Boundary-layer model

CATALYSTS - REGENERATION - FLUID CATALYTIC CRAC KING UNITS] (Vol 5) Turbulent boundary layer model... 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

The process of equilibration of the atmosphere with the ocean is called gas exchange. Several models are available, however, the simplest model for most practical problems is the one-layer stagnant boundary-layer model (Fig. 10-18). This model assumes that a well-mixed atmosphere and a well-mixed surface ocean are... 

In the simplest situation, the CO produced at the particle surface diffuses away from the surface without further reactions. This assumption, known as the single-film or frozen boundary layer model, results in the species profiles shown in Fig. 9.17. 

The approach described above is by no means complete or exclusive. For example, Lamb et al. (1975) have proposed an alternative route to assess the adequacy of the atmospheric diffusion equation. Their approach is based on the Lagrangian description of the statistical properties of nonreacting particles released in a turbulent atmosphere. By employing the boundary layer model of Deardorff (1970), the transition probability density p x, y, z, t x, y, z, t ) is determined from the statistics of particles released into the computed flow field. Once p has been obtained, Eq. (3.1) can then be used to derive an estimate of the mean concentration field. Finally, the validity of the atmospheric diffusion equation is assessed by determining the profile of vertical dififiisivity that produced the best fit of the predicted mean concentration field. 

Boundary layer models take a similar approach but attempt to extend the parameterization of gas exchange to individual micrometeorological processes including transfer of heat (solar radiation effects including the cool skin), momentum (friction, waves, bubble injection, current shear), and other effects such as rainfall and chemical enhancements arising from reaction with water. 

Surface Renewal Model Boundary Layer Model... 

In the seventies, the growing interest in global geochemical cycles and in the fate of man-made pollutants in the environment triggered numerous studies of air-water exchange in natural systems, especially between the ocean and the atmosphere. In micrometeorology the study of heat and momentum transfer at water surfaces led to the development of detailed models of the structure of turbulence and momentum transfer close to the interface. The best-known outcome of these efforts, Deacon s (1977) boundary layer model, is similar to Whitman s film model. Yet, Deacon replaced the step-like drop in diffusivity (see Fig. 19.8a) by a continuous profile as shown in Fig. 19.8 b. As a result the transfer velocity loses the simple form of Eq. 19-4. Since the turbulence structure close to the interface also depends on the viscosity of the fluid, the model becomes more complex but also more powerful (see below). 

C. Relative temperature dependence of Sciw and via calculated for trichlorofluoromethane (CFC-11) from Eqs. 1 and the boundary layer model for moderate and high wind speed (Eq. 20-16) ... 

In the film model of Whitman the water-phase exchange velocity, v,w, is a function of the molecular diffusion coefficient of the chemical, while in Deacon s boundary layer model v[W depends on the Schmidt Number Sc W. Explain the reason for this difference. 

From the viewpoint of the chemical engineer, the application of the fundamentals just discussed takes the form of mass-transfer theory, and the constants Kj are called mass-transfer coefficients. However, some care must be exercised in determining the potential difference between two phases. One cannot simply take the difference between the thermodynamic activities in two phases without ensuring that they are adjusted to the same reference state. The point is illustrated with a brief consideration of the boundary-layer model. 

Stokes models and boundary-layer models, it can be shown that the boundary-layer models are accurate [322]. Moreover the boundary-layer models are considerably faster to solve compared to the Navier-Stokes models, especially when complex gas-phase chemistry is involved. 

There are numerous applications that depend on chemically reacting flow in a channel, many of which can be represented accurately using boundary-layer approximations. One important set of applications is chemical vapor deposition in a channel reactor (e.g., Figs. 1.5, 5.1, or 5.6), where both gas-phase and surface chemistry are usually important. Fuel cells often have channels that distribute the fuel and air to the electrochemically active surfaces (e.g., Fig. 1.6). While the flow rates and channel dimensions may be sufficiently small to justify plug-flow models, large systems may require boundary-layer models to represent spatial variations across the channel width. A great variety of catalyst systems use... 

For relatively minor species, such as the CO mass fractions shown in Fig. 17.20, there are somewhat larger differences between the Navier-Stokes and boundary-layer models. Under these flow conditions the CO mass-fraction peaks just near the leading edge of the active catalyst. As the CO desorbs from the initial region of the catalyst, the shapes of the CO contours show less classical boundary-layer development behavior, especially at low Reynolds number. Nevertheless, the agreement between the two models is still quite good. 

