Effects of Bend Angle

Figure 4.13 shows the resultant polarization curves for three flow patterns (45–135, 60–120 and 90–90) with different bend angles at the conditions specified in Table 4.2. The first number in each flow pattern represents the first angle of the channels, and the second one represents the second angle.

These two are combined to generate a complete U-turn flow channel. The reversible voltage is 1.0404V with cell temperature of 323K and 1.1154V with cell temperature of 353K that are obtained by the equation from reference [33].

As mentioned previously, the pattern of 90–90 is the most conventional one applied in most researches such that it is considered as the reference case.

Table 4.2 Operating conditions

Parameter Value Operating temperatures 323 and 353 (K)

Reversible voltages 1.0404 and 1.1154 (V) Atmosphere pressure 101.3 (kPa)

Outlet pressure 101.3 (kPa)

Flow direction Counter current

Anode inlet conditions

Gas H₂

Relative humidity 100%

Temperature 323 and 353 (K)

Flow rate 796.08 (ml/min)

Cathode inlet conditions

Gas O2

Relative humidity 100%

Temperature 323 and 353 (K)

Flow rate 658.992 (ml/min)

From the comparison of polarization curves, it indicates that the performances are higher at 353K due to the enhanced reaction rates and the increase of reference current densities. The figure also shows that 60–120 pattern achieves the highest performance at low operating voltages ranged from 0.4V to 0.6V. Comparing to 90–90 pattern, this pattern’s performance gives around 5% higher current density with cell temperature of 323K and around 4%

higher with temperature of 353K at 0.4V. It is resulted from the higher Peclet number in the flow channel that will be discussed below. Note that the results show that the performance difference between 45–135 and 90–90 can be ignored because of only about 1% disagreement between these two patterns.

The inverse of local Peclet number (Pe^-1) in streamwise direction at each anodic bend entrance is shown in Fig. 4.14. The operating voltage is 0.4V

because it can achieve the highest power density. This figure indicates that 60–120 pattern has higher mass diffusion rate compared to the ones of 45–135 and 90–90. Comparing to 90–90 pattern, this pattern gives around 3% higher value of Pe^-1 in the bends from the third one to the tenth with cell temperature of 323K and around 2% higher from the third one to the eighth with the temperature of 353K. From the results of [40], the transition of transport mechanism from the diffusive regime to the forced one is situated around Pe^-1=0.04. In convection regime, the higher mass diffusion rate will thus intensify the electrochemical reaction. As the cell temperature is increased from 323K to 353K, the difference of Pe^-1 between 60–120 and 90–90 patterns decreases, indicating that the influence of bend angle on flow mechanism decreases with an increase of cell temperature. However, at the locations near inlets and outlets, Pe^-1’s from different patterns are approximately equal because of the same boundary conditions. For further analyses, the distributions of current density, temperature and water content will be compared.

Figures 4.15 and 4.16 show the distributions of current density in the membrane at an operating voltage of 0.4V with cell temperatures of 323K and 353K, respectively. It can be seen that the current density decreases from anodic inlet toward anodic outlet duo to the consumption of hydrogen as discussed before. These figures also indicate that 60–120 pattern has the considerably highest local current density at bending areas than those of other patterns at both cell temperatures, which result in the improvement of performance. With cell temperature of 323K, the variation of 45–135 is 663 mA/cm², the one of 60–120 is 658 mA/cm², and that of 90–90 is 645 mA/cm². With temperature of 353K, the variation of 45–135 is 548 mA/cm², the one of 60–120 is 514 mA/cm², and that of 90–90 is 502 mA/cm². Comparing to

90–90 flow pattern, even though 60–120 pattern achieves the highest performance, it does not effectively decrease the variation of current density as the change of bend angle.

