CHAPTER 3 EFFECTS OF TEMPERATURE AND
3.6 Summary
The three-dimensional, multi-component and multi-physics model has been applied to explore the temperature gradient and humidification perturbation effects on PEMFCs. This model accounts for various species transport and the two-phase flow problem. The CL local activation overpotential resolution is also achieved. According to the model prediction results and discussion, the following conclusions can be addressed:
1. The anode humidification level bears the impact of concentration and ohmic overpotentials on cell performance at elevated and reduced situations respectively.
2. Proper cathode humidification level reduction benefits cathode reactant transport and improves polarization concentration at a high reaction rate.
3. Despite its nonlinear behavior, a suitable PEMFC humidification scheme can be reached by carefully using the individual humidification level effect on either side of the cell.
4. Temperature gradient effect on cell performance exhibits entirely different behaviors according to its direction and magnitude. When the cathode temperature
is fixed at a lower level, the anode temperature variation has no noticeable change in output current. However, when it is specified at a higher value, a larger temperature gradient is harmful at high current density.
5. Positive cell temperature gradient effect on its performance is found for medium reaction rate at a lower anode temperature. However, this trend is reversed at a higher reaction rate due to membrane dehydration.
6. Local physical property contours demonstrate interrelations among the temperature field, local oxygen concentration, and water saturation level. As a result, cell performance has a close connection with these property variations, and the essential role of existing PEMFC temperature and humidification gradients is elucidated.
0.6 0.8 1 1.2 1.4 1.6 Current Density (A/cm2)
0 0.1 0.2 0.3 0.4 0.5 0.6
Cell Potential (V)
TBA THA THC TBC (K) 353/353/353/353 353/363/353/353 343/343/343/343 343/353/343/343 333/333/333/333 333/343/333/333
Fig. 3.1. Effect of anode enhanced humidification scheme with 10K of anode humidification level greater than cell temperature for cell temperatures 333K, 343K and 353K
0.6 0.8 1 1.2 1.4 1.6 Current Density (A/cm2)
0 0.1 0.2 0.3 0.4 0.5 0.6
Cell Potential (V)
TBA THA THC TBC (K) 353/353/353/353 353/353/363/353 343/343/343/343 343/343/353/343 333/333/333/333 333/333/343/333
Fig. 3.2. Effect of cathode enhanced humidification scheme with 10K of cathode humidification level greater than cell temperature for cell temperatures 333K, 343K and 353K
0.6 0.8 1 1.2 1.4 1.6 Current Density (A/cm2)
0 0.1 0.2 0.3 0.4 0.5 0.6
Cell Potential (V)
TBA THA THC TBC (K) 353/353/353/353 353/343/353/353 343/343/343/343 343/333/343/343 333/333/333/333 333/323/333/333
Fig. 3.3. Effect of anode reduced humidification scheme with 10K of anode humidification level smaller than cell temperature for cell temperatures 333K, 343K and 353K
0.6 0.8 1 1.2 1.4 1.6 Current Density (A/cm2)
0 0.1 0.2 0.3 0.4 0.5 0.6
Cell Potential (V)
TBA THA THC TBC (K) 353/353/353/353 353/353/343/353 343/343/343/343 343/343/333/343 333/333/333/333 333/333/323/333
Fig. 3.4. Effect of cathode reduced humidification scheme with 10K of cathode humidification level smaller than cell temperature for cell temperatures 333K, 343K and 353K
0.6 0.8 1 1.2 1.4 1.6 Current Density (A/cm2)
0 0.1 0.2 0.3 0.4 0.5 0.6
Cell Potential (V)
TBA THA THC TBC (K) 353/353/353/353 353/343/363/353 343/343/343/343 343/333/353/343 333/333/333/333 333/323/343/333
Fig. 3.5. Effect of humidification gradient that combines anode reduced and cathode enhanced schemes for cell temperatures 333K, 343K and 353K
336 340 344 348 352
Anode Side Temperatures (K)
0.8 1 1.2 1.4
C u rr en t D e n s it y ( A /c m 2 )
0.98V
0.9 V
0.8 V
0.7 V
0.6 V
Fig. 3.6. Cell performance at various total overpotentials with 353K cathode temperatures and anode temperatures varied from 333K to 353K
