Simple and Complex Polymer Electrolyte Fuel Cell Stack Models: A Comparison
Authors: Zhang Shidong , Beale Steven B. , Reimer Uwe , Nishida Robert T. , Andersson Martin , Pharoah Jon G. , Lehnert Werner 
Published: February 2020

The High Temperature Polymer Electrolyte Fuel Cell (HT-PEFC) converts chemical energy to electricity and heat. Operating at around 160°C, the heart of a HT-PEFC is a phosphoric-acid-doped polybenzimidazole membrane, which exhibits good protonic conductivity. HT-PEFCs may readily operate with either hydrogen or reformate as fuel. As is the case with most fuel cells, HT-PEFCs are operated in stacks in order to increase the overall electric potential. However, there are few comprehensive models of HT-PEFC stack performance. The results of this research program are among the first to obtain performance calculations for HT-PEFC at the stack scale with experimental validation.
HT-PEFC stacks designed at the Forschungszentrum Jülich are actively cooled with polyalkyline glycol liquid (oil) coolant, flowing in internal passages within the solid bi-polar plates, upon the surfaces of which a complex pattern consisting of straight and serpentine passages have been machined, in order to supply the air and fuel to the cell. Because of the elevated temperature, liquid water is not generally found in the gas channels or porous layers. Considerable experimental data have been previously gathered, in-house, for a 5-cell stack based on this design.
Two high temperature polymer electrolyte fuel cell (HT-PEFC) models of a HT-PEFC stack are described in detail:
(i) A detailed cell-level model where a set of conformal meshes are body-fitted to all the different parts of the stack. The code typically runs, in parallel, on 1000-2000 cores at the Jülich Supercomputer Centre; and,
(ii) A coarse-grid stack model based on a ‘distributed resistance analogy’ whereby rate equations supplant local diffusion terms in selected locations and directions to reduce computational requirements. A multiply-shared space (MUSES) method is employed to obtain simultaneous solutions for concentration, heat and momentum for the different phases occupying the ‘same’ global space.
Both (i) detailed and (ii) MUSES methods are implemented by instantiating 5 distinct meshes corresponding to (i) air, (ii) fuel, (iii) oil (fluid), and (iv) membrane electrode assembly, (v) bipolar plate (solid) regions, and obtaining solutions of the governing equations on these meshes. For both methods a solution is obtained simultaneously for the stack manifolds, cell manifolds (entrance regions) as well as the ‘core’ of the fuel cell stack. Thermal equilibrium between the 3 fluid phases is not presumed, a priori. In both methods, the electric field potential is expressed as the ideal (Nernst) potential less activation, ohmic, and transport losses. Individual cell potentiostatic boundary conditions are iteratively corrected until the desired overall galvanostatic condition is obtained for all cells in the stack. Both codes are developed in the modern open-source object-oriented library, OpenFOAM.
The results of the two models are compared with each other in terms of local current density and species partial pressure distributions. Both models are then compared with experimental data. The results show that the coarse-grid stack model (ii) agrees well, both quantitatively and qualitatively, with the detailed model (i) and experimental results and calculations are performed in two orders of magnitude less computation time. However, neither the experimental results nor the stack model (ii) are able to resolve local extrema in the current density and species mole fraction values that are observed with the detailed model (i). These are due to complex flow regimes associated with the meandering channels and flow bypassing in the porous transport layers. Importantly, these lead to significant local extrema in the local current density and other parameters of significance. These are among the first fully-comprehensive physicochemicohydrodynamic models of a HT-PEFC stack which allows calculations to be performed simultaneously for all the fluid and solids in the manifolds, entrance regions and stack core, together with experimental validation.