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Global modes and nonlinear analysis of inverted-flag flapping

Goza, Andres and Colonius, Tim and Sader, John E. (2018) Global modes and nonlinear analysis of inverted-flag flapping. Journal of Fluid Mechanics, 857 . pp. 312-344. ISSN 0022-1120. https://resolver.caltech.edu/CaltechAUTHORS:20180122-091425148

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Abstract

An inverted flag has its trailing edge clamped and exhibits dynamics distinct from that of a conventional flag, whose leading edge is restrained. We perform nonlinear simulations and a global stability analysis of the inverted-flag system for a range of Reynolds numbers, flag masses and stiffnesses. Our global stability analysis is based on a linearisation of the fully coupled fluid–structure system of equations. The calculated equilibria are steady-state solutions of the fully coupled nonlinear equations. By implementing this approach, we (i) explore the mechanisms that initiate flapping, (ii) study the role of vorticity generation and vortex-induced vibration (VIV) in large-amplitude flapping and (iii) characterise the chaotic flapping regime. For point (i), we identify a deformed-equilibrium state and show through a global stability analysis that the onset of small-deflection flapping – where the oscillation amplitude is significantly smaller than in large-amplitude flapping – is due to a supercritical Hopf bifurcation. For large-amplitude flapping, point (ii), we confirm the arguments of Sader et al. (J. Fluid Mech., vol. 793, 2016a) that classical VIV exists when the flag is sufficiently light with respect to the fluid. We also show that for heavier flags, large-amplitude flapping persists (even for Reynolds numbers < 50) and is not classical VIV. Finally, with respect to point (iii), chaotic flapping has been observed experimentally for Reynolds numbers of O(10^4) , and here we show that chaos also persists at a moderate Reynolds number of 200. We characterise this chaotic regime and calculate its strange attractor, whose structure is controlled by the above-mentioned deformed equilibria and is similar to a Lorenz attractor.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/jfm.2018.728DOIArticle
https://arxiv.org/abs/1709.09745arXivDiscussion Paper
ORCID:
AuthorORCID
Goza, Andres0000-0002-9372-7713
Colonius, Tim0000-0003-0326-3909
Sader, John E.0000-0002-7096-0627
Additional Information:© 2018 Cambridge University Press. Received 27 September 2017; revised 1 August 2018; accepted 6 September 2018; first published online 22 October 2018. A.G. and T.C. gratefully acknowledge the computing resources provided to them through the NSF XSEDE program, and funding from Robert Bosch LLC through the Bosch Energy Research Network Grant (grant number 07.23.CS.15) and from the AFOSR (grant number FA9550-14-1-0328). J.E.S. thanks the ARC Centre of Excellence in Exciton Science and the Australian Research Council Grants Scheme.
Funders:
Funding AgencyGrant Number
Bosch Energy Research Network07.23.CS.15
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0328
Australian Research CouncilUNSPECIFIED
Record Number:CaltechAUTHORS:20180122-091425148
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180122-091425148
Official Citation:Goza, A., Colonius, T., & Sader, J. (2018). Global modes and nonlinear analysis of inverted-flag flapping. Journal of Fluid Mechanics, 857, 312-344. doi:10.1017/jfm.2018.728
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84443
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Jan 2018 14:03
Last Modified:03 Oct 2019 19:18

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