Figure 2.9 depicts the temperature distribution of the cell when the inlet flows are uniform. The isotherm increases from under 600°C close to both the inlets of the anode gas and the cathode gas to 638°C near the corner of both gases outlets . When the anode gas and the cathode gas flow through the reaction area of the cell, they not only supply the reaction species but also carry away the reaction heat in the cell.
Therefore, the anode gas and the cathode gas accumulate all of the reaction heat and reach their maximum temperatures when they flow to the outlets. The temperatures
of the gases also influence the temperature distribution of the cell and separator because coupled heat transfer occurs among them. In this figure, the isotherm in the y direction increases more uniform than that in the x direction. Hence, the cathode gas dominates the cell cooling because it has a higher flow rate than the anode gas.
Figure 2.10 displays the current density distribution on the cell plane under the same conditions as in Fig. 2.9. The minimum current density is 1316A m⋅ −2 in the corner of the cathode gas inlet and the anode gas outlet, and the maximum current density is 1846A m⋅ −2 in the middle-left outlet of the cathode gas. When the cell voltage is set to be a constant, the Nernst voltage and the internal resistance of the cell directly affect the current density according to the Ohmic law. With respect to the relationship between the Nernst voltage and the current density, examining the Eq.
X(2.15)X indicates that the concentration of gas species influences the Nernst voltage, which declines as the concentrations of hydrogen and oxygen drop. Since the cathode gas is easily obtained from the environment and thus has a larger flow rate in order to cool the cell, the variation of the oxygen concentration is less than the hydrogen concentration. Consequently, the current density fell should decrease in the x direction of the anode gas flow, because the Nernst voltage fell with the drop in hydrogen concentration. With respect to the relationship between internal resistance and current density, Fig. 2.11 presents the total internal resistance distribution on the cell plane. The total internal resistance is defined in Eq. X(2.18)X which obtained from Bosio et al [30]. In this figure, the continuous line and dashed line are represented
the results of FORTRAN program and FlexPDE, respectively. The results of FORTRAN program agree well with the results of FlexPDE. In Fig. 2.11, it shows that the distribution of total internal resistance is similar to the distribution of current density, but reaches a minimum in the middle-right outlet of cathode gas. The area of lower internal resistance represents it has higher current density when the cell voltage is set to be constant. When both the effect of the concentration of species and the total internal cell resistance are considered, it is reasonable that the contour with maximum current density moves left as determined by comparing Fig. 2.11 to Fig. 2.10 because of the effect of the concentration of hydrogen.
Figures 2.12(a) to 2.12(h) show the systematic cell temperature distribution of eight patterns with a deviation of 0.5. Meanwhile, T and Δ represent the T average and variation of cell temperature, respectively. In these figures, it shows that the dominated factor on cell temperature distribution is the cathode gas, because the main trend of isotherm is increasing along the y direction of cathode gas flowing.
In Fig. 2.2, Patterns A to B, C to E, and F to H have the same inlet flow profile of the cathode gas in each group. In Figs. 2.12(a) and 2.12(b), the cell temperature distributions of Patterns A and B are similar, and the main trend of cell temperature increases from under 600°C in the inlet of cathode gas to 636-638°C in the outlet of the cathode gas along the y direction, which is close to that in Fig. 2.9 with uniform inlet flow of the anode and the cathode gases. The cell temperature distribution of Patterns C, D, and E are similar to each other, and Figs. 2.12(c) to 2.12(e) show that
the isotherm range is from under 600°C to 638-640°C, and the highest temperature moves from the corner of the outlet of both cathode gas and anode gas to the middle of the cathode gas outlet. Examining the inlet flow profile of Patterns C to E indicates that the flow rate of cathode gas progressively increases in the x direction.
Since the part that is close to the outlet of the anode gas has more cathode gas to cool the cell, the highest temperature in the corner moves to the left, as revealed by comparing Figs. 2.12(a) and 2.12(b), which have uniform cathode inlet flow. In Figs.
