Comparison with Numerical Model

The numerical model developed in Sect. 7.2 was applied to the current system. The geometric characteristics of the flow needed for the simulations, i.e. film thickness (5), length of unit cell (Luc), and plug length (Lp) and the plug velocity (Up), discussed in detail in Chap. 4, are tabulated in Table 7.1. The residence time, (t = Up/Lch) selected for the simulations represents the time that the aqueous plug flows in the extraction channel (Lch = 31.5 cm). The properties of the fluids used for the simulations are shown in Table 7.2. The difiusivity coefficient of UOa in the TBP/IL (30 %, v/v) mixture and in the aqueous nitric acid solution has been selected based on literature information. 

In Pig. 7.3a the recirculation in the plug and the slug for Case 3 as calculated from the model is shown. As shown in Chap. 5 internal circulation is created in both continuous and dispersed phases. According to Gupta et al. (2013), who run CFD 

In Fig. 7.4 the total velocity field for Case 3 as predicted by the numerical model and by the experimental results (Insight 4G, Tecplot) is shown. Similar to experimental results it can be seen that the magnitude of the velocity is maximum at the core of the plug while it is decreasing towards the channel walls and the liquid/Hquid interfaces, i.e. front and rear cap of the plug. 

The evolution of the concentration profile at different residence times from t = 0 until the plug exits the channel (Lch = 31.5 cm) is shown in Fig. 7.5 for Case 3. It can be seen that most of the concentration profile has already been developed within 

The effect of the channel size on extraction efficiency is shown in Fig. 7.6 as a function of residence time (t = Up/Lch). Higher extraction efficiency can be achieved 

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Tence, M., Chevalier, J. P. and Jullien, R. (1986). On the measurement of the fractal dimension of aggregated particles hy electron-microscopy - experimental-method, corrections and comparison with numerical-models. J. Phys., 41, 1989-1998. 

More than one model should be developed if there is uncertainty about the response of some parts of the structure. A sensitivity analysis should be made to provide the basis for this decision and this should also help in the choice of the size, type and number of finite elements if this modelling technique is used. Models should be validated by means of testing or by comparison with numerical models with different formulations in order to resolve possible uncertainties. 

The quantitative computations were conducted using equilibrium thenuodynamic model. The proposed model for thermochemical processes divides layer of the sample into contacting and non-contacting zones with the material of the atomizer. The correlation of all initial components in thermodynamic system has been validated. Principles of results comparison with numerous experimental data to confirm the correctness of proposed mechanism have been validated as well. 

In the first part of this paper, we therefore generalize the analysis of the above-mentioned reaction system. An approximate reaction factor expression is derived without restriction on the reaction regime, and the accuracy of this factor is tested by comparison with numerical solutions of the film-theory model. 

Approximate vs. Numerical Solution. The accuracy of the approximate reaction factor expression has been tested over wide ranges of parameter values by comparison with numerical solutions of the film-theory model. The methods of orthogonal collocation and orthogonal collocation on finite elements (7,8) were used to obtain the numerical solutions (details are given by Shaikh and Varma (j>)). Comparisons indicate that deviations in the approximate factor are within few percents (< 5%). It should be mentioned that for relatively high values of Hatta number (M >20), the asymptotic form of Equation 7 was used in those comparisons. 

The validity of the CSP method for sub-picosecond processes in systems which exhibit moderate quantum effects was established by comparison with numerically exact quantum dynamical calculations for small modell systems [27,49], Good correlation with experiments for large realistic systems is also encouraging [50, 51], Currently, limitations of the CSP scheme given by its separable nature are being overcome by extending the method in the direction of configuration interaction [53],... 

This series of papers " " has presented a detailed picture of how the model Cl + CI2 reaction in rare gas solvent occurs. Such detail can more easily be observed and understood because of the relative simplicity of the solvent-reactant and intrasolvent forces. As we shall discuss later in this section, such a level of detail makes possible a comparison with numerous simple models for solution reaction dynamics. As we shall see presently, this simplicity does not always exist, and the extension of these simple models to more complex chemical reactions in more complex solvents is still to be developed. 

