CHAPTER 3 EFFECTS OF CATHODE HUMIDIFICATION AND
3.7 Summary
An isothermal, multi-dimensional, multi-component, computational fluid
dynamic model was developed to study the effect of the cathode humidification
conditions and the cathode gas diffusion layer porosities on the location of the
interface where the liquid water begins to condense along the flow channel direction
in a PEM fuel cell. The model results support the following conclusions.
(1) The gas-liquid interface location moves from the cathode catalyst layer toward the
gas diffusion layer as the relative humidity of the cathode increases. When the
relative humidity of the cathode reaches 100%, the gas-liquid interface location is
close to the gas flow channel inlet region.
(2) As the condensed water in the pores in the porous media blocks the transport of
fuel gas, the cell performance and power density decrease as the relative humidity
of the cathode increases.
(3) Reducing the cell operating voltage reduces the distance between the gas-liquid
interface and the gas flow channel inlet region, because the higher current density
is associated with a higher electrochemical reaction rate.
(4) The decreased oxygen fraction and the increased water fraction along the flow
channel are related to the electrochemical reaction of the cathode catalyst layer, as
oxygen is consumed and water produced.
(5) The transport of liquid water through the porous media is driven by the capillary
force. Accordingly, the liquid water moves from the cathode catalyst layer toward
the gas diffusion layer and the flow channel.
(6) The diffusion transport of the reactant gas to the cathode catalyst layer and the
production of water via the gas diffusion layer to the flow channel increases with
increasing the cathode gas diffusion layer porosities. Consequently, the cell
performance and power density are increased.
0
0.02 0.03 0.04 0.05 0.06 0.07
Y ( m )
0.02 0.03 0.04 0.05 0.06 0.07
Y ( m )
Figure 3.1 Effects of relative humidity of cathode on the location of the interface where liquid water begins to condense along the conventional flow channel at a cell operating voltage of 0.7 V. (a) RHca = 20~100 % and (b) RHca = 20~60 %.
0.2
Power Density ( W/cm2 )
Current Density ( A/cm2 )
Figure 3.2 Effect of relative humidity of the cathode on cell performance with conventional flow fields. (a) I-V curves and (b) I-P curves.
(b)
(a)
0
0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07
Y ( m )
0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07
Y ( m )
Z ( m )
V = 0.9
V = 0.8
(b)
Figure 3.3 Effect of cell operating voltage on the location of the interface where liquid water begins to condense along the conventional flow channel at a relative humidity of the cathode of 80 %. (a) V= 0.5~0.9 (b) V= 0.8~0.9.
0 0.0002 0.0004 0.0006 0.0008 0.001
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Y ( m )
Z ( m )
0.1182
0.1381
0.15 0.1621
0.1745 0.1863
Figure 3.4 Oxygen fraction in the cathode gas channel and gas diffusion layer along the conventional flow channel at a cell voltage of 0.7 V and cathode relative humidity of 80 %.
0 0.0002 0.0004 0.0006 0.0008 0.001
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Y ( m )
Z ( m )
0.1688
0.18
0.1925
0.2055
0.2178 0.2295
0.2432
Figure 3.5 Water fraction in the cathode gas channel and the gas diffusion layer along the conventional flow channel at a cell voltage of 0.7 V and cathode relative humidity of 80 %.
0 0.0002 0.0004 0.0006 0.0008 0.001
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
0.001166 0.01184 0.02136 0.03003 0.0387 0.04201 0.04565
Y ( m )
Z ( m )
Figure 3.6 Liquid water saturation field in the cathode gas channel and gas diffusion layer along the conventional flow channel at a cell voltage of 0.7 V and cathode relative humidity of 80 %.
Figure 3.7 Oxygen mass fraction contours at the gas diffusion layer as the cathode humidification of (a) 20 % (b) 60 % (c) 100 % for cell voltage of 0.4 V.
(a) (b)
(c)
X
Z
Figure 3.8 Water mass fraction contours at the gas diffusion layer as the cathode humidification of (a) 20 % (b) 60 % (c) 100 % for cell voltage of 0.4 V.
