The 19th International Symposium on Transport Phenomena,
17-20 August, 2008, Reykjavik, ICELAND
Simulation of heat and mass transport in gas flow streams of a PEMFC from water management
perspective
1
1
1
J. LaManna , R. Underhill , and S. G. Kandlikar
1
Department of Mechanical Engineering
Rochester Institute of Technology, Rochester, NY, USA
ABSTRACT
The paper presents an in-depth review of the available
models for simulating heat and water transport in the gas
channels and diffusion layers of a PEMFC. Water
management plays a critical role in the efficient operation
of a fuel cell. Temperature gradients can result in
changes in the concentration and phase of water thus
closely coupling heat transfer with water management.
This paper presents the literature review and basic
governing equations used in each model’s development.
INTRODUCTION
With the current energy outlook and rising concerns for
the environment, alternative energy sources are
currently being sought. Automotives are an area which
uses large amounts of energy and significantly adds to
greenhouse gas emissions. The Proton Exchange
Membrane (PEM) fuel cell is currently under
development as an alternative to the internal
combustion engine. In this role performance will be
critical from the fuel cell. Performance of a PEMFC is
significantly affected by the water content within the cell
and therefore the water management abilities of the cell.
Modeling of the Gas Diffusion Layer (GDL) has
become an important tool within the past few years to
understand water management issues within the fuel
cell. Water management is critical within PEM fuel cells
because of the need to keep the membrane hydrated
while at the same time trying to keep the water levels
as low as possible to allow for unimpeded reactant gas
transport.
Liquid water levels in the GDL are
determined by the temperature gradients experienced
by the water across the GDL. This dependence on
temperature gradients strongly ties heat transfer with
water management
Early models such as by Springer et al. [1] and
Cheng et al. [2] made isothermal assumptions which
did not allow for an accurate insight of water
management. Other authors have shown the effects of
non-isothermal models [3-10]. These non-isothermal
models have shown that temperature gradients could
exist across the GDL and these gradients can be
significant enough to cause phase changes of water.
Single-phase models were used to investigate
diffusion of reactant gases and transport of liquid water
through the GDL. Single-phase models assume that
water remains in the vapor phase as it is transported
out. These models [11-13] do not capture the true
conditions within the fuel cell since liquid water will
inevitably form. Developed from soil mechanics for the
use in fuel cell porous material analyses, pore-network
models [14-17] have been used to track how liquid
water transports through the pore structure of the GDL.
Pore-network models typically assume a generalized
framework that approximates the structure of the GDL.
To determine how liquid water interacts with
oxygen diffusion during cell operation, two-phase
models have been implemented.
These models
account for the removal of product water from the
catalyst layer and the counter-flow of oxygen gas.
Some authors [18-24] analyzed the two-phase flow with
the assumption that water is generated in the liquid
phase and remains in this phase as it transports
through the GDL, while others [25-28] account for the
phase change of water.
Hwang [29] developed a model to investigate the
effects of phase change of water and the formation of
condensation zones within the GDL. The results of
Hwang’s work are significant because it could show that
there is another cause to reactant gas mal-distribution
within the catalyst layer above the channel land areas.
Liu et al. [30] investigated how a mixed-wet GDL
affects the performance of a fuel cell. A mixed-wet
GDL represents a structure consisting of a distribution
of hydrophobic and hydrophilic pores. This framework
better models the actual structure of the GDL as the
Teflon treatment actually leaves regions that are
hydrophilic. The work performed by the authors is
significant as many models assume that the GDL is
strictly hydrophobic which could skew the actual water
saturation levels within the GDL.
Modeling of the cathode gas channel has also
aided in the understanding of water management
issues within PEM fuel cells. The gas channel holds a
significant role in pulling water from the GDL and
allowing for the diffusion of oxygen into the porous
medium. As in the GDL, heat transfer and water
management can be closely coupled in gas channels.
The gas channel is often modeled in terms of its
interface with the GDL as demonstrated by Wang et al.
[24] and Matamoros and Brüggemann [7]. Many models
have gone into greater detail as to the processes within
the channel. Early research within the gas channel
such as Hu et al. [21] and You and Liu [31] focused on
the transport of gases within the channel and at the
GDL interface. Vynnycky and Birgersson [32] and Li et
al. [33] generated greater focus on water vapor in the
channel in their modeling efforts. Lin [34] expanded
upon the diffusion-based models with the inclusion of
convective affects upon gas transport in the channel.
