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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