Recall that the performance curve is simply a plot of the voltage versus the current, usually labeled as the ‘V-i’ curve. For the initial model verification simulation, several input parameters were selected as defining parameters corresponding to the values listed by the experimental results. These parameters include the fuel cell stack power, average stack temperature between top and bottom, steam to carbon ratio, air inlet temperature, fuel inlet temperature, fuel utilization, and temperature difference between the cathode outlet and cathode inlet. Although experimental data for the fuel and air inlet flow rates are available, these values were not included in the initial round of simulation to understand how well the air and fuel flow rate controllers in the model can match the experimental air and fuel inlet flow rates. Therefore, the fuel and air flow rate controllers were left unconstrained for this round of simulations while the important electrochemical parameters were manually adjusted in order to match the performance curves. It is worth noting that when leaving the air flow controller unconstrained, the cathode outlet temperature is always exact because of the nature of the air flow controller. In addition, the exact degree of external reformation was not provided by SolidPower, therefore each simulation represents results for differing degrees of external reformation.For this round of simulations, the electrolyte constant differed very slightly for each degree of external reformation according to the Table 14. As is immediately noticeable,grow trays the power curves match the power demanded on the system model because of the nature of the power controller to match the power demanded on the system.
However, the polarization curves show slight differences from the experimental results for moderate to high current densities, which may be a result of inaccuracies in the calculation of the ohmic and concentration losses. Despite these small differences, it is clear that the model’s polarization curve nearly matches that of the experimental results for all points. With successful matching of the polarization and power curves, of secondary importance is verifying that the anode and cathode outlet temperatures as well as the air and fuel flow rates from the model match that of the experimental data. Reviewing the anode outlet temperature, cathode inlet flow rate, and anode inlet flow rate plotted in Figures 33-36, inaccuracies are immediately apparent. Recall that there is no error with the cathode outlet temperature when the air flow rate is left unconstrained, which explains why the cathode outlet temperature is exact for each simulation point. Of particular interest here is that decreasing the degree of external reformation reduces the anode outlet temperature of the model and brings it closer to the experimental data, which conforms to electrochemical theory. Nevertheless, the cathode and anode inlet flows are consequently much more inaccurate. The theory that explains why the anode outlet temperature is reduced when the degree of external reformation is reduced follows from the fact that for lower degrees of external reformation, lower concentrations of methane are reformed by the steam methane reformation reaction in the external reformer. As a result, higher concentrations of methane enter the anode of the fuel cell stack where it is internally reformed by the high temperature operation of the SOFC.
Recall from thermodynamic theory that the steam methane reformation reaction is a highly endothermic reaction and therefore should result in lower anode outlet temperatures as heat is being absorbed by the steam methane reformation reaction. Due to the limitations in available information provided by SolidPower, the selected electrochemical parameters are educated guesses based upon repeated model simulations following the provided experimental data obtained through experimentation of the Engen-2500 system in the NFCRC lab. Therefore, all selected electrochemical parameters herein are based on educated guesses resulting from repeated model simulations. Furthermore, repeated simulations have consistently shown that the anode outlet temperatures of the model are higher than what the experimental data indicates. To achieve the lowest possible anode outlet temperature, all simulation results shown are performed with air and fuel inlet streams entering the fuel cell stack opposite one another suggesting a counter-flow design for the actual Engen-2500 stack. Of course, no analysis verification is ever complete when there remain pieces of known information that have not been tested. For this round of simulations, the air and fuel inlet flow rates of the model are constrained to the known inlet flow rates provided by the experimental data. Therefore, the air and fuel flow rate controllers are not controlling the inlet flows but instead exactly match the known flow rates for each simulation point. Again, varying degrees of external reformation are plotted because the actual extent of reformation is unknown. According to the following plots, it is evident that the air and fuel inlet flows are constrained to the appropriate molar flow rate values, despite an obvious error in the highest current point where the model and experimental values for current do not quite match.