Berning et al. [3] provided a model for heat transport for
gases in the channel with varying oxygen
concentrations.
Other research has been conducted in the area of
liquid water transport. Jiao and Zhou [35] produced a
three-dimensional model for transport of liquid water
and air. Maharudrayya et al. [36] analyzed flow
The 19th International Symposium on Transport Phenomena,
17-20 August, 2008, Reykjavik, ICELAND
Table 1. Comparison chart of selected papers.
Ref
#
Author
Year
[29] J.J. Hwang 2007
[30]
Z. Liu, Z.
Mao, C.
Wang
2006
V.P. Schulz,
J. Becker, A.
Wiegmann,
[19]
2007
P.P.
Mukherjee,
C.Y. Wang
General
Equations
Model Approach
momentum
equation based
two-phase flow
and nonequilibrium
(LTNE) heat
transfer model
Model simultaneously
tracks velocity,
temperature, and
current. Model is
capable of tracking the
phase equilibrium front
within the GDM
Model Verification
Experimental
verification
GDL
characterizing
[34]
2007
Gas diffusion terms
calculated with
inclusion of axial
convection in the gas
channel
N/A
Found relationships between
contact angle and pressure
drop as well as water content in
Strength lies in
cathode gas channel. Pressure
determination of stress
drop increased with decreasing tensors at liquid water/ air
contact angle. A bell-curve
interface
relationship was formed for
water content.
Darcy flow,
averaged
isotropic
properties
Found oxygen depletion along
Isothermal assumptions
length of gas channel as well as
innapropriate for modelling.
increasing isothermality. Partial
Heat transfer significant in
dehydration of membrane also
water removal calculations
found
N/A
Gas flow modeled from
continuity, momentum
non-isothermal,
Checked results
and Navier-Stokes
T. Berning,
threeagainst existing
[3] D.M. Lu, N. 2002
equations with diffusion
dimensional heat
experimental data,
Djilali
terms obtained through
transfer model
found consistency
solution of StefanMaxwell equations
quasi twodimensional
mass transport
model
Brings in condensation
Found that small hydrophillic
pores are the first pores to
within GDL but seems to
condense water vapor. Vapors
move towards liquid flow
tend to be over-saturated in the once water condenses in the
hydrophobic GDL.
pore
Experimentally
Found capillary pressure
The GDL was scanned
validated physical
Threecalculated in model agreed well
and digitally
analyzed various levels of
properties of carbon
with experiments. Compression
dimensional
reconstructed. The full
compression and its effect
of the GDL redistributes the pore
paper to
stochastic
morphology method
on capillary pressure.
reconstructions, reconstruction of diameters with average moving
simulates the drainage
Strength lies in the 3D
Toray090 and
towards smaller diameters.
also compared to
process through the
reconstruction of the carbon
SGL10BA
Compression results in more
Lattice-Boltzmann
initially wetting phase
paper
and pore network
carbon papers
tortuous paths and higher
saturated GDL
models
capillary pressures
Boundary conditions
established from
isothermal threecontinuity, momentum
P. Quan, M.
dimensional two2007
and Navier-Stokes
[37]
Lai
phase (air and
equations. Model
liquid water) flow
implemented into CFD
software, FLUENT
Y. Lin, C.
Lin, Y.
Chen, K.
Yin, C.
Yang
Comment
Gas velocity fields within the GDL
induce gas flow from the channel Condensation zones above
averaged
to the catalyst which is opposite
lands can reduce oxygen
properties,
diffusion in these areas
Stefan-Maxwell from single-phase models. The
causing slower reaction
multicomponent reactant gases and solid phase
have the same temperature at the
rates
diffusion
catalyst
Accounts for both
two-dimensional
Experimentally
Stefan-Maxwell
hydrophillic and
partial flooding
validated using
multicomponent
hydrophobic pores in the
model
Toray carbon paper
diffusion
GDL
full morphology
model
Results
N/A
characteristics with reference to channel geometries.
Quan and Lai [37] provided a three-dimensional model
of liquid water and air with steady generation of water
from the GDL interface.
