Fluidization disperse phase

Though this new algorithm still requires some time step refinement for computations with highly inelastic particles, it turns out that most computations can be carried out with acceptable time steps of 10 5 s or larger. An alternative numerical method that is also based on the compressibility of the dispersed particulate phase is presented by Laux (1998). In this so-called compressible disperse-phase method the shear stresses in the momentum equations are implicitly taken into account, which further enhances the stability of the code in the quasi-static state near minimum fluidization, especially when frictional shear is taken into account. In theory, the stability of the numerical solution method can be further enhanced by fully implicit discretization and simultaneous solution of all governing equations. This latter is however not expected to result in faster solution of the TFM equations since the numerical efforts per time step increase. 

An alternative treatment for radiative heat transfer in a circulating fluidized bed is to consider the radiation from the clusters (hcx) and from the dispersed phase (i.e., the remaining aspect of gas-solid suspension except clusters, A ), separately [Basu, 1990]... 

In solid-liquid fluidized beds the particle phase is the dispersed phase and the bed usually operates in the particulate (homogeneous) regime. However, for heavy particles (large size and density or high terminal setthng velocity), heterogeneity sets in. 

The preceding mathematical analysis also holds for gas-solid fluidized beds. In this case, the gas phase is the continuous phase and the solid phase is the dispersed phase. The criterion given by Eq. (24) holds where the values of the constants are given in Table I. It may be noted that the terms... 

With this approach, even the dispersed phase is treated as a continuum. All phases share the domain and may interpenetrate as they move within it. This approach is more suitable for modeling dispersed multiphase systems with a significant volume fraction of dispersed phase (> 10%). Such situations may occur in many types of reactor, for example, in fluidized bed reactors, bubble column reactors and multiphase stirred reactors. It is possible to represent coupling between different phases by developing suitable interphase transport models. It is, however, difficult to handle complex phenomena at particle level (such as change in size due to reactions/evaporation etc.) with the Eulerian-Eulerian approach. 

The bubbling fluidized bed (Figure 8.3) is divided vertically into two zones, namely, a dense phase and a freeboard region (also known as lean phase or dispersed phase). The... 

The heat transfer coefficient between vertical heating and cooling surfaces and a dispersed system (gas and liquid fluidized beds, bubble and drop columns) has been determined experimentally. Often, a maximum heat transfer coefficient is found at a certain volume flux v, or of the continuous respectively the dispersed phase (Mersmann and Wunder 1978). Here, only information about this maximum value is provided. 

It may be that the polymer is insoluble in the monomer-solvent mixture from which it is formed. Polypropylene and PVC are two examples where the polymer has very limited solubility in the monomer. As polymerization proceeds, the polymer will precipitate from the reacting mass to form a dispersed phase of polymer swollen with the monomer-solvent mixture. This is called a slurry polymerization. (Phase inversion can occur at high conversions to give a bulk polymerization.) A typical slurry polymerization is autorefrigerated. The heat of polymerization causes the reacting mass to boil it is condensed and returned to the reactor. The gas-phase processes for polyethylene and polypropylene are conceptually similar to slurry polymerizations. The continuous phase is now a gas and the dispersed phase is a fluidized solid, but the heat of polymerization is still removed through the low-viscosity, continuous phase. 

Avhere H is the fractional volumetric hold-up of dispersed phase and Ud and Uc the superficial velocities of dispersed and continuous phases. In the absence of specific data, Elgin and Foust recommend the correlation of Wilhelm and Kwauk (85) for fluidized beds of solids for estimation of the... 

Beginning with the paper by Jackson [20], disturbance stabilization in a fluidized bed is usually associated with the action of specific normal stresses inherent to the dispersed phase. These stresses impede volume deformations of the dispersed phase. Despite this fact having been understood for a long time, comprehensive development of a stability theory is hindered by the almost total absence of reliable information concerning the dependence of dispersed phase stresses (or of the corresponding bulk moduli of dispersed phase elasticity) on the suspension concentration and on the physical parameters. This lack of information partly invalidates all theoretical inferences bearing upon hydrodynamic stability in suspension flow. 

The first parameter appears as a result of quasi-viscous stresses in the dispersed phase affecting the development of initial plane waves. In fact, this parameter characterizes an influence on fluidized bed stability caused by dispersed phase viscosity. The occurrence of the second parameter is due to the restriction imposed from below on permissible wave numbers for these plane waves. Actually, the second parameter descibes a so-called scaling effect of the bed dimensions on bed stability. The curves in Figure 4 correspond to the Carnahan-Starling model, save for the dotted ones which have been drawn when using Equation 4.8 to represent the osmotic pressure correction function and the Enskog factor. 

Dense-phase conveying, also termed "nonsuspension" conveying, is normally used to discharge particulate solids or to move materials over short distances. There are several types of equipment such as plug-phase conveyors, fluidized systems, blow tanks, and, more innovative, long-distance systems. Dilute-phase, or dispersed-phase conveyors, are more versatile in use and can be considered the typical pneumatic conveying systems as described in the literature. The most accepted classification of dilute-phase conveyors comprises pressure, vacuum, combined, and closed-loop systems. 

Among engineers, population balance concepts are of importance to aeronautical, chemical, civil (environmental), mechanical, and materials engineers. Chemical engineers have put population balances to the most diverse use. Applications have covered a wide range of dispersed phase systems, such as solid-liquid dispersions (although with incidental emphasis on crystallization systems), and gas-liquid, gas-solid, and liquid-liquid dispersions. Analyses of separation equipment such as for liquid-liquid extraction, or solid-liquid leaching and reactor equipment, such as bioreactors (microbial processes) fluidized bed reactors (catalytic reactions), and dispersed phase reactors (transfer across interface and reaction) all involve population balances. 

Heat transfer models are usually written in terms of either clusters or dense wall layers, based on the hydrodynamics of fast fluidization. For cluster models (Fig. 26), heat can be transferred between the suspension and wall by (1) transient conduction to particle clusters arriving at the wall from the bulk, supplemented by radiation (2) convection and radiation from the dispersed phase (gas containing a small fraction of solid material). The various components are usually assumed to be additive, ignoring interaction between the convective and radiation components. 

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