Vortex shedding patterns, their competition, and chaos in flow past inline oscillating rectangular cylinders

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.