{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/56157"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/56157","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Shallow vibrated particulate beds - bed dynamics and heat transfer","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Thomas, Benku"],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Chemical Engineering","degree_department":"Chemical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Squires, Arthur M.","Liu, Y.A."],"committee_members":["McGee, Henry A. Jr.","Pell, Melvyn","Wills, George B."],"year":1988,"date_issued":"1988","date_published":"1988","updated_at":"2026-07-22T22:20:21Z","subjects":[],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/56157","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Squires, Arthur M.","Liu, Y.A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["McGee, Henry A. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Shallow vibrated particulate beds - bed dynamics and heat transfer"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Squires, Arthur M.","Liu, Y.A."],"dc:contributor.committeemember":["McGee, Henry A. Jr.","Pell, Melvyn","Wills, George B."],"dc:contributor.department":["Chemical Engineering"],"dc:creator":["Thomas, Benku"],"dc:date.accessioned":["2015-08-07T13:13:05Z"],"dc:date.available":["2015-08-07T13:13:05Z"],"dc:date.issued":["1988"],"dc:description.abstract":["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."],"dc:description.degree":["Ph. D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/56157"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Shallow vibrated particulate beds - bed dynamics and heat transfer"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Chemical Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:21Z"}