This paper will focus on critically reviewing four
current models that discuss a majority of the issues
surrounding PEM fuel cells.
DISCUSSION
Hwang [29] Two-Phase Flow Model
Hwang [29] developed a two-phase flow model to
analyze the effects of condensation and evaporation
and thermal equilibrium boundaries within the GDL.
This model closely couples the two-phase flow of
reactant gases, heat transfer, and current. These
couplings account for the interaction between the
reactant gases, product liquid, and solid structures.
The GDL was assumed to be homogeneous and
therefore modeled with isotropic porosity and
permeability. Water was assumed to be in the liquid
phase when produced within the catalyst layer but
through non-equilibrium evaporation, the water
Found increase in oxygen
content at gas channel/GDL
interface as compared to oneDiffusion model, dimensional models without
averaged
convection. Increased air
properties
velocity in the channel leads to
greater convective effects and
higher oxygen concentrations
downstream
Addition of convective
terms shows need for
increased coupling of
models.
introduced into the GDL is in the vapor phase. Hwang
chose to model the velocity of the gases and liquids
through the GDL using Darcy’s law for each phase.
1
ε
1
ε
∇ ⋅ ( ρu g u g ) = −ε∇p g + ∇ ⋅ ( µ g ∇u g ) −
εµu g
κk rg
(1)
∇ ⋅ (ρuwu w ) = −ε[∇pg + (ρ w − ρ g ) g] + ∇ ⋅ (µw∇u w )
−
εµwuw
κkrw
(2)
Where κ represents the dry electrode permeability and
krg and krw represent the relative permeabilities for the
two phases.
Two phase heat transfer was modeled by
accounting for the effective thermal conductivity of both
the solid structure and the reactant fluids. Equations
were formed for the temperature distributions of the
solid and fluids as seen below in Eq. (3) and Eq. (4):
The 19th International Symposium on Transport Phenomena,
17-20 August, 2008, Reykjavik, ICELAND
where the heat transfer between the solid structure and
fluids and joule heating are represented by the intrinsic
and ohmic terms. The phase change heat transfer term
designates the heat absorbed or released during
evaporation or condensation as shown in Eq. (5).
∇ ⋅ (− k s ,eff ∇Ts ) = − q& int + q& Ω
(3)
( ρc p ) f u ⋅ ∇T f + ∇ ⋅ (− k eff ∇T f ) = q& int + q& phase
(4)
q& phase = m& phase × h fg
(5)
The two-phase current was modeled to represent
the ionic current (im) and the electronic current (is).
Current conservation was related to the local current
density, jct, and was derived from Ohm’s law as shown
in Eqs. (6) and (7).
∇ ⋅ (−σ s ,eff ∇φ s ) = j ct
(6)
∇(−σ m ,eff ∇φ m ) = − j ct
(7)
Numerical implementation of the model relied on a
finite-element solution method. Boundary conditions for
the inlet gas and the bi-polar plate lands were both
fixed at 298 K. Ionic current was set to zero at the
Cathode Catalyst Layer (CCL) and the GDL while the
species fluxes and electronic current were set as
continuous.
Hwang validated the model with experimental data.
The model’s i-V curve output overlaid well with the
experimental curve as seen in Fig. 1.
Fig. 1. Validation results by Hwang [29]
The model was used to find where water vapor
condenses within the GDL. Three cases were tested
which set the channel land temperatures to 298 K, 308
K, and 318 K. It was found that water vapor condensed
in the areas above the lands due to the cooler
temperatures experienced here. As the temperature of
the lands increased, the amount of saturated liquid
water would reduce in this area while the rest of the
GDL remained in the vapor phase.
Fig. 2. Condensation Front @ 298 K by Hwang [29]
Hwang also used the model to track the thermal
equilibrium boundary within the GDL. This is the point
were the fluid temperature transitions from being
greater than the solid temperature above the lands to
less than the solid temperature above the channels. It
was also found that as the land temperature increased
the thermal equilibrium point would shift closer to the
center of the channel.
Fig. 3. Thermal equilibrium front @ 298K by Hwang [29]
This model shows where within the GDL water
management may be an issue, since water only
condenses above the lands. Pore spaces filled with
condensed water may affect cell performance by further
reducing the distribution of reactant gases within the
catalyst layer above the lands leading to uneven
reaction rate distributions.