The reason for the current mismatch for the fifth simulation point is better characterized by looking at the polarization curve plots. As mentioned previously, it is important that for all simulations the polarization curves produced by the model match the experimental data as accurately as possible. The following plots show that after adjusting the electrochemical parameters for each degree of external reformation , the polarization and power curves are quite accurate despite discrepancies at the lowest and highest current density points. Although the polarization and power curves very well match the experimental data, a critical discrepancy occurs at the highest current value. There may be a number of reasons to explain this, however, the most relevant conjecture would be to consider the anode and cathode outlet temperatures and ensure that the temperatures produced by the model match those of the experimental data.At first glance, there is no doubt that the outlet temperatures are far from accurate. What is immediately noticeable is the correlation between lower degrees of external reformation and the lower anode outlet temperature. Recall that from section 6.1.3 Polarization Losses, the activation and concentration over potentials are dependent upon the temperature of the electrolyte. Because of this temperature dependence, it is highly likely that the mismatch in temperature is causing the discrepancy at the lowest and highest current simulation points. It is already known that for very low current levels, the activation over potential plays a major role in limiting the stack voltage and for very high current levels, the concentration over potential acts as the pivotal limiting factor. Therefore, it is imperative that cathode and anode outlet temperatures be as close to exact as possible. It is important to note that matching the air and fuel inlet flows came out nearly perfectly for this round of simulations with no obvious errors at high or low current levels . This happens to be a direct result of reducing the discrepancy between the anode outlet temperature predicted by the model and the actual values specified by the experimental data. Table 16 includes the electrochemical parameters used for each simulation. Referring to the polarization curves, it is evident that there are minor errors with matching the voltage values for the highest and lowest current simulation points. Nevertheless,pruning cannabis the errors do not seem to be as wild as in the previous case – especially when considering the highest current point. As mentioned previously, there may be a number of reasons for the minor errors, but first it is important to compare the anode and cathode outlet temperatures produced by the model to those of the experimental data. Looking at the cathode and anode outlet temperature plots above, an interesting trend is revealed. Before getting into the details of this trend, it is important to mention that the ‘heat loss to the environment’ terms is supposed to simulate convection heat transfer occurring at the immediate surfaces of the fuel cell stack. The heat loss to environment terms simply compares the difference in temperatures between the temperature of the immediate surroundings outside of the fuel cell stack to the temperature of the fuel or oxidant separator plate. This difference in temperature is then multiplied by a convection coefficient for air similar to any simple convection heat transfer problem.
Comparing all of the results for the polarization, power, outlet temperatures, and flow rate plots, it is evident that the simulations made in round three provide the best all-around fit to the experimental data. It is well understood that the electrochemical reaction kinetics are usually limited by cathode reactions. This is because the electrochemical kinetics are primarily involved with the reactions occurring at the triple-phase boundary on the cathode-electrolyte interface. All of the reaction kinetics, however, are exponentially dependent upon temperature. The interesting trend that was realized was that the system model consistently predicts anode and cathode outlet temperatures that are very close to one another. As is evident from round two and round three simulations for the given fixed air and fuel flow rates, the anode and cathode outlet temperatures differed by less than 10 degrees Kelvin. This could be due in large part to the difficulty in accurately measuring heat transfer kinetics especially due to limitations in available information provided by SolidPower. The most revealing piece of information that was provided by SolidPower showed the locations of the fuel inlet and outlet thermocouples in the Engen-2500 stack. However, the air inlet and outlet thermocouples were not labelled in the provided confidential diagram. This leads me to question the veracity of the cathode outlet temperature since the location of the thermocouple could give some additional insight to the heat transfer kinetics. Furthermore, the model predicts the anode and cathode outlet temperatures at the immediate exit of the stack. Therefore, it is possible that if an air or fuel thermocouple is placed a distance away from the immediate stack exit, that the temperature measured by the thermocouple would indeed differ from the temperature at the stack exit because of convection and potentially radiation heat transfer kinetics due to such high operating temperatures. The ultimate goal of this thesis was to prove the validity of implementing a SOFC for handling any kind of dynamic load – even for extreme cases. One extreme case that can be immediately tested using the Engen-2500 system model is the ability for this system to handle the dramatic fluctuations in load-demand such as the power demanded by several computer servers booting up. Microsoft was able to provide the power dynamics for the case of 9 servers powering on, which is shown in the following plot. The reason the SOFC system model predicts perfect load-following capability is because the system model is utilizing air and fuel flow controllers that can respond instantaneously to the dramatic spikes in power demand. Therefore, at any moment the air and fuel flow controllers can instantaneously measure the required air and fuel flow rates necessary for the fuel cell stack to match the power demanded of it – hence why this simulation is an example of a SOFC load-following capability under ideal conditions. Recall from Dr. Zhao’s previous work with utilizing PEMFCs for a similar application, that it was found that the processes inside a fuel cell occur on time scales on the order of milliseconds; however, load following issues arise when the fuel cell system cannot meet both external system and balance of plant power demands. Limitations could result from conservative control techniques or inherently slow response of subsystem components, such as flow or chemical reaction delays associated with fuel and/or air processing equipment. Nevertheless, the Engen-2500 system model is indeed able to tackle even the most severe dynamic loads when considering ideal air and fuel flow rate conditions. Furthermore, snapshots of the temperature gradients across the surface of the five modeled components of a cell can be illustrated in an image. For example, the following images are a snapshot of the temperature gradients across the cathode gas stream, PEN, and anode gas stream. Comparing the temperature gradients of the cathode gas stream to that of the anode gas stream, it is readily noticeable that the rightmost edge of the cathode gas stream experiences much lower temperatures than that of the anode gas stream. This makes sense because it is evident from the label on the x-axis that the air is flowing from right to left and the fuel from left to right.