Instabilities and the formation of bubbles in fluidized beds

1995 ◽  
Vol 303 ◽  
pp. 327-366 ◽  
Author(s):  
K Anderson ◽  
S. Sundaresan ◽  
R. Jackson
Keyword(s):  
Fluidized Beds ◽  
Equations Of Motion ◽  
Glass Beads ◽  
Solid Particles ◽  
The Other ◽  
Ambient Conditions ◽  
Small Perturbations ◽  
Gas Fluidized Beds ◽  
Direct Numerical Integration ◽  
Bed Expansion

As is well known, most gas-fluidized beds of solid particles bubble; that is, they are traversed by rising regions containing few particles. Most liquid-fluidized beds, on the other hand, do not. The aim of the present paper is to investigate whether this distinction can be accounted for by certain equations of motion which have commonly been used to describe both types of bed. For the particular case of a bed of 200 μm diameter glass beads fluidized by air at ambient conditions it is demonstrated, by direct numerical integration, that small perturbations of the uniform bed grow into structures resembling the bubbles observed in practice. When analogous computations are performed for a water-fluidized bed of 1 mm diameter glass beads, using the same equations, with parameters modified only to account for the greater density and viscosity of water and to secure the same bed expansion at minimum fluidization, it is found that bubble-like structures cannot be grown. The reasons for this difference in behaviour are discussed.

Fluidization characteristics of gas-fluidized beds: Air and glass beads system

Energy ◽  
1989 ◽  
Vol 14 (12) ◽  
pp. 811-826 ◽  
Author(s):  
S.C. Saxena ◽  
N.S. Rao
Keyword(s):  
Fluidized Beds ◽  
Glass Beads ◽  
Gas Fluidized Beds

Particle pressures generated around bubbles in gas-fluidized beds

2002 ◽  
Vol 455 ◽  
pp. 103-127 ◽  
Author(s):  
KHURRAM RAHMAN ◽  
CHARLES S. CAMPBELL
Keyword(s):  
Fluidized Bed ◽  
Bubble Size ◽  
Fluidized Beds ◽  
Gas Flow ◽  
Solid Particles ◽  
Particle Phase ◽  
Fluid Mixture ◽  
Maximum Value ◽  
Particle Pressure ◽  
Gas Fluidized Beds

The particle pressure is the surface force in a particle/fluid mixture that is exerted solely by the particle phase. This paper presents measurements of the particle pressure on the faces of a two-dimensional gas-fluidized bed and gives insight into the mechanisms by which bubbles generate particle pressure. The particle pressure is measured by a specially designed ‘particle pressure transducer’. The results show that, around single bubbles, the most significant particle pressures are generated below and to the sides of the bubble and that these particle pressures steadily increase and reach a maximum value at bubble eruption. The dominant mechanism appears to be defluidization of material in the particle phase that results from the bubble attracting fluidizing gas away from the surrounding material; the surrounding material is no longer supported by the gas flow and can only be supported across interparticle contacts which results in the observed particle pressures. The contribution of particle motion to particle pressure generation is insignificant.The magnitude of the particle pressure below a single bubble in a gas-fluidized bed depends on the bubble size and the density of the solid particles, as might be expected as the amount of gas attracted by the bubble should increase with bubble size and because the weight of defluidized material depends on the density of the solid material. A simple scaling of these quantities is suggested that is otherwise independent of the bed material.In freely bubbling gas-fluidized beds the particle pressures generated behave differently. Overall they are smaller in magnitude and reach their maximum value soon after the bubble passes instead of at eruption. In this situation, it appears that the bubbles interact with one another in such a way that the de uidization effect below a leading bubble is largely counteracted by refluidizing gas exiting the roof of trailing bubbles.

The growth, saturation, and scaling behaviour of one- and two-dimensional disturbances in fluidized beds

1998 ◽  
Vol 362 ◽  
pp. 83-119 ◽  
Author(s):  
M. F. GÖZ ◽  
S. SUNDARESAN
Keyword(s):  
Fluidized Bed ◽  
Growth Rates ◽  
Fluidized Beds ◽  
Secondary Growth ◽  
Two Dimensional ◽  
Small Perturbations ◽  
One Dimensional ◽  
Gas Fluidized Beds ◽  
The Waves ◽  
Primary Instability

It is well-known that fluidized beds are usually unstable to small perturbations and that this leads to the primary bifurcation of vertically travelling plane wavetrains. These one-dimensional periodic waves have been shown recently to be unstable to two-dimensional perturbations of large transverse wavelength in gas-fluidized beds. Here, this result is generalized to include liquid-fluidized beds and to compare typical beds fluidized with either air or water. It is shown that the instability mechanism remains the same but there are big differences in the ratio of the primary and secondary growth rates in the two cases. The tendency is that the secondary growth rates, scaled with the amplitude of a fully developed plane wave, are of similar magnitude for both gas- and liquid-fluidized beds, while the primary growth rate is much larger in the gas-fluidized bed. This means that the secondary instability is accordingly stronger than the primary instability in the liquid-fluidized bed, and consequently sets in at a much smaller amplitude of the primary wave. However, since the waves in the liquid-fluidized bed develop on a larger time and length scale, the primary perturbations need longer time and thereby travel farther until they reach the critical amplitude. Which patterns are more amenable to being visually recognized depends on the magnitude of the initially imposed disturbance and the dimensions of the apparatus. This difference in scale plays a key role in bringing about the differences between gas- and liquid-fluidized beds; it is produced mainly by the different values of the Froude number.

An Application of Mixture Theory to Particulate Sedimentation

1980 ◽  
Vol 47 (2) ◽  
pp. 261-265 ◽  
Author(s):  
C. D. Hill ◽  
A. Bedford ◽  
D. S. Drumheller
Keyword(s):  
Particle Concentration ◽  
Equations Of Motion ◽  
Mixture Theory ◽  
Solid Particles ◽  
Two Phase ◽  
Small Perturbations ◽  
One Dimensional ◽  
Blood Sedimentation ◽  
The One ◽  
Extended Variational Principle

Equations for two-phase flow are used to analyze the one-dimensional sedimentation of solid particles in a stationary container of liquid. A derivation of the equations of motion is presented which is based upon Hamilton’s extended variational principle. The resulting equations contain diffusivity terms, which are linear in the gradient of the particle concentration. It is shown that the solution of the equations for steady sedimentation is stable under small perturbations. Finally, finite-difference solutions of the equations are compared to the data of Whelan, Huang, and Copley for blood sedimentation.

The height of expansion in bubbling fluidized beds

1987 ◽  
Vol 52 (5) ◽  
pp. 1178-1185
Author(s):  
Miloslav Hartman ◽  
Václav Veselý ◽  
Otakar Trnka ◽  
Karel Svoboda
Keyword(s):  
Bubble Size ◽  
Bubble Growth ◽  
Fluidized Beds ◽  
Empirical Correlation ◽  
Gas Fluidized Beds ◽  
Bed Expansion ◽  
Semi Empirical

A theory of bubble growth due to coalescence in gas fluidized beds was employed to predict the bed expansion. Using the semi-empirical correlation of bubble size by Mori and Wen, an equation for the height of expanded beds has been developed and verified by experiment. Predictions of the proposed formula were compared with the predictions of recent bed expansion correlations.

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