The study performed by Wang and Nehrir [68] serves as a benchmark case for verifying the present model’s dynamic behavior. Wang and Nehrir developed a dynamic, tubular, pressurizedSOFCmodel based on electrochemical, species mass balance, and energy balance equations. These authors investigated the voltage response of theSOFCto step changes in the current density on small, medium, and large timescales, corresponding to electrochemical, mass flow, and thermal processes, respectively. The operating conditions adopted in the present study are presented in Table 4.3. The flow configuration, inlet gas temperatures and pressures, and the air ratio are identical to those of Wang and Nehrir. The inlet fuel composition, fuel flow rate, and the current density, on the other hand, are based on theIEA
benchmark study (and the results thereof), as the corresponding conditions were either not specified by Wang and Nehrir, or they were not appropriate for use in the present model. Throughout this section, the settling time is estimated as the time required for the SOFC
operating voltage to reach a uniform (constant-slope) profile after experiencing a step change in the current density. Figures 4.3–4.5 present the voltage responses of the SOFC model. Settling times estimated from Wang and Nehrir’s results are indicated by red, dashed lines
Figure 4.3 Electrochemical voltage response. The red, dashed line indicates the es- timated electrochemical voltage response time from Wang and Nehrir’s results. The double layer polarization (axially averaged) is shown for Cdbl = 10 mF.
for comparison with the present model. In addition, as part of each simulation, a quantity is shown indicating the physical process associated with each transient phenomenon.
The model’s electrochemical voltage response is shown in Fig. 4.3. The current density decreases from 3000 A/m2 to 2500 A/m2 at 50 ms, and the double layer capacitance is varied between 0.1 mF and 10 mF. The electrochemical voltage settling time for Cdbl = 10 mF is found to be approximately 50 ms. This result agrees with the settling time obtained by Wang and Nehrir, who also found a settling time of approximately 50 ms [68]. Notice, also, that the voltage settling time is very close to the double layer polarization settling time, indicating that the charge double layer is associated with the SOFC’s dynamic behavior on the electrochemical timescale. It can furthermore be seen from Fig.4.3that the shape of the voltage profile depends on the value of the double layer capacitance. Higher values of the double layer capacitance lead to smoother (flatter) voltage profiles. This result also agrees with that of Wang and Nehrir. Finally, notice that the charge double layer polarization continues to increase even after settling has occurred. This longer transient behavior likely demarcates the beginning of the mass flow dynamic response, which characteristically occurs on the second timescale.
Figure 4.4 Mass flow voltage response. The red, dashed line indicates the mass flow voltage settling time estimated from Wang and Nehrir’s results. The H2 mole fraction (axially averaged) is also shown.
The model’s mass flow voltage response is shown in Fig. 4.4. The current density de- creases from 3000 A/m2 to 2500 A/m2 at 5 sec. The mass flow voltage settling time is found to be approximately 2 sec. The mass flow voltage settling time estimated from Wang and Nehrir’s results is also approximately 2 sec. [68]. Evidently, differences in the inlet fuel composition, while leading to different reactions inside the fuel cell (particularly the steam reforming and water-gas shift reactions), yields a negligible effect in terms of the mass flow voltage settling time. The choice of discretized vs. single-node domains also yields a negli- gible effect on the results, as Wang and Nehrir’s model included only a single node, while the present model discretizes the domain along the flow path. Notice, also, that the voltage settling time is very close to the H2 mole fraction settling time, indicating that the change in the gas composition is associated with the SOFC’s dynamic behavior on this timescale.
Finally, the fuel cell’s thermal voltage response is shown in Fig.4.5. The current density decreases from 3000 A/m2 to 2500 A/m2at 3000 sec. (50 min.). The thermal voltage settling time is approximately 600 sec. (10 min.). The thermal voltage settling time estimated from Wang and Nehrir’s results, on the other hand, is approximately 1500 sec. (25 min.). One possible explanation for this discrepancy is the choice of fuel. The reforming reaction is
Figure 4.5 Thermal voltage response. The red, dashed line indicates the thermal voltage settling time estimated from Wang and Nehrir’s results. The PENtemperature (axially averaged) is also shown.
highly endothermic, leading to faster thermal settling times when the temperature is reduced (i.e., the load is decreased). Wang and Nehrir assumed an inlet fuel composition of H2 and
H2O, whereas the present study assumed a pre-reformed fuel mixture, which then undergoes internal reforming. This difference may help to explain why Wang and Nehrir’s results exhibit a significantly slower thermal settling time compared to the present study. Martinez, et al. [23] observed a similar phenomenon. These authors compared the performance of an
H2-fueledSOFCsystem to that of a natural gas-fed system, finding that theH2-fueled system exhibited larger overshoots than the natural gas system during load decreases. Notice, also, that the thermal voltage settling time of the present model is very close to the averagePEN
temperature settling time, indicating that the average PEN temperature is associated the
4.5 SUMMARY
This chapter performed several checks on theSOFC model prior to simulation in later chap- ters. In particular, the present chapter demonstrated the fuel cell’s mesh-independence. The
PENtemperature, current density, composition, and PENtemperature gradient distribution exhibited only slight changes beyond 40 nodes. The present chapter also verified the SOFC
model during both steady-state and dynamic operation. During steady-state operation, re- sults from the model agree reasonably well with those from the benchmark case. Slight differences in the power and voltage likely arise from different polarization models. During dynamic operation, the fuel cell exhibits electrochemical (fast), mass flow (slower), and ther- mal (slowest) settling times that are on the same order of magnitude as those obtained by Wang and Nehrir [68]. The present model’s shorter settling times on the thermal timescale likely arise from the endothermic reforming reaction. In the next chapter, the fuel cell model is incorporated into two larger system models.