(160t) Voidage Wave Instability in a Vibrated Liquid-Fluidized Bed

Authors: 
Lim, E. W. C., National University of Singapore
Wang, C., National University of Singapore


Fluidized beds show different regimes of hydrodynamic behavior above the minimum fluidization velocity. The stable, uniform and homogenous state of fluidization is seldom found in practical applications. On the other hand, it is well established that liquid-fluidized beds exhibit more stable fluidization behaviors but may develop a type of instability known as voidage-wave instability under certain conditions. Such instabilities are of considerable interests to many researchers and have been studied using both experimental and theoretical approaches. Voidage waves were observed to be one-dimensional in narrow beds (Duru et al., 2002; Ham et al., 1990; Nicolas et al., 1996; Nicolas et al., 1999). In such cases, concentration plane waves propagated along the bed in the form of alternating dense and dilute layers. However in wider beds, transverse structures were found to develop as a result of secondary instabilities (Duru & Guazzelli, 2002).

The focus of the present study is on the first type of voidage instability observed in liquid-fluidized beds. The objective is to investigate the nature of these unstable flow structures and also its responses to external harmonic forcing. A combination of experimental study using Particle Image Velocimetry (PIV) and numerical investigation with Computational Fluid Dynamics and the Discrete Element Method (CFD-DEM) is applied. In both experimental and numerical studies, the fluidized bed system used consisted of a glass tube of 2 cm diameter and 1 m height fluidized by water at ambient condition. The bed suspension is supported by a piston which can be set to oscillate vertically at a given frequency and amplitude. The granular material used was glass beads of specific gravity 2.5 and diameter 1 mm. The column was filled with glass beads up to a height of about 12 cm and fluidized by water at a flow velocity of 0.03 m/s.

The instantaneous velocity vectors of particles in a section of the system about 5 cm above the vibrating base obtained from the CFD-DEM simulation and PIV experiments illustrate the unique behavior of solid particles in a liquid fluidization system in the presence of voidage waves. Here, adopting an Eulerian point of view, it may be seen that particles switch periodically between generally upward and downward motions. These correspond to the passage of dense and dilute phases of the voidage wave through the particles respectively. In other words, when a dense phase of the wave propagates through a section of the bed, particles in that section were observed to be moving in the upward direction and vice versa. For the present case studied, the frequency and amplitude of the vibrating base were 2 Hz and 1.5 mm respectively. The characteristic frequency of the periodic motion of the solid particles is also about 2 Hz. The characteristic frequency of such oscillatory motions of solid particles was obtained by a fast Fourier Transform of the vertical component of solid velocities and observed to match the vibrating frequency of the base. Similarly, the characteristic frequencies of solid fraction which also exhibited periodic variations with respect to time were found to be equal to the vibrating frequency of the base. Thus, the voidage waves formed as a result of instability in such liquid fluidized bed systems are traveling waves with dense and dilute phases being convected along the bed.

Despite the convective nature of the voidage waves which originate at the vibrating base and travel up along the length of the fluidized bed, one interesting feature of such instabilities observed in the present CFD-DEM simulations is the highly localized motion of individual particles. As discussed earlier, solid particles move upwards when a dense phase of the voidage wave passes through and settle downwards in the dilute phase of the wave. However, the overall motion of each individual particle was observed to be highly restricted to a small region within the system. Taking a Lagrangian point of view, the positions of four arbitrarily selected particles were tracked for a period of 6 s corresponding to 12 cycles of the vibrating base. Regardless of the precise starting location of the particle within the system, it may be seen that there is very restricted motion in both the axial (vertical) and lateral (horizontal) directions. Each particle seems to be ?trapped' within a small cell whose dimensions are similar to those of the Eulerian cells used previously to illustrate the periodic nature of solid motions. However, when the base is vibrated at a frequency of 1 Hz, with all other operating parameters unchanged, the size of the cell in which each particle is trapped remains substantially similar. The extent of motion of individual particles does not seem to be significantly affected by the frequency of the vibrating base. Similar observations were made from the experiments conducted where a few arbitrarily selected particles were dyed and tracked visually for a short period of time. This phenomenon of localized solid motion over short time scales in a liquid fluidized bed exhibiting voidage wave instabilities does not seem to have been reported previously.

Following the previous qualitative discussion on localization of solid motion, a more quantitative approach was used to characterize the nature of such motions. Solids drifted away from their initial positions gradually much like the diffusion of material from a region of high concentration to another of lower concentration. In order to characterize this phenomenon quantitatively, the concept of dispersion was used to examine this drifting behavior of particles within the liquid fluidized bed.

The mean squared vertical displacement of an arbitrarily selected particle over a 3-second interval exhibited a linear relationship with respect to time. The excellent fit between the simulation data and the dispersion model used in the present study confirms that particles in the bed indeed exhibited a diffusion type of motion. To the knowledge of the present authors, this has not been reported in previous studies of voidage wave instabilities in liquid fluidized beds. The corresponding dispersion coefficient can be calculated from the gradient of the straight line fitted to the mean squared vertical displacement data. Dispersion coefficients were found to be larger at higher bed levels.

References:

Duru, P. and E. Guazzelli. Experimental investigation on the secondary instability of liquid-fluidized beds and the formation of bubbles. J. Fluid Mech., 470, 359?382. 2002.

Duru, P., M. Nicolas, J. Hinch, E. Guazzelli. Constitutive laws in liquid-fluidized beds. J. Fluid Mech., 452, 371?404. 2002.

Ham, J. M., S. Thomas, E. Guazzelli, G. M. Homsy, M.-C. Anselmet. An experimental study of the instability of liquid-fluidized beds. Int. J. Multiphase Flow, 16, 171?185. 1990.

Nicolas, M., J.-M. Chomaz, D. Vallet, E. Guazzelli. Experimental investigations on the nature of the first wavy instability in liquid fluidized beds. Phys. Fluids, 8, 1987?1989. 1996.

Nicolas, M., J. Hinch, E. Guazzelli. Wavy instability in liquid-fluidized beds. Ind. Eng. Chem. Res., 38, 799?802. 1999.

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