No abstract

No abstract

A model is presented of a polymer electrolyte fuel cell including slow transient effects of liquid water accumulation and evaporation in gas diffusion electrodes ͑GDEs͒ and gas channels. The model is reduced dimensionally, coupling a one-dimensional ͑1D͒ model of gas and coolant channel flow to 1D models of transport through the membrane electrode assembly ͑MEA͒ and bipolar plates. An asymptotic reduction of the two-phase flow to a sharp interface model is used, in which phase change occurs at a front that evolves in time. The asymptotic reduction is based on an immobile water fraction in the GDE and a large capillary pressure. The water content in the membrane and channels is also tracked in time. Gas and thermal transport are taken to be at quasi-steady state on the time scale of liquid accumulation. The model is fit to Ballard Mk9 cells and validated against experimental measurements of both steady-state and transient MEA water content distributions along the length of the channel. Predictions of slow cyclovoltammograms are presented based on the model. Polymer electrolyte membrane ͑PEM͒ fuel cells are complex electrochemical devices that display transient behavior and hysteresis on a wide range of time scales. We present a model that captures the slow transient behavior associated to the accumulation of liquid water within the membrane electrode assembly ͑MEA͒ and gas flow fields of PEM fuel cells. Liquid water is widely known to play a critical role in overall cell performance, influencing the protonic conductivity of the Nafion membrane, the transportation of oxygen to reaction sites within the catalyst layers, 1 and the transportation of gases within the flow fields. Moreover, the time scale for liquid water buildup, on the order of tens of minutes, has an important impact on the dynamic loading of fuel cells typical for driving cycles. 2,3 Indeed, any predictive model designed for the optimization of automotive and other nonstationary applications of PEM fuel cells must resolve the transients and hysteresis on these time scales.There is substantial literature on computational fluid dynamicsbased models for PEM fuel cells that include two-phase effects ͑see for example, Ref. 4-9, and references therein͒. These models resolve various subcomponents of PEM fuel cells, or even the full cell. More recent work has included transient, two-phase effects; however, they either consider analysis of a single component 10,11 or present a full three-dimensional simulation without rigorous reduction, 12 for which the computational requirements are unsuitable for optimization schemes requiring extensive parameter testing or for upscaling to stack-level codes. Models that use analytical reductions of the subscale processes within the fuel cell, particularly the 1 + one-dimensional ͑1D͒ models, which exploit the nearly 1000:1 aspect ratio of the MEA thickness vs the along-the-channel distance of PEM unit cells, are well suited for these tasks. Several authors have proposed 1 + 1D models, 13-17 which couple 1D through-plane ...

We extend the renormalization group method, developed for the study of pulse interaction in damped wave equations, to the study of oscillatory motion of supercritical pulses in the parametrically forced nonlinear Schrödinger equation (PNLS). We construct a global manifold which asymptotically attracts the flow into an O(r 4 ) neighbourhood in the H 1 norm, where r is the amplitude of the internal oscillations. The oscillatory and translational dynamics of the pulses are rigorously recovered as a finite-dimensional flow on the manifold. The normal form for the projected dynamics of the oscillatory pulse shows that it is created in a supercritical Poincaré-Hopf bifurcation.