0 0.01 0.02 0.03 0.04 0.05 X Position (m)
7 8 9 10 11 12 13 14 15
Ionic Phase Conductivity (I/Ωm)
TBA THA THC TBC (K) 333/333/353/353 338/338/353/353 343/343/353/353 348/348/353/353 353/353/353/353
Fig. 3.7. Ionic Phase conductivity along central channel direction on membrane middle section for cases in Fig. 3.6
336 340 344 348 352
Cathode Side Temperatures (K)
0.8 1 1.2 1.4
C ur rent D e ns it y ( A /c m 2 )
0.98V
0.9 V
0.8 V
0.7 V
0.6 V
Fig. 3.8. Cell performance at various total overpotentials with 353K anode temperatures and cathode temperatures varied from 333K to 353K
336 340 344 348 352
Cathode Side Temperatures (K)
0.8 1 1.2 1.4
C ur rent D e ns it y ( A /c m 2 )
0.98V
0.9 V
0.8 V
0.7 V
0.6 V
Fig. 3.9. Cell performance at various total overpotentials with 333K anode temperatures and cathode temperatures varied from 333K to 353K
0 0.01 0.02 0.03 0.04 0.05 X Position (m)
10 11 12
Ionic Phase Conductivity (1/Ωm)
TBA THA THC TBC (K) 333/333/333/333 333/333/338/338 333/333/343/343 333/333/348/348 333/333/353/353
Fig. 3.10(a). Ionic phase conductivity along central channel direction on membrane middle section for cases in Fig. 3.9 at total cell overpotential of 0.6V
0 0.01 0.02 0.03 0.04 0.05 X Position (m)
10 11 12
Ionic Phase Conductivity (1/Ωm)
TBA THA THC TBC (K) 333/333/333/333 333/333/338/338 333/333/343/343 333/333/348/348 333/333/353/353
Fig. 3.10(b). Ionic phase conductivity along central channel direction on membrane middle section for cases in Fig. 3.9 at total cell overpotential of 0.98V
(a)
(b)
Fig. 3.11. Local temperature contours in cathode GDL at section of x=0.025m with 353K anode temperatures and cathode temperatures (a) 343K (b) 333K
(a)
(b)
Fig. 3.12. Local oxygen mass fractions in cathode GDL at section of x=0.025m with 353K anode temperatures and cathode temperatures (a) 343K (b) 333K
(a)
(b)
Fig. 3.13. Local water saturation in cathode GDL at section of x=0.025m with 353K anode temperatures and cathode temperatures (a) 343K (b) 333K
0.3 0.4 0.5 0.6 0.7 0.8
Ce ll P o ten tia l ( V )
0.8 1 1.2 1.4 1.6
Current Density (A/cm2) T
BAT
HAT
HCT
BC(K)
343/343/313/343 343/343/323/343 343/343/333/343 343/343/343/343 343/343/353/343
Fig. 3.14 Experimental results of Wang et al. (2003) on the effects of cathode humidification schemes. The cell temperature is set at 343K and the cathode humidification temperatures varied from 313K to 353K
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Ce ll P o te n tia l (V )
0.2 0.4 0.6 0.8 1
Current Density (A/cm2)
T
BAT
HAT
HCT
BC(K) 343/358/348/343 343/368/358/343
Fig. 3.15 Experimental results of Lee et al. (1999b) on the effects of anode and cathode enhanced humidification schemes. The cathode humidification temperatures vary from 348K to 358K while the anode humidification temperatures vary from 358K to 368K
CHAPTER 4
TRANSPORT COMPONENT DESIGN EFFECTS ON PROTON EXCHANGE MEMBRANE FUEL CELL PERFORMANCE
4.1 Introduction
As introduced in chapter 2, the main components of PEMFCs consist of bipolar plates, flow channels, gas diffusion layers, catalyst layers and membrane.
Reactant gases and charged species move along individual route to complete the functions of electrochemical reaction as well as product discharge. In order to reach an optimal characteristic of the cell performance, it is vital to carefully examine the individual effects of transport component design. The most important issues are those which can evenly and efficiently deliver various species to the reaction sites, such that the cell can release the largest fraction of the chemical energy stored in the reactants.
Meanwhile, the movement of the water vapor or liquid, product of cell reaction, is also essential because the transport passage could be clogged and the diffusion rate of reactants is reduced if no additional attention is addressed at high reaction rate condition. In this chapter, the influences of transport component design such as channel aspect ratio and GDL thickness are investigated and described in detail.
