Invasion percolation with inlet multiple injections and the water management problem in proton exchange membrane fuel cells

Liquid water transport in the diffusion porous layers of polymer electrolyte membrane fuel cells (PEMFC) is analyzed as a process of quasi-static invasion from multiple interfacial injection sources. From pore network simulations based on a new version of the invasion percolation algorithm it is shown that a porous layer acts as a two-phase filter: the number of breakthrough points is significantly lower that the number of injection points owing to the merging of liquid paths within the porous layer. The number of breakthrough points at the gas diffusion layer/gas channel interface obtained with this model is consistent with the available experimental observations.     

A simple model for evaluation of contribution factors to skin melt formation in gas-assisted injection molding

A simple formulation based on a non-isothermal power-law fluid model was derived in order to evaluate the effect of various processing parameters as well as melt rheological behavior on the skin melt formation during gas-assisted injection molding. From this model, effect of molding conditions including melt temperature, mold temperature, delay time and gas injection pressure as well as shear-thinning behavior of polymer melt on the formation of skin melt thickness was numerically evaluated in a quasi-quantitative manner. Calculated results from this model predict similar dependence of skin thickness variation on contributing parameters as those observed from experiments. The analysis also indicates that the transient nature of melt flow caused by gas penetration may exist in actual molding process.     

A two-phase flow and transport model for the cathode of PEM fuel cells

A unified two-phase flow mixture model has been developed to describe the flow and transport in the cathode for PEM fuel cells. The boundary condition at the gas diffuser/catalyst layer interface couples the flow, transport, electrical potential and current density in the anode, cathode catalyst layer and membrane. Fuel cell performance predicted by this model is compared with experimental results and reasonable agreements are achieved. Typical two-phase flow distributions in the cathode gas diffuser and gas channel are presented. The main parameters influencing water transport across the membrane are also discussed. By studying the influences of water and thermal management on two-phase flow, it is found that two-phase flow characteristics in the cathode depend on the current density, operating temperature, and cathode and anode humidification temperatures.     

The gas diffusion layer in polymer electrolyte membrane fuel cells: A process model of the two-phase flow

A two-phase flow process model for the gas diffusion layer (GDL) of a polymer electrolyte membrane fuel cell, considering also the cathode catalyst layer (CL), is presented. For this purpose, a systematic analysis of the factors affecting flooding and drying, including the liquid accumulation in the gas channel (CH), was performed using a one-dimensional reference model for the GDL and a compact channel model. The treatment proposed for the CH-GDL interface was compared with other boundary conditions in the literature. It was concluded that the liquid accumulation in the channel is determinant for estimating the steady state and transient GDL flooding, but that predicting the saturation level in the CL can help for determining operation policies for precluding flooding in the GDL-CL composite, in the absence of an adequate channel model. Bifurcation behavior, associated with the water phase change, was identified by means of the compact model.     

Two-phase flow and maldistribution in gas channels of a polymer electrolyte fuel cell

Liquid water transport in a polymer electrolyte fuel cell (PEFC) is a major issue for automotive applications. Mist flow with tiny droplets suspended in gas has been commonly assumed for channel flow while two-phase flow has been modeled in other cell components. However, experimental studies have found that two-phase flow in the channels has a profound effect on PEFC performance, stability and durability. Therefore, a complete two-phase flow model is developed in this work for PEFC including two-phase flow in both anode and cathode channels. The model is validated against experimental data of the wetted area ratio and pressure drop in the cathode side. Due to the intrusion of soft gas diffusion layer (GDL) material in the channels, flow resistance is higher in some channels than in others. The resulting flow maldistribution among PEFC channels is of great concern because non-uniform distributions of fuel and oxidizer result in non-uniform reaction rates and thus adversely affect PEFC performance and durability. The two-phase flow maldistribution among the parallel channels in an operating PEFC is explored in detail.     

Multiscale modeling of particle–solidification front dynamics,Part I: Methodology

The interaction between an advancing solidification front and a micron-size particle is an inherently multiscale heat and mass transport problem. Transport at the micro-scale (i.e. the scale of the particle dimension) couples with intermolecular interactions and lubrication forces in a thin layer of melt between the particle and the front to determine the overall dynamics of the interaction. A multiscale model is developed to simulate such front–particle interactions. The solution to the lubrication equations in the melt layer is coupled to the solution of the Navier–Stokes equations for the overall particle–front system. Techniques are developed for coupling the dynamics at the two disparate scales at a common “matching plane”. All interfaces are represented and tracked using the level-set approach. A sharp-interface technique is employed for solution of the governing equations in the resulting moving boundary problem. Validation of the coupling strategy and results for the particle–front interaction phenomenon with the multiscale approach are presented.     

