A Machine Learning Accelerated Hierarchical 3D+1D Model for Proton Exchange Membrane Fuel Cells

Abstract

Physics-based continuum models for proton exchange membrane fuel cells (PEMFCs) are an essential tool for fuel cell design and management. To date, many continuum models, ranging from 1D to 3D, have been developed for PEMFCs. Although computationally efficient, 1D models do not account for heterogeneity in flow fields, which negatively impact their accuracy. In contrast, 2D and 3D models are usually more representative of actual operating conditions but computationally intensive due to the coupled partial differential equations and large number of mesh elements involved. To overcome these issues, a hierarchical approach that combines a 2D/3D description of flow fields, gas diffusion layers (GDLs) and a simplified microporous layer (MPL)/catalyst layer (CL)/membrane sub-model has been proposed in the literature. However, studies based on this method often use a simplified or 0D MPL/CL/membrane sub-model, whose results may deviate from a full 1D description due to the neglected nonlinearity, especially at higher loads.In this study, we present a computationally efficient 3D+1D hierarchical model for PEMFCs accelerated by machine learning. The 3D model, which captures the two-phase flow in the gas channels and GDLs, is coupled with a full 1D description of the MPLs, membrane, CLs, and CL agglomerates by exchanging boundary values and fluxes, as shown in the figure. To avoid the high computing cost increase associated with the full 1D description, we develop a physics-informed neural network to replace the 1D sub-model for coupling with the 3D model, while maintaining the full description of fuel cell internal states. Large synthetic datasets are generated using the 1D model for training the neural network, ensuring the accuracy of the model. The proposed 3D+1D model is validated against experimentally obtained polarization curves and high frequency resistances under different relative humidities. The proposed model is then used to study the nonlinear distribution of the internal states along the thickness direction of the membrane electrode assembly as well as in the 3D flow field. The model is also highly effective in elucidating the dominant voltage loss factor under different operating conditions. Our developed model offers high accuracy at low computing cost under a wide range of operating conditions, potentially aiding the rapid optimization of both the membrane electrode assembly and the gas channel geometry and advance the water and thermal management of existing fuel cell designs. Figure 1