4.2 Cell Performance Subjected to Transport Component Design
Flow channel geometry is important for optimizing cell performance with delivery of sufficient reactant to the reaction sites. Various configurations with different channel aspect ratios are investigated to explore the effects of channel geometry design. The aspect ratio (AR) is defined as the height (in Z-direction) of the channel divided by the width (in Y-direction) of the channel. Channel height and width are modified according to the AR, such that the channel cross-sectional area is fixed. Hence, the reactant mass flow rate at the inlet and the channel hydraulic diameter are the same in all case studies. To maintain a fixed cell width, the shoulder width is also changed. Detailed channel geometries for each considered AR are listed in Table 4.1 and Fig.4.1..
4.2.1 Effect of Channel Aspect Ratio
Fig. 4.2(a) shows the relationships between output current densities and AR at moderate and low cell voltages. Clearly, cell performance dependence on the channel aspect ratio varies with operating conditions. The cell output current density is larger at moderate cell voltage and performance declines rapidly in the high reaction rate region, when the AR is large as in the case of 1.5. However, despite poor performance at cell potentials of 0.42V to 0.62V when the channel is flat, such as at AR =0.5, current density exceeds that obtained with other channel geometries at 0.14V.
4.2.2 Effect of Diffusion Layer Thickness
Figure 4.2(b) displays cell current density curves with five GDL thicknesses. A thinner diffusion layer is generally believed to reduce the reactant vertical diffusion path such that more oxygen arrives at the catalyst layer to gain more current. In contrast, cell performance varies with increased thickness of the diffusion layer because the reactant is transported through a longer distance and the flooding problem occurs. However, the data in Fig. 4.2(b) reveals that optimal thickness increases from 152 m at 0.62V to 254 m at 0.22V, beyond which potential, it decreases. The tendency is slightly different from the work of Jeng et al. (2004)] with a monotonously decreased performance when GDL thickness increases for a low - porosity GDL. By using a high-porosity GDL however, the trends coincide.
μ μ
Fuel cell output is controlled by three degrading mechanisms- loss associated with reactant activation energy at the electrodes; loss associated with transport of the current in the electrically conducting media, and loss associated with the transport of reactant gases in the cell. These are called activation overpotential, ohmic overpotential, and concentration overpotential, respectively. The AR and GDL thickness influences relative magnitudes of these three irreversibilities according to the operating voltage, as is obvious from the data in Fig. 4.2. Local variations of these factors may also play an important role on the trend transition shown in the figure. A fixed cell overpotential is notably designated on the cathode BP surface in the present
study. The current conservation equation solution provides detailed information of potential distribution throughout the domain. Therefore ohmic overpotential and activation overpotential can be resolved and compared with the oxygen concentration for different operating voltage. Without generality loss, representative locations in the cell domain are assigned to investigate the effects of these two parameters and various transport properties on cell performance variation in the following sections.
4.3 Local Properties Variations in Transverse Direction 4.3.1 Membrane Conductivity and Potential
A series of demonstrations involving the most important transport quantities, such as phase potentials, reactant concentrations at selected locations, and cell voltages are performed to elucidate the cause of the forgoing results. All of the data are mirrored to yield results for a complete channel and a pair of half shoulders adjacent to the channel. Notably, the negatively charged electrons move from low potential to high potential and the positively charged proton move oppositely. The main concern in the potential variation discussion is that the passages with lowest electron potential increase from the cathode boundary, and the ionic potential decrease from the anode catalyst layer. Therefore, ohmic overpotential decreases, and the absolute value of the electrochemical reaction driving force, the activation
overpotential, in Eq. (14) increases. Fig. 4.3 plots and compares the membrane potential and conductivity in the transverse direction of the middle X-Y plane of the membrane for AR=0.5, 1, and 1.5, and cell voltages of 0.62V and 0.14V at Z-coordinate of 2.152mm. The short bars on the plot indicate the interfaces between channel and shoulder for each AR. At a cell voltage of 0.62V, the membrane conductivity patterns in the channel region and the shoulder differ, according to the AR value. At the membrane location of the channel region, conductivity is greater at a lower AR. Membrane conductivity is a function of water activity, so increasing the channel transverse dimension at AR=0.5 facilitates water transport at the anode through the channel to the membrane, causing water activity in the central region to exceed that in the shoulder region. Trends are reversed at the other AR values because of local current density effect. Membrane phase potential variations are strongly related to the conductivities; a lower conductivity is responsible for a larger membrane ohmic loss at a moderate reaction rate at which the local change in current density is expected to be small. However, the data in Fig. 4.3(b) indicate that at a high reaction rate, higher membrane conductivity locations exhibit a larger membrane ohmic loss because the local current density varies markedly at this cell voltage. The ohmic law and the fact that a large current density variation outweighs the trivial local
conductivity fluctuation demonstrate that ohmic loss in the membrane phase is consistent with local current density.