Characterization of flooding and two-phase flow in polymer electrolyte membrane fuel cell stacks

A partially flooded gas diffusion layer (GDL) model is proposed and solved simultaneously with a stack flow network model to estimate the operating conditions under which water flooding could be initiated in a polymer electrolyte membrane (PEM) fuel cell stack. The models were applied to the cathode side of a stack, which is more sensitive to the inception of GDL flooding and/or flow channel two-phase flow. The model can predict the stack performance in terms of pressure, species concentrations, GDL flooding and quality distributions in the flow fields as well as the geometrical specifications of the PEM fuel cell stack. The simulation results have revealed that under certain operating conditions, the GDL is fully flooded and the quality is lower than one for parts of the stack flow fields. Effects of current density, operating pressure, and level of inlet humidity on flooding are investigated.     

Ex situ and modeling study of two-phase flow in a single channel of polymer electrolyte membrane fuel cells

In this study, we investigate the air-water two-phase flow in a single flow channel of polymer electrolyte membrane (PEM) fuel cells. In the ex situ study, both straight and serpentine channels with various gas diffusion layer (GDL) surfaces are studied. Focus is placed on the two-phase flow patterns, which are optically characterized using a microscope with a high-resolution camera, and the two-phase pressure amplifiers. We find that the GDL surface properties slightly affect the flow pattern and two-phase pressure amplifier in the flow field configuration. Flow pattern transition occurs at the superficial gas velocity of around 1 m s⁻¹, and the pressure amplifier can reach as high as 10. A two-fluid model is also presented together with one dimensional (1-D) analytical solution, and acceptable agreement is achieved between the model prediction and experimental data at high gas flow rates.     

Interface resolving two-phase flow simulations in gas channels relevant for polymer electrolyte fuel cells using the volume of fluid approach

With the increased concern about energy security, air pollution and global warming, the possibility of using polymer electrolyte fuel cells (PEFCs) in future sustainable and renewable energy systems has achieved considerable momentum. A computational fluid dynamic model describing a straight channel, relevant for water removal inside a PEFC, is devised. A volume of fluid (VOF) approach is employed to investigate the interface resolved two-phase flow behavior inside the gas channel including the gas diffusion layer (GDL) surface. From this study, it is clear that the impact on the two-phase flow pattern for different hydrophobic/hydrophilic characteristics, i.e., contact angles, at the walls and at the GDL surface is significant, compared to a situation where the walls and the interface are neither hydrophobic nor hydrophilic (i.e., 90° contact angle at the walls and also at the GDL surface). A location of the GDL surface liquid inlet in the middle of the gas channel gives droplet formation, while a location at the side of the channel gives corner flow with a convex surface shape (having hydrophilic walls and a hydrophobic GDL interface). Droplet formation only observed when the GDL surface liquid inlet is located in the middle of the channel. The droplet detachment location (along the main flow direction) and the shape of the droplet until detachment are strongly dependent on the size of the liquid inlet at the GDL surface. A smaller liquid inlet at the GDL surface (keeping the mass flow rates constant) gives smaller droplets.     

Water dynamics inside a cathode channel of a polymer electrolyte membrane fuel cell

The present study focuses on the investigation of water dynamics inside a polymer electrolyte membrane fuel cell using two different modelling approaches: Eulerian two-phase mixture and volume of fluid interface tracking models. The Eulerian two-phase mixture model has provided overall information of species distribution inside a fuel cell and identified that the liquid water usually accumulates under the land area. The volume of fluid interface tracking model has then been implemented to investigate the emergence of water droplets from the gas diffusion layer into the cathode channel and the subsequent removal of water from the channel. Further, the effects of the location of water emergence in the cathode channel on the dynamic behavior of liquid water have been investigated. The present study shows that the water emerging into the channel near the side walls greatly reduces the surface water coverage of the channel. In order to control the water path into the channel near side walls, a further discussion has been provided that a gas diffusion layer design based on hydrophilic fibres distributed inside a hydrophobic fibre matrix could provide a precisely controlled water path through the gas diffusion layer.     

