under the lands and reactant channel differently as shown in
Fig. 6. It was observed that Φav,land decreased with the increased
in-plane conductivity of the GDL whereas Φav,ch increased. The
ratio between Φav,land and Φav,ch remained the same with Q.
However, this ratio can only be affected by the type of GDL.
Φav,land/Φav,ch is 192% and 140% for the isotropic and
anisotropic GDLs respectively.
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Copyright © 2012 by ASME
pores will affect Deff used in this model locally. Therefore, the
results presented here are only guidelines to predict which areas
are prone to suffer more from flooding under the lands.
It can be concluded from Fig. 9 that the flooding under the
lands that becomes significant at the downstream can be
prevented by operating the coolant stream at a minimum Q of
1.2x10-6 m3/s. Switching from the lowest to the highest Q
reduced ψland from 24.2% to 10.8 and from 22.6% to 3.5% for
isotropic and anisotropic GDLs respectively. This reduced the
non-uniformity of vapor flux along the reactant channel. The
remaining non-uniformity, clearly shown at the land-reactant
channel boundaries in Fig. 7, can be reduced by the use of
GDLs with higher in-plane thermal conductivities.
FIGURE 8: Φav IN THE STRAIGHT PASS COOLANT
CHANNEL DESIGN.
The Φav values presented in Fig. 8 and their variations due
to GDL type and Q are comparable with water generation rates
in a typical PEMFC. As stated by Owejan et al., the water
generation rate at 1.5 A/cm2 corresponds to around 1.4 g/(m2.s)
[3]. Owejan et al. achieved this flux of water vapor across a
Toray TGP-H-060 GDL with a microporous layer by imposing
a ΔT of 4 oC across the GDL while both sides of it were at
100% RH [3]. In Fig. 8, similar vapor fluxes are obtained under
the lands by having a ΔT of 3-4 oC with the compensation effect
of a higher diffusivity used in this work.
The area averaged vapor flux non-uniformity values, ψ are
presented for the straight pass design in Fig. 9. This parameter
depicts how non-uniformly the vapor flux was distributed in
subdomains under the lands and reactant channel. All ψ values
shown in Fig. 9 are decreased by the increased Q. This is the
result of smaller temperature rises taking place in the coolant
fluid. Therefore, a warmer GDL led to higher vapor fluxes as
shown in Fig. 5 and 8 and this decreased the relative magnitude
of non-uniformities. It can be concluded from Fig. 9 that all the
non-uniformities along the reactant channel direction can be
prevented by reaching to a coolant flow rate of 1.2x10 -6 m3/s.
Even though the lands of the anisotropic GDL show a
decreasing trend after 1.2x10-6 m3/s, the ψ value under 5%
makes it negligible.
Figure 9 demonstrates that in the isotropic GDL, the
subdomain under the reactant channel is occupied by the
highest ψ. The subdomains under the lands of the isotropic
GDL and under the reactant channel of the anisotropic GDL
share the same ψ. The land of the anisotropic GDL has the
lowest ψ in the whole range of Q.
In addition to the trends discussed above, it is important to
state that the non-uniformities of vapor flux under the reactant
channel is not as important as lands because channel interfaces
may provide open surfaces for vapor to be carried away by
convection. However, the vapor flux under the lands will either
be distributed to reactant channels by in-plane diffusion or lead
to condensation and capillary forces will start taking effect. In
the condensation case, the pores in the GDL will be saturated
which was not taken into consideration here. The saturation in
FIGURE 9: ψ IN THE STRAIGHT PASS COOLANT CHANNEL
DESIGN.
The area averaged vapor fluxes in Fig. 10 show very
similar trends to those shown Fig. 8. The major difference
between Fig. 8 and Fig. 10 is the fact that the serpentine coolant
design offered a more uniform temperature distribution on the
heated GDL surface and this is why the serpentine design led to
7% and 8.3% increases of Φland,av and Φchannel,av respectively for
both types of GDLs at the highest flow rate.
Another contribution of the serpentine channel coolant
design compared to straight pass coolant channel design is
shown in Fig. 11 with the surface averaged relative vapor flux
non-uniformity parameter, ψ. The trends of Fig. 9 are observed
also in Fig. 11. However, non-uniformities at low Q are lower
in Fig. 11 than in Fig. 9. For instance, at the lowest Q,
serpentine coolant channel design decreased ψland by 6.3% and
7.5% in isotropic and anisotropic GDLs respectively. For Q
higher than 0.6x10-6 m3/s, the non-uniformity differences are
negligible.
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Copyright © 2012 by ASME
FIGURE 10: Φav IN THE SERPENTINE COOLANT CHANNEL
DESIGN.
FIGURE 11: ψ IN THE SERPENTINE COOLANT CHANNEL
DESIGN.
From the non-uniformity results presented in Fig. 9 and 11
it can be inferred that the coolant plates should run at a
minimum value Q of 1.2x10-6 m3/s to eliminate nonuniformities of vapor flux along the reactant channel. In order
to identify the functionality of the remaining non-uniformities,
more complex numerical simulations should be performed. It
was shown in Fig. 6 and 7 that in the isotropic GDL case, the
vapor flux under the lands and reactant channel is concentrated
at land-reactant channel boundaries. This condition may have
advantages and disadvantages to be identified by further
simulations. On the one hand, the consequent condensation
concentrated under the land-reactant channel boundary can be
pushed into the reactant channel easier compared to uniformly
distributed condensation under the land; and on the other, the
concentrated condensation under the land-reactant channel may
need to build a thicker condensation front which may block the
reactant diffusion more adversely.
CONCLUSIONS
A 3D, steady-state, numerical model was solved by
COMSOL Multiphysics 4.2a for the full length cathode side of
a PEMFC. The model incorporated two different designs of
water utilized coolant plates, namely straight pass and
serpentine coolant channel. The thermal effects of the coolant
plate designs, their operating conditions and the anisotropy of
GDL thermal conductivity were analyzed by temperature
distributions, thermal gradients, through-plane vapor fluxes and
their non-uniformities in the GDL. The following conclusions
are derived from the results obtained:
The uniformity of temperature is essential in the GDL to
maximize the available vapor flux capacity. This uniformity can
be achieved by high coolant flow rates (larger than 1.2x10-6
m3/s for a 50 cm2 active area cell) and improved by preferring a
serpentine coolant channel design over a straight pass design.
This ensures the cell two-phase transport dynamics show
smaller variations along the reactant channels.
The effect of GDL anisotropy, in other words, higher inplane thermal conductivity is twofold: Firstly, it smoothes out
the thermal gradient peaks formed under the isotropic GDL
boundaries between UPP lands and reactant channels.
Therefore, vapor fluxes are distributed more evenly under the
lands and reactant channel than the isotropic GDL case.
Secondly, GDL anisotropy increases vapor fluxes under the
channels and while decreasing the fluxes under the lands.
The results presented in this paper did not incorporate a
coupled heat transfer with the mass transport. In a coupled
model, heat can be removed through GDL by the diffusion of
vapor in addition to conduction. Therefore, the effect mass
transport on the thermal profiles in the GDL will be
investigated in the future work.
ACKNOWLEDGMENTS
Support for this project was provided by the US
Department of Energy under award number: DE-EE0000470.
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