Computationally Efficient Pseudo-2D Non-Isothermal Modeling of Polymer Electrolyte Membrane Fuel Cells with Two-Phase Phenomena

Abstract

In this article, a computationally efficient pseudo-2D model for real-time dynamic simulations of polymer electrolyte membrane fuel cells (PEMFCs) is developed with a specific focus on water and thermal management. The model accounts for temperature dynamics, two-phase flow and flooding in the diffusion media, and membrane water crossover as well as absorption and desorption processes. Computational efficiency is achieved by leveraging the disparate time scales within the system dynamics, in addition to exploiting the large aspect ratio of the cell layers to create a spatio-temporal decoupling. Taking advantage of such decoupling, the model yields a computationally efficient solution while providing detailed information about the state of water and temperature throughout the cell. Through this approach, the current implementation of the model is found to be about twice faster than real time. Moreover, a case study is carried out where different mechanisms contributing to overall water balance in the cell are investigated. The results are shown to be in qualitative agreement with published experimental data, thereby providing a preliminary validation of the modeling approach. Finally, using the modeling results, an equivalent electrical circuit model is proposed to help elucidate water transport inside various cell layers. Real-time estimation, prediction, and control of cell hydration and temperature distribution is essential for optimizing the performance of polymer electrolyte membrane fuel cells (PEMFCs), as well as avoiding critical conditions and mitigating cell degradation. These applications necessitate mathematical models that not only run in real time, but also incorporate the important physical phenomena related to water transport and thermal management. However, including such phenomena comes at the cost of higher computational requirements, resulting in a trade-off between model accuracy and computational speed, which must be carefully balanced based on the desired application. As a result of these competing requirements, developing mathematical models that achieve a balance between the needs for high fidelity and low computational demand remains an active area of research.Within the context of this paper, a fuel cell model is considered to have high fidelity if it incorporates the following phenomena: i) 3-D effects including anisotropic material properties 1-3 to resolve transport phenomena in all physical directions; ii) transient behavior; iii) detailed multistep hydrogen oxidation reaction (HOR) and oxygen reduction reaction (ORR) kinetics; 4,5 iv) multiphase flow in gas channels and porous media; v) non-isothermal effects; 6 and vi) multicomponent diffusion.7,8 A more detailed explanation of these considerations follows.In terms of dimensionality, 3-D models are of highest fidelity, because they are capable of capturing transport in both through-themembrane and along-the-channel directions and also account for the channel-land effects in the third dimension. Moreover, these models can easily in...

Along-the-channel modeling and analysis of PEFCs at low stoichiometry: Development of a 1+2D model

“…Along-the-channel marching methods combined with MEA cross-section models have been extensively used to model complete cells [42,[54][55][56][57][58][59][60][61].…”

A Real Time Capable Quasi 3D System Level Model of PEM Fuel Cells

“…These two contributions are in the case of a full analytic solution an infinite series of Fourier terms [23] whereas in the case of HAN-RT only the first two terms are taken into account and, using the expressions for the concentration and velocity profile given in Eqs. (17) and (14), respectively, are computed as follows:…”

“…The so called reduced dimensionality models in their broader sense, i.e., any model that does not address all three dimensions equally, are a typically answer to the need for a balance between computational speed and accuracy of results. Common reduced dimensionality models are the 2D models (e.g., , ), combined 2D and 1D models and the so called 1D+1D models (e.g., , , ), which are a simplification of the 2D models (models where only the most dominant physical phenomena – e.g., mass transport via bulk gas flow in channel – are addressed in the dimension that runs along direction of gas flow). The 2D modeling approach leads to certain systematic discrepancies that are sometimes compensated by means of correction parameters yielding the pseudo 3D modeling approach (e.g., , , the Sherwood number adjusted 2D model in and the model of ).…”

A Mathematical Model toward Real-Time Monitoring of Automotive PEM Fuel Cells

“…In particular, earlier models were mostly lumped parameter with no distribution [4], or 1D, capturing the distributions in either the through-the-membrane [7] or along-the-channel [8] directions. More recently, most of the models have evolved to 2D computational domains capturing land-channel variations [9][10][11] or along the channel distributions [12][13][14].…”

“…Here, our specific focus is on capturing temperature and water distributions throughout the cell, which is achieved through a pseudo-2D bi-domain modeling approach. In particular, this work draws from our earlier effort in this area [13,27] and enhances it as follows: i) the bi-domain modeling approach allows for capturing of the in-plane distributions, ii) the microporous layer (MPL) is explicitly accounted for and is no longer lumped with the gas diffusion layer (GDL), while the catalyst layer (CL) is treated as a component with finite thickness rather than an interface, iii) the counter-flow configuration is modeled while maintaining real-time computation capabilities, iv) the model is more efficiently implemented to allow for significant savings in computation time, and v) the model is experimentally validated with performance data from a differential cell and an automotive short stack under a variety of operating conditions. These modifications render the model suitable for real-time monitoring of unmeasured and critical states within the fuel cell stack.…”