Experimental Study of a Periodical Flapping Flag

Bai Ye; Jia Yong-Xia; Li Cun-Biao; Zhu Yi-Ding

doi:10.7498/aps.65.124701

Abstract

A flag flapping in the wind is a classical fluid-structure interaction problem that concerns the interaction of elastic bodies with ambient fluid. The fluid-flag interaction can give rise to three self-sustained oscillation states under certain conditions, i.e., stretched-straight state, periodic state, and chaotic state. This paper reports an experimental study of a cantilevered polydimethylsiloxane (PDMS) flag flapping in a uniform flow at a periodic state. A heavy flag is well designed, with metal strips imbedded in the PDMS sheet. Immersing the elastic but self-sustaining flag into the water flow, we use the time-resolved particle image velocimetry (PIV) and visualization techniques to obtain the whole flow field around the midspan of the flapping flag. A unique PIV image processing method is used to measure the near-wall flow velocities around the flap-ping elastic flag at the periodic state. The image processing technique adopts a radon transform technology to determine the moving interface in the particle images. The interface velocity distribution is subsequently calculated. Artificial particles of uniform size with the interface velocity are added into the flag region. Therefore, the whole velocity field over a flapping period is accurately obtained, giving the basic data to analyze the flag flapping. It is found that there exists an inflection point in the envelope curve of the flag flapping. Based on the analyses of the flapping states and velocity fields, a unified flapping Strouhal number (St = 2Af/U) is proposed by choosing the amplitude of the inflection point as the characteristic length, which is similar to the Strouhal number of the flow around a circular cylinder over the same range of Reynolds number.

Keywords:

Authors and contacts

1.
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China

Corresponding author: Jia Yong-Xia, yongxiajia@pku.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 109103, 010062), the National Climb-B Plan, China (Grant No. 2009CB724100), the Group Project (Grant Nos. 10921202，11221062，11521091), and the National Natural Science Funds for Distinguished Young Scholar Group, China (Grant No. 10921202).

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Cited By

[1]	Eloy C, Schouveiler L 2011 J. Non-Linear Mech. 46 568
[2]	Hellum A, Mukherjee R, Hull A 2011 J. Fluid. Struct. 27 1086
[3]	Jafferis N T, Sturm J C 2013 J. Microelectromech. S. 22 495
[4]	Akcabay D T, Young Y L 2012 Phys. Fluids 24 054106
[5]	Doar O, Michelin S 2011 J. Fluid. Struct. 27 1357
[6]	Dunnmon J, Stanton S, Mann B, Dowell E 2011 J. Fluid. Struct. 27 1182
[7]	Giacomello A, Porfiri M 2011 Proceedings of SPIE 7976 797608
[8]	Michelin S, Doar O 2013 J. Fluid Mech. 714 489
[9]	Balint T, Lucey A 2005 J. Fluid. Struct. 20 893
[10]	Huang L 1995 J. Fluid. Struct. 9 127
[11]	Howell R, Lucey A, Carpenter P, Pitman M 2009 J. Fluid. Struct. 25 544
[12]	Zhang J, Childress S, Libchaber A, Shelley M 2000 Nature 408 835
[13]	Watanabe Y, Suzuki S, Sugihara M, Sueoka Y 2002 J. Fluid. Struct. 16 529
[14]	Shelley M, Vandenberghe N, Zhang J 2005 Phys. Rev. Lett. 94 302
[15]	Abderrahmane H A, Padoussis M P, Fayed M, Ng H D 2012 J. Wind Eng. Ind. Aerod. 107108 225
[16]	Eloy C, Lagrange R, Souilliez C, Schouveiler L 2008 J. Fluid Mech. 611 97
[17]	Eloy C, Souilliez C, Schouveiler L 2007 J. Fluid. Struct. 23 904
[18]	Huang W X, Sung H J 2010 J. Fluid Mech. 653 301
[19]	Yu Z, Wang Y, Shao X 2012 J. Sound Vib. 331 4448
[20]	Eloy C, Kofman N, Schouveiler L 2012 J. Fluid Mech. 691 583
[21]	Gibbs S C, Wang I, Dowell E 2012 J. Fluid. Struct. 34 68
[22]	Tang D, Yamamoto H, Dowell E 2003 J. Fluid. Struct. 17 225
[23]	Gao T G, Qin F H, Huang W X, Sun D J 2012 Chin. Phys. Lett. 29 094702
[24]	Michelin S, Smith S L, Glover B 2008 J. Fluid Mech. 617 1
[25]	Tang L, Padoussis M 2007 J. Sound Vib. 305 97
[26]	Tang L, Padoussis M 2008 J. Sound Vib. 310 512
[27]	Gordnier R E, Visbal M R 2002 J. Fluid. Struct. 16 497
[28]	Banerjee S, Connell B S H, Yue D K P 2015 J. Fluid Mech. 783 103
[29]	Gibbs S C, Fichera S, Zanotti A, Ricci S, Dowell E H 2014 J. Fluid. Struct. 48 507
[30]	Cao H C, Shi S X, Liu Y Z 2013 J. Exp. Fluid Mech. 27 58 (in Chinese) [曹洪才, 施圣贤, 刘应征 2013 实验流体力学 27 58]
[31]	Taylor G K, Nudds R L, Thomas A L R 2003 Nature 425 707
[32]	Shelley M J, Zhang J 2011 Annu. Rev. Fluid Mech. 43 449
[33]	Connell B S H, Yue D K P 2007 J. Fluid Mech. 581 33
[34]	Zhu Y D, Yuan H J, Zhang C H, Lee C B 2013 Meas. Sci. Technol. 24 125302
[35]	Lee C B, Su Z, Zhong H J, Chen S Y, Zhou M D, Wu J Z 2013 J. Fluid Mech. 732 77
[36]	Zhong H J, Lee C B, Su Z, Chen S Y, Zhou M D, Wu J Z 2013 J. Fluid Mech. 716 228
[37]	Shelley M J, Zhang J 2011 Annu. Rev. Fluid Mech. 43 449
[38]	Rohr J J, Fish F E 2007 J. Exp. Biol. 207 1633
[39]	Virot E, Amandolese X, Hemon P 2013 J. Fluid. Struct. 43 385

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Vol. 65, Issue 12 - 2016-06-20

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