Direct numerical calculation of the kinematic tortuosity of reactive mixture flow in the anode layer of solid oxide fuel cells by the lattice Boltzmann method

Mathematical models that predict performance can aid in the understanding and development of solid oxide fuel cells (SOFCs). Of course, various modeling approaches exist involving different length scales. In particular, very significant advances are now taking place using microscopic models to understand the complex composite structures of electrodes and three-phase boundaries. Ultimately these advances should lead to predictions of cell behavior, which at present are measured empirically and inserted into macroscopic cell models. In order to achieve this ambitious goal, simulation tools based on these macroscopic models must be redesigned by matching them to the complex microscopic phenomena, which take place at the pore scale level. As a matter of fact, the macroscopic continuum approach essentially consists of applying some type of homogenization technique, which properly averages the underlying microscopic phenomena for producing measurable quantities. Unfortunately, these quantities in the porous electrodes of fuel cells are sometimes measurable only in principle. For this reason, this type of approach introduces additional uncertainties into the macroscopic models, which can significantly affect the numerical results, particularly their generality. This paper is part of an ongoing effort to address the problem by following an alternative approach. The key idea is to numerically simulate the underlying microscopic phenomena in an effort to bring the mathematical description nearer to actual reality. In particular, some recently developed mesoscopic tools appear to be very promising since the microscopic approach is, in this particular case, partially included in the numerical method itself. In particular, the models based on the lattice Boltzmann method (LBM) treat the problem by reproducing the collisions among particles of the same type, among particles belonging to different species, and finally among the species and the solid obstructions. Recently, a model developed by the authorswas proposed which, based on LBM, models the fluid flowof reactive mixtures in randomly generated porous media by simulating the actual coupling interaction among the species. A parallel three-dimensional numerical code was developed in order to implement this model and to simulate the actual microscopic structures of SOFC porous electrodes. In this paper, a thin anode (50 m) of Ni-metal/YSZ-electrolyte cermet for a high-temperature electrolyte supported SOFC was considered in the numerical simulations. The three-dimensional anode structure was derived by a regression analysis based on the granulometry law applied to some microscopic pictures obtained with an electron microscope. The numerical simulations show the spatial distribution of the mass fluxes for the reactants and the products of the electrochemical reactions. The described technique will allow one to design new improved materials and structures in order to statistically optimize these fluid paths.