Fundamental and phenomenological models for cells, stacks, and complete systems of PEFC and SOFC are reviewed and their predictive power is assessed by comparing model simulations against experiments. Computationally efficient models suited for engineering design include the (1+1) dimensionality
approach, which decouples the membrane in-plane and through-plane processes, and the volume-averaged-method (VAM) that considers only the lumped effect of pre-selected system components. The former model was shown to capture the measured lateral current density inhomogeneities in a PEFC and
the latter was used for the optimization of commercial SOFC systems. State Space Modeling (SSM) was used to identify the main reaction pathways in SOFC and, in conjunction with the implementation of geometrically well-defined electrodes, has opened a new direction for the understanding of
electrochemical reactions. Furthermore, SSM has advanced the understanding of the COpoisoning-induced anode impedance in PEFC. Detailed numerical models such as the Lattice Boltzmann (LB) method for transport in porous media and the full 3-D Computational Fluid Dynamics (CFD) Navier-Stokes
simulations are addressed. These models contain all components of the relevant physics and they can improve the understanding of the related phenomena, a necessary condition for the development of both appropriate simplified models as well as reliable technologies. Within the LB framework,
a technique for the characterization and computer-reconstruction of the porous electrode structure was developed using advanced pattern recognition algorithms. In CFD modeling, 3-D simulations were used to investigate SOFC with internal methane steam reforming and have exemplified the significance
of porous and novel fractal channel distributors for the fuel and oxidant delivery, as well as for the cooling of PEFC. As importantly, the novel concept has been put forth of functionally designed, fractal-shaped fuel cells, showing promise of significant performance improvements over the
conventional rectangular shaped units. Thermo-economic modeling for the optimization of PEFC is finally addressed.
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