Homogeneous fluidized bed

Smooth fluidization In fine particle A beds, a limited increase in gas flow rate above minimum fluidization can result in smooth, progressive expansion of the bed. Bubbles do not appear as soon as the minimum fluidization state is reached. There is a narrow range of velocities in which uniform expansion occurs and no bubbles are observed. Such beds are called a particulate fluidized bed, a homogeneously fluidized bed, or a smoothly fluidized bed. However, this regime does not exist in beds of larger particles of 13 30 B and D, in these cases bubbles do appear as soon as minimum fluidization is reached. 

In one of the proposed modeling approaches the production of granular temperature represented by the gas-particle velocity covariance term is interpreted as a mechanism that breaks a homogeneous fluidized bed with no shearing motion into a non-homogeneous distribution. Koch [74] proposed a closure for these gas-particle interactions for dilute suspensions. Koch and... 

The general approach in dealing with pseudo-turbulent fluctuations was already outlined in great detail [9,14,23] and thereafter applied to homogeneous fluidized beds [25]. A serious deficiency in the latter analysis [25] lies in the fact that the authors... 

The fact that the total number of particles must be conserved during the development of occasional disturbances in a uniform vertical flow or in a homogeneous fluidized bed in itself results in the formation of kinematic waves of constant amplitude, as was first demonstrated by Kynch [48]. Both particle inertia and the nonlinear dependence of the interphase interaction force on the suspension concentration cause an increase in this amplitude. This amounts to the appearance of a resultant flow instability with respect to infinitesimal concentration disturbances and with respect to other mean flow variable disturbances. Various dissipative effects can slow the rate at which instability develops, but cannot actually prevent its development. Therefore, investigating the linear stability of a flow without allowing for interparticle interaction leads inevitably to the conclusion that the flow always is unstable irrespective of its concentration and the physical parameters of its phases. This conclusion contradicts experimental evidence that proves suspension flows of sufficiently small particles in liquids to be hydrodynamically stable in wide concentration intervals [57-59]. Moreover, even flows of large particles in gases may be stable if the concentration is either very low or very high. 

Equations 8.4 hold true for unperturbed states of a homogeneously fluidized bed the stability of which is under question. When the bed consists of small particles, these equations yield... 

Since V is the volume of a representative particle in a homogeneously fluidized bed, the representative volume of liquid associated with this particle (in a unit cell so circumscribed that the liquid-to-solid ratio is the same as in the bed as a whole) is Ee/(1—e) and the correspondingly representative volume of bed is simply V/ —e) [= Fe/(1 — e) -I- E]. 

The Purasiv HR process is an improved fluidized bed, activated carbon process based on the use of a spherical beaded adsorbent developed by Kureha Chemical of Japan. The process was introduced in the United States and Canada by Union Carbide Corporation in 1978 (Union Carbide Corp., 1983). The unique form of the carbon adsorbent represents the key feature of the process. The beads, which are about 0.7 mm in diameter, create a homogeneous fluidized bed in the adsorption section and a free-flowing dense bed in the desorption section while providing a much higher resistance to attrition than conventional granular or pelletized material. The beads are produced by a proprietary process that involves shaping molten petroleum pitch into spherical particles which are subsequently carbonized and activated under controlled conditions. 

The Ergun equation has been extensively verified for packed beds of spheres and near spheres, for which the void fraction variation remains small e 0.4. Some measurements, which we discuss later in this chapter, have been reported for beds artificially expanded by various mechanical means to much higher void fractions homogeneously fluidized beds can attain void fractions of 0.9 and more. These situations call for a re-examination of the derived dependence of AP on void fraction. 

The expansion characteristics of homogeneously fluidized beds have been the subject of far more empirical study than theoretical analysis. This could be due to the uncomplicated nature of the experimental procedure, which involves simply the measurement of steady-state bed height Lg as a function of volumetric fluid flux U. The results are usually presented as the relation of U with void fraction e, which, unlike Lg, is independent of the quantity of particles present. The constant particle volume relation. 

Once again we have arrived, quite independently, at a result for the expansion characteristics of homogeneous fluidized beds which is in compete agreement with the Richardson-Zaki relation, this time for inertial flow conditions eqn (4.4), = 2.4. The unhindered-particle limit, 1, yields, as it must, the inertial regime relation of eqn (2.13) for Uf... 

The response of homogeneously fluidized beds to sudden changes in fluid flux... 

Consider a homogeneously fluidized bed of void fraction ei in equilibrium with a fluid flux of U. At time zero the flux is suddenly switched to a lower value U2, causing the bed to contract, eventually attaining a new equilibrium at void fraction 2. 

Figure 5.6 Gravitational instabilities in expanding, homogeneously fluidized beds.

Although the bed surface response represents the most obvious and easily measurable manifestation of the transient behaviour of homogeneously fluidized beds, it is the response of the other interface, that separating the two equilibrium zones, which provides a key component for a comprehensive analysis of the fluidized state. The velocity of this interface, dLjjdt, follows immediately from the above relations eqn (5.5) links it to the bed surface velocity, eqn (5.6), thereby yielding ... 

We shall see that this relation, which was first derived somewhat differently by Slis et al. (1959), plays a central role in the analysis of the fluidized state. It stipulates the velocity at which long-wavelength void fraction perturbation waves travel, always in the upward direction, through homogeneously fluidized beds. Perturbations represent an ever present reality in physical systems, created as a result of the imperfect nature of the fluid distributor and other imponderables. 

We now consider the counterpart experiment performed on the particle-phase of a homogeneously fluidized bed. The piston in this case is, in effect, the distributor (which acts like the sieve in the compression experiment... 

Figure 8.2 Idealized particle layer description of a homogeneously fluidized bed.

Rietema, K. and Mutsers, S.M.P. (1978). The effect of gravity upon the stability of a homogeneously fluidized bed, investigated in a centrifugal field. Fluidization. Cambridge University Press. 

Consider a homogeneously fluidized bed in equilibrium. If the particles are now subjected to a small force, they will move to restore the equilibrium condition. How fast they do this will depend on the specific system properties the greater the velocity of the particles, the more uniformly held together will be the suspension, and vice versa. A parameter that could provide a measure of this effect, the bulk mobility Bp of the particles , has been proposed by Batchelor (1988) in the development of a model for fluidization that is structurally similar to the particle bed model. He defines Bp as the ratio of the (small additional) mean velocity, relative to zero-volume-flux axes, to the (small additional) steady force applied to each particle of a homogeneous dispersion . For a bed initially in a state of equilibrium, this becomes ... 

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