Fuel cell model

Finally, for relevant fuel cell modeling, the kinetic model studies should be performed under similar temperature and pressure conditions, i.e., at temperatures in the range of 80-120 °C and pressures up to 3 bar, and at comparable space velocities. The first flow-cell and DBMS measurements under such temperature and pressure conditions are currently underway in our laboratory. 

Comprehensive discussions of fuel cells and Camot engines Nemst law analytical fuel cell modeling reversible losses and Nemst loss and irreversible losses, multistage oxidation, and equipartition of driving forces. Includes new developments and applications of fuel cells in trigeneration systems coal/biomass fuel cell systems indirect carbon fuel cells and direct carbon fuel cells. 

Through the use of a transparent fuel cell, Spernjak et al. [87] were able to visualize the anode FF plate (and DL without MPL) while operating the fuel cell with a cathode that had MPL on the DL. It was observed that liquid water was present in the anode flow field only when an MPL on the cathode side was used. Again, this is an indication that the cathode side creates a pressure barrier that pushes the water toward the anode. These observations agree with the ones presented mathematically by Weber and Newman [148]. Although they did not do any experimental work, their two-phase fuel cell model concluded that the MPL acts as a valve that pushes water away from the DL toward the anode though the membrane. 

Pasaogullari, Wang, and Chen [149] also presented a two-phase fuel cell model in which the effect of MPL was studied. They concluded that the water flux toward the anode is enhanced when the following MPL characfer-isfics are used smaller pore size, lower porosity, larger thickness, and higher hydrophobicity. It is important to note that similar conclusions have been presented in studies related to MPLs used in direct methanol fuel cells (see Section 4.3.3.5 for more information). 

The focus of this review is to discuss the different fuel-cell models with the overall goal of presenting a picture of the various types of transport in fuel cells. Although the majority of the literature fuel-cell models have been examine, there are rmdoubtedly some that were left out. In terms of time frame, this review focuses mainly on models that have been published through the end of 2003. 

The number of published fuel-cell-related models has increased dramatically in the past few years, as seen in Figure 2. Not only are there more models being published, but they are also increasing in complexity and scope. With the emergence of faster computers, the details of the models are no longer constrained to a lot of simplifying assumptions and analytic expressions. Full, 3-D fuel-cell models and the treatment of such complex phenomena as two-... 

Figure 2. Bar graph showing the number of polymer-electrolyte related fuel-cell models published per year.

The beginning of modeling of polymer-electrolyte fuel cells can actually be traced back to phosphoric-acid fuel cells. These systems are very similar in terms of their porous-electrode nature, with only the electrolyte being different, namely, a liquid. Giner and Hunter and Cutlip and co-workers proposed the first such models. These models account for diffusion and reaction in the gas-diffusion electrodes. These processes were also examined later with porous-electrode theory. While the phosphoric-acid fuel-cell models became more refined, polymer-electrolyte-membrane fuel cells began getting much more attention, especially experimentally. 

In 2000 and 2001, fuel-cell models were produced by the dozens. These models were typically more complex and focused on such effects as two-phase flow ° where liquid-water transport was incorporated. The work of Wang and co-workers was at the forefront of those models treating two-phase flow comprehensively. The liquid-water flow was shown to be important in describing the overall transport in fuel cells. Other models in this time frame focused on multidimensional, transient, and more microscopic effects.The microscopic effects again focused on using an agglomerate approach in the fuel cell as well as how to model the membrane appropriately. 

Recently. Weber and Newman " " introduced a framework for bridging the gap between the Bernard and Verbrugge and the Springer et al. membrane approaches. The membrane model was used in a simple fuel-cell model, and it showed good agreement with experimentally measured water-balance data under a variety of conditions. The fuel-cell model was similar to the model of Janssen. who used chemical potential as a driving force in the... 

Within the last five years, many fuel-cell models have come out of the Research Center in Julich, Germany. These models have different degrees of complexity and seek to identify the limiting factors in fuel-cell operation. The model of Kulikovsky et al. examined a 2-D structure of rib and channel on the cathode side of the fuel cell, and is similar to that of Springer et al. Other models by Kulikovsky included examination of depletion along long feed channels and effects in the catalyst layers.The most recent model by Kulikovsky relaxed the assumption of constant water content in the membrane and examined quasi 3-D profiles of it. Also at the research center, Eikerling et developed many... 

As noted in the Introduction, one of the defining characteristics of any fuel-cell model is how it treats transport. Thus, these equations vary depending on the model and are discussed in the appropriate subsections below. Similarly, the auxiliary equations and equilibrium relationships depend on the modeling approach and equations and are introduced and discussed where appropriate. The reactions for a fuel cell are well-known and were introduced in section 3.2.2. Of course, models modify the reaction expressions by including such effects as mass transfer and porous electrodes, as discussed later. Finally, unlike the other equations, the conservation equations are uniformly valid for all models. These equations are summarized below and not really discussed further. 

Because a large electrical force is required to separate charge over an appreciable distance, a volume element in the electrode will, to a good approximation, be electrically neutral. For fuel-cell models, electroneutrality is often assumed for each phase... 

