| dc.description.abstract | The swimming motion of fishes have long fascinated scientists and engineers. Over
the past few decades, researchers have studied physical models mimicking the tail beat
of fishes in an effort to extract key physical principles behind the swimming of fishes
with a view to develop more efficient underwater vehicles. In this thesis, we study two
idealized models related to the propulsive force generated by the oscillating tail and the
turning manoeuvre of a fish. We use experimental studies involving force measurements,
velocity fi eld measurements and the recently developed tool called Lagrangian Coherent
Structures (LCS) to understand the developing vortical
flow and the forces acting on the
unsteady physical models.
In the first experimental study, we investigate thrust production from a pitching
flexible foil in a uniform
flow which can be seen as idealized model of a swimming fish.
The
flexible foils studied comprise of a rigid foil in the front (chord length cR) that
is pitched sinusoidally at a frequency f, with a
flexible
flap of length cF and
flexural
rigidity EI attached to its trailing edge. We investigate thrust generation for a range
of
flexural rigidities (EI) and
flap length to total chord ratio (cF =c), with; the former
being varied over 4 orders in magnitude and the later varied from 0 to about 0.7. In
each case, the mean thrust (CT ) and the efficiency of thrust generation ( ) are directly
measured. We nd that using a non-dimensional
exural rigidity parameter (R ) de fined
as R = EI=(0:5 U2c3
F ) appears to combine the independent effects of variations in EI
and cF =c at a given value of the reduced frequency (k = fc=U) for the range of cF =c
values studied here. At k 6, the peak mean thrust coefficient is found to be about
100% higher than the rigid foil thrust, and occurs at R value of about 8, while the
peak efficiency is found to be about 300% higher than the rigid foil efficiency, and occurs
at a distinctly different R value of close to 0.01. Corresponding to these two optimal
flexural rigidity parameter values, we nd two distinct
flap mode shapes; the peak thrust
corresponding to a mode 1 type simple bending of the
flap, while the peak efficiency
corresponds to a mode 2 type bending of the
ap. The peak thrust condition is found to
be close to the `resonance' condition for the first mode natural frequency of the
flexible
flap in still water. PIV measurements for the
flexible cases show signi ficant differences
in the strength and arrangement of the wake vortices in these two cases.
In the second study, we present a combined experimental and numerical study of
an idealized model of the propulsive stroke of the turning manouevre known as C-start
in sh. Speci fically, we use the framework of Lagrangian Coherent Structures (LCS) to
describe the kinematics of the
flow that results from a thin-plate performing a large angle
rotation about its tip in still
fluid. Temporally and spatially well-resolved velocity fields
are obtained using a two-dimensional, incompressible finite-volume solver. We then
implement the recently proposed variational theory of LCS to extract the hyperbolic
and elliptic LCSs in the numerically generated velocity fields. Detailed LCS analysis is
performed for a plate motion pro le described by _(t) =
max sin2(!t) during 0 t to
and zero otherwise. The stopping time to is given by to = =! = 10s, the value of
max chosen to give a stopping angle of max = 90 , resulting in a Reynolds number
Re = c2
max= = 785:4, where c is the plate chord length and = 106m2=s the
kinematic viscosity of water. The
flow comprises a starting and a stopping vortex,
resulting in a pair of oppositely signed vortices of unequal strengths that move away
from the plate in a direction closely aligned with the nal plate orientation at t=to 2.
The hyperbolic LCSs are shown to encompass the
fluid material that gets advected away
from the plate for t > to, henceforth referred to as the advected bulk. The starting and
stopping vortices, identi ed using elliptic LCSs and hence more objective than Eulerian
vortex detection methods, constitute only around (2=3)rd of the advected bulk area. The
advected bulk is traced back to t = 0 to identify ve distinct lobes of
fluid that eventually
form the advected bulk, and hence map the long-term fate of various regions in the
fluid
1
at t = 0. The ve different lobes of
uid are then shown to be delineated by repelling
LCS boundaries at t = 0. We provide the first ever direct experimental evidence for the
relevance of hyperbolic and elliptic LCSs using novel dye visualization experiments, and
also show that attracting hyperbolic LCS provide objective characterization of the spiral
structures often observed in vortical
flows. We also show that qualitatively similar LCSs
persist for several other plate motion pro les and stopping angles as well.
Lastly, as a continuation of the second study, we present the
flow and forces created
by partially and fully
exible (cF =c = 0:5 ; 1) rotating plates using experiments. But
to begin with, we present a numerical study to bring out the connection between the
flow and the forces acting on the rigid rotating plate and an experimental study that
brings out the weak dependence of the problem on the Reynolds number in the range of
5000 < Re < 16000. The partially and fully
flexible plates performs a 90o rotation about
the hinge using a angular velocity pro le _(t) =
max sin2(!t) during 0 t to. A
non-dimensional stiffness parameter, EI = EI=0:5 c2
2
maxc3
F is de fined to characterize
the
flexible plate, where c is the total chord, cF is the
flap length, EI the
flap stiffness
and
max the maximum angular velocity of the imposed rotation at the hinge. It is
found that both the partially and fully
flexible
aps generate a vortex pair as a result of
the imposed rotation at the hinge. A momentum parameter, Svp = j(dV 1j+jdV 2j)d=c is
defi ned to qualitatively relate to the momentum associated with the bulk
flow generated
along the stopping angle of the plate. It was found that Svp has a broad peak around
EI 0:5 with cases in the range of 0:1 < EI < 6 having 60% more Svp than the
rigid case. The parameter EI was found to collapse data from force measurements for
the partially and fully
flexible rotating plates with low, medium and high stiffness
aps.
Mean forces in the direction of the stopping angle of the plate, CX, was found to take
higher values than the rigid case in the range of 0:3 < EI < 1.
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