The implementation of phenomenological membrane models within computational fluid dynamics (CFD) codes requires coupling of the conservation equation for water content within the membrane to the conservation equations for species mass outside the membrane. It is common practice to treat water and current transport within the membrane as one-dimensional (1D), i.e., normal to the membrane surface only. The purpose of this study is to investigate the accuracy and efficiency of various strategies of implementing a phenomenological membrane model within the framework of a two-dimensional (2D) CFD code. Springer’s membrane model was compared against two other models available from the literature, and the accuracy of each model was assessed by comparing predicted results against experimental data. Results appear to indicate that the Springer model and the Nguyen and White model over-predict the drying of the membrane, while the Fuller and Newman model provides the best match with experimental data. Following these studies, three strategies for implementation of the membrane model were investigated: (1) 2D transport in membrane, (2) 1D transport in membrane and (3) 1D transport with approximate transport properties. Fuller and Newman’s membrane model was used for these studies. The results obtained using the three approaches were found to be within 4% of each other, while there was no significant difference in the computational time required by the three models, indicating that an analytical 1D transport model for the membrane that uses approximate properties is adequate for describing transport through it.
The flooded agglomerate model has found prolific usage in modeling the oxygen reduction reaction within the cathode catalyst layer of a polymer electrolyte membrane fuel cell (PEMFC). The assumption made in this model is that the ionomer-coated carbon-platinum agglomerate is spherical in shape and that the spheres are non-overlapping. This assumption is convenient because the governing equations lend themselves to closed-form analytical solution when a spherical shape is assumed. In reality, micrographs of the catalyst layer show that the agglomerates are best represented by sets of overlapping spheres of unequal radii. In this article, the flooded agglomerate is generalized by considering overlapping spheres of unequal radii. As a first cut, only two overlapping spheres are considered. The governing reaction-diffusion equations are solved numerically using the unstructured finite-volume method. The volumetric current density is extracted for various parametric variations, and tabulated. This sub-grid-scale generalized flooded agglomerate model is first validated and finally coupled to a computational fluid dynamics (CFD) code for predicting the performance of the PEMFC. Results show that when the agglomerates are small (< 200 nm equivalent radius), the effect of agglomerate shape on the overall PEMFC performance is insignificant. For large agglomerates, on the other hand, the effect of agglomerate shape was found to be critical, especially for high current densities for which the mass transport resistance within the agglomerate is strongly dependent on the shape of the agglomerate, and was found to correlate well with the surface-to-volume ratio of the agglomerate.
The effect of the cathode catalyst layer’s structure and composition on the overall performance of a polymer electrolyte fuel cell (PEMFC) is investigated numerically. The starting point of the sub-grid scale catalyst layer model is the well-known flooded agglomerate concept. The proposed model addresses the effects of Nafion loading, platinum loading, platinum/carbon ratio, agglomerate size and cathode layer thickness. The sub-grid scale model is first validated against experimental data and previously published results, and then embedded within a two-dimensional validated computational fluid dynamics code that can predict the overall performance of the fuel cell. The integrated model is used to explore a wide range of the compositional and structural parameter space, mentioned earlier. In each case, the model is able to correctly predict the trends observed by past experimental studies. The studies show that the presence of an optimal performance with varying Nafion content in the cathode is more due to the local agglomerate-level mass transport and conductivity losses in the polymer coating around the agglomerates than due to the amount of Nafion within the agglomerate. It was also found that platinum mass loading needs to be at a moderate level in order to optimize fuel cell performance. Cathode tortuosity has a significant effect on fuel cell performance at low values of agglomerate radius.
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