Rigorous 3-D Mathematical Modeling of PEM Fuel Cells

Abstract

In this part of the paper, we present a model to treat formation and transport of liquid water in proton exchange membrane ͑PEM͒ fuel cells ͑FCs͒ in three-dimensional ͑3-D͒ geometry. The performance of modern-day PEM FCs at high current density are largely dictated by the effective management of liquid water. In the first part of this paper, a rigorous model was presented to model PEM FCs using a computational fluid dynamic technique. It was found that under the assumption of no liquid water formation, the model consistently overpredicted measured polarization behavior. In the model presented here, the phase change process is modeled as an equilibrium process, while the transport of liquid water is governed by pressure, surface tension, gravity and electro-osmotic drag. Results show that the inclusion of liquid water transport greatly enhances the predictive capability of the model and is necessary to match experimental data at high current density.Despite several studies on water management in proton exchange membrane ͑PEM͒ fuel cells ͑FCs͒ within the past decade, effective water management has remained elusive. This is partly due to the fact that once liquid water is formed, it is transported within the membrane-electrode-assembly ͑MEA͒ by several co-existing and comparable forces, and therefore, it is extremely difficult to control its motion. The other complication results from the conflict that while liquid water is necessary to maintain high electrical conductivity of the membrane, excessive water can result in clogging of the electrodes. In particular, in a hydrogen-air PEM FC operating at high loads, water is generated at the cathode due to electrochemical reactions, and significant condensation and clogging can occur within the cathode if the liquid water is not managed properly. Thus, it is neither desirable to remove water completely, nor is it desirable to have it in excessive amounts, and this poses a design challenge. The best scenario is to have liquid water in optimum amounts in certain regions of the MEA only, and this is almost impossible to achieve. One can only hope to alleviate the problem by understanding how much water is produced, where it finally resides within the cell, and what effects it has on the performance of the cell. Part of the role of modeling and simulation is to answer these questions.Modeling of liquid water formation and transport has been a topic of intense debate and discussion in the past five years. While such modeling can be extremely useful in understanding some of the aforementioned issues, the models available today are by no means predictive in the truest sense of the word. In this paper, we carefully explore the various ''gray areas'' associated with liquid water formation and transport that make the modeling difficult, and point out their repercussions in the prediction of performance of the FC.Several examples of mathematical modeling of water transport in PEM FCs can be found in the literature. The earliest models 1-3 were semi-empirical in nature, and attempte...

A model for hydrogen sulfide poisoning in proton exchange membrane fuel cells

“…It assumed that the net water produced is in liquid form. Condensation and evaporation are modelled using the approach in [25][26][27], and references therein, . Mass balance equations in gas phase are derived by taking into account transport by diffusion and convection, and mass transfer to and from the electrolyte:…”

Transient non-isothermal model of a polymer electrolyte fuel cell

“…The GDL must allow sufficient oxygen from the cathode channel to enter the CCL, but must be sufficiently hydrophobic to expel any build-up of liquid water beyond that required for optimal hydration of the membrane. The importance of water management explains the emphasis placed on capturing the effects of (particularly) liquid water in modelling studies [1][2][3][4][5][6][7][8][9]. However, a lack of understanding of the interaction between, and transport of, the three phases of water continues to retard progress towards a predictive model.…”

“…We assume that the net water produced is in dissolved form, consistent with the reaction location and the strongly hydrophillic nature of the ionomer. Condensation and evaporation are modelled using the approach in [2,4,5], and references therein. In this representation the transfer occurs at a finite rate, dictated by the deviation of the local thermodynamic state from equilibrium.…”

“…A great deal of debate surrounds both the form and magnitude of the permeability and capillary pressure. Mazumder [4], compares the Leverette model employed in [9] with the empirical relationship in [5], in which both of these quantities assume entirely different forms, yielding markedly different predicted levels of saturation. There are also other models of liquid transport in porous media, of varying degrees of sophistication.…”

“…The liquid-vapour phase-change term, derived from that given in [4] and references therein, is driven by the deviation from equilibrium, RTC v − P sat , where P sat is the saturation pressure of water and the first term is equivalent to the partial pressure of the vapour. The latter is defined by X v P, where P is the pressure of the gas phase and X v is the molar fraction of vapour.…”