2.12(f) to 2.12(h), Pattern F, G, and H also have analogous temperature distribution of the cell, and these figures show that the temperature distribution of the cell is from under 600°C to 648-649°C, and the highest temperature occurs in the corner of the outlet of the cathode gas and the anode gas. Notably, the variation of cell temperature in Patterns F to H is about 58°C, and it is wider than that in Patterns A to E, so this is the worst temperature distribution. Patterns F to H have the same inlet flow profile of the cathode gas, which is progressively decreasing in the x direction.
This non-uniform inlet flow causes less cathode gas to flow through the part with higher temperature on the cell, where is near the outlet of the anode gas. Therefore, the highest temperature in Figs. 2.12(f) to 2.12(h) rises more than those in Figs. 2.12(a) to 2.7(e). This study selects the cell temperature field of Pattern B and F, which has the least and most temperature variation, to subtract the cell temperature field in uniform pattern, and then show the results in Fig. 2.13. In this figure, the temperature difference of Pattern B related to uniform pattern is between -3 and 5°C,
as well as the largest temperature difference of Pattern F related to uniform pattern occurs at the corner of gas outlet and it is over 12°C.
Figure 2.14 plots the systematic cell current density distribution of eight inlet flow patterns with a deviation of 0.5. Meanwhile, i and Δi represent the average and the variation of current density, respectively. In this figure, the current density distribution of Pattern A is similar to those of Patterns D and G, and that of the current density distribution of Pattern B is analogous with those of Patterns E and H.
Similarly, the current density distribution of Pattern C is similar to that of Pattern F.
The inlet flow profile of each pattern in Fig. 2.2 indicates that Patterns A, D, and G, Patterns B, E, and H, and Patterns C and F represent three groups whose members have same profile of anode gas inlet flow in each group. Therefore, the inlet flow pattern of the anode gas dominates the current density distribution. As mentioned in the second paragraph of this section, the concentration of hydrogen and the total resistance of the cell influence the current density. An anode gas flows faster with a less varying hydrogen concentration, and with a more uniform current density distribution as the uniformity of the Nernst voltage increases. On the contrary, an anode gas flows more slowly and with a greater change in the hydrogen concentration because of the consumption of hydrogen in the chemical reaction, with a greater change of current density in the direction of flow of the anode gas. In Figs. 2.14(c) and 14(f), the current density distributions are similar to that in Fig. 2.10 because the inlet flows of anode gas have the same uniform profile. In Figs. 2.14(a), 2.14(d), and
2.14(g), it is clear that the current density distribution at the top half of the cell is clearly more uniform than that in the bottom half of the cell, because the inlet flow of anode gas in Patterns A, D, and G progressively increase in the y direction. Figures 2.14(b), 2.14(e), and 2.14(h) show that the distributions of current density in the bottom half are more uniformly than the distributions of current density in the top half of the cell, because Patterns B, E, and H have a progressively decreasing inlet flow rate of the anode gas in the y direction. Figure 2.14 shows that the current density difference of Pattern D and F related to the uniform pattern, because Pattern D and Pattern F have the most and least current density variation in Fig. 2.14. In Fig.
2.15(a), the current density difference of Pattern D is between –365 and 173A m⋅ −2, and the maximum difference occurs near the outlet of anode gas. The current density difference of Pattern F related to uniform pattern is between –30 and 53
A m⋅ −2, so it seems flat in Fig. 2. 15 (b).
This study calculates all patterns in Fig. 2.2 with three deviations of 0.25, 0.5 and 0.75. Table 2.3 presents the results, and Fig. 2.16 presents them as histograms.
