Ind. Eng. Chem. Process Des. Dev. 1905, 2 4 , 719-725
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Fluid Mechanics of Crossflow Magnetically Stabilized Fluidized Beds Nlcholas P. CheremlsInoff,+ Jeffrey H. Siegell,” and Costas A. Coulaloglou~ Exxon Research and Engineering Company, Florham Park, New Jersey 07932
From the analogy of laminar flow through a circular pipe, a simple model describing the fluid mechanics of a crossflow magnetically stabilized fluidized bed (MSB) in an inclined channel was developed. Predictions from the model compared favorably with experimental data for the bed top surface and solids velocity profiles. It was found that the flow of MSB sollds can be described as a non-Newtonian fluid, where standard rheological models such as power law or Blngham plastic apply. The effective viscosity of an MSB was found to decrease with increasing channel shear rate. Thus, a magnetically stabilized bed of solids appears as a “shear thinning fluid”. High yield stresses are the controlling mechanism at low bed flow rates, while a truly vlscous flow exists once the bed solids establish steady-state flow. The decrease in bed fluidity with Increasing magnetic field was confirmed and further quantified.
Introduction Fluidization has found wide application throughout the process industries. In these operations, passage of some of the fluid phase through the bed in the form of bubbles produces potentially disadvantageous effects. There is a wide range of residence times of both the fluid and solid phases, thus lowering the contacting efficiency. In addition, agitation of the bed particles is high, causing attrition of the material. Application of a magnetic field to stabilize a fluidized bed of magnetizable particles has been shown to reduce these detrimental effecta while maintaining the advantage of bed flowability (Rosensweig, 1979; Lucchesi et al., 1979; Rosensweig et al., 1981). The magnetic stabilization produces a nonbubbling quiescent fluid state termed a magnetically stabilized fluidized bed (MSB). The MSB solids resemble a liquid and are easily transported. Similar to unmagnetized fluidized beds the pressure drop is independent of particle size or fluid throughput, and both fluid and solids backmixing which normally occur in bubbling fluidized beds are absent. Properties of the MSB Figure 1shows that the fluid/solids/magnetic system exists in one of three regimes. Below the minimum fluidization velocity, the pressure drop across the bed is less than the bed weight per unit area and the bed is “unfluidized”. In the stably fluidized, MSB regime, the bed is free of backmixing patterns. In the regime denoted bubbling magnetized, the bed bubbles even though magnetized. The transition between each of these regimes is rather sharp and reproducible. The MSB regime existing a t velocities between the minimum fluidization velocity and transition velocity to bubbling is the operating regime of interest in this paper. When increasing the gas velocity in an MSB, as shown in Figure 2, the breakpoint of the pressure drop curve corresponds to the minimum fluidization velocity Ump Thereafter, as in unmagnetized bubbling fluidized beds, the pressure drop through the MSB equals the weight of bed solids per unit bed area independent of particle size or gas velocity. This is an indication that although there may be substantial interparticle forces within the bed, the magnetic field exerts no net external force on the MSB.
* Corporate Research Science Laboratories. t Chemical Engineering Technology Division. Present address:
Exxon Chemical Co., Elastomers Technology Division, Linden, NJ. Chemical Engineering Technology Division.
*
0196-4305/85/1124-0719$01.50/0
Crossflow fluidized beds, where solids flow in a transverse direction to the ascending flow of the fluidizing fluid, are attractive to a variety of applications. Examples of these include dryers, classifiers, roasting furnaces, and a variety of pneumatic channel transfer devices. Besides the fluid bypassing and vertical solids backmixing experienced in other configurations, there is considerable horizontal mixing of the solids. Thus, there are substantial differences in solids residence times. Vertical baffles are normally located within these beds to reduce the amount of horizontal mixing and to provide a staging effect. Continuous solids throughput of crossflow magnetically stabilized fluidized beds has been demonstrated (Siegell and Coulaloglou, 1984). The crossflow MSB was found to experience near plug flow of the bed particles, including those adjacent to the wall, thus eliminating the horizontal as well as the vertical backmixing of the solids in addition to the fluid bypassing. The bed of solids was found to move faster a t higher gas velocities and lower magnetic fields. Continuous operation at high magnetic fields was limited due to high particle-to-particle attractive forces, which impeded solids flow. Modeling The mathematical model describing the flow of an MSB with solids moving in a transverse direction to the ascending flow of fluidized gas is derived herein. The crossflow MSB is operated in a vessel tilted slightly from the horizontal so that the solids flow is assisted by gravity. Woodcock and Mason (1978), Ishida et al. (1980), and Singh et al. (1978), have modeled air-assisted solids flow down inclined open channels and described such behavior as being homogeneous. Materials used in these studies were different grades of sand. The flow of magnetized fluidized solids, however, is more complex in that their flowability is not only a function of the fluidization velocity, the bed angle, and the properties and size of solids, but also, as shown by Siegell and Coulaloglou (1984), of the strength of the applied magnetic field. Following the analogy of Woodcock and Mason (1978), the crossflow stabilized bed is considered to be represented by a differential slice of homogeneous fluid flowing down a channel, as described by the coordinates in Figure 3. Assuming the flow to be at steady state for a constant set of operating conditions, the overall mechanical energy balance may be written as
+ A(gy) +
1 2 v dP + CF + Wf
@ 1985 American Chemlcal Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 SDLIDS IN
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