Hydrodynamic flow models

The discussion above suggests a hydrodynamic flow model based on two distinct regions in the fluidized bed a bubble region made up mostly of gas, but also containing solid... 

Hydrodynamic Flow Models. The discouraging result with the previous approaches lead us reluctantly to the conclusion that we must know more about what goes on in the bed if we hope to develop a reasonable predictive flow model. In particular we must learn more about the behavior of rising gas bubbles, since they probably cause much of the difficulty. 

Table 8.1 The pore structure of the carbon nanotube membrane and the enhancement of flows over the calculated values based on Knudsen and hydrodynamic flow model...

The solution flow is nomially maintained under laminar conditions and the velocity profile across the chaimel is therefore parabolic with a maximum velocity occurring at the chaimel centre. Thanks to the well defined hydrodynamic flow regime and to the accurately detemiinable dimensions of the cell, the system lends itself well to theoretical modelling. The convective-diffiision equation for mass transport within the rectangular duct may be described by... 

The basic model equations for a description of hydrodynamical flow are the Navier-Stokes equations, representing momentum conservation in the fluid... 

As a result of asperity contact, the nominal contact zone is split into a number of discrete areas that can be cataloged either to the lubrication region or asperity contact area (Fig. 2). The mean hydrodynamic pressure in the lubrication regions, pi, can be calculated by the average flow model, while contact pressure is estimated via Eq (7). Consequently, the film thickness is determined through numerical iterations to... 

Patir, N. and Cheng, H. S., "Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication, ASME J. Lubr. Technol., Vol. lOO.No. 1,1978,pp. 12-17. 

The UASB tractor was modeled by the dispensed plug flow model, considering decomposition reactions for VFA componaits, axial dispersion of liquid and hydrodynamics. The difierential mass balance equations based on the dispersed plug flow model are described for multiple VFA substrate components considaed... 

Resulting maps of the current density in a random-site percolation cluster both of the experiments and simulations are represented by Figure 2.9.13(b2) and (bl), respectively. The transport patterns compare very well. It is also possible to study hydrodynamic flow patterns in the same model objects. Corresponding velocity maps are shown in Figure 2.9.13(d) and (c2). In spite of the similarity of the... 

Models available to explain the CHF phenomenon are the hydrodynamic instability model and the macrolayer dryout model. The former postulates that the increase in vapor generation from the heater surface causes a limit of the steady-state vapor escape flow when CHF occurs. The latter postulates that a liquid sublayer (macrolayer) formed on the heating surface (see Secs. 2.2.5.5 and 2.4.1.2)... 

Annular flow. Modeling the interfacial shear is central to the problem of modeling hydrodynamics and transport during annular flow. The mechanisms are not clear, and the extent of basic modeling that has appeared is still very limited (Dukler and Taitel, 1991b). Only empirical treatments are currently available (see Sec. 3.5.3.3). 

Flow boiling of other alkali metals CHF data for other alkali metals were reported by Fisher et al. (1964, 1965), who tested rubidium and cesium in axial and swirl flow and potassium in swirl flow. The data were correlated by postulating a mist or fog flow model for the hydrodynamic situation in the heated section in which CHF occurs. These investigations were motivated by the potential use of alkali metals as Rankine cycle working media in space applications and have not been pursued further, because there is no longer interest in such concepts. 

Lionbashevski et al. (2007) proposed a quantitative model that accounts for the magnetic held effect on electrochemical reactions at planar electrode surfaces, with the uniform or nonuniform held being perpendicular to the surface. The model couples the thickness of the diffusion boundary layer, resulting from the electrochemical process, with the convective hydrodynamic flow of the solution at the electrode interface induced by the magnetic held as a result of the magnetic force action. The model can serve as a background for future development of the problem. 

Hydrodynamic type flow models can be developed to represent the BFB, based on the above two seemingly simple findings. Let us consider and develop the simplest of these, the K-L BFB model. 

By converting the governing hydrodynamic equations for a particular system into nondi-mensional ones, Horio et al. (1986) and Glicksman (1988) derived the so-called scaling laws for fluidized beds. These laws should be seen as a guide to design small-scale, cold-flow models, which simulate the hydrodynamic behavior of the commercial units (Knowlton et al., 2005). 

The third region of flow near the front is of special interest. The important feature of this region is the fountain effect, which must be considered in modelling all types of mold filling. It is important not only for estimating the hydrodynamic flow pattern, but also because the deformation of the macromolecules near the front influences their orientation and the properties of the end product. 

The heat and mass transfer properties can be represented by heat and mass transfer coefficients, which are commonly given in empirical or semiempirical correlation form. The transfer coefficient is defined in terms of flow models under specific flow conditions and geometric arrangements of the flow system. Thus, when applying the correlations, it is necessary to employ the same flow model to describe the heat and mass transfer coefficients for conditions comparable to those where the correlations were obtained. An accurate characterization of the heat and mass transfer can be made only when the hydrodynamics and underlying mechanism of the transport processes are well understood. 

In the development of these processes and their transference into an industrial-scale, dimensional analysis and scale-up based on it play only a subordinate role. This is reasonable, because one is often forced to perform experiments in a demonstration plant which copes in its scope with a small produdion plant ( mock-up plant, ca. 1/10-th of the industrial scale). Experiments in such plants are costly and often time-consuming, but they are often indispensable for the lay-out of a technical plant. This is because the experiments performed in them deliver a valuable information about the scale-dependent hydrodynamic behavior (arculation of liquids and of dispersed solids, residence time distributions). As model substances hydrocarbons as the liquid phase and nitrogen or air as the gas phase are used. The operation conditions are ambient temperature and atmospheric pressure ( cold-flow model ). As a rule, the experiments are evaluated according to dimensional analysis. 

Let us first consider the simple flat plate with a liquid metal flowing across it. The Prandtl number for liquid metals is very low, of the order of 0.01. so that the thermal-boundary-layer thickness should be substantially larger than the hydrodynamic-boundary-layer-thickness. The situation results from the high values of thermal conductivity for liquid metals and is depicted in Fig. 6-15. Since the ratio of 8/8, is small, the velocity profile has a very blunt shape over most of the thermal boundary layer. As a first approximation, then, we might assume a slug-flow model for calculation of the heat transfer i.e., we take... 

Suppose the fluid is highly conducting, such as a liquid metal. In this case, the thermal-boundary-layer thickness will be much greater than the hydrodynamic thickness. This is evidenced by the fact that the Prandtl numbers for liquid metals are very low, of the order of 0.01. For such a fluid, then, we might approximate the actual fluid behavior with a slug-flow model for energy transport in the thermal boundary layer, as outlined in Sec. 6-5. We assume a constant velocity profile... 

Determinations of Peclet number were carried out by comparison between experimental residence time distribution curves and the plug flow model with axial dispersion. Hold-up and axial dispersion coefficient, for the gas and liquid phases are then obtained as a function of pressure. In the range from 0.1-1.3 MPa, the obtained results show that the hydrodynamic behaviour of the liquid phase is independant of pressure. The influence of pressure on the axial dispersion coefficient in the gas phase is demonstrated for a constant gas flow velocity maintained at 0.037 m s. 

As part of the work undertaken by APCI under contract to the DOE, to develop a slurry phase Fischer-Tropsch process to produce selectively transportation fuels, a study of the hydrodynamics of three phase bubble column reactors was begun using cold flow modelling techniques (l ). Part of this study includes the measurement of solid concentration profiles over a range of independent column operating values. 

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