Formulating Reduced-Order Models to Include Mesoscale Methods in Full Proton Exchange Membrane Fuel Cell Models
Authors: Grunewald Jonathan B , Mistry Aashutosh N , Verma Ankit , Goswami Navneet , Mukherjee Partha P. , Fuller Thomas F. 
Published: February 2020

As the scales vary wildly in proton exchange membrane fuel cells (PEMFCs), from the nano and mesoscale in the cathode catalyst layer (CCL) to meter scale for the cell components of the membrane electrode assembly (MEA) themselves, it would not be feasible to run mesoscale models along with any kind of 1D, 1+1D, or 3D model of the entire PEMFC. In some of our previous work, we built a model of liquid and vapor distributions and electrochemical phenomena in a PEMFC electrode through a Lattice-Boltzmann-Method (LBM)-Direct-Numeical-Simulation (DNS) framework. However, as both LBM and DNS are computationally intensive, it would be far too computationally expensive to use these for a full cell model. While advances in computational power has alleviated some of the computing challenges, it does not allow for running computationally impractical experiments. To counter this, we suggest using the reduced-order modeling techniques used in machine learning, such as Bayesian linear regressions or neural networks for cases such as different RH levels, under rib, or different tortuosities and incorporating these into the larger model instead. These methods, especially Bayesian ones, account for the fact that getting accurate tomography data through focused ion beam scanning electron microscopy (FIB-SEM) is quite difficult and still give insight into physics for different microstructures. The idea behind these models would be to collect effective properties from the LBM-DNS framework such as effective diffusivity, conductivity, Dijkstra tortuosity, among others to make accurate predictions without running either LBM or DNS. Doing this allows larger models to incorporate accurate pore-scale information for the CCL while still accounting for global PEMFC issues, such as anode drying, water electro-osmosis, and water back diffusion not modeled by the framework.
The ability to build these reduced-order models based off of the real microstructure gives us a major advantage over the field, which currently gloss over microstructure detail. It also allows us to model long-term phenomena, such as carbon corrosion, more effectively because the framework gives more accurate results, but the model allows these results to be accessed much more quickly for new conditions. Since the models utilize information from an actual PEMFC, we can deploy our model predictions to inform practitioners on what type of microstructures they need to build. While it is admittedly difficult to control the individual pore distribution over the whole CCL experimentally, the model predictions can inform what kind of distribution promotes the best performance. While this approach has begun to be adopted in other fields in engineering, it has not been applied to PEMFCs yet – possibly due to the difficulty in obtaining the necessary microstructure data on the CCL. As a proof of concept, this is done on the capillary pressure vs saturation curves – an example parity plot for a GPR (Gaussian Process Regression) and linear regression are shown below in Figure 1 based on the principle components scores from several of the FIB-SEM geometries. One can see that the general shape of the curve is captured with relatively low differences.

Figure 1