Single-Phase Modeling

Unlike the cases of the single-phase models above, the transport properties are constant because the water content does not vary, and thus, one can expect a linear gradient in pressure. However, due to Schroeder s paradox, different functional forms might be expected for the vapor- and liquid-equilibrated membranes. 

The single-phase model described herein considers the total water amount without distinguishing liquid water from water vapor. This approach is valid under the condition that liquid saturation within the gas... 

The bulk of our knowledge regarding thermal oxidation has been derived from studies with model systems of fatty acids and their derivatives, or with individual natural oils (2,3,6,12,13,14,15,16). However, in biological systems as complex as food, lipids usually exist in a complicated environment markedly different from that of the single phase model system. In cell membranes, for example, the lipid molecules are highly ordered, relatively restricted in distance and mobility, and closely associated with different neighboring molecules, e.g., other lipids, protein, cholesterol, water, pro- and antioxidants. What influence does such an environment have on the oxidation of the lipids at elevated temperature Even in less organized systems, e.g., depot fat from animal or plant, the lipids... 

This relation corresponds to exchange-coupled crystallites diluted in an ideally soft magnetic matrix. The only modification made over the original single phase model is the inclusion of the crystalline volume fraction xcr. It should be noted that is scaling with the volume fraction in the same way as with the crystalline volume 1f. 

An introductory summary of the basic ideas underlying the conventional single phase modeling concepts is given to emphasize the inherent limitations reflected by the different continuum model formulations [173]. It is generally... 

The two-phase k — e model analyzed was based on the Favre averaged transport equation for turbulent kinetic energy developed by [73, 74]. The resulting transport equation for kinetic energy is similar to the one obtained from the single phase model (5.2), supporting the semi-empirical modification introduced in that model. 

The formulation of a proper e - equation for the case of bubbly flow was found to be more severe. As a first approach they adopted the above equation developed from the single phase transport equations (5.3). However, analyzing the two physical situations mentioned above, they found that this model formulation fails to produce both the asymptotic value and the time constant of homogeneous decay of grid generated bubbly flow turbulence. That is, the modified single-phase model did not break down, but it gave rise to unphysical solutions for such cases. 

The Cb parameter takes values between 0 and 1, and generally depends on bubble size and shape, and on the turbulent length scale. The empirical coefficients in the turbulence model were kept equal to the standard values for the original single phase model. 

Much of the understanding of the solid state mechanism of heterogeneous catalysis stems from fundamental studies of single phase model compounds (1-5). In many cases, the role of a metal component in a catalytic process has been discerned through its incorporation into solid solutions of relatively inert host matrices (O. In the case of the selective oxidation and... 

Developed a 3-D model for hydrogen feed with constant over-potential across the catalyst layer. Developed a 2D two-phase flow model with variable over-potential across the catalyst layer. Substantially extended and improved the 3-D single phase model, including the variation of overpotential across the catalyst layers. 

Developed a 3-D single-phase model for reformate feed in the anode. 

Further develop the 3-D single-phase model improve on reformate feed and for different flow fields. Improve the fuel cell stack model. 

A fast, reliable, and specialized CFD model for PEM fuel cell simulation can be very useful in fuel cell design optimization and operation control. In this project, a unified PEM fuel cell simulation model has been successfully established. This project started in FY 2000 with 2-D single-phase models. In FY 2001, the 2-D models were successfully transformed into a unified 3-D model for hydrogen feed. In FY 2002, this established 3-D model was extended to include reformate feed, accounting for the poisonous effect of carbon monoxide as well as the dilution effect of the reformate gas stream on the anode side. Based on this 3-D model with the geometry of a single fuel cell, a preliminary stack model was established. Extensive experiments in our lab and industry interactions were carried out to improve and calibrate the computation model. 

The geometry of a single fuel cell is shown in Figure 1. The PEM fuel cell is divided into 9 regions according to the material properties and flow characteristics. In FY 2000, this project started with 2-D single-phase models that included 2 sub-models... 

