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Levitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters

hal.structure.identifierLaboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
dc.contributor.authorCHAMPMARTIN, Stéphane
hal.structure.identifierLaboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
dc.contributor.authorAMBARI, Abdelhak
hal.structure.identifierDepartment of Chemical Engineering [Kanpur]
dc.contributor.authorCHHABRA, R. P.
dc.date.accessioned2021-05-14T10:00:21Z
dc.date.available2021-05-14T10:00:21Z
dc.date.issued2012
dc.identifier.issn0034-6748
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/78121
dc.description.abstractEnIn this study, a theoretical framework is developed to predict the equilibrium conditions of a non-neutrally buoyant sphere placed in a vertical conical tube as encountered in liquid rotameters. The analysis presented herein is applicable for a sphere heavier than the surrounding fluid, situated on the axis of a slightly tapered tube. The sphere is subject to the laminar flow conditions with the Reynolds numbers ranging between the Stokes type regimes up to values corresponding to slightly inertial regimes. In this work, we assume that the aperture angle of the tube is small and that the drag force is mainly due to the dissipation located in the gap between the tube and the sphere. Under these conditions, it is possible to consider the tube as locally cylindrical and we can use the results previously obtained for the correction factor of the Stokes force on a sphere subject to a Poiseuille flow in a tube of constant cross-section. We obtain an equation relating the flow rate to the vertical position of the sphere in the tube and the validity of this analysis is demonstrated by applying it to a commercially available rotameter. The present study provides a simple but sound theoretical method to calibrate such flowmeters.
dc.language.isoen
dc.publisherAmerican Institute of Physics
dc.subject.enFlow rate measurement
dc.subject.enReynolds stress modeling
dc.subject.enCalibration
dc.subject.enStokes flows
dc.subject.enPoiseuille flow
dc.title.enLevitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters
dc.typeArticle de revue
dc.identifier.doi10.1063/1.4769053
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
bordeaux.journalReview of Scientific Instruments
bordeaux.page125103.1-125103.7
bordeaux.volume83
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.issue12
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-01061933
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01061933v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Review%20of%20Scientific%20Instruments&rft.date=2012&rft.volume=83&rft.issue=12&rft.spage=125103.1-125103.7&rft.epage=125103.1-125103.7&rft.eissn=0034-6748&rft.issn=0034-6748&rft.au=CHAMPMARTIN,%20St%C3%A9phane&AMBARI,%20Abdelhak&CHHABRA,%20R.%20P.&rft.genre=article


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