The model also
demonstrates the effects of cooling on liquid water
saturation levels.
The strength of this model lies in its ability to track
the phase change front within the GDL. This ability
shows an effect of phase change that is not captured in
many models with liquid water forming above the lands.
Liquid water formation above the lands can result in
mal-distribution of reaction gases on the catalyst layer
which will affect the overall performance of the cell.
Also, the ability of the model to track the thermal
equilibrium line can help to increase the understanding
between the temperature differences that exist between
the solid structures and the reactant fluids.
Weaknesses of this model include the isotropic
assumption and the gas inlet and bi-polar plate
temperature constraints. The GDL should not be
modeled as isotropic as its structure is inherently
anisotropic which can greatly affect the temperature
distribution and water saturation levels within the fuel
cell. The bi-polar plate temperature constraint should
be modeled so as the temperature of the plate can be
calculated by the model as this temperature will be
dependant on actual operational conditions.
The 19th International Symposium on Transport Phenomena,
17-20 August, 2008, Reykjavik, ICELAND
Liu et al. [30] Partial Flooding Model
Liu et al. [30] developed a partial flooding model to
determine the effects of mixed-wet GDL. This model
takes into account the uneven distribution of Teflon
within the carbon fibers which results in a distribution of
hydrophilic and hydrophobic pores.
The model’s
purpose is to investigate the condensation process
within the mixed-wet GDL.
The model was represented by an even number of
hydrophilic and hydrophobic pores in varying pore
diameters. Pore diameter distributions were set equal
for both the hydrophilic and hydrophobic pores. This
representation is illustrated in Fig. 4.
Fig. 4. Pore structure representation by Liu et al. [30]
The model assumed that water cannot condense
within the flow channels and water flows in slugs within
the flow channels. To avoid modeling flow within the
catalyst layer, the catalyst layer is assumed to be ultra
thin. Oxygen and hydrogen are assumed to not diffuse
through water.
An experimental test was developed to validate the
model. The experimental setup consisted of a 5cm2
fuel cell that was tested using Arbin test equipment.
The test cell and the model were run through the same
base case to perform the validation. Model agreement
with the experimental data is marginal in that the
severity
of
mass
concentration
loses
are
underestimated and the limiting current value is
overestimated by 0.2 A/cm2 in the model. The model
does agree to a better extent with general trends in the
i-V curve when compared to the experimental data.
The model was used to investigate the effect of cell
temperature, reactant humidity, reactant flow rates, and
GDL properties on cell current density. For the effects
of cell temperature, the cell was simulated at 40, 50, 60,
and 70°C. It was found that cell performance increas es
with cell temperature.
For the inlet gas humidification, it was found that
the cell performance would drop if the inlet gases were
oversaturated. When the gases were oversaturated the
GDL would flood and the reaction rate would suffer
further down the channel from the inlet. The authors
state that the model seems to underestimate the
dehydration in the cell and overestimate the flooding
effects.
Mass transport in the GDL was modeled using the
Maxwell-Stefan equation which was modified to include
the relationships for the fluxes of hydrogen and water.
This equation was then integrated to solve for position
along the channel and modified to include the molar
fraction gradients across the GDL for each species.
The final result can be seen in Eq. (8).

X
 − X n − (4α + 2) X O − w,c
cDon
cDow
cDow

 NO 

X N (4α + 2) X O
d 
j 
−
 NN  =

dy 
4F 
cDon
cDnw

 N w ,c 
X
 (4α + 2) X O
(4α + 2) X n
+ w ,c +

cDow
cDow
cDnw










(8)
The model was then developed to calculate current
density. The Butler-Volmer equations were chosen by
Liu et al. to calculate the current density as seen in Eq.
(9) and (10).