In addition to the statistical translation of model output, the forecasters in weather services apply subjective judgments to the model forecasts. In the early days of numerical prediction, subjectively corrected forecasts often beat the score of pure model products. The subjective judgments were based on past performance of the model and comparison with other model forecasts. However, the involvement of forecasters in the daily forecast process is decreasing steadily with time. This is due to improvement in the short- to mediinn-tange prediction systems and the need for more research and development for long-range and seasonal forecasts as well as for severe storm forecasts. 

The mesh contains 35,149 nodes, 158,022 tetrahedra, and 33,532 triangles. Figure 26.5 showed the comparisons. The numerical model had to rotate the hull (trim) around the center of gravity. The agreement with the measured values was reasonable. 

Recently, robust developments in the capabilities of computers have led to the modeling of transient turbulent flows becoming much less challenging. The experimental analysis of PCD, which requires sophisticated measurements (e.g., LDA, PDA, pressure, temperature, noise, etc.) is difficult, hostile (e.g., high noise level, around 110-130 dB) and expensive to carry out in comparison with numerical simulations (Zbicinski, 2002). Computational fluid dynamics (CFD) models for a steady or transient flow, for example, as generated by the pulse combustor, differ... 

Figure 3.45b shows the spatial dependence of carrier concentration across the EMCD device. A comparison with accurate model is also shown. It can be seen that at a certain distance from the top surface (right side of the diagram corresponds to the top surface) the numerically calculated concentration (dashed) becomes significantly larger than the analytical approximation (solid). This distance is equal to the critical thickness. 

Fig. 3.45 Results of approximate analytical model of magnetoconcentration detector and their comparison with numerical simulation according to full mode, a Critical thickness versus bias for a magnetoconcentration HgCdTe p-type photodetector for different values of magnetic induction r = 220 K, X = 0.187, d = 15 pm,...

Laser ablation is a relatively new, not fully investigated, and not widely used (in comparison with numerous chemical methods) method for the synthesis of nanoparticles. Reports on catalytic application of nanopartides made by laser ablation are limited.li65 A particular disadvantage is the slow preparation, although the laser beam can be split into several beams. Typically, only 4-5 mg of Pt nanop>articles is produced after 1 hour of laser work. This can be accepted in the case of model catalysts, where the material demonstrates excellent catalytic properties or high metal loadings are not needed. 

FIG. 8 — COMPARISON OF NUMERICAL MODEL RESULTS WITH LABORATORY FIVE-SPOT WATER-FLOOD DATA ... 

Application of the Thermodynamic Theory to the Selkov Model and Comparison with Numerical Results... 

Numerical Modeling of eddy current steam generator inspection Comparison with experimental data, P.O. Gros, Review of Progress in Quantitative Nondestructive Evaluation, Vol 16 A, D.O. Thompson D. Chimenti, Eds (Plenium, New York 1997) pp 257-261. 

This paper is structured as follows in section 2, we recall the statement of the forward problem. We remind the numerical model which relates the contrast function with the observed data. Then, we compare the measurements performed with the experimental probe with predictive data which come from the model. This comparison is used, firstly, to validate the forward problem. In section 4, the solution of the associated inverse problem is described through a Bayesian approach. We derive, in particular, an appropriate criteria which must be optimized in order to reconstruct simulated flaws. Some results of flaw reconstructions from simulated data are presented. These results confirm the capability of the inversion method. The section 5 ends with giving some tasks we have already thought of. 

The statistics literature presents numerous reviews of comparing the description of one model against another. Watanabe and Himmel-blau (1984) present a list of review articles. The judgment criterion is based on a comparison of the model predictions against the measurements. These comparisons are related to the general statistic given below, developed tor each model with its corresponding parameter set. 

Analysis of realistic aspects of fabrication and performance of plastic materials involves the combination of complex geometrical, material and physical factors. The identification of the material mechanisms responsible for a specific phenomenon requires the development of relatively complex numerical models which accommodate the critical factors. Once the model is in place, it is possible to simulate different material mechanisms and verify their predictions through a comparison with experimental results. 

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