Figure 4.4 plots the membrane phase conductivity and potential at GDL thicknesses of 152 m, 203 m and 356 μ μ μ m and cell voltages of 0.62V and 0.14V, to examine GDL thickness and cell voltage effects on the various transport properties.
The data were obtained from the same position as in Fig. 4.2. A thick GDL stabilizes transverse variation of local conductivity. Reducing this parameter leads to a highly non-homogeneous local conductivity distribution at a cell voltage of 0.14V. The data in Fig. 4.4 indicates that conductivity is related to membrane potential in a manner similar to that in Fig. 4.3. At a low reaction rate, these two variables vary oppositely, but at a high reaction rate, they vary similarly.
4.3.2 Solid Phase Potential and Activation Overpotential
Solid-phase potential and activation overpotential in the transverse direction for various AR at the interface between the cathode catalyst layer and the GDL are described in Fig. 4.5. The data in Fig. 4.5(a) reveal that the shoulder area exhibits a small ohmic overpotential from the outer surface of the cathode BP. The longer electron passage in the catalyst layer beneath the channel region corresponds to greater potential variation on the way to this location. Consequently, the activation
overpotential absolute value in the shoulder region exceeds that in the channel region, indicating that the electrochemical reaction driving force is stronger there. This finding of non-uniform activation overpotential is consistent with that of Kulikovsky
et al. (1999) and Sun et al. (2005b). Comparing the potential variation effects in the
three selected designs of the channel AR, show that a slender channel design exhibits a smaller ohmic overpotential, and a larger absolute activation overpotential at all positions of interest. This result is explained by the wide electron transport passage along the shoulder height and the reduced average distance between the shoulders and the channel center, leading to a reduced current resistance. Variation of these two potentials at 0.14V appears initially to be similar to that in Fig. 4.5(a). The channel with AR =1.5 has a stronger driving force of electrochemical reaction in the shoulder region as it has the smallest membrane and solid phase ohmic overpotential compared to the other two channel designs.
Figure 4.6 compares the transverse variation in the solid phase potential and the activation overpotential at the location between the cathode GDL and the catalyst layer at three GDL thicknesses and two operating potentials. The GDL thickness effect on ohmic overpotential is clearly demonstrated in the data in Fig. 4.6(a).
Despite the fact that the catalyst layer shoulder area exhibits minor ohmic overpotential in the design with a thickness of 152 mμ , the potential increases
abruptly toward the channel central region, because the height and cross-sectional area of the electron transverse transport passage are small in this thinnest design. For the design with the thicker GDL, the larger ohmic overpotential in the catalyst layer shoulder region is problematic, but the moderate potential variation toward the central channel is advantageous. Accordingly, the activation overpotential variation exhibits the same tendency as that of the solid phase potential. These situations are similar at the two operating voltage, but the absolute values and variations are greater in the 0.14V case.
4.3.3 Water Saturation Level
Channel geometry effects on the transverse saturation level of the cathode GDL along the channel direction is presented in Figure 4.7. The flat channel advantage is evidenced by liquid water accumulation. The relatively short distance through which water is transported at AR=0.5 leads to the low saturation level in the channel direction even at a high reaction rate. That means the fast diffusion associated with the flat channel design causes the local partial pressure of water vapor to be low.
In contrast, saturation level at the rear section of the channel with AR=1.5 is high, as the water vapor cannot easily escape from GDL under the shoulder. In this scenario, effective pore space in the porous medium is reduced considerably, and more mass
transport overpotential is activated, so cell performance is drastically degraded at low cell voltage.
