caa a22 4500 605466475 CHVBK 20210128100307.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s00397-014-0831-x doi (NATIONALLICENCE)springer-10.1007/s00397-014-0831-x Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number [Elektronische Daten] [Isaías Garduño, Hamid Tamaddon-Jahromi, Michael Webster] This study investigates the numerical solution of a viscoelastic flow for an Oldroyd-B model, due to the rotation of a sphere about its diameter. Analysis of the elastic-viscous problem had been reported by Thomas and Walters (Q J Mech Appl Math 17:39-53, 1964), Walters and Savins (J Rheol 9:407-416, 1965) and Giesekus (Rheol Acta 9:30-38, 1970). In this respect, three different flow patterns (types 1-3) predicted by Thomas and Walters (Q J Mech Appl Math 17:39-53, 1964) have been successfully reproduced when using an Oldroyd-B fluid to represent a Boger fluid. Initially, solutions for the Oldroyd-B model were calibrated in the second-order regime against the analytical solution. Then, the work is extended 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 revealed that the distinctive symmetrical shape formed in the second-order regime was not preserved, but an elliptical shape was acquired. Moreover, for general and transitional flow regimes, a new and third vortex was identified in the polar region of the sphere. The adjustment of this feature between two different fluid compositions, with solutions for high-solvent and high-polymeric versions (low-high polymeric contributions), was contrasted. The second normal stress difference (N 2) on the field was increased as the m parameter developed across the different flow regimes. Different torque values for several m values were compared against the theory, demonstrating the expected linear behaviour. The numerical algorithm involved a hybrid sub-cell finite-element/finite volume discretisation (fe/fv), which solved the system of momentum-continuity-stress equations. It is based on 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 were addressed discretely through finite volume upwind Fluctuation Distribution techniques and inhomogeneity calls upon Median Dual Cell approximation. Springer-Verlag Berlin Heidelberg, 2015 Rotating sphere nationallicence Secondary flow field nationallicence Transitional and general flow nationallicence Oldroyd-B model nationallicence Garduño Isaías College of Engineering, Swansea University, SA2 8PP, Swansea, UK aut Tamaddon-Jahromi Hamid College of Engineering, Swansea University, SA2 8PP, Swansea, UK aut Webster Michael College of Engineering, Swansea University, SA2 8PP, Swansea, UK aut Rheologica Acta Springer Berlin Heidelberg 54/3(2015-03-01), 235-251 0035-4511 54:3<235 2015 54 397 https://doi.org/10.1007/s00397-014-0831-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00397-014-0831-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Garduño Isaías College of Engineering, Swansea University, SA2 8PP, Swansea, UK aut NATIONALLICENCE 700 1- Tamaddon-Jahromi Hamid College of Engineering, Swansea University, SA2 8PP, Swansea, UK aut NATIONALLICENCE 700 1- Webster Michael College of Engineering, Swansea University, SA2 8PP, Swansea, UK aut NATIONALLICENCE 773 0- Rheologica Acta Springer Berlin Heidelberg 54/3(2015-03-01), 235-251 0035-4511 54:3<235 2015 54 397