Numerical modeling

A special two-dimensional (2D) gcisdynamic code is developed to model multiphase flows. It allows for an arbitrary number of condensed and gaseous components, homogeneous and heterogeneous chemical reactions, interactions between condensed particles, and an arbitrary number of mesh refinement levels. 

The traditional burning-time equation is used for decomposition and burning of condensed particles, and an Arrhenius-type global equation is used for homogeneous reactions. To analyze the flow pattern and compare computations (wave velocities and impulses) with the experiment, the following problems are solved  

Modeled also are detonations of stoichiometric hydrogen-air and propane-air mixtures in a 0.8-meter-long tube. 

A simple analysis suggests that to generate an intense initial shock wave the pressure in the injector must be high. However, in contrast to low-pressure jets, in the high-pressure case the products expand at almost equal velocities in the axial and radial directions. Thus, the products are expected to expel a significant portion of air from the tube. 

Numerical computations are performed to assess the fuel fraction not participating in the reaction with air and to find ways of increasing the burning efficiency. Unfortunately, the process within the injector is not amenable to modeling. Therefore, in order to fit the pressure at which the injector diaphragm bursts, it was assumed that initially 10% of the propellant reacts at a constant volume. Further on, it was also assumed that the initial size of liquid drops in the jet was 25 fim. This allows the wave velocities to be approximately fitted to the experiment. 

P Oligo- and Poly thiophene Field Effect Transistors Oligo- and poly thiophene field effect 

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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. 

Numerical Modeling of Elastic Wave Propagation in Inhomogeneous Anisotropic Media. 

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 NMR experimental methods for studying chemical exchange are all fairly routine experiments, used in many other NMR contexts. To interpret these results, a numerical model of the exchange, as a frmction of rate, is fitted to the experimental data. It is therefore necessary to look at the theory behind the effects of chemical exchange. Much of the theory is developed for intennediate exchange, and this is the most complex case. However, with this theory, all of the rest of chemical exchange can be understood. 

Two-dimensional models can be used to provide effective approximations in the modelling of polymer processes if the flow field variations in the remaining (third) direction are small. In particular, in axisymraetric domains it may be possible to ignore the circumferential variations of the field unlaiowns and analytically integrate the flow equations in that direction to reduce the numerical model to a two-dimensional form. 

Andre, J. M. ct al., 1998. Numerical modelling of the polymer film blowing process. Int. J. Forming Processes 1, 187-210. 

Quahtative simulation is a specific KBS model of physical processes that are not understood well enough to develop a physics-based numeric model. Corrosion, folding, mechanical wear, equipment failure, and fatigue are not easily modeled, but decisions about them can be based on qualitative reasoning. See Refs. 178 and 292. 

For the analysis heat and mass transfer in concrete samples at high temperatures, the numerical model has been developed. It describes concrete, as a porous multiphase system which at local level is in thermodynamic balance with body interstice, filled by liquid water and gas phase. The model allows researching the dynamic characteristics of diffusion in view of concrete matrix phase transitions, which was usually described by means of experiments. 

Davison, L., Numerical Modeling of Dynamic Material Response, in Shock Waves in Condensed Matter—1983 (edited by Asay, J.R., Graham, R.A., and Straub, G.K.), North-Holland Physics, Amsterdam, 1984, pp. 181-186. 

Flynn et al." applied a finite element based numerical model to solve the problem of a push-pull flow with cross-drafts and demonstrate that the results show good agreement with experimental data. They note, however, that the numerical method is time consuming and therefore computationally expensive. 

The engineer decides when to do a numerical simulation. He or she will consider numerical modeling when one or several of the following apply ... 

Ventilation components with small geometric detail Numerical modeling of diffusers with complex geometry is difficult. Therefore, it is more reliable to measure airflow around such devices at full scale. 

The last advantage, parameter variations, is in fact common to all the numerical models but is a main advantage over an experimental investigation, as the time effort for changing parameters is very small. 

Nielsen, P. V. Description of supply openings in numerical models for room air distribution. ASHRAE Trans., vol. 98, pp. 963-971, 1992. 

For simplicity, the basic theoretical considerations of electrostatic precipitation are given in terms of cylindrical geometry, i.e., pipe-type electrostatic precipitation. This makes it possible to show most of the basic principles without numerical modeling. 

Brayshaw, M.D., 1990. Numerical model for the inviscid flow of a fluid in a hydrocyclone to demonstrate the effects of changes in the vorticity function of the flow field on particle classification. International Journal of Mineral Processing, 29, 51. 

Q. Han, J. D. Hunt. Numerical modelling of the growth of a cellular/dendritic array in multi-component alloys. Mater Sci Eng A 255 192, 1997. 

To overcome this problem, they proposed a working-fluid heat-addition model. This model implies that the gas dynamics are not computed on the basis of real values for heat of combustion and specific heat ratio of the combustion products, but on the basis of effective values. Effective values for the heat addition and product specific heat ratios were determined for six different stoichiometric fuel-air mixtures. Using this numerical model, Luckritz (1977) and Strehlow et al. (1979) systematically registered the properties of blast generated by spherical, constant-velocity deflagrations over a large range of flame speeds. 

The benefit of such LFERs is that they establish patterns of regular behavior, isolating apparent simplicity and defining normal or expected reactivity. Against such patterns it becomes possible to detect widely deviant or unexpected behavior. As we saw in Chapter 7, we cannot expect great generality from the extrathermodynamic approach, so it may be necessary to define numerous model processes so as to fit a full range of situations. 

For more precise work, micro hot stage methods under a microscope are used. For all compds, except those which are isotropic or become so on heating, the mp can best be observed by means of a polarizing microscope, since the temp at which color disappears arid the space lattice is ruptured is the true mp. Among numerous models of micro-hot stages, the Kofler micro-hot stage has attained widespread use and is commercially available (Refs 3 4)... 

A numerical modeling of physical properties of a ternary surfactant mixture more typical of commercial products can be achieved on the basis of the parameter characteristics of the binary peripheral systems alone. 

Fig. 4.1a-c Different heating cases in experiments and numerical modeling. Reprinted from Lelea (2005) with permission... 

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