The vertical axis represents the relative variation of temperature or current density in non-uniform patterns to uniform pattern. Meanwhile, TΔ and Δi represent the difference between the maximum and minimum temperature and current density on the cell. In Fig. 2.16(a), the relative variation between average cell temperature and that in the uniform inlet flow is always ±0.4% for all deviations. Consequently, the non-uniform inlet flow affects slightly the average cell temperature and this effect can
be ignored. In Fig. 2.16(b), the absolute relative variation between the average current density and that in uniform inlet flow is always lower than 5% for all deviations. The variations of average current density in Pattern C and Pattern F are very small and there are almost to be zero. That means the more uniform the inlet of the anode gas is, the smaller the average current density will be. Moreover, the inlet of the cathode gas is non-uniform. Additionally, the relative variations of average current density in Pattern B, Pattern E and Pattern H are much worse than in the other patterns, and are close to –5% at a deviation of 0.75. Examining the patterns in Fig.
2.2 shows that all of them have progressively decreasing inlet flow in anode gas.
Based on the Eq. X(2.15)X and Eq. X(2.18)X, increasing the cell temperature increases the Nernst voltage and reduces the total cell resistance. Therefore, the current density increases with the cell temperature as the Nernst voltage gets increases and total cell resistance in Eq. X(2.17)X declines. According to the results in Fig. 2.12 and Fig. 2.14, the temperature and the current density in the top part of the cell plane are higher than those in the bottom part. The higher current density causes more hydrogen to be consumed in this area. Therefore, the consumption of hydrogen in this area is more than that in other area due to the higher current density. In Pattern B, E, and H, since the mole flow rate in the top part is less than that in the bottom part due to the progressively decreasing inlet profile of anode gas, the average current density will drop due to the lack of hydrogen. Therefore, the progressively decreasing inlet flow profile in anode gas is the worst for average current density.
Figures 2.16(c) and 2.16(d) represent the relative variation of cell temperature and current density distribution related to those in uniform inlet flow. The distribution of temperature is worst in Pattern F with a deviation of 0.75, for which the relative variation is 37%. The distribution of current density is worst in Pattern D with deviation of 0.75, for which the relative variation is 179%. Furthermore, authors find that some relative variations are negative in Figs. 2.16(c) and 2.16(d), indicating that the variation of temperature or current density in the non-uniform inlet flow is less than that in uniform flow. In Fig. 2.16(c), Pattern B exhibits a better distribution of temperature because the temperature difference decreases as the deviation of non-uniform profile increases. Moreover, Pattern F has a more intensive current density distribution than that in uniform in Fig. 2.16(d), because the values of relative variations are –3%, -6%, and –10% with deviations of 0.25, 0.5, and 0.75, respectively. Although the uniformity of temperature distribution in Pattern B is better than others flow patterns, the uniformity of current density distribution is the worthiest than others flow patterns. The uniformity of current density distribution in Pattern B is the worthiest, because there is a non-uniform inlet flow of the anode gas channel. The uniformity of current density distribution in Pattern F is better than other flow patterns, but the uniformity of temperature distribution is the worthiest than others flow patterns. The uniformity of temperature distribution in Pattern F is the worthiest, because its inlet flow pattern of the cathode gas channel is non-uniform.
In Figs. 2.16(c) and 2.16(d), note that both Patterns A and B have better temperature
distribution than the other non-uniform patterns, and both Patterns C and F have a better current density distribution than the other non-uniform patterns. Examining the inlet flow profile in Fig. 2.2 indicates that Pattern A and B have uniform inlet flow of cathode gas, and Pattern C and F have uniform inlet flow of anode gas. Therefore, the uniform inlet flow in both the anode side and the cathode side is the best profile from the perspective cell temperature and current density distribution. In industrial applications, the position of the inlet manifold affects primarily the inlet flow distribution and the uniform inlet profile is difficult to obtain. Therefore, the uniform inlet flow is the goal of the design of an MCFC with a cross-flow configuration, and designers must avoid putting the inlet manifolds of the anode gas and the cathode gas too close to the side of another gas inlet, which would produce non-uniform inlet flow with a progressively decreasing profile. Such poor positions of manifolds would further reduce average current density, as shown in Pattern B and Pattern E in Fig. 2.16(b), and widen the cell’s temperature distribution, as shown in Patterns F to H in Fig. 2.16(c).