An experimental study of the stability of liquid-fluidized beds

Ham, J.M.; Thomas, Subin; Guazzelli, Élisabeth; Homsy, G. M.; Anselmet, M.-C.

doi:10.1016/0301-9322(90)90052-k

Cited by 62 publications

(41 citation statements)

References 12 publications

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“…Homogeneous fluidized beds and sedimenting suspensions with monodisperse, spherical particles can be subject to instabilities in the form of long-range number density variations that appear as one-dimensional traveling waves, the magnitude of which can grow with time. [56][57][58] It should be noted that we see no evidence of such inhomogeneities at the conditions of particle Reynolds number, particle-to-fluid density ratio, and simulation cell size explored in our study. The pair distribution functions decay with radial position approaching P͑r , ͒ = 1 before reaching radial positions comparable with L / 2.…”

Section: ͑17͒mentioning

confidence: 54%

Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers

2007

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Lattice-Boltzmann simulations are employed to determine the mean settling velocity and pair distribution function for spheres settling in a liquid. The Reynolds number based on the terminal velocity ranges from 1 to 20, the solid-to-fluid density ratio is p / f = 2.0, and the solid volume fraction is varied from 0.005 to 0.40. At volume fractions larger than about 0.05, the ratio of the mean settling velocity to the terminal velocity u * can be fit by a power-law expression u * = k͑1 − ͒ n , where k and n are functions of the Reynolds number based on the terminal velocity. The constant k is typically about 0.86-0.92 and u * deviates from the power-law behavior in dilute suspensions. The extent of this deviation increases with increasing Reynolds number. We show that the hindered settling velocity follows a power law when the particle microstructure is similar to that in a hard-sphere suspension. The deviation from the power-law behavior can be correlated with an anisotropic microstructure resulting from wake interactions among the spheres. This microstructure, which occurs in dilute suspensions and is most pronounced at the higher Reynolds numbers explored in our study, consists of a decreased pair distribution function for pairs with vertical separation vectors and a peak in the pair distribution function for horizontal separations corresponding to about two particle diameters.

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Section: ͑17͒mentioning

confidence: 54%

Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers

2007

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“…It has also been recognized that particle-phase pressure is crucial to the stability of particle-fluid flows. 3 Kinetic theory of granular flows ͑KTGF͒ has been widely used to predict particle-phase stresses, and how to quantify particle fluctuation velocity or granular temperature is the central problem for the theory. However, most research thus far has focused on shear-induced particle velocity fluctuations ͑see Sangani 4 and references therein͒.…”

mentioning

confidence: 99%

Collisional particle-phase pressure in particle-fluid flows at high particle inertia

Wang

2005

Physics of Fluids

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Particle-phase pressure has to be considered in two-fluid models describing particle-fluid flows, and is important for the stability of such flows. However, most research so far has focused on its dependence on shear-induced particle velocity fluctuations. This Brief Communication proposes a simple model to predict collisional particle-phase pressure at high particle inertia due to microscopic particle number and velocity fluctuations in the absence of any large-scale shearing. The results are in good agreement with the experimental data of Zenit et al. ͓J. Fluid. Mech 353, 261 ͑1997͔͒.Particle-fluid two-phase flows are widely encountered in both natural and industrial processes. Two-fluid models 1,2 are mainstream simulation approaches to such systems, which treat both the particle and fluid phases as interpenetrating continua. Therefore, quantification of the particle-phase stresses generated by particle velocity fluctuations and hence collisions among the particles, becomes a necessity of the establishment of a two-fluid model. It has also been recognized that particle-phase pressure is crucial to the stability of particle-fluid flows. 3 Kinetic theory of granular flows ͑KTGF͒ has been widely used to predict particle-phase stresses, and how to quantify particle fluctuation velocity or granular temperature is the central problem for the theory. However, most research thus far has focused on shear-induced particle velocity fluctuations ͑see Sangani 4 and references therein͒. Theoretical works on particle velocity fluctuations in response to microscopic particle number fluctuations in the absence of largescale shearing have received much less attention, especially at high particle inertia. 5 For particles with small inertia, the characteristic viscous relaxation time is very short compared with the characteristic particle collision time, and the particle fluctuation velocity is dominated by anisotropic and long-range correlated particlefluid interactions, which can be well predicted by Segrè's model. 6 The model has been based on the balance between the rate of gravitational potential increment in a correlated spatial region and the rate of viscous dissipation. At the other extreme, direct interparticle collisions should be the dominant mechanism for random and isotropic particle velocity fluctuation and energy exchange, if the collisions are nearly elastic. 7 Koch 8 analyzed dilute gas-solid flow with ideal interparticle collisions by the kinetic theory, and then extended his theory to dense gas-solid flows at small particle Reynolds numbers ͑Re= g U p d p / g , where g is fluid density, U p is particle velocity, d p is particle diameter, and g is fluid viscosity͒, and finite Stokes numbers ͓St= p U t d p / ͑9 g ͒, where p is particle density, U t is particle terminal velocity͔ with inelastic interparticle collisions. 9 Buyevich and Kapbasov 10 showed that their model can qualitatively reproduce Zenit's experimental data 11 with an adjustable numerical coefficient. However, as Sundaresan concluded in a recent re...