In FY 2002, the 3-D single-phase model was significantly improved in several aspects. Specifically, instead of assuming constant overpotential across the catalyst layer, the variation... 

The calculation principle on which the assessment of design for such reactors is based is a substitution of the multi-phase reaction system by a quasi-single-phase model. In two-phase systems both reactants have to get into contact at a certain place. Consequently a reaction and a transport phase are distinguished. If the mass transfer rate from the transport to the reaction phase is veiy fast compared to the actual reaction rate, the process in total is dominated by the reaction kinetics. In order to discriminate this situation from one taking the mass transfer into account, it is referred to as micro-kinetically dominated In this ease all formal kinetic laws presented for homogeneous systems may be applied directly. 

It can be generalized somewhat more by accounting for the Prandtl number dependence power. The correlation is based on a pseudo-single-phase model. It follows from the correlation that the gas approaches the temperature of the solid in the very first centimeters of the bed. This is confirmed by a recent correlation of Balakrishnan and Pei [20]... 

The thickness, dispersion of refractive index, and absorption of the obtained films were measured on a spectral elUpsometer FIlipw developed at the AV.Rzhanov Institute of Semiconductor Physics SB RAS (http //www.isp.nscru/). The optical parameters of the film according to ellipsometric parameters delta (A) and p i ( P) were found by approximating the single-phase model of the Si-substrate/ absorbing film. 

In a single-phase model, the fluidized bed is regarded essentially as a continuum (Figure 8.4). Heat and mass balances are applied over the fluidized bed. It is assumed that particles in the bed are perfectly mixed. Equations 8.22 and 8.23 are the equations of moisture balance and energy balance, respectively [34]. 

FIGURE 8.4 Schematic diagram of the single-phase model of FED. 

Heat balance for the single-phase model gives the following energy balance ... 

The considerations of Read and Dean are, however, moving away from the spirit of the aggregate model, which is essentially a single phase model, and it is appropriate to consider them as a link with composite structure models, which will now be discussed in some detail. 

The form of Eq. (5.9) models a retum-to-isotropy effect due to fluctuating interfacial momentum coupling and reduces the turbulent viscosity from that predicted by the single-phase model. The turbulence energy exchange rate coefficient Ey is given by... 

Dohle et al. presented a one-dimensional model for the vapor-feed DMFC, including a description of the methanol crossover [158]. The effects of methanol concentration on the cell performance were studied. Scott et al. also developed several simplified single-phase models to study transport and electrochemical processes in liquid-feed DMFC and showed that the cell performance is limited by the slow diffusion of methanol in the liquid [13, 159-171]. Siebke et al. presented a ID mathematical model and a numerical simulation to explore the influence of different physical and electrochemical phenomena in the MEA of the liquid feed DMFC [162]. Dohle et al. presented a model to describe the heat and the power management of a DMFC system [163]. 

Using as a basis the single-phase model presented in section 3, a multi-phase model has been developed that accounts for both the gas and liquid phase in the same computational domain and thus allows for the implementation of phase change inside the gas diffusion layers. The model includes the transport of liquid water within the porous electrodes as well as the transport of gaseous species, protons, energy, and water dissolved in the ion conducting polymer. 

The same boimdaiy conditions are applied as in the single-phase model (section 3). Again, symmetry boimdary conditions are applied in the y and the z directions, thereby redueing the size of the computational domain and computational costs. In the x direction, zero flux conditions are applied at all interfaces except for the flow channels. At the inlets of the gas-flow charmels, the incoming velocity is calculated as a function of the desired current density and stoichiometric flow ratio, as described in section 3.7. The gas streams entering the cell are fully humidified, but no liquid water is contained in the gas stream. At the outlets, the pressure is prescribed for the momentum equation and a zero gradient conditions are imposed for all scalar equations. 

The same computational procedure and algorithm are used as in the single-phase model (section 3). Due to the complexity of this model with a large spatial variation in competing transport and phase-change mechanisms, the computational time required was about three times greater than in single-phase. 

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