Critical control volume sizing for improved transient thermal modeling of PEM fuel cells
Many control-oriented models represent the entire fuel cell stack's thermal response with a single lumped temperature. While this simplification greatly reduces the computational expense of these models, it does not afford any information regarding cell-to-cell differences. In many cases, the operating conditions in the outermost (inlet and outlet) cells are significantly different from the rest of the stack. As a result, these cells also often limit the stack performance. Previous experiments performed by the authors have shown this phenomenon, particularly in the inlet cells. Poor performance in these cells led to a gradual decline in the stack average voltage at high loads, and caused the inaccuracy of the lumped fuel cell model prediction. These results suggest a need for individual modeling of the end cells to properly model performance in these areas, particularly during high demand phases. In this paper, the necessity of multiple thermal control volumes (CVs) in the cathode channel is investigated to address the spatial gradients. A method to improve the thermal modeling accuracy near the cathode inlet of the fuel cell stack by using un-evenly spaced CVs to represent the channel is presented. Analysis is performed starting with the 1D heat transfer equation for the cathode channel. By using scaling arguments to remove extraneous terms, a simplified 1D solution for the temperature profile in the cathode channel is developed. From this result, the necessary CV sizes to remain within a critical band of the actual spatial temperature profile can be calculated.
International Journal of Hydrogen Energy
Headley, A., & Chen, D. (2015). Critical control volume sizing for improved transient thermal modeling of PEM fuel cells. International Journal of Hydrogen Energy, 40 (24), 7762-7768. https://doi.org/10.1016/j.ijhydene.2014.12.123