Operation thickness models
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In terms of cell-level models with thin or variable-thickness catalyst layers, the most comprehensive were those of Nandy et al.
In this scheme, under the presence of temperature gradients, liquid water moves from the colder to hotter side of the membrane — in a direction that increases the entropy. Next, the model is used to describe the impacts of catalyst-layer thickness on performance.
In terms of modeling, both pore-scale and continuum models have been generated, although only the latter are germane to understanding cell water and thermal management. Kongkanand et al. Since the focus of the study is on the impact of catalyst-layer thickness, especially thin ones, the model was first validated by comparison to data from NSTF cells. Currently, the transport mechanisms of water removal behind possible mitigation strategies for thin electrodes are not well understood. The other relevant parameters are reported in Table VII. For the cathode, the oxygen reduction reaction ORR is modeled with a double-trap kinetic model initially developed by Wang et al.
It should be noted that although water-retention curves are useful, there is some debate of their applicability when applied locally, 33 a topic of future study.
Polymer-electrolyte fuel cells PEFCs have emerged as a promising zero-emission technology for energy conversion due to their thermodynamic efficiency and high energy density. For numerical reasons, a negligible permeability at saturation equal to zero is added.
This temperature sensitivity is attributed to poor water management and is discussed in more detail in the later sections and is a key factor that the model should capture. It is the goal of this article to elucidate the key transport mechanisms and component de parameters to explain experimental trends and help guide future studies, as well as present a comprehensive modeling framework.
It is well known that droplets along this interface in higher dynamic liquid pressures before the droplet is removed. Below, we discuss each major phenomenon in turn. Last, the ultrathin NSTF thickness is used as a case study to explore the impact of various material parameters in the hope of determining how one can increase its low-temperature performance. This is an open access article distributed under the terms of the Creative Commons Attribution 4. These and the model kinetic parameters are reported in Table VII. To capture the heterogeneous structure of the CL, an agglomerate model is used, which is only implemented on the cathode side, as mass-transport losses on the anode side due to hydrogen dissolution into agglomerates are assumed to be negligible.
The energy balance is solved on all of the domains with Eq. On the right-side of Eq. In this work, experimental values are used extensively whenever possible as shown in Table V. The GDL MRC used in this modeling study thermal conductivity in the in-plane direction is reported to vary with liquid-water saturation and is incorporated into the model as For the energy-balance boundary conditions, the temperatures are set at the outside edge of Plate as reported in Table III.
The effective gas permeability, k effof the porous domains is assumed to be a product of saturated permeability, k satand relative permeability, k rG which depends on operation liquid saturation value, S L. The effective diffusion coefficient,s for gas-species transport through porous and tortuous pathways of porous media and is described as The mass fraction of oxygen is computed from the sum of all mass fractions equals one. If the direction of the flux of water is into the GDL, then a no-flux boundary thickness is set.
To determine the chemical potentials, thermodynamics is used. In terms of Chan and Eikerling, they used a simplified model focused on water transport with ultra-thin-film catalyst layers and the related impacts of liquid-water transport, but did not examine what happens as a function of catalyst-layer thickness as the layer was treated as an interface. This order of magnitude was also adopted in a recent modeling work by Alink and Gerteisen.
The base-case thickness subdomain dimensions and type of materials used are shown in Table I. The model s for different phases present in a particular domain as listed in Table I. For the study in this paper, the catalyst-layer thickness was varied; for the NSTF case study, it is set to the measured value of 0. First, the model framework is presented with a discussion of all relevant physics and parameters.
The two pathways — O-orption and OH-orption, as model as four elementary operations with labels are. This enabled ease of data storage in a form of structures through a Matlab interface. The agglomerate current is given by Assuming a first-order oxygen dependence, the analytical solution for the reaction effectiveness factor, E r The mesh was generated with 5, triangular and quadrilateral elements, where increased mesh density was introduced within and near CL domains.
The findings provide understanding and guidance to optimize fuel-cell performance with thin electrodes. The Electrochemical Society was founded in to advance the theory and practice at the forefront of electrochemical and solid state science and technology, and allied models. The various empirical findings of NSTF as well as traditional supported thin electrodes 8 can be much better understood by examining the various tradeoffs engendered and complications arising from the use of thin catalyst layers.
A hybrid approach is used here, as proposed by Weber and Newman, 52 where the membrane has two transport modes: vapor- and liquid-equilibrated. Iryna V. Zenyuk 4,1,2Prodip K. Das 3 and Adam Z. Weber 4,5,1. No-flux boundary conditions are applied on the outside surfaces of the CLs. Conservation of charge applies to operation transport as shown by Eq. The outside edge of the anode Plate is kept as a reference at 0 V, whereas either potential potentiostatic mode of operation or current galvanostatic mode was applied at the outside edge of the cathode Plate, depending on the operation mode.
The reference point for the x-direction is set at the aCL PEM interface; for the y-direction, the model spans from the mid-plane of the channel, where the reference is set to 0, to the mid-plane of the land.
The PEFC model framework presented in this work is based on the model developed by Balliet and Newman 1718 and ly by Weber and coworkers. Typically, thinner electrodes are susceptible to severe flooding due to their inherently low water capacity and perhaps lack of hydrophobic zones.
Such phenomena are particularly pronounced when PEFCs operate at lower temperatures or during startup. In the following sections the model and relevant discussion are presented.
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In particular, the tradeoffs between water production and removal through transport or evaporation are highlighted, with a focus on low-temperature performance. The most common strategy for such catalyst thrifting is to fabricate thinner catalyst layers. A continuous transition is assumed between the two modes using a fraction of expanded channels, S.
Explicit membrane swelling effects are neglected in this model treatment since the feeds are fully humidified. The model is a two-phase, two-dimensional, cross-sectional sandwich model where model domains are shown in Figure 1. These tradeoffs were not explored for higher temperature operation tradeoffs nor for more realistic startup conditions.
The article is organized as follows. In this article, we report on findings of water and thermal management as a function of catalyst-layer thickness, with a focus on the complications with thin electrodes, using a two-dimensional, transient, nonisothermal, full-cell model. The prototypical example of this approach is the nano-structured thin-film NSTF electrode, which has several advantages compared to standard carbon-supported Pt electrodes.
The governing equations, model boundary conditions and associated source terms are summarized in Tables II through IV. Mass, electronic and ionic charge, and energy are conserved within the model with the use of second-order partial differential equations.
For multiphase properties, the saturation is determined using water-retention curves that plot the saturation as a function of the capillary pressure. In this manuscript, a liquid-pressure boundary condition is adopted using the approach of Weber and Newman 39 as Table III shows. approaches include setting the liquid pressure at this boundary to one that corresponds to a small saturation value about 0. The effective liquid permeability, k effof the porous domains is treated in a similar manner to that of gas permeability. The model assumes no reservoir of liquid water is present in the channel; therefore, the only physically meaningful direction of liquid-water flux is out from the GDL and into the channel.
The boundary condition at the CH GDL for liquid pressure is not trivial and requires additional attention as we believe it to be of crucial importance. Agglomerates are assumed to be of constant size and covered by a thin continuous ionomer film. For the latter, a case study of an ultra-thin catalyst layer is undergone to explore how various material properties alter the steady-state and startup performance of a cell. One can set the two chemical potentials equal to each other to calculate the vapor pressure, which can be corrected for meniscus effects using the Kelvin equation In the membrane, transport of water and protons is considered.
Published by ECS. Zenyuk et al J. Received 1 March Published 30 April Buy this article in print.
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