A Transient Three-Dimensional Mathematical Model for the Local Impedance and Polarization Performance of Planar SOFCs
Authors: Sezer Hayri , Mason Jerry H , Celik Ismail Bektas , Abernathy Harry W. , Epting William K , Kalapos Thomas , Hackett Gregory A 
Published: July 2021

Electrochemical impedance spectroscopy is an invaluable tool for understanding the various processes and their relative effective resistances within electrochemical energy devices such as fuel cells. Due to their large surface area, the overall resistance of planar cells is relatively small especially for cells that are not electrolyte supported. This makes experimental measurements of planar cell impedance difficult as the noise and disturbances external to the cell is more likely to distort or even dominate the measurement. It is expected that impedance spectra in planar cells will differ from button cells due to the additional considerations of processes occurring in the flow channels such as sudden variations in gas velocity and density or that temperature gradients will play a role. Theoretically, a comprehensive Multiphysics model can be used to interrogate the impact of these factors more clearly than what can be achieved experimentally. In the present work, a transient three-dimensional multi-physics model is used to predict the impedance and polarization behavior of a planar solid oxide fuel cell (SOFC) utilizing hydrogen under varying operation conditions and flow configurations. The mathematical model solves for species, charge, momentum and energy transport in the cell components and interconnects. The mathematical model presented in this work is used to investigate the local impedance spectra and the current density distribution in different regions of the cell. The polarization and impedance simulations are performed for the full 3D domain and locally by dividing the cell into three regions along the flow direction. Computationally, it is expensive to simulate transients occurring within the 3D geometry of SOFCs. The model must be able to capture processes occurring over several different time scales in order to capture the full range of relevant processes. To overcome this impediment, the impedance calculations applied in this study employ Bessler’s fast impedance modeling technique[1], in which a current stimulation is applied to obtain the corresponding potential relaxation. The polarization curve is generated in increments of 0.01 A/cm2 starting at 0.005 A/cm2 until the limiting current is reached. With each current increase, the simulation continues until the cell reaches a steady state voltage. Due to the presence of gradients of current, species concentration, temperature, and current density along the flow direction within the cell layers, results show significant difference between the cell global and local polarization performance and global and local impedance spectra along the channel flow direction. Figure 1 shows an example of an impedance spectra obtained from a simulation of a planar fuel cell operating at 0.4 A/cm2, 40% hydrogen utilization. As shown, the relative polarization resistance of the cell increases from the fuel inlet to outlet. The goal of the present study is to gain a deeper understanding of the impedance spectra of planar SOFCs by systematically exploring the relationship between certain operating conditions and the impedance of planar cells both globally and locally. Parametric studies on key operating conditions such as fuel utilization, air utilization, gas flow rates and composition are performed and the relative contributions to the polarization resistance of each parameter are quantified.
References
[1] W. G. Bessler. J. Electrochem. Soc., 154, B1186 (2007). doi:10.1149/1.2772092.

Figure 1