Teitl: Numerical Investigation of Sedimentation in Viscoelastic Fluids using Spectral Element Methods

Arianwyr
Engineering and Physical Sciences Research Council

Prif Ymchwiliwr

Cyd-Ymchwilwyr
Phillips, Timothy

Manylion y Prosiect
Dyddiad dechrau: 01.10.2008
Dyddiad gorffen: 28.06.2013
Crynodeb



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 ow 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 constitutive 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.


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