Homogeneous Fluidized Bed Research Articles

A coherent representation of pressure drop in fixed beds and of bed expansion for particulate fluidized beds

A coherent representation of pressure drop in fixed beds and of fluidized bed expansion is derived on the basis of an analysis of the Navier—Stokes equations. This representation combines an Euler-number, a Reynolds-number and a characteristic dimensional ratio r 0/δ. Empirical relations for fixed bed pressure drop usually are based on the mean hydraulic diameter concept. The mean hydraulic diameter concept is originally based on certain assumptions. There is no doubt that none of these assumptions is valid for fixed beds of particles. On the other hand, expansion of homogeneous fluidized beds is described by the well known empirical Richardson—Zaki equation, which at least describes fluidized bed behaviour as a deviation from single particle behaviour. Both phenomena, fixed bed and fluidized bed, however, are not so different that two completely different approaches may be regarded as physically meaningful. Therefore a coherent description of both phenomena is derived. A cell model is derived which leads to a characteristic dimensional ratio r 0/δ containing a packing parameter ξ which can be determined by pressure drop measurements in fixed beds and by bed expansion measurements in fluidized beds. Consideration of the Navier—Stokes equations describing the flow around a sphere in a close packing yields relations between the Euler-number, the Reynolds-number and the characteristic dimensional ratio. Inspection of own measurements and of measurements found in literature confirms the validity of this concept. For fixed beds and for fluidized beds of spherical particles different packings parameters ξ are determined. A more general application of the results obtained, in particular to the flow of concentrated suspensions, appears to be possible.

Local structure of a binary finely dispersed fluidized bed

Results are given of calculations of the quantities characterizing the random pseudoturbulent motions of the phases in a homogeneous fluidized bed consisting of particles of two sorts, differing in size. The dependence of the coefficients of pseudoturbulent diffusion of the particles, the mean-square velocities of the pulsations, etc., on the partial concentrations of the particles, the ratio of their sizes, and other parameters is evaluated. For granular beds, fluidized by a gas or a drop-type liquid, intense chaotic fluctuations of both phases are characteristic; these determine to a considerable degree the observed macroscopic properties of the bed and affect its effectiveness as a working body in various types of heat exchangers and chemical reactors. Such random (“pseudoturbulent”) motions are particularly considerable for beds of small particles under homogeneous fluidization conditions, where mixing due to the rise of cavities in the bed, filled only with the fluidizing medium, is practically absent. A similar situation is encountered in reactor and regenerating units for catalytic cracking [1, 2], in beds with a drop-type liquid phase, in rarefied two-phase systems under the conditions of strong fluidization or of the transport of bulk materials in a dilute phase, etc. The characteristics of pseudoturbulence in locally homogeneous flows of monodisperse two-phase systems have been investigated, for example, in [3–5]. However, real fluidized beds are generally polydis-perse; the presence of particles of different sizes in the bed has a very considerable effect, on the intensity of the pulsations, the effective diffusion coefficients of the phases of the bed, the effective viscosities, etc. [1, 6]. In addition, the chaotic mixing in polydisperse beds determines some of the technological characteristics, specifically, the rate of entrainment of small particles by the flow of the fluidizing medium and the settling of large particles, the degree of separation of the fractions of the disperse phase, which is very important in determination of the limits of the existence of the fluidized state, and in the modeling of numerous processes of the separation of particles with respect to size or density [1, 6].

Momentum, heat, and mass transfer for fixed and homogeneous fluidized beds

AbstractThe Carman channel model for flow in packed beds is shown to apply for the minimum fluidization velocity and homogeneous fluidized beds. The channel model also provides correlations for mass transfer in the laminar flow region and heat and mass transfer for turbulent flow in a packed bed. Tube bundle data for pressure drop and heat transfer are also evaluated as a packed bed with the channel model.

The interrelationship between bubble motion and solids mixing in a gas fluidized bed

AbstractThe stochastic differential equations for particle motion in a homogeneous fluidized bed have been modified to incorporate a bubble‐particle interaction. In a freely bubbling bed this interaction causes an instantaneous random step upwards when a particle collides with a bubble. In addition the particles are subject to a Brownian Motion due to particle‐particle interactions and to a vertical drift velocity. The particle motion was modeled by the set of stochastic differential equations where N and W are Poisson and Wiener processes respectively. U is the velocity vector, X the vertical coordinate, Y and Z the horizontal coordinates. This set of equations has been solved and the form of the probability density function p(x, t) has been obtained. Predictions are in terms of the mean bubble frequency at a point λ the average displacement associated with a particle‐bubble collision, and the dense phase diffusion coefficient.The main result is that the effective diffusion coefficient in the vertical direction is given by where E is the dense phase diffusion coefficient and 1/α is the average displacement suffered by a particle on collision with bubble.The model was tested experimentally using random forcing function techniques. All parameters were evaluated independentely; λ by direct measurement and the other two inferred from available published data. The predictions of the theory agreed well with experimental observations of the solids dispersion.