X Z
(c)
(a) (b)
Figure 3.9 Liquid saturation contours at the gas diffusion layer as the cathode humidification of (a) 20 % (b) 60 % (c) 100 % for cell voltage of 0.4 V.
(a) (b)
X Z
(c)
Z Y
Z Y
Figure 3.10 Two-phase mixture velocity field in the gas diffusion layer and flow channel of the cathode at the cell voltage of 0.7 V and cathode relative humidity of 80 %.
Figure 3.11 Effects of porosity of the gas diffusion layer on the location of the interface where liquid water begins to condense along the conventional flow channel at a cell voltage of 0.7 V and cathode relative humidity of 80 %.
0 0.0002 0.0004 0.0006 0.0008 0.001
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
ε = 0.3 ε = 0.4 ε = 0.5
ε = 0.6 ε = 0.7 ε = 0.8
Y ( m )
Z ( m )
Figure 3.12 Effect of porosity of the gas diffusion layer on cell performance with conventional flow fields at cathode relative humidity of 80 %. (a) I-V curves and (b) I-P curves.
0
Power Density ( W/cm2 )
Current Density ( A/cm2 )
Figure 3.13 Oxygen fraction at various porosities of the gas diffusion layer at an operating voltage of 0.7 V and cathode relative humidity of 80 %.
0 0.0002 0.0004 0.0006 0.0008 0.001
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
ε =0.3 ε =0.4 ε =0.5
ε =0.6 ε =0.7 ε =0.8
Y ( m )
Z ( m )
Figure 3.14 Water fraction at various porosities of the gas diffusion layer at an operating voltage of 0.7 V and cathode relative humidity of 80 %.
0 0.0002 0.0004 0.0006 0.0008 0.001
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
ε =0.3 ε =0.4 ε =0.5
ε =0.6 ε =0.7 ε =0.8
Y ( m )
Z ( m )
CHAPTER 4
EFFECTS OF TEMPERATURE ON THE LOCATION OF THE GAS–LIQUID INTERFACE IN A PEM FUEL CELL
4.1 Introduction
During the operation of a PEM fuel cell, the production of electrical energy is
accompanied by the release of thermal energy. The generated heat in a fuel cell
includes entropic heat of reactions, the irreversible heat of electrochemical reactions,
and Joule heating. It is crucial to keep the cell temperature of the PEM fuel cell within
safe levels through proper thermal management to maintain the cell performance
properly. This is because a too high cell temperature may lead to membrane
dehydration and a too low cell temperature may result in water condensation or even
electrodes flooding phenomenon. In order to ensure proper water and thermal
managements for the PEM fuel cell, it is essential to predict the water and temperature
distributions inside the PEM fuel cell. The formation of liquid water depends on the
saturation vapor pressure, which is strongly dependent on the temperature. Therefore,
the temperature factor is an inevitable consideration in water management
investigations because the phase change of water such as condensation and/or
evaporation closely relates to the corresponding saturation pressure.
In this chapter, the non-equilibrium conditions of partial pressure deviation
from saturation pressure have been considered. Our quest to delineate the effects of
the gas-liquid interface on a PEM fuel cell has involved the following two parts. First,
as a preliminary study, the cell temperature and humidification temperature were set
as being equal. Second, we considered a scenario whereby cell temperatures were
altered at a fixed humidification temperature. For all of the calculations carried out in
this study, the fuel flows were co-flows and inlet stoichiometric ratios of 1.5 and 3
were used for the anode and cathode sides based on a reference current density of
1 A/cm2. Furthermore, fully humidified hydrogen and oxygen were fed to the anode
and cathode inlets, respectively.
