Transient simulation of a tubular micro-solid oxide fuel cell
Introduction
The transient behavior of a solid oxide fuel cell (SOFC) has a significant practical interest, more so as the commercialization of this technology becomes more viable. The operation of an SOFC is by nature transient; the current and voltage can change significantly during its operation as a result of changing load requirements. Critical components of a SOFC power generation system, such as the control and power conditioning sub-units, are typically designed to handle transients. As the load changes in the SOFC, concomitant changes in operating parameters are required to keep it running both effectively and within the acceptable range. For example, a load increase requires a higher flow rate of reactants to maintain the same utilization and efficiency. Furthermore, to avoid temperatures that exceed permissible limits, the extra thermal energy generated at higher load levels must be removed, for example by increasing the air circulation rate. Managing and controlling such transient is vital to proper operation of the SOFC system [1]. During start-up and shut down cycles thermal transients are usually significant, and it is important to manage the thermal stresses so as to ensure mechanical stability and safe operation. Optimum control of such transients will maximize the efficiency of the SOFC system [2].
Computer simulation is a powerful tool that can be used to improve understanding of SOFC transients, how to predict them, and to control them effectively. There are many SOFC models reported in the literature, and these show variations which vary in their details, designs, and purposes. Bhattacharyya et al. [3] provide a detailed review of a wide range of these models. One of the main purposes of transient modelling is effective SOFC control, and many dynamic models have been used to study and optimize control strategies [2,[4], [5], [6], [7], [8]]. A simplified model that correlates the SOFC input parameters to parameters that need to be controlled, for example, power, voltage, current and temperature, might be sufficient for this purpose. For this reason, control based models are often simplified zero [[9], [10], [11], [12], [13]] or one-dimensional [[14], [15], [16], [17], [18]]. Transient models have been used to study the systems aspect of the SOFC operation, i.e. the balance of plant, which focuses on the interaction of the components [19,20], the control and optimization of the overall system [[21], [22], [23], [24], [25], [26]], to analyze system performance in the grid [27], to understand the effect of load transients [28], and to develop load-following strategies [[29], [30], [31]]. In addition, dynamic models based on physics have been developed that model SOFC in two dimensions [32,33], quasi-three dimension [34,35], and three dimensions [[36], [37], [38]]. Some transient models are used to gain a better understanding of various SOFC operational details such as startup conditions [39,40], carbon deposition [41], effect of flow configuration [42], and the induced mechanical stress effects [42]. Models simulating transient behavior of SOFCs go beyond the time-domain transient simulations in cases where in frequency domain the impedance response of SOFC cells and electrodes are modeled [33,[43], [44], [45], [46], [47], [48], [49], [50], [51]].
The significant phenomena observed in a fuel cell have widely differing transient time-scales. The electrochemical reaction steps are very fast and have time constants on the order of a fraction of a second [52]. The mass transport phenomena at high temperatures are quite fast and sub-second as well [52]. The slowest are the thermal transients, which are highly dependant on factors such as the design and architecture of the cell, and typically greater than 100 s [52]. Transient time constants, especially the ones for heat and mass transport, depend on the design and operating conditions of the cell. For example, cells with thicker electrodes or lower gas velocities have slower mass transport transients. The thermal transients are often the controlling ones, and therefore they are most importance from a practical point of view. This observation has induced some modellers to include only the thermal transients in their models. One of the earliest dynamic SOFC only modeled temperature distribution and electrochemical reactions [53,54]. Furthermore, there are even transient models that assume isothermal conditions [55,56].
TμSOFCs offer several advantage compared to other geometries. Because of the micro deign, they have small thermal mass, and also the thermal gradients across the cell are minimized. Both these advantages makes them superior for rapid star-up, shut-down, and fast load-following applications, which are all inherently transient phenomenon.
In this paper, the TμSOFC steady-state model reported previously [57] is extended to predict transient behavior. The resulting transient model comprehensively captures all of the relevant phenomena in detail. The transient transport phenomena within the gas channels and the electrodes are included. A unique aspect of the presented transient model is its experimental validation. Experimental validation is a significant aspect of any simulation work, to ensure the relevance and applicability of the results. However, little work has been done on experimental validation of transient models [56], which makes a simulation work presented along with experimental validation, such as this work noteworthy. Hence, this work is significant because it presents such details in the transient model along with the presentation of a comprehensive experimental validation; it is one of the few if not the only paper in that regard.
Section snippets
Experimental
The tubular micro-solid oxide fuel cell that is the subject of this work is shown in Fig. 1. The cell was developed at the Alberta Research Council using the electrophoretic deposition technique (EPD). EPD allows for fabricating very thin layers of anode and electrolyte as shown in Fig. 1(b). The cell is anode supported, with a Ni/YSZ anode, YSZ electrolyte, and LSM/YSZ cathode and has one end closed. A diffuser tube was used to inject hydrogen to the closed end which flowed back along the
Results and discussion
The effect of various quantities on the thermal and voltage transients to a step change in the current load from 0 to 1 A was simulated. Because the behavior of the TμSOFC itself is the focus, the results presented are for the case without a thermocouple effect.
As a general rule, the time constant for a transient thermal system is proportional to its thermal mass, mcp, and to the inverse of the heat transfer coefficient [61]:
The heat transfer coefficient increases when
Conclusion
A transient model for a TuSOFC was developed and solved. As no parameter fitting was done, the simulation results were purely predictive. Simulations were validated against experimental results and were found to make reliable predictions. When the effect of thermocouples attached to the cell was included, the model predictions were closer to the experimental values.
The thermal behavior of the system was distinguished by two transients. The faster transient corresponded to the cell, and a slow
Acknowledgement
This work was financially supported by the Alberta Ingenuity Fund in Nanotechnology, and the Natural Science and Engineering Council of Canada (NSERC) strategic grant.
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