A.M. Squires

Identifying States in Shallow Vibrated Beds

Abstract Shallow particulate beds on surfaces vibrating at ca. 25 Hz and an amplitude of a few millimetres display several states, in order of increasing bed depth: two ‘Newtonian states’ in which freely bouncing particles obey simple Newtonian mechanics; a ‘coherent—expanded (CE) state’ in which particles move together in loosely organized packets to form a turbulent shallow layer; and a ‘coherent—condensed (CC) state,’ either beneath or replacing the CE state, in which particles move together in a compacted layer. In the CC state, neighboring particles tend to remain in close company. Which states are present, as well as whether a gap forms beneath the vibrated bed, depends on bed depth and particle and gas properties. Transitions between the states appear to be sharp and quantifiable, but further investigation, both theoretical and experimental, is needed before the transitions are fully understood. The CE state provides intense solid mixing and appears likely to provide superb contacting of a solid with a gas in the space above a shallow vibrated bed. The CE state may provide an opportunity for developing a family of microreactors for kinetic studies. The CC state is characterized by a bulk solid-circulation pattern, generally stable over a long time interval, as well as by a relatively low porosity.

Some behaviors of shallow vibrated beds across a wide range in particle size and their implications for powder classification

Abstract Vertical sinusoidal vibration (25 Hz) was imposed upon two-dimensional beds of particulate matter (30-mm bed average depth), particle sizes ranging from ∼1 to 707 μm. Behaviors of coarse- and fine-powders are in sharper contrast than in gas-fluidized beds. A vibrated-bed powder classification, analogous to Geldarts for fluid beds, will be complex; yet the present work suggests opportunities for refining fluid-bed powder classification. Before lift-off, 707- and 177-μm alumina ‘Beads’ pull in gas during a “lift-off-delay interval”, creating an absolute porosity increase of ∼0.13% and ∼0.8%, respectively. For ‘Beads’ of size 177-μm and larger, a high-speed cinematograph of a bed–floor collision discloses passage of a compaction front reversing the earlier porosity increase. No front can be seen in 88-μm ‘Beads’ (although other data indicate its existence); in these ‘Beads’, porosity waxes and wanes during each vibration cycle by an absolute 2%. Evidence is given for further bed expansion during flight. In non-aeratable powders, all circulation is stop–go: particles move only during flight. An aeratable powder (Geldart Group A) “breathes”: it imbibes gas over many cycles and then quickly releases it in the form of bubbles. In aeratable and cohesive powders (Geldart A, A–C, and C), a spout can be created by extending a vertical pipe from near the floor to beyond the bed surface. Such a spout appears to be suitable for controlled feeding of matter as small as ∼1 μm.

Heat transfer in shallow vibrated beds

Abstract Coefficients are reported for transfer of heat from a horizontal cylinder and from vertical, flat surfaces (paired back-to-back, closely spaced-apart) to 30-mm deep vibrated beds (25 Hz) of alumina spheres and high- and low-density glass beds (at sizes from 63 to 707 μm). In general, the flat surfaces afford higher coefficients, but heat transfer is sensitive to pattern and vigor of powder circulation. No broadly general explanation or correlation of vibrated-bed heat transfer can be given; but the body of data provides leads for the engineer wishing to develop a vibrated-bed-heat-exchanger design for non-sticky particulate matter. The leads hold promise of coefficients beyond 500 W/m2K, even perhaps approaching 1000.

A method for observing phase-dependent phenomena in cyclic systems: Application to study of dynamics of vibrated beds of granular solids

Abstract A technique is described which uses a digital circuit based on a phase-locked loop to permit viewing, photographing, or measuring phase-dependent phenomena in cyclic systems. This eliminates the need for expensive and tedious high-speed cinematographic methods that have been used thus far for visual observations of cyclic systems. The technique provides accurate quantitative data on visual cyclic phase-dependent phenomena that occur within the system with the same frequency as the forcing vibration. The technique has been used in studies of a vibrated bed. It may also be used with vibrating gas-fluidized beds. With little modifications, the technique may be applied to study phase-dependent phenomena in other cyclic systems. In direct observations at a series of phase angles, using a strobe light activated by the digital circuit, particle-free air gaps appear above and below a horizontal heat-transfer tube placed within a two-dimensional vibrated bed. The time-integrated percentage of heat-transfer surface blanketed by air, estimated from back-lit photographs, explicates trends in the heat-transfer data. A rarefied zone of reduced particle density forms at the top surface of a vibrated bed. In a bed in which solid circulates, down at walls and upward at the center, the rarefied zone is the major path for return flow of solids from the center to wall. Phase-shift photographs show that the rarefied zone develops during lift-off of the bed from the vibrating plate, indicating that rarefaction occurs because a downward flow of gas, necessary to supply gas to the gap forming between the bed and plate, exerts a lesser drag on the top layer of particles in the bed that it does on the remainder of the bed. The phase-delayed trigger system ha also been used to facilitate measurements of non-visual phase-dependent properties such as gas pressures below the bed throughout a cycle of vibration.

Pressure drop across shallow fluidized beds: Theory and experiment

A special manometer system has been developed to permit an accurate measurement of average pressure drop across shallow fluidized beds, despite the possible pressure fluctuations and oscillations caused by the vigorous solid mixing and gas bubbling commonly observed in such beds. Quantitative measurements have been made of bed pressure drop over wide ranges of superficial gas velocities, static-bed heights, distributor design characteristics, and particle types and properties. By making a macroscopic momentum balance over the fluidized-bed control volume, a simple model for correlating and predicting the pressure-drop ratio (i.e., the ratio of bed pressure drop to static-bed pressure) has been developed. The model indicates that the pressure-drop ratio PR is linear in the reciprocal of static-bed height (Hs): PR = ‡ α — β/Hs, where α and β are constants which can be predicted a priori from known experimental variables and common dimensionless groups such as Reynolds and Froude numbers based on the gas velocity passing through the distributor. A comparison between model predictions and experimental data shows that the proposed model can accurately correlate and predict the bed pressure drop across shallow fluidized beds.