 X cat
j a = f a j a0  href
 Xh
j c = f c j c0




0.5
 αa F 
 (1 − α a ) F 
η a  − exp −
η a 
exp
RT



  RT
(9)
X 0cat   α c F 
 (1 − α c ) F 
exp
η c  − exp −
η c 
ref 
RT
X 0   RT



(10)
Fig. 5. Effect of inlet gas humidification by Liu et al. [30]
Pore geometry was investigated to find the effects
that pore size distribution and average pore diameter
have on current density. For the pore size distribution
case, a normal distribution was chosen with a
multiplicity factor, ω. It was found that with a higher
value of ω, the fuel cell performed better. With the
average pore diameter case, pore diameters of 6, 8, 10,
12, and 14 µm were chosen. As shown below in Fig. 6,
the smaller pore diameters favor higher current
densities. This occurs because of the higher pressures
placed on the water vapor which restricts the
condensation in the hydrophilic pores reducing flooding.
The 19th International Symposium on Transport Phenomena,
17-20 August, 2008, Reykjavik, ICELAND
Liquid water was neglected in the gas channel in terms
of heat transfer characteristics. For simplicity, the
authors assumed that water vapor existed at saturation
throughout the length of the channel, allowing the molar
fraction of water to then be calculated:
x gw =
p wsat (T )
pg
(13)
Where pwsat is the saturation pressure of water and pg is
total vapor pressure in atmospheres. Saturation
pressure was approximated by a log base ten function
of temperature (K) at the given location.
log10 p wsat (T ) = −2.1794 + .02953T − 9.1837T 2
Fig. 6. Effect of average pore diameter by Liu et al. [30]
The model developed by Liu et al. provides a case for
further investigation into the effects of mixed-wet GDL.
As the GDL is inherently not uniformly hydrophobic
from the Teflonation process, hydrophilic pores should
be accounted for in the models.
The main strength of this model is in elucidating
how water condenses within a mixed-wet GDL. How
water prefers to condense within a GDL structure can
change how liquid water is removed from the cell.
Understanding of this is critical to developing models
with increased accuracy.
The main weakness of this model is the
discrepancy between the model output and the
experimental data. The model describes a process that
is not well understood within the GDL and lays a good
base for future work but should be able to predict the
experimental data with better accuracy. Also, assuming
that the catalyst layer is ultra thin does not account for
catalyst occupation and could be a reason for the
discrepancy between the model and experimental data.
Berning et al. [3] Heat Transfer Model
Berning et al. [3] have developed a model for heat and
species transport through the channels, diffusion layers,
and membrane of a PEMFC. The model accounts for
three-dimensional heat and mass transport through the
entire cell. In determining these characteristics, gas
concentrations and resultant properties were of main
focus.
The authors established a series of governing
equations and boundary conditions and implemented
them into computational fluid dynamics software. As
pertaining to the gas channel, flow characteristics were
derived from continuity and Navier-Stoke’s equations:
∇ ⋅ (ρ g u g ) = 0
+ 1.4454T 3
For this model, air was assumed to be a mixture of
three gases: Oxygen, Nitrogen, and water vapor. The
concentration of Nitrogen was assumed constant
throughout the channel and oxygen concentration was
obtained through an advection-diffusion equation and
the solution of the Stefan-Maxwell equations:
∇ ⋅ (ρ g u g y gi ) − ∇ ⋅ (ρ g D g ∇y gi ) = S gi
[
2


T
− ∇ ⋅  p + µ g ∇ ⋅ u g  + ∇ ⋅ µ g (∇u g )
3


]
(15)
From the molar fraction of each species, the mass
fraction and resulting overall bulk density could be
calculated. The actual temperature profile was obtained
through the convective energy equation:
∇ ⋅ (ρ g u g H g − λ g ∇Tg ) = 0
(16)
The model is subject to inlet velocity and pressure
conditions required for a given power density within the
fuel cell as well as diffusion of oxygen at the channelGDL interface.
The model currently yields results for a straight,
three-dimensional channel in coordination with the
remainder of the cell. Figure 7 shows oxygen
concentration at slices along the gas channel. A steady
decrease in oxygen content through the length of the
channel is shown in Fig. 7.
(11)
∇ ⋅ (ρ g u g × u g − µ g ∇u g ) =
(14)
(12)
Fig. 7. Oxygen Concentration in Cathode [3]
The 19th International Symposium on Transport Phenomena,
17-20 August, 2008, Reykjavik, ICELAND
It is also shown that there is a slight increase in
mean temperature along the length. Furthermore, the
model demonstrates an increase in uniformity from inlet
to outlet. The cathode gas channel is represented in
the bottom of Fig. 8 below.