The other type of model is the macrohomogeneous model. These models are macroscopic in nature and, as described above, have every phase defined in each volume element. Almost all of the models used for fuel-cell electrodes are macrohomogeneous. In the literature, the classification of macrohomogeneous models is confusing and sometimes contradictory. To sort this out, we propose that the macrohomogeneous models be subdivided on the basis of the length scale of the model. This is analogous to dimensionality for the overall fuel-cell models. 

The simplest way to treat the catalyst layers is to assume that they exist only at the interface of the diffusion media with the membrane. Thus, they are infinitely thin, and their structure can be ignored. This approach is used in complete fuel-cell models where the emphasis of the model is not on the catalyst-layer effects but on perhaps the membrane, the water balance, or multidimensional effects. There are different ways to treat the catalyst layer as an interface. 

Due to the complexity and interconnectivity of the governing equations and constitutive relationships, most fuel-cell models are solved numerically. Al-... 

For most numerically solved models, a control-volume approach is used. This approach is based on dividing the modeling domain into a mesh. Between mesh points, there are finite elements or boxes. Using Taylor series expansions, the governing equations are cast in finite-difference form. Next, the equations for the two half-boxes on either side of a mesh point are set equal to each other hence, mass is rigorously conserved. This approach requires that all vectors be defined at half-mesh points, all scalars at full-mesh points, and all reaction rates at quarter-mesh points. The exact details of the numerical methods can be found elsewhere (for example, see ref 273) and are not the purview of this review article. The above approach is essentially the same as that used in CFD packages (e.g.. Fluent) or discussed in Appendix C of ref 139 and is related to other numerical methods applied to fuel-cell modeling. ... 

Other types and aspects of polymer-electrolyte fuel cells have also been modeled. In this section, those models are quickly reviewed. This section is written more to inform than to analyze the various models. The outline of this section in terms of models is stack models, impedance models, direct-methanol fuel-cell models, and miscellaneous models. 

The next set of models examined in this section is impedance models. Impedance is often used to determine parameters and understand how the fuel cell is operating. By applying only a small perturbation during operation, the system can be studied in situ. There are many types of impedance models. They range from very simple analyses to taking a complete fuel-cell model and shifting it to the frequency domain. The very simple models use a simple equivalent circuit just to understand some general aspects (for examples, see refs 302—304). 

Finally, there are some miscellaneous polymer-electrolyte fuel cell models that should be mentioned. The models of Okada and co-workers - have examined how impurities in the water affect fuel-cell performance. They have focused mainly on ionic species such as chlorine and sodium and show that even a small concentration, especially next to the membrane at the cathode, impacts the overall fuelcell performance significantly. There are also some models that examine having free convection for gas transfer into the fuel cell. These models are also for very miniaturized fuel cells, so that free convection can provide enough oxygen. The models are basically the same as the ones above, but because the cell area is much smaller, the results and effects can be different. For example, free convection is used for both heat transfer and mass transfer, and the small... 

The review is organized as follows. Section 2 defines a systematic framework for fuel cell modeling research, called computational fuel cell dynamics (CFCD), and outlines its four essential elements. Sections 3—5 review work performed in the past decade on PEFCs, DMFCs, and SOFCs, respectively. Future research needs and directions of the three types of fuel cells are pointed out wherever applicable and summarized separately at the end of each section. 

Section 2.1 gives a generalized summary of fuel cell models, while section 2.2 discusses the need for employing large numerical meshes and hence advanced numerical algorithms for efficient fuel cell simulations. Section 2.3 briefly reviews the efforts, in the literature, to measure basic materials and transport properties as input to fuel cell models. 

A fundamental fuel cell model consists of five principles of conservation mass, momentum, species, charge, and thermal energy. These transport equations are then coupled with electrochemical processes through source terms to describe reaction kinetics and electro-osmotic drag in the polymer electrolyte. Such convection—diffusion—source equations can be summarized in the following general form... 

Main source terms prevailing in most transport equations for a fuel cell model are due to electrochemical reactions occurring in the electrode comprised of three phases electronic (s), electrolyte (e), and gas ( ). Electrochemical reactions occur at the triple-phase boundary according to the following general formula... 

The importance of materials characterization in fuel cell modeling cannot be overemphasized, as model predictions can be only as accurate as their material property input. In general, the material and transport properties for a fuel cell model can be organized in five groups (1) transport properties of electrolytes, (2) electrokinetic data for catalyst layers or electrodes, (3) properties of diffusion layers or substrates, (4) properties of bipolar plates, and (5) thermodynamic and transport properties of chemical reactants and products. 

The most important electrokinetic data pertinent to fuel cell models are the specific interfacial area in the catalyst layer, a, the exchange current density of the oxygen reduction reaction (ORR), io, and Tafel slope of ORR. The specific interfacial area is proportional to the catalyst loading and inversely proportional to the catalyst layer thickness. It is also a strong function of the catalyst layer fabrication methods and procedures. The exchange current density and Tafel slope of ORR have been well documented in refs 28—31. 

Transport Phenomena in Direct Methanol Fuel Cells. Modelling and Experimental Studies. 

A two-dimensional, electrochemical, and transport-coupled transient fuel cell model is developed based on the laws of conservation of species and charge14 ... 

T.E. Springer, T.A. Zawodzinski, S. Gottesfeld, Polymer electrolyte fuel cell model. J. Electrochem. Soc. 138, 2334 (1991)... 

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