Confirmation of Faraday's explanation of bunkering in vibrated granular beds

Abstract Faraday, like Chladni earlier, saw a shallow layer of a fine powder collect in a circular heap (a ‘minibunker’) at an antinode of a vibrating plate. He saw ‘Faraday circulation’: powder motion in a shallow surface layer of the heap, downward from its center to its edge; inward motion centerward at the edge; by inference, motion upward toward the middle of the heaps interior. What he saw led him to postulate formation of a partial vacuum beneath the powder heap, creating (1) an external wind blowing the powder toward an antinode and (2) a flow of air inward from the heaps edge, driving powder toward its center. Although some experimentalists have recently advanced alternative explanations of vibrated-bed heaping (‘bunkering’), we are able to confirm the essentials of Faradays thought. At suitable amplitude and frequency, vertical sinusoidal vibration of a fine-powder bed causes it, in each vibration cycle, to experience a free-flight interval during which pressure gradients in its interior drive powder centerward. A center-high bunker forms, displaying Faraday circulation. When bed-floor collision terminates flight, pressure gradients reverse direction; but passage of a compaction front has locked particles against further movement. Before a next flight interval, an increase in porosity will reverse the compaction that accompanied heap-floor collision. In particles 177-μm and larger, we see the compaction front cinematographically; in 88-μm particles, we infer it from floor-pressure data. Although, given sufficient time, a bed of large particles (e.g., 707 μm) will form a bunker, it displays the wall-friction-driven circulation elucidated by Muchowski, not the Faraday pattern.

A vibrofluidized-bed heat exchanger for heat recovery from a hot gas II. Heat-transfer evaluation of a pilot-scale system

Abstract The objective of this work is to experimentally evaluate a process for recovering the thermal energy from a hot exhaust gas by direct contact of the gas with a countercurrently flowing vibrofluidized bed of solids. This portion of the two-part paper presents the results of heat-transfer studies on a pilot-scale vibrofluidized-bed heat-exchanger system described in Part I. Based on the phenomenon of spray zone formation observed in Part I together with results from gas-temperature measurements and cold-flow experiments, a model was proposed for the effective convective heat-transfer coefficient between the hot supernatant gas and the vibrofluidized solid. By using a factorial design of experiments, high effective heat-transfer coefficients were obtained with high air and solid flow rates, low baffle heights and high vibrational intensities. Under the ranges of operating conditions investigated, a maximum heat-transfer coefficient of 268 ± 5 W/(m2·K) was obtained with an effective heat-exchange area of 0.11 m2. The resulting pressure drop across the gas-deflection baffle is relatively low, being less than 350 Pa. Convective heat-transfer results from a supernatant gas to a flowing vibrofluidized bed of solids represent the only data reported thus far, and have led to a better understanding of the proposed vibrofluidized-bed system for heat-recovery applications.

A simple light-probe method for quantitative measurements of particle volume-fractions in fluidized beds

Abstract A simple light-probe method has been developed for quantitative measurements of particle volume-fractions in fluidized beds. The method consists of an improved light-probe design and two calibration techniques which quantitatively relate the particle volume-fraction to output voltage from the light probe. The first calibration technique utilizes a theoretical particle volume-fraction distribution derived from optical theory and particle properties. The second technique uses the light probe in conjunction with a vibro-fluidized-bed system and takes advantage of the unique ability of vibrofluidization to provide a homogeneous bed of particles of a known porosity. The use of an IBM PC interfacing system further facilitates the data acquisition and analysis, and permits the accurate measurements of both the particle volume-fraction and its statistical (microscopic) fluctuation with a response time as fast as 30 μs. The method has been successfully applied experimentally to fluidized beds of building sands and fused-alumina particles (‘Norton Master Beads’), but it can be readily adapted for measurements with other fluidizing solids. It is shown that the proposed method provides an effective, efficient and inexpensive means for quantitative measurements of particle volume-fractions in fluidized beds.

A vibrofluidized-bed heat exchanger for heat recovery from a hot gas I: Feasibility study of a pilot-scale system

Abstract The purpose of this study is to experimentally evaluate a process for recovering the thermal energy from a hot exhaust gas by direct contact of the gas with a counter-currently flowing vibrofluidized bed of solids. This portion of the two-part paper describes a pilot-scale experimental system for heat-transfer studies and feasible operating conditions under which experiments are performed. Key variables that are tested in the vibrofluidized-bed heat-exchanger system include the gas flow rate, solid flow rate, height and number of gas-deflection baffles, and vibrational conditions (for example, throw angle, frequency, and amplitude). Tests demonstrate the importance of selecting the correct height of a gas-deflection baffle so that a ‘solid flooding’ condition does not exist within the heat exchanger. Results show that a prototype system using multiple baffles operates similarly to a single-baffle system, except in the case of high air flow rates, where a ‘multiple retardation’ effect prevents a major portion of solid particles from exiting the heat exchanger. A ‘flooding’ diagram is presented that summarizes the range of feasible operating conditions for steady-state operations. In addition, under vibrational conditions where solids are truly vibrofluidized, a ‘spray zone’ is observed which can greatly increase gas—solid mixing and enhance gas-to-bed heat transfer.