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Effect of morphology on the large-amplitude flapping dynamics of an inverted flag in a uniform flow

Fan, Boyu and Huertas-Cerdeira, Cecilia and Cossé, Julia and Sader, John E. and Gharib, Morteza (2019) Effect of morphology on the large-amplitude flapping dynamics of an inverted flag in a uniform flow. Journal of Fluid Mechanics, 874 . pp. 526-547. ISSN 0022-1120. doi:10.1017/jfm.2019.474.

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The stability of a cantilevered elastic sheet in a uniform flow has been studied extensively due to its importance in engineering and its prevalence in natural structures. Varying the flow speed can give rise to a range of dynamics including limit cycle behaviour and chaotic motion of the cantilevered sheet. Recently, the ‘inverted flag’ configuration – a cantilevered elastic sheet aligned with the flow impinging on its free edge – has been observed to produce large-amplitude flapping over a finite band of flow speeds. This flapping phenomenon has been found to be a vortex-induced vibration, and only occurs at sufficiently large Reynolds numbers. In all cases studied, the inverted flag has been formed from a cantilevered sheet of rectangular morphology, i.e. the planform of its elastic sheet is a rectangle. Here, we investigate the effect of the inverted flag’s morphology on its resulting stability and dynamics. We choose a trapezoidal planform which is explored using experiment and an analytical theory for the divergence instability of an inverted flag of arbitrary morphology. Strikingly, for this planform we observe that the flow speed range over which flapping occurs scales approximately with the flow speed at which the divergence instability occurs. This provides a means by which to predict and control flapping. In a biological setting, leaves in a wind can also align themselves in an inverted flag configuration. Motivated by this natural occurrence we also study the effect of adding an artificial ‘petiole’ (a thin elastic stalk that connects the sheet to the clamp) on the inverted flag’s dynamics. We find that the petiole serves to partially decouple fluid forces from elastic forces, for which an analytical theory is also derived, in addition to increasing the freedom by which the flapping dynamics can be tuned. These results highlight the intricacies of the flapping instability and account for some of the varied dynamics of leaves in nature.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Sader, John E.0000-0002-7096-0627
Gharib, Morteza0000-0002-2204-9302
Additional Information:© 2019 Cambridge University Press. Received 30 October 2018; revised 3 June 2019; accepted 7 June 2019; first published online 10 July 2019. We acknowledge funding from the Gordon and Betty Moore Foundation, the Lester Lees Aeronautics Summer Undergraduate Research Fellowship, the Australian Research Council Centre of Excellence in Exciton Science (CE170100026) and the Australian Research Council grants scheme.
Funding AgencyGrant Number
Gordon and Betty Moore FoundationUNSPECIFIED
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Australian Research CouncilCE170100026
Record Number:CaltechAUTHORS:20181210-110613444
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Official Citation:Fan, B., Huertas-Cerdeira, C., Cossé, J., Sader, J., & Gharib, M. (2019). Effect of morphology on the large-amplitude flapping dynamics of an inverted flag in a uniform flow. Journal of Fluid Mechanics, 874, 526-547. doi:10.1017/jfm.2019.474
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91638
Deposited By: Tony Diaz
Deposited On:10 Dec 2018 19:32
Last Modified:16 Nov 2021 03:43

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