Figure 4.8 plots the saturation level in the transverse direction of the cathode GDL at three positions x=0.05m, 0.025m and 0.045m, to elucidate GDL thickness effects on liquid water distribution. The plot demonstrates that the thinner GDL design has the lowest saturation level since water vapor produced in the cell reaction easily transports to the channel and outside the cell. On the contrary, the longer path and water vapor lower diffusion rate in the design with the 356 μ m-thick GDL results in greater water vapor concentration with a high probability of over-saturation and liquid water formation, contributing to concentration overpotential and performance reduction, especially at x=0.45m at a cell potential of 0.14V.
Note that in the discussing of saturation level in the electrodes, the temperature field may also be an influential factor. At locations where the electrochemical reaction rate is high, the enthalpy as well as temperature increase accordingly. The higher temperature region corresponds to a greater saturation pressure of water and lower local partial pressure, causing a lower water saturation level. However, the high production rate of water vapor at this region causes a counter effect.
4.3.4 Oxygen Concentration and Current Density
Figure 4.9 depicts oxygen mass fraction distribution and local current density under the same condition and at the same location as in Fig.4.5. Intuitively, the flat channel supplies more oxygen to the catalyst layer and a high current density is expected. However, calculations reveal entirely different trends between channel and shoulder region catalyst layers. The design with AR=0.5 generates the lowest local current density in the channel region, despite its having the largest oxygen mass fraction, and the expected relationship between reactant concentration and the reaction rate is not observed except at the shoulder center. On average, the slender design with AR=1.5 generates more current at moderate cell voltage. This phenomenon is explained by the fact that in this scenario, the reaction is relatively slow and the high reactant concentration is not as important as low ohmic overpotential and high activation overpotential provided by slender channel geometry such as AR=1.5. This design has a wider rib zone than those of other designs, providing a small increase and variation in the solid phase potential as well as large absolute activation overpotential, causing high current density and favorable cell performance. At a high reaction rate as shown in Fig. 4.9(b), the dominant mechanism of local current density transits from electric potential at the channel region, to oxygen concentration at the shoulder region at AR=1.5. This transition is also found when AR=1. The design with AR=0.5 exhibits the same local current density variation trend as in the case of o.62V. At AR=1.5, a
high reactant concentration need outweighs a high activation overpotential need, so the expected relationship between the concentration and the local reaction rate appears earlier. The large shoulder area width hinders reactant transport, resulting in a relatively low level of local oxygen mass fraction and a sharp decline in the local current density under the shoulder area. In contrast, the sufficient oxygen provided by the flat channel such as AR=0.5 causes most of the region to exhibit a potential controlled state and on average, produces a greater current than that generated by other designs.
GDL thickness effects on transverse distribution of oxygen concentration and current density is plotted in Fig. 4.10. Exhibiting a trend opposite to that of the potential, a thinner GDL provides more oxygen to the channel region catalyst layer.
The thickest design is associated with a greater concentration in the shoulder region.
These variations are related to the vertical depth and transverse cross-section of reactant delivery. In the case in which GDL thickness is 152μ m, the vertical path is short and oxygen concentration is high at the catalyst layer beneath the channel.
Nevertheless, the transverse transport cross-section is reduced and oxygen concentration falls substantially at the shoulder region. With reference to local current density distribution, mechanisms of activation overpotential mechanism and oxygen concentration have different effects in different regions. The activation overpotential
dominates the reaction in the catalyst layer under the channel region because oxygen concentration fulfills the requirement for electrochemical reaction. Accordingly, the current density trend is consistent with that of the activation overpotential throughout the entire region in the 356μ m case and in most of the region in the 203μ m and 152 m cases at 0.62V. A peak point in the concave pattern of the local current density appears only near the central shoulder region in the 152
μ
μ m cases, suggesting that from this point to the central shoulder, oxygen deficiency forces the current density to drop according to the oxygen mass fraction, and local performance is dominated by oxygen concentration. Nevertheless, most current density gain in the shoulder region catalyst layer arises from higher activation overpotential for the design with the 152
μ m cases, suggesting that from this point to the central shoulder, oxygen deficiency forces the current density to drop according to the oxygen mass fraction, and local performance is dominated by oxygen concentration. Nevertheless, most current density gain in the shoulder region catalyst layer arises from higher activation overpotential for the design with the 152