Numerical modelling underestimation

Numerical models are used to predict the performance and assist in the design of final cover systems. The availability of models used to conduct water balance analyses of ET cover systems is currently limited, and the results can be inconsistent. For example, models such as Hydrologic Evaluation of Landfill Performance (HELP) and Unsaturated Soil Water and Heat Flow (UNSAT-H) do not address all of the factors related to ET cover system performance. These models, for instance, do not consider percolation through preferential pathways may underestimate or overestimate percolation and have different levels of detail regarding weather, soil, and vegetation. In addition, HELP does not account for physical processes, such as matric potential, that generally govern unsaturated flow in ET covers.39 42 47... 

In the field of N2 adsorption, the development of model mesoporous materials like MCM-41 and SBA-15, showing a uniform mesopore size distribution in the range of 2 - 20 nm, has led to numerous studies to determine the PSD accurately. Since it is widely known that the BJH model underestimates the mesopore size, these studies resulted in adaptation of existing models and development of new... 

According to Bernoulli s principle, the pressure will decrease which will make the ship sink more. Numerical models have to take into account this over squat to precisely calculate ship squat in all channel configurations. So when a first squat result has been found, the model has to check that this squat is not disturbing the hydrodynamics in such a way that squat could increase more. This checking is important to ensure a reliable result from the numerical model. As these commercial numerical models do not perform squat checking, they may not be very efficient in restricted water. The user has to be very careful and take the result with reservations since the numerical model could in these conditions underestimate ship squat. 

The first of the shortcomings of the Lindemann theory—underestimating the excitation rate constant ke—was addressed by Hinshelwood [176]. His treatment showed that ke can be much larger than predicted by simple collision theory when the energy transfer into the internal (i.e., vibrational) degrees of freedom is taken into account. As we will see, some of the assumptions introduced in Hinshelwood s model are still overly simplistic. However, these assumptions allowed further analytical treatment of the problem in an era long before detailed numerical solution was possible. 

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. 

In these equations summations over repeated indices are implied. The values for the empirical constants Cu = 1.44, C2e = 1.92, Gi = 1.0, and ce = 1.3 are widely accepted (Launder and Spaulding, The Numerical Computation of Turbulent Flows, Imperial Coll. Sci. Tech. London, NTIS N74-12066 [1973]). The k-e. model has proved reasonably accurate for many flows without highly curved streamlines or significant swirl. It usually underestimates flow separation and overestimates turbulence production by normal straining. The k-e model is suitable for high Reynolds number flows. See Virendra, Patel, Rodi, and Scheuerer (A1AA J., 23, 1308-1319 [1984]) for a review of low Reynolds number k-e. models. 

Two experimental runs were performed. The H2S- and CO2 mole fluxes were obtained from the measured concentration curves by numerical differentiation and are plotted in figure 8a,b together with penetration and film model calculations. It is evident that forced desorption can be realized under practical conditions and can be predicted by the model. In general, measured H2S mole fluxes are between the values predicted by the models, whereas the CO2 forced desorption flux is larger than calculated by the models. The CO2 absorption flux, on the other hand, can correctly be calculated by the models. This probably implies that the rate of the reverse reaction, incorporated in equation (5), is underestimated. Moreover, it should be kept in mind that especially the results of the calculations in the forced desorption range are very sensitive to indirectly obtained parameters (diffusion, equilibrium constants and mass transfer coefficients) and the numerical differentiation technique applied. 

In the first place, the averaged model equations are highly nonlinear and require sophisticated numerical analysis for solution. For example, the attempt to obtain numerical solutions for motions of polymeric liquids, based upon simple continuum, constitutive equations, is still not entirely successful after more than 10 years of intensive effort by a number of research groups worldwide [27]. It is possible, and one may certainly hope, that model equations derived from a sound description of the underlying microscale physics will behave better mathematically and be easier to solve, but one should not underestimate the difficulty of obtaining numerical solutions in the absence of a clear qualitative understanding of the behavior of the materials. 

The numerical results of evaluating Equation (26)-(29) and its INM equivalent, Equation (17), are shown in Fig. 11 for a model diatomic solute dissolved in Xe (76). Consider first the behavior inside the INM band, the region below 120 cm 1 shown in the bottom panel. The original INM theory, which relies on the complete set of collective harmonic solvent modes, actually does rather well here, whereas the IP theory, for all its anharmonic enhancements, tremendously underestimates the vibrational friction. Liquid motion within the spectral range of the solvent band evidently has some profoundly collective features, despite the fact that the coupling to the solute is often funneled through a few key solvents. 

Thus, the possibility to hide the effects of dynamic correlation in a small set of intuitively appealing semiempirical parameters is very attractive. This procedure to connect the microscopic and model physics through effective Hamiltonians brings a large amount of clarity and order into both theoretical and experimental results, which is a feature that, in our opinion, should not be underestimated in its importance - in particular, in modem times where the temptation to mistake numerical agreement between calculated and measured numbers for understanding appears to be widespread. 

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