A numerical study of laminar to turbulent evolution and free-surface interaction of a vortex ring

Archer, Philip John (2008) A numerical study of laminar to turbulent evolution and free-surface interaction of a vortex ring. University of Southampton, School of Engineering Sciences, Doctoral Thesis , 154pp.


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Direct numerical simulation was used to study various aspects of vortex ring evolution
and interaction with a free surface. An investigation of a single unbounded
vortex ring at various Reynolds numbers and core thicknesses showed qualitative
dierences between the evolution of thin- and thick-core rings, leading to a correction
factor to the classical equation for the ring translational velocity. The
obtained linear modal growth rates were compared with previous work, highlighting
the role of the wake in triply periodic numerical simulations. The transition
from a laminar to a turbulent ring is marked by the rearrangement of the outer
core vorticity into a clearly dened secondary structure. The onset of the fully
turbulent state is associated with shedding of the structure in a series of hairpin
vortices. A Lagrangian particle analysis was performed to determine the ring entrainment
and detrainment properties and to investigate the possibility of an axial
flow being generated around the circumference of the core region prior to the onset
of turbulence.

The orthogonal interaction of laminar, transitional and turbulent rings with an
initially undesturbed free surface was investigated. At small depths, the expanding
ring is unstable to the Crow instability but its dominant mode is predetermined by
the prior development of the Widnall instability. The presence of opposite-signed
vorticity, due to surface curvature, aects the ring dynamics at the surface. The
interaction of a transitional ring modies the surface displacements, refecting the
structure of the ring below. The secondary structure associated with a transitional
ring reconnects to the surface in addition to the inner core. In the presence of the
surface, the turbulent ring nds greater coherency of the core due to stretching and
aligning of vorticity laments. The addition of a planar surface wave field modied
the ring interaction greatly due to the higher surface curvature and associated
surface vorticity. The ring expands asymmetrically and even rebounds locally if
sufficient opposite-signed vorticity is generated. The ring diffracts the surface wave
field and the generation of secondary small-amplitude waves was noted.

Item Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
T Technology > TL Motor vehicles. Aeronautics. Astronautics
Divisions : University Structure - Pre August 2011 > School of Engineering Sciences > Aerodynamics & Flight Mechanics
ePrint ID: 63999
Accepted Date and Publication Date:
June 2008Made publicly available
Date Deposited: 19 Jun 2009
Last Modified: 31 Mar 2016 12:48
URI: http://eprints.soton.ac.uk/id/eprint/63999

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