()
r
rr
r r
∂ ( ρv )
+ ∇(ρv v ) = −∇p + ∇ τ + ρg + F
∂t
(18)
Where:
τ = µ (∇v + ∇v T ) − µ∇v I
r
r
2
3
r
(19)
r
Where F accounts for surface tension and porous
affects, µ is dynamic viscosity, and I the unit tensor.
Porous affects were determined through Navier-Stokes
calculations resulting in:
r
µr
S =− v
(20)
κ
Fig. 8. Temperature Distribution in Stack [3]
This model presents an advantage over many
previous models in that it accounts for the nonisothermal nature of the cathode. The determination of
a temperature profile in the gas channel results in
greater accuracy pertaining to oxygen diffusion and
resultant water vapor content. This will benefit the
understanding of water removal characteristics in PEM
fuel cells.
Weaknesses of the model include the assumption
of no interaction of liquid water in the cathode channel
with reference to heat transfer and flow characteristics.
The presence of water in liquid form can severely alter
the pressure drop along the channel and will also have
significant effects upon the rate of heat and species
transport. The assumption of complete humidification
may also lead to false heat transfer characteristics,
particularly in the entrance region.
Quan and Lai [37] Liquid Water Transport Model
Quan and Lai [37] have developed a model for twophase transport in the cathode gas channel, accounting
for hydrophilicity, water content, velocity and pressure
drop. This model also takes into account various
channel geometries. Modeling was completed with the
use of the computational fluid dynamics software,
FLUENT.
The model assumes isothermal conditions
throughout the gas channel. This yields constant
viscosities of air and liquid water as well as other fluid
properties. In coordination with this assumption, it is
also assumed that there is no phase change present in
the channel. Liquid water and air are considered to be
immiscible.
Resultant water transport equations are derived
from continuity and momentum equations in the forms:
r
∂ρ
= ∇ ( ρv ) = 0
∂t
(17)
Where κ is the viscous resistance coefficient.
In order to further simplify the model, a constant
water flux over the channel area was assumed. This
value was determined from a given current density of
the fuel cell. Liquid water generation occurs on the
channel/ GDL interface.
From the water flux provided, a volume fraction of
water and air can be calculated.
∂
(Fi pi ) + ∇(Fi pi vi ) = 0
∂t
n
∑F
i =1
i
=1
(21)
(22)
The model was able to determine liquid water buildup points through the channel as well as determine
pressure drop changes due to varying levels of
hydrophilicity. It was observed that the greater contact
angle of a more hydrophilic channel surface produces
less drag upon the gas, resulting in a decreased overall
pressure drop through the length of the channel. A
relationship for water content and contact angle was
also established that displays the history of water
content for each of the five contact angles examined
(See Fig. 9).
This model allows for improvements in the
understanding of two-phase flow in the cathode gas
channel of a PEM fuel cell. Stress tensor calculation as
well as the established relationships between
hydrophilicity and flow characteristics improves
understanding of the factors involved in PEM fuel cell
performance. The work will also lead to more effective
design of cathode gas channels.
Weaknesses of this model pertain greatly to the
isothermal assumption. The lack of heat flux leads to
incorrect property calculations of the fluids. The
assumption of immiscibility alters the volume fraction of
liquid water in the channel along with the make-up of air.
The model also neglects the presence of liquid water on
surfaces other than the gas channel/ GDL interface.
The presence of liquid water on other surfaces may
result from evaporation on one face and subsequent
condensation on others.
The 19th International Symposium on Transport Phenomena,
17-20 August, 2008, Reykjavik, ICELAND
Fig. 9. Water content in gas channel as function of contact angle [37]
Need for Future Work
Current modeling of the GDL indicates a need for future
work. This work will be critical to further developing the
knowledge base and understanding of the transport
processes that occur within a fuel cell. As it is difficult
to measure data within the layers of an operational fuel
cell, it is uncertain the exact phase of water as it leaves
the catalyst layer and transports to the gas channels.
Because of this uncertainty in the phase of water, it will
be necessary to develop further models exploring the
phase change effects of water within the GDL and
incorporate them into suitable two-phase flow models.
