Output, simulation chemical kinetic outputs

In this code, a 1-dimensional electrochemical element is defined, which represents a finite volume of active unit cell. This 1-D sub-model can be validated with appropriate single-cell data and established 1-D codes. This 1-D element is then used in FLUENT, a commercially available product, to carry out 3-D similations of realistic fuel cell geometries. One configuration studied was a single tubular solid oxide fuel cell (TSOFC) including a support tube on the cathode side of the cell. Six chemical species were tracked in the simulation H2, CO2, CO, O2, H2O, and N2. Fluid dynamics, heat transfer, electrochemistry, and the potential field in electrode and interconnect regions were all simulated. Voltage losses due to chemical kinetics, ohmic conduction, and diffusion were accounted for in the model. Because of a lack of accurate and detailed in situ characterization of the SOFC modeled, a direct validation of the model results was not possible. However, the results are consistent with input-output observations on experimental cells of this type. 

Very briefly, this rather large subject in the general area of chemical kinetics [43-45] was carried into electrochemistry in the studies by Bieniasz et al. [46-48]. It asks the question, when fitting some parameter to a proposed mechanism by means of simulation using some simulation output (concentrations or current or some other result), how sensitive to the changes in the output is the value of the fitted parameter. This is expressed in the form of a sensitivity function s. If the simulation yields, for example, an array of concentrations c x,t,p), where x are positions in space, t the time (which may enter the problem) and the parameter(s) p, then the function is defined [46] as 5 = dc/dp, which is an expression of the sensitivity to changes in concentration. This can be useful in estimating the reliability of fitted parameters by a series of simulations. This subject will not be persued further here. 

We shall present here an equilibrium simulation of the transport of a solute across a liquid-liquid interface, which permits to measure the rate constant. This work has been done with the same rationale than other recent molecular dynamics studies of chemical kinetics /5,6/. The idea is to obtain by simulation, at the same time, a computation of the mean potential as a function of the reaction coordinate and a direct measure of the rate constant. The mean potential can then be used as an input for a theoretical expression of the rate constant, using transition state /7/, Kramers /8/ or Grote-Hynes /9/ theories for instance. The comparaison can then be done in order to give a correct description of the kinetics process. A distinct feature of molecular dynamics, with respect to an experimental testing of theoretical results, is that the numerical simulations have both aspects, theoretical and experimental. Indeed, the computation of mean potentials, as functions of the microscopic models used, is simple to obtain here whereas an analytical derivation would be a heavy task. On the other hand, the computation of the kinetics constant is more comparable to an experimental output. 

In the following sections, further methods are presented which result neither in a smaller reaction mechanism nor in a new set of differential equations. Instead, these methods provide a numerical relationship between a vector that defines the state of the model and the outputs of the chemical kinetic model. These reduced models will be termed here as numerical reduced models. Such relationships can be obtained directly from the kinetic and thermodynamic equations that define the system (see this section) or can be deduced by processing simulation results (see Sects. 7.11-7.13). 

The relationship between the state of a model and the vector of chemical kinetic information can be stored in tables. Such tables are called look-up tables in the simulation of turbulent flames. When the simulation code receives the input vector, it locates points within the table that are close to the input point within a highdimensional space. The output vector is composed using linear interpolation between the output vector elements at the storage points. 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

Nevertheless, a number of problems remain in modelling both the physical processes (fluid dynamics, heat transfer), the complex chemistry and the coupling between them. There are major limitations on the applicability of computer models and in the accuracy which simulations can achieve. It is of the utmost importance for model users to be aware of the main sources of error blind belief in the output from models can be dangerous and expensive. In this chapter we consider the major source of uncertainty in chemical simulations, whether full or reduced mechanisms are used, namely the quality and quantity of the available kinetics data. 

Solution of the model for a particular problem requires specification of the chemical species considered, their respective possible reactions, supporting thermodynamic data, grid geometry, and kinetics at the metal/solution interface. The simulation domain is then broken into a set of calculation nodes that may be spaced more closely where gradients are highest (Fig. 6.22). Fundamental equations describing the many aspects of chemical interactions and species movement are finally made discrete in readily computable forms. The model was tested by comparing its output with the results of several experiments with three systems ... 

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