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OpenFCST: An Open-Source Mathematical Modelling Software for Polymer Electrolyte Fuel Cells

OpenFCST is a finite element method based, open-source, mathematical modeling software for polymer electrolyte fuel cells. The aim of the software is to develop a platform for collaborative development of fuel cell models and for assessing the impact of different models in the literature. The software is well documented, contains several sample models, and it is available for download online at http://www.openfcst.mece.ualberta.ca/. The software currently contains a library of governing equations that includes Fick's law of diffusion, Ohm's law, the adsorbed water transport model proposed by Springer et al. [2], a thermal model including thermal osmosis and heat of sorption, and a database of electrochemical equations including models for multi-step reaction mechanisms for the oxygen reduction reaction and the hydrogen oxidation reaction. The software also contains a database of fuel cell materials including several catalyst layer representations such as a macro-homogeneous catalyst layer, an ionomer-filled agglomerate based catalyst layer, and a water-filled agglomerate based catalyst layer.

Using openFCST, a multi-scale agglomerate model framework has been proposed to analyze any type of spherical agglomerate regardless of composition and electrochemical reactions [3]. Using this framework, different agglomerate models such as ionomer-filled [3] and water-filled [4] models can be analyzed under the same macro-scale conditions, e.g., same mass and heat transport models, in order to assess their impact on fuel cell performance and reaction distribution inside the catalyst layer. In this study, several agglomerate models are analyzed using different reaction kinetic models including the use of a cathode multi-step reaction kinetics model. Results show that, in ionomer-filled agglomerate models, the kinetic model used has the largest impact on fuel cell performance predictions, followed by the rate of oxygen dissolution. Proton transport has a negligible effect. A comparison of ionomer and water-filled agglomerate models is also presented. Using openFCST, an MEA model using the two types of agglomerate models is developed assuming a Tafel electrochemical model. Figure 1 shows the overall cell performance, the current produced inside a single agglomerate, and the macroscopic current distribution. The results show that, for a fuel cell with a conventional electrode, i.e. 10µm in thickness, even though the current produced by the agglomerates might be remarkably different (Fig. 2), the predicted cell performance, under most operating conditions, is not significantly affected by the agglomerate model. This is because of a macroscopic rearrangement of the current density as shown in Figure 3. In thin electrodes, the macroscopic rearrangement might not be possible leading to very different results.

In summary, an overview of the first open-source, multi-dimensional, finite element based, polymer electrolyte fuel cell software in the literature is presented. The software can be used to analyze any type of membrane electrode assembly. In this presentation, it is used to analyze the effect of different kinetic models, boundary conditions, and agglomerate composition recently proposed in the literature.

**References**

[1] Weber, A.Z. and Newman, J. Modeling transport in polymer-electrolyte fuel cells, *Chemical Reviews*, 104(10):4679-4726, 2004.

[2] Springer, T.E. et al. Polymer electrolyte fuel cell model, *Journal of the Electrochemical Society*, 138(8):2334-2342, 1991.

[3] M. Moore et al., Understanding the effect of kinetic and mass transport processes in cathode agglomerates, *Journal of the Electrochemical Society*, 161(8), 2014.

[4] Wang, Q. et al., Structure and performance of different types of agglomerates in cathode catalyst layers of PEM fuel cells, *Journal of Electroanalytical Chemistry*, 573(1):61-69, 2004.