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Oldroyd-B numerical solutions about a rotating sphere at low Reynolds number
Rheologica Acta, Volume: 54, Issue: 3, Pages: 235 - 251
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DOI (Published version): 10.1007/s00397-014-0831-x
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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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.
rotating sphere, secondary flow field, transitional and general flow, Oldroyd-B model
College of Engineering