4.2 Effects of temperatures scheme
Figure 4.1 shows the polarization curves of the cell at equal cell and
humidification temperatures of 323, 333, and 343 K. The results reveal that the cell
performance improves as the temperature is increased because a higher temperature
results in higher catalytic activity and a higher capacity for water removal by
evaporation. Hence, increasing the temperature is helpful in reducing the level of
flooding. Moreover, a higher cell temperature increases the membrane conductivity
and mass diffusivity, and decreases the mass transport resistance. Figure 4.2 presents
the effect of temperature on the location of the interface at which liquid water begins
to condense along the cathode flow channel direction at a cell voltage of 0.7 V. Indeed,
the interface is defined as the location where the liquid water begins to condense, and
so the saturation value behind this interface is greater than zero and this gives rise to
the two-phase flow region. The horizontal dotted line indicates the interface between
the flow channel and the gas diffusion layer of the cathode. The results reveal that the
gas-liquid interface location moves toward the flow channel inlet region as the
temperature is decreased, because the formation of liquid water depends on the
saturation pressure, which is strongly dependent on the temperature. Liquid water is
more easily and quickly condensed at a lower temperature. Additionally, the formation
of liquid water may block pore paths for mass transport through the porous diffusion
layer to the cathode catalyst layer, thereby reducing cell performance. An increase in
temperature increases the saturation pressure of water vapor, in turn increasing the
evaporation capacity of the gas stream. However, although not shown here, a high
temperature may result in the membrane drying out.
4.3 Effects of cell temperatures scheme
In the second part of this study, the effect of cell temperature was investigated
for a fixed inlet gas humidification temperature. As the stoichiometric flow ratio and
the humidification temperature do not change in this phase of simulation, the reactant
flow rates were kept constant. Polarization curves at Th = 323 K and Th = 343 K at
various cell temperatures are plotted in Fig. 4.3. The curves in Fig. 4.3 (a) reveal that
the cell performance improves as the cell temperature is increased from 323 to 333 K,
but deteriorates as the temperature is further increased from 333 to 343 K. This result
probably follows from the fact that the humidification temperature is less than the cell
temperature, and the inlet fuel gases are therefore unsaturated. Therefore, water is
almost entirely present in vapor form. Accordingly, the mass fraction of water vapor
increases along the channel because of evaporation of liquid water from the cathode
catalyst layer. Hence, a high temperature reduces the water content of the membrane,
dehydrating it, and reducing its ionic conductivity. Figure 4.3 (b) indicates the positive
effect of cell temperature on cell performance. Since the humidification temperature
exceeds the cell temperature, liquid water forms when the inlet gases enter the flow
channel. Some of the liquid water keeps the membrane moist and improves its ionic
conductivity. Accordingly, the cell performance improves as the cell temperature is
increased.
Some experimental investigations [46−48] have demonstrated that the best
working conditions for the single cell are those under which the humidification
temperature slightly exceeds the cell temperature. The objective of this study has been
to investigate the impact of the formation of liquid water on cell performance.
Therefore, the case in which the humidification temperature exceeds the cell
temperature has been considered. Figures 4.4 (a) and (b) show the location of the
gas-liquid interface along the flow channel direction at a cell operating voltage of
0.7 V and a humidification temperature of 343 K as the cell temperature is varied. The
results reveal that the gas-liquid interface location gradually moves to the gas inlet
region as the cell temperature is decreased, which may be ascribed to the following
two reasons. (1) Reducing the cell temperature reduces the saturation pressure,
increasing the amount of liquid water generated, shifting the gas-liquid interface
location closer to the gas channel inlet region. (2) Some of the water produced in the
cathode catalyst layer by the electrochemical reaction is evaporated because the cell
temperature is higher and, therefore, the gas-liquid interface location moves closer to
the cathode catalyst layer. Figure 4.4 (b) shows an enlarged portion of the curves
along the channel from 0 to 0.08 cm. In conclusion, reducing the cell temperature can
reposition the gas-liquid interface and cause liquid water to appear, which is
detrimental to cell performance, since this water may occupy the pores in the porous
medium, reducing the amount of fuel gases that can reach the cathode catalyst layer.
4.4 Three-dimensional species field
Figure 4.5 displays the liquid water saturation field in the gas flow channel
and the gas diffusion layer on the cathode side at various cell temperatures. Each of
the figures reveals that liquid water saturation increases along the flow channel
direction, because water is generated in the cathode catalyst layer by an
electrochemical reaction. Therefore, liquid water may first appear near the interface
between the membrane and the cathode catalyst layer close to the channel outlet
region. Consequently, the liquid water saturation level in the catalyst layer is higher
than that in the gas diffusion layer on the cathode side. Liquid water is transported
from the cathode catalyst layer towards the gas diffusion layer only by capillary action;
when the liquid water has reached the interface between the flow channel and the gas
diffusion layer, it is transported along the channel by the drag force arising from the
convective flow of gas.
