State Of Uniform Fluidization Research Articles

A comparison of one-dimensional traveling waves in inverse and normal fluidized beds

The state of uniform fluidization is usually unstable to small disturbances, and this can lead to the formation of vertically traveling voidage waves. In inverse fluidization, when particle density is less than fluid density ( ρ s < ρ f ), particles fluidize in the direction of gravity when the drag force exerted by the fluid overcomes buoyancy. Inverse fluidization thus provides a unique parameter space, which augments the study of instability behavior in normal fluidization when ρ f < ρ s . Using continuum equations of continuity and motion, we compared the linear stability of normal and inverse bed modes to examine the effect of the Froude number ( Fr) and fluid to solid density ratio ( δ = ρ f / ρ s ). Making use of numerical bifurcation analysis and continuation, periodic solutions in the form of one-dimensional traveling waves (1D-TWs) were computed. Based on wave growth rates and bifurcation structure, we identified the Fr as an important parameter for predicting instability strength. However, δ affects instability onset, or the point at which the base state is rendered unstable. In the case studies we examined, traveling waves were shown to propagate in the direction of fluidization, and asymmetrical, high amplitude 1D-TW profiles suggest fully developed bubble-like structures are oriented in the direction of fluidization.

Transverse instability of plane wavetrains in gas-fluidized beds

Using a two-fluid model of gas-fluidized beds, it is shown that periodic plane voidage waves travelling against gravity are unstable to perturbations with large transverse wavelength. This secondary instability sets in at arbitrarily small amplitudes of the plane wave and correspondingly small transverse wavenumbers of the two-dimensional perturbation. More precisely, if the bed is wide enough to accommodate sufficiently long horizontal waves, then the plane wave becomes unstable as soon as its amplitude has grown to the order of the square of the transverse wavenumber. The instability can be stationary or oscillatory in nature and has its origin in the interaction between the plane wave and four least-stable modes with small transverse wavenumber. Two of them represent a pair of bubble-like ‘mixed modes‘; the other two are initially, i. e. at the onset of the primary wave, pure transverse modes, one consisting only of an initially pure vertical velocity perturbation of the state of uniform fluidization. Depending on a relation between the eigenvalues of the least-stable modes at the primary bifurcation point, either one of these can be the dominant mode, which becomes (most) unstable along the growing vertically travelling plane wave. While the transverse modes gain longitudinal structure during this process, the mixed modes obtain a vertical component of the vertically averaged velocity as well, so that it appears that the secondary instability described here is a variant of Batchelor &amp; Nitsche's (1991) ‘overturning’ instability found recently for unbounded stratified fluids, see also Batchelor (1993).

Effect of the lift force on the stability of uniform fluidization

The state of uniform fluidization, where the uniform upflow of a fluid balances the weight of a bed of particles, it shown to be unstable to small disturbances when the effect of the lift force on the particles is included. The lift force is dominant during the initial growth of the disturbances. The lift force on the particles is assumed to be proportional to the slip and to the one-half power of the shear rate. Perturbations from the state of uniform fluidization are studied. The resulting perturbation problem is such that the evolution of the smallest disturbances is governed by a nonlinear equation. Particular initial conditions corresponding to growing solutions are found.