Enhancing under-rib mass transport in proton exchange membrane fuel cells using new serpentine flow field designs

New flow field configurations are developed to improve the performance of polymer electrolyte membrane fuel cells (PEMFCs). The developed designs aim to uniformly distribute the reactants over the reaction area of the catalyst layer surface, boost the under-rib convection mass transport through the gas diffusion layer, decrease the water flooding effect in the gas diffusion layer-catalyst layer interface, and maintain the membrane water content within the required range to augment protonic conductivity. To evaluate the performance parameters of a PEMFC, a comprehensive three-dimensional, two-phase mathematical model has been developed. The model includes the charge transport, electrochemical reactions, mass conservation, momentum, energy, and water transport equations. The results signify that the improved flow field patterns attain a considerable boosting of the output power, the under-rib convection mass transport, improvement of the reactant distribution over the catalyst layer surface and decline of the liquid water saturation in the gas diffusion layer-catalyst layer interface. The developed configurations achieve a higher power density of 0.82 W/cm² at a current density of 1.74 A/cm², compared to the standard serpentine configuration, which attains about 0.67 W/cm² at a current density of 1.486 A/cm².Accordingly, the develop configurations demonstrate a 22.6% enhancement in power density.     

Multiscale modeling of particle–solidification front dynamics. Part II: Pushing–engulfment transition

The interaction between a particle and an advancing solidification front is studied using a multi-scale computational model developed in Part I. The flow and temperature fields are solved separately at two disparate scales, i.e. at the overall system scale (“outer region”) and in the thin melt layer (“inner region”) between the particle and the front. The solutions from the inner and outer regions are coupled at a matching region. The coupled dynamics of the particle and phase boundary motion, including lubrication and disjoining pressure effects in the premelted film between the particle and the front is captured in the simulations. Results show that particle pushing (as opposed to particle engulfment) can occur when the ratio of thermal conductivity of the particle to the melt, k_p/k_l < 1. The velocity of the solidification front at which the transition from particle pushing to particle engulfment occurs, i.e. the critical velocity for particle engulfment, is naturally obtained from the coupled dynamics. No ad hoc assumptions to identify the critical velocity need be made. The results also provide insights into the physics of particle–solidification front interactions.     

Transport Phenomena Within the Cathode for a Polymer Electrolyte Fuel Cell

A one-dimensional two-phase steady model is developed to analyze the coupled phenomena of cathode flooding and mass-transport limitation for a polymer electrolyte fuel cell. In the model, the liquid water transport in the porous electrode is driven by the capillary force based on Darcy's law, while the gas transport is driven by the concentration gradient based on Fick's law. Furthermore, the catalyst layer is treated as a separate computational domain. The capillary pressure continuity is imposed on the interface between the catalyst layer and the gas diffusion layer. Additionally, through Tafel kinetics, the mass transport and the electrochemical reaction are coupled together. The saturation jump at the interface between the gas diffusion layer and the catalyst layer is captured in the results. Meanwhile, the results further indicate that the flooding situation in the catalyst layer is much more serious than that in the gas diffusion layer. Moreover, the saturation level inside the cathode is largely related to the physical, material, and operating parameters. In order to effectively prevent flooding, one should first remove the liquid water residing inside the catalyst layer and keep the boundary value of the liquid water saturation as low as possible.     

Three-dimensional numerical simulations of water droplet dynamics in a PEMFC gas channel

The dynamic behavior of liquid water emerging from the gas diffusion layer (GDL) into the gas flow channel of a polymer electrolyte membrane fuel cell (PEMFC) is modeled by considering a 1000 μm long air flow microchannel with a 250 μm × 250 μm square cross section and having a pore on the GDL surface through which water emerges with prescribed flow rates. The transient three-dimensional two-phase flow is solved using Computational fluid dynamics in conjunction with a volume of fluid method. Simulations of the processes of water droplet emergence, growth, deformation and detachment are performed to explicitly track the evolution of the liquid–gas interface, and to characterize the dynamics of a water droplet subjected to air flow in the bulk of the gas channel in terms of departure diameter, flow resistance coefficient, water saturation, and water coverage ratio. Parametric simulations including the effects of air flow velocity, water injection velocity, and dimensions of the pore are performed with a particular focus on the effect of the hydrophobicity of the GDL surface while the static contact angles of the other channel walls are set to 45°. The wettability of the microchannel surface is shown to have a major impact on the dynamics of the water droplet, with a droplet splitting more readily and convecting rapidly on a hydrophobic surface, while for a hydrophilic surface there is a tendency for spreading and film flow formation. The hydrophilic side walls of the microchannel appear to provide some benefit by lifting the attached water from the GDL surface, thus freeing the GDL-flow channel interface for improved mass transfer of the reactant. Higher air inlet velocities are shown to reduce water coverage of the GDL surface. Lower water injection velocities as well as smaller pore sizes result in earlier departure of water droplets and lower water volume fraction in the microchannel.     