At very high Reynolds number the boundary-layer model is likely preferable to the Navier-Stokes model. The assumptions on which it is based are excellent and the computation cost is greatly reduced. Again, judgment is required as to the specific interest in the simulation and the appropriate scales involved. For example, even at very high Reynolds numbers, if the objective is to study the fine details around the leading edge of the catalyst, then the Navier-Stokes models must be used. 

Develop a boundary-layer model of the process, using an elementary gas-phase reaction mechanism H202Mech.txt but neglecting heterogeneous chemistry at the surface. Simulate the process over a range of potential process pressures. 

Rehder et al. (2004) measured the dissociation rates of methane and carbon dioxide hydrates in seawater during a seafloor experiment. The seafloor conditions provided constant temperature and pressure conditions, and enabled heat transfer limitations to be largely eliminated. Hydrate dissociation was caused by differences in concentration of the guest molecule in the hydrate surface and in the bulk solution. In this case, a solubility-controlled boundary layer model (mass transfer limited) was able to predict the dissociation data. The results showed that carbon dioxide hydrate dissociated much more rapidly than methane hydrate due to the higher solubility in water of carbon dioxide compared to methane. 

Concentration polarization can dominate the transmembrane flux in UF, and this can be described by boundary-layer models. Because the fluxes through nonporous barriers are lower than in UF, polarization effects are less important in reverse osmosis (RO), nanofiltration (NF), pervaporation (PV), electrodialysis (ED) or carrier-mediated separation. Interactions between substances in the feed and the membrane surface (adsorption, fouling) may also significantly influence the separation performance fouling is especially strong with aqueous feeds. 

II is a function of hydrodynamic parameters of the model. Unfortunately, these parameters which describe the effect of hydrodynamics do not correspond to any physical quantity nor can they be Independently evaluated. For some models, the value of w is a constant. For example, the penetration and surface renewal models (Danckwerts, 31) predict w 0.5, while for the boundary layer model w 2/3. The film-penetration model, on the other hand, predicts that w varies between 0.5 and 1 (Toor and Marchello, 32). Knowledge of the effect of dlffuslvlty on k Is needed in evaluating the various mass transfer models. Calderbank (13) reported a value of 0.5 Linek et al. (22) used oxygen, Helium and argon. The reported diffusion coefficients for helium and similar gases vary widely. Since in the present work three different temperatures have been used, the value of w can be determined much more accurately. Figure 4... 

Assuming a simple boundary layer model and a constant inlet flow rate of reactants, the growth rate of GaN is independent of reactor pressure in the mass-transport limited regime. The experimental data shown in FIGURE 2 for various reactor pressures is consistent with this behaviour. 

Equation (3.58) and Equation (3.61) are the Hixson and Crowell cube-root and the Higuchi and Hiestand two-thirds-root expressions, respectively. The cube-root and the two-thirds-root expressions are approximate solutions to the diffusional boundary layer model. The cube-root expression is valid for a system where the thickness of the diffusional boundary layer is much less than the particle radius whereas the two-thirds-root expression is useful when the thickness of the boundary layer is much larger than the particle radius. In general, Equation (3.57) is more accurate when the thickness of the boundary layer and the particle size are comparable. 

Fig. 2 A schematic diagram of the boundary layer model showing the reaction zones for Al Og coating.

Young, T. C., and W. E. Stewart, Correlation of fractionation tray performance via a cross-flow boundary-layer model, AIChE J., 38, 592-602 (1992) Errata, 38, 1302 (1992). 

Allan W., Lowe D. C., and Cainey J. M. (2001b) Active chlorine in the remote marine boundary layer modeling anomalous measurements of C in methane. Geophys. Res. Lett. 28, 3239-3242. 

Hedgecock I. M. and Pirrone N. (2001) Mercury and photochemistry in the marine boundary layer-modelling studies suggest the in situ production of reactive phase mercury. Atmos. Environ. 35, 3055-3062. 

There is a great deal of theoretical and experimental information from micrometeorological research on the transfer of momentum, heat, and mass at solid and liquid surfaces and across their associated air boundary layers (hence the term boundary layer models for relationships arising from this approach). Based on the analogy between transfer of momentum and mass, it has been shown that k is proportional to the friction velocity in air (u ) and that k is also proportional to Sc. Apart from an assumption that the surface was smooth and rigid, it was also necessary to assume continuity of stress across the interface in order to convert the velocity profile in air to the equivalent profile in the water (Deacon, 1977). The relationship developed by Deacon is as follows ... 

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