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Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number

I. Garduno, H.R. Tamaddon-Jahromi, Michael Webster Orcid Logo, Hamid Tamaddon-Jahromi

Rheologica Acta, Volume: 54, Issue: 3, Pages: 235 - 251

Swansea University Authors: Michael Webster Orcid Logo, Hamid Tamaddon-Jahromi

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DOI (Published version): 10.1007/s00397-014-0831-x

Abstract

This study investigates the numerical solution of creeping viscoelastic flow for an Oldroyd-B model due to the rotation of a sphere about its diameter. Analysis of the elastico-viscous problem has been reported by Thomas and Walters (1964), Walters and Savins (1965), and Giesekus (1970). In this res...

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Published in: Rheologica Acta
Published: 2015
URI: https://cronfa.swan.ac.uk/Record/cronfa24185
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spelling 2016-04-29T16:15:52.3616563 v2 24185 2015-11-08 Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number b6a811513b34d56e66489512fc2c6c61 0000-0002-7722-821X Michael Webster Michael Webster true false b3a1417ca93758b719acf764c7ced1c5 Hamid Tamaddon-Jahromi Hamid Tamaddon-Jahromi true false 2015-11-08 EEN This study investigates the numerical solution of creeping viscoelastic flow for an Oldroyd-B model due to the rotation of a sphere about its diameter. Analysis of the elastico-viscous problem has been reported by Thomas and Walters (1964), Walters and Savins (1965), and Giesekus (1970). In this respect, three different flow patterns (Types 1-3) predicted by Thomas and Walters (1964) have been successfully reproduced when using an Oldroyd–B fluid to represent a Boger fluid. First, solutions for the Oldroyd-B model are calibrated in the second-order regime against those from the analytical solution. Then, the work is broadened to cover three different flows regimes: second-order regime, transitional and general flow; and two settings of polymeric solvent-fraction. Analysis based on the bounding sphere-radius, associated with Type-2 flow and through different flow regimes, reveals that the distinctive symmetrical-shape formed in the second-order regime is not preserved; instead, acquiring elliptical-shape. Moreover, for general and transitional flow regimes, a new and third vortex is identified in the polar region of the sphere. This feature is contrasted in its adjustment between two different fluid compositions - with solutions for highly-solvent and highly-polymeric versions (low-high polymeric contributions). The numerical algorithm involves a hybrid subcell finite-element/finite volume discretization (fe/fv), which solves the system of momentum-continuity-stress equations. This employs a semi-implicit time-stepping Taylor-Galerkin/pressure-correction parent-cell finite element method for momentum-continuity, whilst invoking a sub-cell cell-vertex fluctuation distribution finite volume scheme for the stress. The hyperbolic aspects of the constitutive equation are addressed discretely through finite volume upwind Fluctuation Distribution techniques and inhomogeneity calls upon Median Dual Cell approximation. Journal Article Rheologica Acta 54 3 235 251 rotating sphere, secondary flow field, transitional and general flow, Oldroyd-B model 31 12 2015 2015-12-31 10.1007/s00397-014-0831-x COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2016-04-29T16:15:52.3616563 2015-11-08T17:15:33.6954113 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised I. Garduno 1 H.R. Tamaddon-Jahromi 2 Michael Webster 0000-0002-7722-821X 3 Hamid Tamaddon-Jahromi 4
title Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number
spellingShingle Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number
Michael Webster
Hamid Tamaddon-Jahromi
title_short Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number
title_full Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number
title_fullStr Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number
title_full_unstemmed Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number
title_sort Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number
author_id_str_mv b6a811513b34d56e66489512fc2c6c61
b3a1417ca93758b719acf764c7ced1c5
author_id_fullname_str_mv b6a811513b34d56e66489512fc2c6c61_***_Michael Webster
b3a1417ca93758b719acf764c7ced1c5_***_Hamid Tamaddon-Jahromi
author Michael Webster
Hamid Tamaddon-Jahromi
author2 I. Garduno
H.R. Tamaddon-Jahromi
Michael Webster
Hamid Tamaddon-Jahromi
format Journal article
container_title Rheologica Acta
container_volume 54
container_issue 3
container_start_page 235
publishDate 2015
institution Swansea University
doi_str_mv 10.1007/s00397-014-0831-x
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 0
active_str 0
description This study investigates the numerical solution of creeping viscoelastic flow for an Oldroyd-B model due to the rotation of a sphere about its diameter. Analysis of the elastico-viscous problem has been reported by Thomas and Walters (1964), Walters and Savins (1965), and Giesekus (1970). In this respect, three different flow patterns (Types 1-3) predicted by Thomas and Walters (1964) have been successfully reproduced when using an Oldroyd–B fluid to represent a Boger fluid. First, solutions for the Oldroyd-B model are calibrated in the second-order regime against those from the analytical solution. Then, the work is broadened to cover three different flows regimes: second-order regime, transitional and general flow; and two settings of polymeric solvent-fraction. Analysis based on the bounding sphere-radius, associated with Type-2 flow and through different flow regimes, reveals that the distinctive symmetrical-shape formed in the second-order regime is not preserved; instead, acquiring elliptical-shape. Moreover, for general and transitional flow regimes, a new and third vortex is identified in the polar region of the sphere. This feature is contrasted in its adjustment between two different fluid compositions - with solutions for highly-solvent and highly-polymeric versions (low-high polymeric contributions). The numerical algorithm involves a hybrid subcell finite-element/finite volume discretization (fe/fv), which solves the system of momentum-continuity-stress equations. This employs a semi-implicit time-stepping Taylor-Galerkin/pressure-correction parent-cell finite element method for momentum-continuity, whilst invoking a sub-cell cell-vertex fluctuation distribution finite volume scheme for the stress. The hyperbolic aspects of the constitutive equation are addressed discretely through finite volume upwind Fluctuation Distribution techniques and inhomogeneity calls upon Median Dual Cell approximation.
published_date 2015-12-31T03:28:38Z
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score 11.037056

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