Figures 4.6 and 4.7 show plots of the distributions of liquid water saturation
and temperature in the X-Y section of the cathode gas diffusion layer in the inlet
region at a cell voltage of 0.7 V and a humidification temperature of 343 K at various
cell temperatures. Figure 4.6 reveals that the liquid water saturation increases under
the land and that the amount of liquid water decreases as the cell temperature is
increased. In the gas diffusion layer, two transport mechanisms operate — gas-phase
diffusion as a result of the concentration gradient from the channel to the land and
liquid water transport by capillary forces from the land to the channel. The liquid
water cannot be discharged by the land, so the liquid water saturation on the land is
higher than that in the channel. Additionally, the amount of liquid water decreases as
the cell temperature is increased because the saturation pressure increases. Figure 4.7
shows that the temperature gradually decreases from the channel to the land. This
result has two explanations. (1) Gas-phase diffusion occurs from the channel area to
the land; (2) heat produced in the cathode catalyst layer by the electrochemical
reaction causes the temperature gradient. Additionally, the degree of temperature
variation is greater when there is a larger difference between the cell temperature and
the humidification temperature.
4.5 Temperature field in the membrane
Figure 4.8 compares the temperature distributions in the membrane from 323
to 343 K. Each of these figures reveals that the temperature distributions in the
membrane gradually decline along the flow channel, and that the distribution is
symmetric about the z-center line. Since the inlet gas is fully humidified, the rate of
the reaction and the temperature are higher at the inlet. The temperature variation
involves irreversible heat, entropic heat, Joule heating, and latent heat. Additionally,
the degree of temperature variation in the membrane is greater when there is a larger
difference between the cell temperature and the humidification temperature.
4.6 Summary
A three-dimensional, non-isothermal, multi-component, and two-phase
mathematical model has been developed in the framework of the computational fluid
dynamics code. The effects of temperature on the location of the gas-liquid interface
along the flow channel direction have been investigated. According to the presented
results and the analysis, when the anode and cathode humidification temperatures are
equal to or higher than the cell temperature, the gas-liquid interface location moves
toward the flow channel inlet region as the temperature is decreased. Since the
formation of liquid water may block pore paths for mass transport through the porous
diffusion layer to the cathode catalyst layer, cell performance is reduced. An increase
in temperature increases the saturation pressure of water, in turn increasing the
evaporation capacity of the gas stream. The temperature distributions in the
membrane gradually decline along the flow channel direction. The distribution is
symmetric about the z-center line because the cell reaction rate and the temperature
are higher at the inlet region. Numerical analysis of the results of this study has also
shown that gas-phase fluid diffuses from the channel to the land and that the
capillary-driven liquid water is transported in the opposite direction. Additionally, the
degree of temperature variation is greater when there is a large difference between the
cell temperature and the humidification temperature.
0 0.2 0.4 0.6 0.8 1 1.2
0 0.2 0.4 0.6 0.8 1 1.2
Th=Tcell= 323 K Th=Tcell= 333 K Th=Tcell= 343 K
Volta g e ( V )
Current Density ( A/cm
2)
Figure 4.1 Polarization curves at various cell temperatures with equal humidification temperature.
0 0.02 0.04 0.06 0.08 0.1
0 1 2 3 4 5 6 7
Th = Tcell = 323 K Th = Tcell = 333 K Th = Tcell = 343 K
Y ( c m )
Z ( cm )
Figure 4.2 Effect of cell temperature on the location of the interface where liquid water begins to condense along the flow channel at a cell operating voltage of 0.7 V.
(a)
Th=323 K ; Tcell=323 K Th=323 K ; Tcell=333 K Th=323 K ; Tcell=343 KVo lt ag e ( V )
Th=323 K ; Tcell=323 K Th=323 K ; Tcell=333 K Th=323 K ; Tcell=343 KVo lt ag e ( V )
Th=343 K ; Tcell=323 K Th=343 K ; Tcell=333 K Th=343 K ; Tcell=343 KVo lt ag e ( V )
Th=343 K ; Tcell=323 K Th=343 K ; Tcell=333 K Th=343 K ; Tcell=343 KVo lt ag e ( V )
Current Density ( A/cm
2)
Figure 4.3 Polarization curves for various cell temperatures at (a) Th = 323 K, (b) Th = 343 K.
