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Wake states and frequency selection of a streamwise oscillating cylinder

Leontini, Justin S. and Lo Jacono, David and Thompson, Mark C. Wake states and frequency selection of a streamwise oscillating cylinder. (2013) Journal of Fluid Mechanics, 730. 162-192. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/jfm.2013.332

Abstract

This paper presents the results of an in-depth study of the flow past a streamwise oscillating cylinder, examining the impact of varying the amplitude and frequency of the oscillation, and the Reynolds number of the incoming flow. These findings are presented in a framework that shows that the relationship between the frequency of vortex shedding fs and the amplitude of oscillation A* is governed by two primary factors: the first is a reduction of fs proportional to a series in A*2 over a wide range of driving frequencies and Reynolds numbers; the second is nonlinear synchronization when this adjusted fs is in the vicinity of N = (1 - fs/fd)-1, where N is an integer. Typically, the influence of higher-order terms is small, and truncation to the first term of the series (A*2) well represents the overall trend of vortex shedding frequency as a function of amplitude. However, discontinuous steps are overlaid on this trend due to the nonlinear synchronization. When fs is normalized by the Strouhal frequency fSt (the frequency of vortex shedding from an unperturbed cylinder), the rate at which fs/fSt decreases with amplitude, at least for fd/fSt = 1, shows a linear dependence on the Reynolds number. For a fixed Re = 175, the truncated series shows that the rate of decrease of fs/fSt with amplitude varies as (2 - fd/fSt)-1/2 for 1 < or egal fd/fSt < or egal 2, but is essentially independent of fd/fSt for fd/fSt < 1. These trends of the rate of decrease of fs with respect to amplitude are also used to predict the amplitudes of oscillation around which synchronization occurs. These predicted amplitudes are shown to fall in regions of the parameter space where synchronized modes occur. Further, for the case of varying fd/fSt, a very reasonable prediction of the amplitude of oscillation required for the onset of synchronization to the mode where fs = 0.5fd is given. In a similar manner, amplitudes at which fs = 0 are calculated, predicting where the natural vortex shedding is completely supplanted by the forcing. These amplitudes are found to coincide approximately with those at which the onset of a symmetric vortex shedding mode is observed. This result is interpreted as meaning that the symmetric shedding mode occurs when the dynamics crosses over from being dominated by the vortex shedding to being dominated by the forcing.

Item Type:Article
Additional Information:Thanks to Cambridge University Press. The definitive version is available at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8959859
HAL Id:hal-00858320
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Monash University (AUSTRALIA)
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Deposited On:05 Sep 2013 08:35

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