Figures 4.17 and 4.18 show the distributions of temperature in the membrane. From Fig. 4.17, it indicates that the temperature reaches the highest value, 326K, in the area above the second anodic channel for all cases and then slowly decreases toward anodic outlet. Figure 4.18 shows that the temperature reaches the highest value, 356K, in the area above the second, third and fourth anodic channels, then, decrease slowly to the exit region. The simulations reveal that the three patterns have similar temperature distributions, implying that the change of bend angle does not significantly improve the temperature uniformity. This also indicates that there exists a limit to how much the improvement of temperature uniformity can be obtained from the change of bend angle.

Figure 4.19 shows the average temperature in the membrane as a function of the current density. It shows that the average temperature increases positively with the current density because of the increasing chemical reaction rate. The average temperature of 60–120 is comparatively higher than that of the other patterns, especially at the higher current densities, due to the higher performance.

This figure also indicates that the difference between the average temperatures of 45–135 and 90–90 is very small with both cell temperatures that are consistent with their performances.

Figure 4.20 and 4.21 present the distributions of water content in the membrane. From the comparison of these two figures, it indicates that overall water content decreases as the operating temperature is increased from 323K to 353K because liquid water formation is inversely proportional to the cell

temperature as mentioned before. Both figures show that 45–135 and 90–90 patterns with different bend angles have similar water content distributions at the same cell temperature. With cell temperature of 323K, the local water content can reach around 9 near the area above the inlet region, then drops gradually toward the exit region. For the temperature of 353K, the local water content can only reach around 6 in the area above the marginal rib and drop to 4 at the one third of the anodic channel, then maintain this value through the exit region. Moreover, both Figs. 4.20 and 4.21 show high water content uniformity in the membrane with only about 5 for the variation that is beneficial for flooding prevention.

Figure 4.22 and 4.23 show the average water content in the membrane and the corresponding electrical resistance at each current density in this study.

The figures reveal that all the three patterns have approximately equal water content under the same cell temperature since the difference between their performances are not great. Also, Fig. 4.22 shows that as current density increases, the membrane water content decreases with cell temperature of 323K.

The decrease in water content at increasing current density is because of an increase in net proton flux that drags water from the anode to the cathode with increasing current density, and therefore, dehydration happens in the membrane.

The intensified water transport from anode to cathode results in membrane dehydration because the hydration state of membrane is a stronger function of anode water activity rather than cathode one. However, with the cell temperature of 353K, the average water contents of the three patterns slowly increase with their current densities, indicating that water content is dictated by reaction intensity rather than proton flux within the membrane. It is resulted from insufficient liquid water formation when cell temperature goes beyond

348K that reduces the electro-osmotic drag force. Usually, the value of water content can reach as high as 22 when at water boiling temperature and current density of 2000 mA/cm² mentioned in reference [5]. However, in this study, the water content is much lower than 22 because the cell temperatures are below boiling point and the current density is comparatively lower than 2000 mA/cm². With such small water content, flooding effect does not appear or cause a substantial voltage drop near the end of the polarization curves. Moreover, it is indicated that higher water content leads to lower membrane electrical resistance since the proton conductivity is proportional to the water content inside the membrane.

Figure 4.24 and 25 show the distributions of saturation on the interface between cathodic GDL and catalyst layer. Patterns with cell temperature of 323K are clearly having higher saturation level compared to the temperature of 353K, since the temperature below 348K is favorable for liquid water formation.

Also, the first rib from the left is considered as dead-end zone where saturation level is high because of limited convection in the region. However, the distributions between different patterns are similar under the same operating temperature, since the flooding effect is not significant.

From above comparisons, it is noted that 60–120 pattern has the highest performance compared to 45–135 and 90–90 patterns duo to the increase of mass diffusion rate. The local uniformities of current density, temperature and water content are improved incrementally along the anodic channel with the increase of mass diffusion rate. However, the improvement for the overall uniformity of current density distribution owing to the change of bend angle is limited. Also, the results between 45–135 and 90–90 are more or less similar for the performances and all variable distributions.