Macroscopic upscaling

Key words polymer electrolyte membrane fuel cell, PEMFC, two-phase transport, porous media, pore network model, lattice Boltemarm model, direct numerical simulation, macroscopic upscaling. 

In this chapter we have shown the scope of multi-scale modeling in PEM fuel cells. The multi-scale modeling consists of pore-scale modeling and macroscopic upscaling. Pore network model and lattice Boltzmann model were specifically discussed in the context of two-phase transport in the PEMFC gas diffusion layer... 

As shown in Figure 26.1, the wide gap opens up between the particle and continuum paradigms. This gap cannot be spanned using statistical mechanical methods only. The existing theoretical models to be applied in the mesoscale are based on heuristics obtained via downscaling of macroscopic models and upscaling particle approach. Simphfied theoretical models of complex fluid flows, e.g., flows in porous media, non-Newtonian fluid dynamics, thin film behavior, flows in presence of chemical reactions, and hydrodynamic instabilities formation, involve not only vah-dation but should be supported by more accurate computational models as well. However, until now, there has not been any precisely defined computational model, which operates in the mesoscale, in the range from 10 A to tens of microns. 

The typical situation in porous reactors is that one has an idea about the physical and chemical processes taking place in the interior of the pores and how these interact with the surfaces of the pellets or their interior. Obviously, there is absolutely no hope for modelling theses processes in all pores of a real reactor simultaneously since the number of pores may be extremely large. Therefore, there is a need for a macroscopic description of the physics and chemistry in such reactors. The mathematical theory dealing with this upscaling and correct averaging is called homogenization, a theory that has... 

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