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Numerical investigation of sedimentation in viscoelastic fluids using spectral element methods

Kynch, Ross 2013. Numerical investigation of sedimentation in viscoelastic fluids using spectral element methods. PhD Thesis, Cardiff University.
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Abstract

In this thesis we consider the problem of a falling sphere within a fluid. We are primarily interested in incompressible fluids exhibiting so-called viscoelastic properties in which a range of phenomena have been observed experimentally. These phenomena are typically manifest in the presence of a negative wake, an overshoot of the velocity of the falling sphere and drag reduction as well as enhancement in some cases. We consider fluid models which have been designed to capture these effects and use them to simulate the flow numerically with the intention of gaining an insight into the observed phenomena. We begin with the most basic fluid models in order to validate our scheme, considering both Stokes and Newtonian fluids before progressing to viscoelastic fluid models in a range of problems to ensure the robustness of our solver. Our scheme ultimately utilises the Spectral Element Method(SEM) combined with a Discontinuous Galerkin(DG) treatment of the constituitive equation along with a DEVSS-G stabilisation term in the momentum equation. We employ an Arbitrary Lagrangian Eulerian(ALE) scheme when simulating a falling sphere. Our simulations successfully capture the drag reduction when moving fluid past a fixed sphere as well as velocity overshoot for the sedimenting sphere, although we have failed to capture the presence of a negative wake thus far. Excellent agreement with the literature is demonstrated for the benchmarks considered in both planar and axisymmetric geometries.

Item Type: Thesis (PhD)
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Funders: EPSRC
Date of First Compliant Deposit: 30 March 2016
Last Modified: 10 Oct 2017 15:10
URI: http://orca-mwe.cf.ac.uk/id/eprint/48949

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