Numerical modelling experimental error

Quantitative Structure-Activity Relationship studies search for a relationship between the activity/toxicity of chemicals and the numerical representation of their structure and/or features. The overall task is not easy. For instance, several environmental properties are relatively easy to model, but some toxicity endpoints are quite difficult, because the toxicity is the result of many processes, involving different mechanisms. Toxicity data are also affected by experimental errors and their availability is limited because experiments are expensive. A 3D-QSAR model reflects the characteristics of... 

To make a more formal assessment of the possible errors (a combination of numerical modeling errors) in the calculations of DREAM-SOFC, here we treat the other eight results as outcomes from eight repetitions of a virtual experiment, the differences being a result of experimental uncertainty. With this assumption, we can calculate the 90% confidence interval for the true error in the DREAM results using the t-distribution as ... 

The Fluent code with the RSM turbulence model, predict very well the pressure drop in cyclones and can be used in cyclone design for any operational conditions (Figs. 3, 5, 7 and 8). In the CFD numerical calculations a very small pressme drop deviation were observed, with less than 3% of deviation at different inlet velocity which probably in the same magnitude of the experimental error. The CFD simulations with RNG k-e turbulence model still yield a reasonably good prediction (Figs. 3, 5, 7 and 8) with the deviation about 14-20% of an experimental data. It considerably tolerable since the RNG k-e model is much less on computational time required compared to the complicated RSM tmbulence model. In all cases of the simulation the RNG k-< model considerably underestimates the cyclone pressme drop as revealed by Griffiths and Boysan [8], However under extreme temperature (>850 K) there is no significant difference between RNG k-< and RSM model prediction. 

A further comparison of calculated and measured CO-concentrations and temperatures, given in Figure IS. show also a good correspondence. Differences between measured and calculated data, especially for the temperatures can be put down to the already mentioned fact of an incorrect predicted size of the recirculation zone in the upper left part of the burnout zone by the numerical model. However, the experimental determination of gas concentrations as well as of gas and wall temperatures is often in involved with uncertainties and measuring errors, especially under the prevailing instationary conditions within a domestic wood heater. 

The recent progress in experimental techniques and applications of DNS and LES for turbulent multiphase flows may lead to new insights necessary to develop better computational models to simulate dispersed multiphase flows with wide particle size distribution in turbulent regimes. Until then, the simulations of such complex turbulent multiphase flow processes have to be accompanied by careful validation (to assess errors due to modeling) and error estimation (due to numerical issues) exercise. Applications of these models to simulate multiphase stirred reactors, bubble column reactors and fluidized bed reactors, are discussed in Part IV of this book. 

In the interpretation of the numerical results that can be extracted from Mdssbauer spectroscopic data, it is necessary to recognize three sources of errors that can affect the accuracy of the data. These three contributions to the experimental error, which may not always be distinguishable from each other, can be identified as (a) statistical, (b) systematic, and (c) model-dependent errors. The statistical error, which arises from the fact that a finite number of observations are made in order to evaluate a given parameter, is the most readily estimated from the conditions of the experiment, provided that a Gaussian error distribution is assumed. Systematic errors are those that arise from factors influencing the absolute value of an experimental parameter but not necessarily the internal consistency of the data. Hence, such errors are the most difficult to diagnose and their evaluation commonly involves measurements by entirely independent experimental procedures. Finally, the model errors arise from the application of a theoretical model that may have only limited applicability in the interpretation of the experimental data. The errors introduced in this manner can often be estimated by a careful analysis of the fundamental assumptions incorporated in the theoretical treatment. 

It is seen that the numerical and experimental results are comparable in most cases. However, the model over-predicts the anode overpotential at low concentrations. Baschuk and Li [21] explained that this over-prediction could be due to oxygen crossover from the cathode while the experimental data was collected. Oxygen crossover and its effects on CO poisoning has been investigated experimentally by Zawodzinski et al. [97]. The slight discrepancy between the model predictions and the experimental results at high temperatures is mostly attributed to error in reproducing the experimental data points from the published article. 

This result was regarded as a confirmation of the experimental observation that for a given concentration the increase in surface tension is the same for all uni-umvalent electrolytes examined, within the limits of the experimental error . Besides, the numerical results from the model were in qualitative agreement with experimental results [7, 8] reported by Schwenker and Heydweiller Schwenker s values, likely to be the more reliable ones, were about 20-30% in excess over the theoretical OS values. 

In according to Figure 3.3, good agreement between experimental and numerical results about fuel consumption can be observed. The averaged error between numerical and experimental results is about 7 percent which shows verification of the selected model. 

The output from the modeling tools is often not used to the extent possible. Often, the FITEQL results used are the numerical values of the optimized parameters and the overall goodness of fit. Sometimes, also the standard deviations are considered. The numerical value of the goodness-of-fit parameter and the standard deviations are dependent on the defined experimental error estimates. The values for these, which are most frequently used, are the standard values, which may not at all be reasonable for the actual equilibrium problem treated [36]. 

The evaluation of electrolyte-binding constants is typically restricted to graphical approaches and numerically fitting experimental data. This implies the same problems discussed earher. Attempts have been published to measure electrolyte adsorption. This commonly involves the measurements of a very small amount adsorbed compared to relatively high solution concentrations. Thus, experimental results are expected to be associated with relatively large experimental errors. Even if reliable results were obtained, the question is, what is actually measured In terms of the models, one would... 

Numerical and statistical errors in processing the spectrum. The quality of the final fit depends on the fitting procedure and the amount of detail in the mathematical model. The precision of each peak determination also depends on the quality of the statistics in the experimental spectrum. Peaks with few counts will not be fitted so well as intense peaks. 

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