dc.identifier.citation |
Srikanth, T. 2011, Vortex shedding patterns, their competition, and chaos in flow past inline oscillating rectangular cylinders, MS Engg thesis, Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru |
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dc.description.abstract |
In this thesis, vortex shedding from hxed and inhne oscillating rectangular cylinders is investigated for the first time to our knowledge. This is a numerical study, and the Lattice Boltzmann
method has been used for simulations. Grid stretching was employed to reduce computation
time. Cylinders of different aspect ratios, defined here as the ratio of height to width, namely:
1, 2, 4, 6 and 8 have been used in this study. Critical Reynolds numbers {Rccr) for fixed rectangular cylinders in uniform flow have been calculated, and it is shown that Rccr decreases slightly
with increasing D/h. It is also shown that the growth rates of disturbance in the wake varies
Hnearly with [Re—Beer) for rectangular geometries too when Re is close to Recr as predicted by
Landau (Landau k Lifshitz 2005a) and later confirmed by the experiments of Sreenivasan et al.
(1987) and Provansal et al. (1989) on a circular cylinder. The variation of Strouhal number [St)
with Re has also been discussed for different rectangular cylinders.
In flow past a fixed cylinder, the mode of vortex shedding is always antisymmetric, named
the Karman street. However, with the cyUnder oscillating in the streamwise direction, the
mode of shedding can be either antisymmetric, symmetric or chaotic depending on the forcing
parameters. Previous studies by Barbi et al. (1986) and Ongoren fc Rockwell (1988) have
found different antisymmetric and synmietric modes in these kinds of flows. Chaotic flow in the
wake of an inline oscillating circular cylinder received renewed attention after its rediscovery
by Perdikaris et al. (2009), who attributed it to mode competition between antisymmetric and
symmetric modes, but the data presented by them do not indicate this.
In this thesis, we have reproduced all the symmetric modes reported in the literature, and
also discovered a new symmetric mode, named S-III. To our knowledge, this is the first luuuerical
study to report the S-II mode of vortex shedding. A study of occurrence of different modes for
varying forcing frequency at fixed Re and A/D has been done, and it shown that different modes
of shedding (antisymmetric, mixed, ST, S II, S-III) exist in different geometries. A physical
mechanism based on 'ground effect' has been proposed to explain the S-II and S-III modes of
shedding in tall cylinders. We also report chaotic flow for certain values of forcing frequency
and amplitude, and show clear evidence that this is due to mode competition in the sense of
Ciliberto & GoUub (1984), who were the first to report mode competition leading to chaos in
another context.
Also, a Fourier-Spectral code developed to study the merger of vortices has been validated
using existing results in the literature and some preliminary results have been presented. |
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