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“…In this connection, different points of view were expressed until the experiments carried out in [7] confirmed very convincingly the presence of such a region . The simple physical explanation is that at values of p fairly close to p the bulk modulus of the dispersed phase, which is proportional to the derivative of its pressure with respect to concentration, is arbitrarily large and sufficient to stabilize the flow near the close-packed (or initial fluidization) state .…”

Section: Scale Effectmentioning

confidence: 88%

“…The analogous relations for the dimensionless frequency and phase velocity of the waves of maximum growth under the same conditions are reproduced in Figs stability curves the frequency of the waves of maximum growth can be approximated by linear relations of the type obtained experimentally in [7] . The propagation velocity of the waves of maximum growth, directed along the flow, i .e ., upwards when x =1, decreases from a finite value on the left-hand branch of the neutral stability curve and reaches a minimum at a concentration very close to the close-packing concentration .…”

Section: Waves Of Maximum Growthmentioning

confidence: 89%

Stability of a vertical high-concentration fine suspension flow

Buevich¹,

Kapbasov²,

Макаров³

1994

Fluid Dyn

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The neutral stability conditions are found with allowance for the effects associated with the disappearance of the particle free volume on transition to the close-packed state and the characteristics of the disturbances with the maximum growth rate are investigated on the interval of intermediate and high particle concentrations . Results relating to the effect of quasi-viscous stresses and Brownian motion on flow stabilization on this concentration interval are obtained . The stability of a bounded uniform vertical flow of not too small particles is investigated and the well-known scale effect, associated with the phenomenon of increasing instability on transition from laboratory to geometrically similar industrial apparatus, is examined .There have been numerous attempts to investigate the hydraulic stability of concentrated suspension and fluidized bed flows (for a partial bibliography see [1,2]) . However, these attempts have not led to success, even in the case of one-dimensional vertical flows, for the simple reason that adequate rheological models of the disperse systems are lacking . Indicative in this respect is the study [1], in which the forces and stresses affecting the flow of the dispersed phase are very carefully discussed . Nevertheless, the lack of reliable information about the most important quantitythe normal stress in that phase -made it impossible to draw any final conclusions concerning the conditions of stability of the vertical flow even in that otherwise very interesting investigation .The paper [2] deals with this problem as it relates to colloids and suspensions of very fine particles, in which there are no direct interparticle collisions . The use of the normal stress in a system of particles in thermal and pseudoturbulent motion following from the model proposed in [3] made it possible completely to close the equation of motion and eliminate the indeterminacies inherent in all previous investigations of the problem .However, in [2] the effects associated with the disappearance of the particle free volume on transition to the closepacked state were not considered . Therefore the results are not applicable to flows with a fairly high concentration . Moreover, it has recently proved possible to eliminate certain inaccuracies in the determination of the essentially unsteady part of the interphase interaction force [4] . The aim of the present investigation is to extend the results of the theory [2] into the region of high concentrations and to introduce corrections associated with the refinement of the above-mentioned force and the computational procedure employed in [2], the need for which was noted in [2] itself . . FREE VOLUME EFFECTS AND REFINEMENT OF THE INTERPHASE INTERACTION FORCEAs in [2, 3], we will consider monodisperse suspensions of spheres of radius a in a fluid of viscosity q o ; the phase densities are p o and p t. We will enumerate the changes which must be introduced into the theory [2] in order to extend it to suspensions with a high concentration approaching the concen...

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An experimental study of the stability of liquid-fluidized beds

Cited by 62 publications

References 12 publications

Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers

Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers

Collisional particle-phase pressure in particle-fluid flows at high particle inertia

Stability of a vertical high-concentration fine suspension flow

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