Bed dynamics and heat transfer in shallow vibrated particulate beds

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Virginia Polytechnic Institute and State University


A vibrated bed is a mobile layer of solid particles contained in a vessel that is vibrated vertically. This study investigates bed dynamics and heat transfer from a vertical surface in shallow vibrated beds in absence of aeration. In general, "shallow" means a depth-to-width ratio less than one. In this study, bed depth is 30 mm, and this ratio is about 0.2. All experiments are at 25 hertz and at vibrational amplitudes affording peak accelerations between 2 and 7 times gravity. The study uses spherical glass beads of two densities and "Master Beads," nearly spherical particles of a crude, dense alumina, in size fractions from 63 to 707 micrometers.

A disc embedded in the vessel floor, vibrated at 4.5 kilohertz, gives data on bed-vessel separation, showing it to occur later than predicted by plastic, single-mass models. The delay is attributed to bed expansion, monitored by piezoelectric force gauges mounted on floor and wall of the vessel. In large-particle beds, bed-vessel collision occurs simultaneously everywhere. In small-particle beds, exhibiting an uneven top surface, collision occurs first at the side walls and moves toward the center.

In small-particle beds, pressure gradients appearing during the bed's free flight drive a horizontal component of particle circulation from the vessel's side walls toward its center. An apparent viscosity of the bed, estimated crudely by pulling a rod through it, influences this component's velocity. In beds of large particles, circulation is almost entirely vertical, a layer of two or three particles moving downward at a wall, and a slow return flow moving upward elsewhere. The study confirms the downward wall motion to be driven by friction.

Heat transfer closely follows trends in rate of circulation. Greater dependence upon vibrational intensity is seen in small-particle beds. Values as high as 578 W/m²-K are measured.

Comparison of vertical-surface heater geometry with an earlier horizontal tube shows the former to be generally superior for surface-to-bed heat transfer.