Complex Dynamics of Solid-Fluid Systems: Applications of Dynamic Systems Theory to Fluid Dynamics

Research output: ThesisDoctoral Thesis

Abstract

The focus of this thesis was the investigation of the complex dynamics of
solid-fluid systems. These systems are of great industrial importance, such
as in methane clathrate formation in sub-sea pipelines, [22]. As well as being
crucial to furthering our understanding of various natural phenomena,
such as the rate of rain droplet formation in clouds, [86].
We began by considering the problem of the orbits tracked by ellipsoids
immersed in viscous and inviscid environments. This investigation
was carried out by a combination of analytical and numerical techniques:
direct numerical simulations of resolved full-coupled solid-fluid systems,
analysis the Kirchhoff-Clebsch equations for the case of inviscid flows, and
characterising dynamics through advanced techniques such as recurrence
quantification analysis. We demonstrate that the ellipsoid tracks a chaotic
orbit not only in an inviscid environment but also when submerged in
a viscous fluid, under specific conditions. Under inviscid environments,
an ellipsoid subject to arbitrary initial conditions of linear and angular
momentum demonstrates chaotic orbits when all the three axes of the ellipsoid
are unequal, in agreement with the Kozlov and Onishchenko [55]’s
theorem of non-integrability of Kirchhoff’s equations and also with Aref
and Jones [3]’s potential flow solution.
We then extended our methodology to understand the dynamics of
a single ellipsoid tumbling in a viscous environment with the presence
of both passive and viscosity-coupled tracers in addition to the chaotic
dynamics predicted by the Kirchhoff-Clebsch equations. Our results show
that the bodies move along from viscosity gradients towards minima of the
viscous stress. These bodies might become trapped in unstable minima.
However, more work is needed to understand the long-term mixing of
viscosity coupled tracers. Our direct numerical solver was also extended
to include contact models for solid-solid interactions in the simulation
domain. The validation of the contact models was presented.
Finally, we expand, the theoretical framework of the Kirchhoff-Clebsch
equations to account for the presence of multiple bodies. This extension
was done by using Hamiltonian mechanics to extend the derivation proposed
by Lamb [61]. We present our preliminary result of simulating two
solids systems using the extended Kirchhoff-Clebsch equations. The relative
orientations of the two solids were found to regularly switch from
being correlated to anti-correlated in an otherwise chaotic system. Further
work is required to understand the mechanism behind this behaviour.
Original languageEnglish
QualificationPh.D.
Awarding Institution
  • University of Edinburgh
Supervisors/Advisors
  • Valluri, Prashant, Supervisor
  • Krueger, Timm, Supervisor
Award date14 Jun 2020
Publisher
DOIs
Publication statusPublished - 2020

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