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A mathematical model for two-phase flow and flooding dynamics in polymer electrolyte fuel cells ͑PEFCs͒ has been developed based on recent experimental observations. This three-dimensional PEFC model consists of four submodels to account for two-phase phenomena, including a catalyst coverage model in the catalyst layer, a two-phase transport model in the gas diffusion layer ͑GDL͒, a liquid coverage model at the GDL-channel interface, and a two-phase flow model in the gas channel ͑GC͒. The multiphase mixture ͑M 2 ͒ model is employed to describe liquid water transport in the GDL while a mist flow model is used in the gas channel. An interfacial coverage model by liquid water at the GDL/GC interface is developed, for the first time, to account for water droplet emergence on the GDL surface. The inclusion of this interfacial model not only gives the present two-phase model a capability to predict the cathode flooding effect on cell performance, but also ultimately removes the inability of prior two-phase models to correctly capture effects of the gas velocity ͑or stoichiometry͒ on cell performance.Water management is a central issue in design and optimization of polymer electrolyte fuel cells ͑PEFCs͒. There are two wellunderstood reasons: first, the proton conductivity of the electrolyte membrane depends strongly on hydration; second, the presence of excessive liquid water covers catalyst sites in the catalyst layer as well as blocks the oxygen transport in the gas diffusion layer ͑GDL͒, resulting in substantial concentration polarization. Therefore, a delicate balance of water in the cell must be maintained to ensure proper operation. Because the oxygen reduction reaction ͑ORR͒ in the cathode catalyst layer produces water, prevention of liquid water flooding is especially crucial on the cathode side of the cell.In the past decade, numerical modeling of PEFCs has received much attention. Many two-and three-dimensional models have been developed in which the computational fluid dynamics ͑CFD͒ method has been rigorously coupled with electrochemical phenomena. 1-5 Electron transport and heat-transfer phenomena have also been incorporated. 6-10 A parallel computing methodology has recently been introduced for large-scale PEFC simulations. 11 Although these single-phase or pseudo single-phase numerical models have already provided significant capabilities to study a multitude of physical phenomena in PEFCs, they are unable to capture the physics of liquid water formation and transport as well as the ensuing flooding effects.Much effort has also been expended on the development of rigorous physical models for two-phase flow and flooding prediction. Wang et al. 12 first studied two-phase flow and liquid water transport on the cathode side of a PEFC based on the multiphase mixture model ͑M 2 model͒ originally developed by Wang and Cheng 13 and summarized by Wang and Cheng. 14 Although liquid water transport and two-phase formation were handled successfully, the predicted liquid water saturation could only reach a maximum val...

A three-dimensional, single-phase, isothermal numerical model of polymer electrolyte fuel cell ͑PEFC͒ was employed to investigate effects of electron transport through the gas diffusion layer ͑GDL͒ for the first time. An electron transport equation was additionally solved in the catalyst and gas diffusion layers, as well as in the current collector. It was found that the lateral electronic resistance of GDL, which is affected by the electronic conductivity, GDL thickness, and gas channel width, played a critical role in determining the current distribution and cell performance. Under fully-humidified gas feed in the anode and cathode, both oxygen and lateral electron transport in GDL dictated the current distribution. The lateral electronic resistance dominated the current distribution at high cell voltages, while the oxygen concentration played a more decisive role at low cell voltages. With reduced GDL thickness, the effect of the lateral electronic resistance on the current distribution and cell performance became even stronger, because the cross-sectional area of GDL for lateral electron transport was smaller. Inclusion of GDL electron transport enabled the thickness of GDL and widths of the gas channel and current collecting land to be optimized for better current distribution and cell performance. In addition, the present model enables: ͑i͒ direct incorporation of contact resistances emerging from GDL/catalyzed membrane or GDL/land interface, ͑ii͒ implementation of the total current as a more useful boundary condition than the constant cell voltage, and ͑iii͒ stack modeling with cells connected in series and hence having the identical total current.

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The evolution of a cryogenic fluid jet initially at a subcritical temperature and injected into a supercritical environment, in which both the pressure and temperature exceed the thermodynamic critical state, has been investigated numerically. The model accommodates full conservation laws and real-fluid thermodynamics and transport phenomena. All of the thermophysical properties are determined directly from fundamental thermodynamics theories, along with the use of the corresponding state principles. Turbulence closure is achieved using a large-eddy-simulation technique. As a specific example, the dynamics of a nitrogen fluid jet is studied systematically over a broad range of ambient pressure. Owing to the differences of fluid states and flow conditions between the jet and surroundings, a string of strong density-gradient regimes is generated around the jet surface and exerts a stabilizing effect on the flow development. The surface layer acts like a solid wall that transfers the turbulent kinetic energy from its axial to radial component. The spatial growth rate of the surface instability wave increases with increasing pressure. The frequency of the most unstable mode exhibits a weak pressure dependence at high pressures. It, however, decreases significantly in the near-critical regime due to the enhanced effect of density stratification and increased mixing-layer momentum thickness. The result agrees well with the linear stability analysis. The jet dynamics is largely dictated by the local thermodynamic state through its influence on the fluid thermophysical properties. When the fluid temperature transits across the inflection point on an isobaric density-temperature curve, the resultant rapid property variations may qualitatively modify the jet behavior compared with its counterpart at low pressures. An increase in the ambient pressure results in an earlier transition of the jet into the self-similar regime.