An area for further work will be the development of
accurate scanning techniques so that the actual
structure of the GDL is used in the model. Techniques
for reconstruction have been discussed in literature [19,
38]. Phase change could then be modeled within this
reconstruction which could yield more condensation
zones as the actual pore structure could permit this.
Adding in the dimension of mixed-wet surfaces within
this
reconstruction
would
further
push
the
understanding of water transport within the GDL.
Within the cathode gas channel, research is
needed in furthering the understanding of liquid water
transport with inclusion of heat transfer characteristics.
In order to better predict the transport of water, a phase
change condition must be applied to the flow.
Future modeling efforts should combine the liquid
water flow and heat transport characteristics. The
inclusion of liquid water in a heat transport model will
allow for more accurate conditions along the GDL
interface. Such a coupled model would also more
accurately describe water removal through the inclusion
of phase change. This would be accomplished through
analyzing evaporation at the liquid water surface and
subsequent condensation upon lower temperature
surfaces.
In order to develop a complete model of the cathode
side of the fuel cell, proper coupling of the GDL and
flow channels must be completed. This coupling will
allow for proper heat and species transfer across the
interface. Coupling will also allow for the removal of
excess boundary conditions with improved temperature
profiles across the components. The bi-polar plate
temperature should also be calculated as it could be
dependant on cell operational conditions.
CONCLUSION
An in-depth review has been conducted for four models
which demonstrate current understanding of transport
processes within the GDL and cathode gas channels of a
PEMFC. The discussion brings forth describes the
modeling methods implemented and important equations
from each of the reviewed models. Heat transfer is
crucial to water management as it can induce
temperature gradients through the components and
along the length of the gas channels in a fuel cell. These
temperature gradients can then result in condensation or
evaporation of water which will affect the flow
characteristics of reactant gases.
Hwang [29] found the possible formation of
condensation zones above the land structures within the
GDL. This is significant to water management as water
will be difficult to remove from this location and could
cause further oxygen concentration distribution issues in
these areas. Liu et al. [30] investigated mixed wet
effects in the GDL. This work is important as it shows
the preferred order of condensation in a more realistic
description of the GDL.
Berning et al. [3] described heat transfer within the
gas channel as a function of varying oxygen and water
vapor content. This model demonstrates temperature
gradients in the channels and will allow for better
understanding of water management in these channels.
Quan and Lai [37] determined flow characteristics of
The 19th International Symposium on Transport Phenomena,
17-20 August, 2008, Reykjavik, ICELAND
liquid water and gas in the gas channel. This work
demonstrates the effects of hydrophilicity and volume
fractions upon water removal and pressure drop through
a given channel.
Based on these models and the literature review
performed, recommendations for possible work have
been made. These recommendations highlight some of
the weaknesses within current models and describe the
need to couple GDL and flow channel analyses.
As PEM fuel cells come closer to possible
implementation in automotives it will be essential to
understand the transport processes within the fuel cell.
Modeling will be one of the primary ways to accomplish
this understanding. Therefore, appropriate assumptions
and boundary conditions will need to be selected to
insure that the proper understanding is gained.
NOMENCLATURE
c
molar concentration, mol m-3
cp specific heat, J kg-1K-1
D
diffusivity of species, m2 s-1
F
Faraday constant, (C mol-1) in eq. 8,9,10
Volume fraction in eq. 22, 23
r
F r momentum source term
g, g gravitational force
H
I
j
k,λ
N
p
q&
R
r
total enthalpy, J
unit tensor
transfer current density, A m-3
thermal conductivity, W m-1 K-1
flux of species, mol s-1 cm-2
pressure, Pa
heat generation, W m-1
universal gas constant, W mol-1 K-1
S, S source terms
T
r temperature,-1K
u, v velocity, m s
v
specific volume, m3 kg-1
x,X molar fraction
y
mass fraction
Greek symbols
α
water drag coefficient, (H2O/H+)
ε
porosity
η
overpotential, V
κ
permeability, m2
µ
dynamic viscosity, N s m-2
ρ
density, kg m-3
σ
electrical conductivity, Ω-1 m-1
τ
φ
stress tensor
phase potential, V
Subscripts/Superscripts
a
anode
c
cathode
g
gas
i
species
N
nitrogen
O oxygen
sat @ saturation
w
water
T
transpose
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