Shallow vibrated particulate beds - bed dynamics and heat transfer

Particulate beds which are mobilized and expanded by the application of mechanical vibrations are called vibrated beds. These beds are generally defined as shallow, if the depth-to-width ratio is less than unity. The dynamics of shallow vibrated beds and the heat transfer from immersed tubes to such beds are investigated using a vibrational frequency of 25 Hz.

The vibration equipment is designed to minimize distortions in the applied displacement waveform. Transducers used are of a sufficiently high frequency response to accurately follow the variation of bed properties over a vibrational cycle. An electronic circuit is designed to exactly phase-match data collected by a transducer with the vibrational displacement. The circuit may also be used to trigger a strobe lamp at any phase angle, thus permitting an accurate examination of the evolution of bed characteristics over a cycle.

Measurements of floor pressures beneath the bed, indicate cyclic characteristics, caused by the bed motion. Horizontal floor-pressure gradients cause the bed to pile up or bunker within the vessel. In bunkered beds, particle motion is determined by horizontal gas flows, and a compaction wave which propagates diagonally through the bed during the bed-vessel collision. In non-bunkered beds, particle motion is driven largely by wall friction.

The observed instant of bed-vessel separation lags the theoretical prediction by several degrees, most likely because of bed expansion associated with the bed lift-off.

Different "states" of shallow vibrated beds are identified, each with a unique set of characteristics. One state which exists in ultra-shallow beds of depths between 6 and 15 particle diameters is characterized by a high porosity and good gas-solid interaction, making it potentially useful for studies of reaction kinetics.

Surface-to-bed heat-transfer coefficients are measured for Master Beads and glass beads, and found to vary with particle size and vibrational intensity. Heat-transfer coefficients as high as 484 W/m²-K are obtained. Heat transfer depends on particle circulation and the formation of air gaps which periodically surround the heater surface.

A simplified theoretical formulation for the heat-transfer coefficient appears to qualitatively predict observed trends in heat transfer.