Combined Levenberg-Marquardt calibration algorithm and CFD modelling for solid oxide fuel cell analysis

Electrochemical data including impedance spectra and polarization curves, when numerically calibrated and combined with proper computational fluid dynamics (CFD) tools, can serve as a deeper understanding of gas flow dynamics in the anodic and cathodic chambers of a solid oxide fuel cell (SOFC). In the related literature, both approaches (calibration and CFD modelling) were usually performed separately. In this work, these two tools were combined to create a detailed framework for SOFC performance analysis. Considering the electrochemical lab measurements made on a SOFC button cell under three working temperatures and for two different gas feeding cases, a calibration approach based on the Levenberg-Marquardt algorithm allowed estimating the main parameters governing the polarization of the cell. Furthermore, a deeper focus is made on the gas dynamics inside the feeding channels and on the porous electrodes through a CFD model built on COMSOL Multiphysics. The CFD model is set up by coupling various modules that describe gas species transport and their diffusion in porous materials as well as gas flow inside the channels and through the electrodes. Using a simplified analytical formulation, the Levenberg-Marquardt algorithm proves its effectiveness by successfully fitting I-V curves with a mean fitting error of less than 2 %. Added to exploring gas flow dynamics, the CFD model is addressed to carrying out an analysis of fuel diffusion and partial pressure evolution along the anode thickness. It was concluded that the Maxwell-Stefan formulation, used in the CFD model, showed better precision in describing gas diffusion compared to the simpler Fick model usually used for analytical calculations. For instance, a saturation current density that was found to be around 1,8 Acm⁻² based on the Fick's law , was obtained to reach around 2 Acm⁻² when the Maxwell-Stefan model was used. The latter value is seen to be more realistic since the area specific resistance plots compare better with experimental data when the Maxwell-Stefan formulation was applied.