Zero-dimensional models

Clean Air Models. Models developed to simulate clean air chemistry generally have the least amount of chemical parameterization. Several recent zero-dimensional models (95,155,156) and one-dimensional models (157,158) have presented calculated HO concentrations for clean air. Two dimensional models have also provided predictions for global [HO ] (58,159,160,161). Three dimensional models that provide information... 

Well-defined stable isotope profiles may be used to provide quantitative information on fluid fluxes such as the direction of fluid flow and the duration of infiltration events (Baumgarmer and Rumble 1988 Bickle and Baker 1990 Cartwright and Valley 1991 Dipple and Ferry 1992 Baumgartner and Valley 2001). In well constrained situations, fluid flow modeling permits estimation of fluid fluxes that are far more realistic than fluid/rock ratios calculated from a zero-dimensional model. 

The simplest case of a ROM would be lumped models or zero-dimensional models where the fuel cell is modeled as a single set of control volumes one for each component, e.g. air gas channel, fuel gas channel, PEN, interconnect, etc. (see for example Elizalde-Blancas et al., 2007a). This hides most of the details of what occurs inside the fuel cell but allows for fast simulation times. Lumped models are appropriate for use in system modeling applications where the fuel cell interacts with other devices such as heat exchangers, combustors, turbines, etc. This kind... 

Current density and voltage are assumed to be constant throughout the cell (zero-dimensional model). 

A simulation of LV performance based on the above assumption, with linkage to a simple arterial model (Windkessel), is shown in Figure 2. The simulated pressure volume, pressure-time, flow-time, volume-time and stress-time, for different values of the preload are consistent with physiological measurements and show that the global LV function can be adequately described by an average zero-dimensional model. 

Archibald et al. [48] also investigated the impacts of OH formation from HO2 + RO2 reactions, epoxide chemistry, and 1,5-H and 1,6-H shifts in ISOPO2 radicals, using a zero-dimensional model with chemistry based on the MCMv3.1. Inclusion of OH-producing channels in HO2 + RO2 reactions in which OH formation is expected to occur gave increases in OH concentrations of 7%, compared to a 16% increase on consideration of the epoxide chemistry and 330% for the 1,5-H and 1,6-H shifts in ISOPO2. 

St-Pierre (2009) developed a zero-dimensional model that considers competitive adsorption for a contaminant with O2 or H2 at the cathode or anode side, respectively. This model assumes that contaminant transport through the gas flow channels, GDLs and ionomer in the catalyst layers is much faster compared to surface kinetics. The rate determining step is considered to be due to contaminant reaction or desorption of reaction product from the platinum surface. Other model assumptions include the absence of lateral interaction between adsorbates, first-order reaction kinetics, constant pressure, and constant temperature at the cathode/anode sides. Using a set of parameters, St-Pierre (2009) successfully used his model in order to describe experimental transient data obtained in the presence of SOj, NOj, and HjS in the cathode airstreams. 

To provide an overview on cell-level models, in this chapter the dimensionality of the models is used as the criterion. On the cell level, zero-dimensional to fully three-dimensional approaches are known. These dimensions are illustrated in Figure 15.2 Whereas zero-dimensional models are single equations and one-dimensional approaches describe processes orthogonal to the electrolyte, simulations in two and more dimensions also include the mass, heat, and charge transport in the plane of the flow field. 

There are in general several steps of refinement to model a gasification system. Zero-dimensional models show the lowest complexity, and rely on empirical correlations or thermodynamic equilibrium calculations. The next step is a onedimensional model that usually requires kinetic expressions either to resolve the space or time coordinate using idealized chemical reactor models. Approaching two- or three-dimensional calculations provokes the use of computational fluid dynamics (CFD) that may incorporate either equiUbriiun or kinetics-based turbulence chemistry interactions. Each step of modeling adds significant complexity and calculation time. 

Prepare a list of experimental tests that must be completed and the parameters you will vary during testing (e.g., you will need to determine kinetic parameters as a function of temperature and species mole fraction). List the methods you will use and the tests that must be performed to obtain all of the values and functional dependencies you will need to completely define a zero-dimensional model of this new fuel cell. 

Zero-dimensional model is a concentrated parameter model and can be simnlated conveniently. Thus it is commonly applied in the cases where only dynamic behaviors of a PEMFC are dealt with. 

In Fig. 4 (Ljungemyr, pers. comm.), the one dimensional lake model presented above is compared to the zero dimensional model discussed in Section 2.1. The lake considered is the eastern part of Lake V9nem, a large and deep lake in the central part of Sweden. From the figure we can notice that the slab model does not simulate summer temperatures correctly, but comes close during autumn and winter periods when the whole lake is vertically mixed. 

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