3D unsteady numerical analysis of conjugate heat transport and turbulent/laminar flows in LEC growth of GaAs crystals

We present the conjugated 3D unsteady numerical analysis of industrial-scale LEC GaAs crystal growth, including the calculation of heat transfer in the crystal and crucibles, melt convection, and the encapsulant flow. The analysis of unsteady turbulent melt convection is performed in terms of the large eddy simulation approach. A special procedure was introduced into the calculations to predict the geometry of the crystallization front. The results of the 3D unsteady calculations are compared to the results obtained in terms of the conventional steady-state Reynolds averaged approach with respect to the calculation of the geometry of the crystallization front. The effect of convective heat transfer in the encapsulant is specially studied using the 3D unsteady analysis. To investigate details of dynamic interaction between two immiscible liquids having a plane interface, preliminary computational tests were performed in a model setup.     

Transition from natural to mixed convection for steam–gas flow condensing along a vertical plate

An analysis method based on two-phase boundary layer analysis has been developed to study the effects of superimposed forced convection on natural convection steam–gas flow condensing along a vertical plate. The mechanism by which superimposed forced convection enhances heat transfer is evaluated: the bulk flow blows away non-condensable gases accumulating near the interface, resulting in an elevated condensation driving force. Further, this bulk flow blowing capability may be characterized by a conventional mass transfer driving potential. Results of the new model are shown to be consistent with experimental data. Finally, a simple criterion was developed to identify transition to mixed convection from natural convection steam–gas flow.     

Comparison of a Reaction Front Model and a Finite Difference Model for the Simulation of Solid Absorption Process

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Gas flow rate distributions in parallel minichannels for polymer electrolyte membrane fuel cells: Experiments and theoretical analysis

In the present work, instantaneous gas flow rates in each of two parallel channels of gas-liquid two-phase flow systems were investigated through measurements of the pressure drop across the entrance region. Liquid flow rates in two branches were pre-determined through liquid injection independently into each channel. Experiments were conducted in two different manners, i.e., the gas flow rate was varied in both ascending and descending paths. Flow hysteresis was observed in both gas flow rate distributions and the overall pressure drop of two-phase flow systems. Effects of liquid flow rates on gas flow distributions were examined experimentally. The presence of flow hysteresis was found to be associated with different flow patterns at different combinations of gas and liquid flow rates and flow instability conditions. A new and simple method was developed to predict gas flow distributions based on flow regime-specific pressure drop models for different experimental approaches and flow patterns. In particular, two different two-phase pressure drop models were used for slug flow and annular flow, separately. Good agreement was achieved between theoretical predictions and our experimental data. The developed new method can be potentially applied to predict gas flow distributions in parallel channels for fuel cells.     

Melting of a vertical plate in porous medium controlled by forced convection of a dissimilar fluid

In this paper a boundary layer analysis is presented for the problem of melting of a flat plate embedded in a porous medium. The melting phenomenon is induced by forced convection of the ambient fluid. The ambient fluid and the melt are dissimilar. The density difference between the melt and the ambient fluid is responsible for the boundary layer flow in the melt region. The results of this paper document the dependence of the temperature and flow fields in the system, as well as the dependence of the local heat transfer rate at the solid/ melt interface on the dimensionless groups describing the physics of the problem.     

An enhanced thermal conduction model for the prediction of convection dominated solid–liquid phase change

An enhanced thermal conduction model for predicting convection dominated solid–liquid phase change is presented. The main feature of the model is to predict (1) the overall thermal behavior of the system and (2) the phase front position without recurring to the full solution of the Navier–Stokes equations. The model rests entirely on the conduction equation for both the solid and liquid phases. The effect of convection in the melt is mimicked via an enhanced thermal conductivity that depends on the dimensionless numbers and the geometry of the flow. The model is tested and confronted to full CFD solutions for a freezing duct flow problem and for buoyancy driven melting in an enclosure. In both cases, the predictions of the enhanced thermal conduction model show excellent agreement with that of the CFD model. Not only is the enhanced thermal conduction model simpler to implement but its simulations run at least ten times as fast as those of the CFD model. Consequently, the enhanced thermal conduction model is well suited for controlling real-time solid–liquid phase change processes that occur in industrial applications as well as in latent heat thermal energy storage systems.