0
Figure 4.4 Effects of cell temperature on the location of the interface where liquid water begins to condense along the flow channel at a cell operating voltage of 0.7 V and a humidification temperature of 343 K. (a) Z = 0 to 7.112 cm, (b) Z = 0 to 0.08 cm.
0
Figure 4.5 Liquid water saturation field in the cathode gas channel and diffusion layer along the flow channel at a cell voltage of 0.7 V and a humidification temperature of 343 K. (a) Tcell = 323 K, (b) Tcell = 333 K, (c) Tcell = 343 K.
0.07 0.09 diffusion layer in the inlet region at a cell voltage of 0.7 V and a
humidification temperature of 343 K. (a) Tcell = 323 K, (b) Tcell = 333 K, (c) Tcell = 343 K.
Y
X
Channel Land
Figure 4.7 Temperature distributions in a cross-section of the cathode gas diffusion layer in the inlet region at a cell voltage of 0.7 V and a humidification temperature of 343 K. (a) Tcell = 323 K, (b) Tcell = 333 K, (c) Tcell = 343 K.
X Y
0
Figure 4.8 Temperature contours in the membrane at a cell voltage of 0.7 V and a humidification temperature of 343 K. (a) Tcell = 323 K, (b) Tcell = 333 K, (c) Tcell = 343 K.
CHAPTER 5
CONCLUSIONS AND FUTURE PERSPECTIVES
5.1 Concluding Remarks
In this dissertation, a single-domain formulation has been developed to
comprehensively describe the electrochemical kinetics, current distribution,
hydrodynamics, thermal flow, and multi-component transport in a PEM fuel cell. The
governing equations considering the mass, momentum, species, charge, and energy
conservation with their related boundary conditions are solved using a commercial
code based on the SIMPLE algorithm for convection-diffusion problems. A
computational fluid dynamics (CFD) technique is successfully adapted to simulate
multi-dimensional behaviors of the PEM fuel cell. It is able to predict not only the
polarization curves which are consistent with the experimental work of Squadrito et al.
[44] but also the detailed reactant and product distributions inside the fuel cell.
The scope in this study has included three crucial topics, namely the effects of
cathode humidification level, cathode gas diffusion layer porosity and operating
temperature on the gas-liquid interface location along the flow channel direction in a
PEM fuel cell. The effects of cathode humidification are investigated firstly. It is
found that the cell performance decreases as the relative humidity of the cathode
increases, because the amount of liquid water increases with the relative humidity.
Accordingly, the pores in the porous media are obstructed by liquid water at the
cathode-side, reducing the amount of reaction gas to the cathode catalyst layer.
Therefore, the performance of the cell gradually decreases. The phenomena have also
been expounded from the gas-liquid interface location. The gas-liquid interface
location moves from the cathode catalyst layer toward the gas diffusion layer and the
flow channel as the relative humidity of the cathode increases. Furthermore, when the
relative humidity of the cathode reaches 100%, the gas-liquid interface location is
close to the gas flow channel inlet region. Hence, the two-phase region appears early
to cause the clogging effect of the reactant transport, resulting in the deteriorations of
cell performance and power density. Moreover, the cell operating voltage also
influences the gas-liquid interface location. Because of the higher cell operating
voltage indicates that the lower current density, namely lower electrochemical
reaction rate and less water generation rate. Hence, the gas-liquid interface location
gradually moves to the gas flow channel inlet region as the operating voltage
decreases, because reducing the operating voltage increases the current density and
electrochemical reaction rate. The cathode gas diffusion layer porosity also influences
the gas-liquid interface location. When the gas diffusion layer porosity decreases, the
gas-liquid interface location appears early in the cathode gas diffusion layer because
of the liquid water transport by capillary force is not easy to pass through the gas
diffusion layer and spread throughout in it. Hence, the liquid water occupies the pores,
diffusion layer and spread throughout in it. Hence, the liquid water occupies the pores,