Abstract
Herein, the dynamics and flow fields of an inverted flag are studied using hydrogen bubble flow visualization and particle image velocimetry technologies at different height-to-length ratios and flow velocities in a water tunnel. Results show that the height-to-length ratio of the inverted flag at which the critical flow velocity remains nearly constant is approximately 1.4. Moreover, a nonperiodic flapping phenomenon is observed under various height-to-length ratios. This phenomenon may be attributed to the existence of multiple equilibrium solutions to the self-excited vibration system, thus engendering chaos in the system comprising an inverted flag and surrounding fluid. Other indications that the system has entered chaos include multiple frequencies, non-overlapping phase diagram, and positive Lyapunov exponent. Further discussion of the flow fields around the inverted flag reveals that the large-amplitude oscillation is due to the flow separation, while the flapping instability is a static divergence instability. In the large flapping mode, the starting leading-edge vortex (LEV) is wrapped by Kelvin-Helmholtz instabilities, which are arranged at almost uniform spacing along a circular path. In addition, the variation in position, circulation, and radius of the starting LEV are discussed in detail.
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References
B. L. Partridge, and T. J. Pitcher, Nature 279, 418 (1979).
M. J. Shelley, and J. Zhang, Annu. Rev. Fluid Mech. 43, 449 (2011).
S. Taneda, J. Phys. Soc. Jpn. 24, 392 (1968).
Y. Watanabe, S. Suzuki, M. Sugihara, and Y. Sueoka, J. Fluids Struct. 16, 529 (2002).
Z. W. Wang, Y. L. Yu, and B. G. Tong, Sci. China-Phys. Mech. Astron. 61, 74721 (2018).
W. Hu, Q. Tian, and H. Y. Hu, Sci. China-Phys. Mech. Astron. 61, 044711 (2018).
S. Michelin, and O. Doare, J. Fluid Mech. 714, 489 (2013), arXiv: 1210.2171.
S. Orrego, K. Shoele, A. Ruas, K. Doran, B. Caggiano, R. Mittal, and S. H. Kang, Appl. Energy 194, 212 (2017).
X. Wang, S. Alben, C. Li, and Y. L. Young, Phys. Fluids 28, 023601 (2016), arXiv: 1509.06726.
J. A. Paradiso, and T. Starner, IEEE Perv. Comput. 4, 18 (2005).
Z. L. Wang, G. Zhu, Y. Yang, S. Wang, and C. Pan, Mater. Today 15, 532 (2012).
C. Eloy, R. Lagrange, C. Souilliez, and L. Schouveiler, J. Fluid Mech. 611, 97 (2008), arXiv: 0804.0774.
M. Shelley, N. Vandenberghe, and J. Zhang, Phys. Rev. Lett. 94, 094302 (2005).
C. Eloy, N. Kofman, and L. Schouveiler, J. Fluid Mech. 691, 583 (2011), arXiv: 1109.4196.
H. Kim, S. Kang, and D. Kim, J. Fluids Struct. 71, 1 (2017).
J. J. Allen, and A. J. Smits, J. Fluids Struct. 15, 629 (2001).
D. Kim, J. Cosse, C. Huertas Cerdeira, and M. Gharib, J. Fluid Mech. 736, R1 (2013).
G. Li, and X. Liu, Acta Astronaut. 67, 596 (2010).
R. Dyal, Int. J. Math. Trends Technol. 48, 229 (2017).
J. E. Sader, J. Cosse, D. Kim, B. Fan, and M. Gharib, J. Fluid Mech. 793, 524 (2016).
P. S. Gurugubelli, and R. K. Jaiman, J. Fluid Mech. 781, 657 (2015).
Y. Yu, Y. Liu, and Y. Chen, Phys. Fluids 29, 125104 (2017).
K. Shoele, and R. Mittal, J. Fluid Mech. 790, 582 (2016).
C. Tang, N. S. Liu, and X. Y. Lu, Phys. Fluids 27, 073601 (2015).
J. Ryu, S. G. Park, B. Kim, and H. J. Sung, J. Fluids Struct. 57, 159 (2015).
B. S. H. Connell, and D. K. P. Yue, J. Fluid Mech. 581, 33 (2007).
S. Alben, and M. J. Shelley, Phys. Rev. Lett. 100, 074301 (2008).
J. Zhang, S. Childress, A. Libchaber, and M. Shelley, Nature 408, 835 (2000).
H. A. Abderrahmane, M. P. Paidoussis, M. Fayed, and H. D. Ng, J. Wind Eng. Indust. Aerodyn. 107–108, 225 (2012).
Y. Yu, Y. Liu, and Y. Chen, Phys. Fluids 30, 045104 (2018).
F. Champagnat, A. Plyer, G. Le Besnerais, B. Leclaire, S. Davoust, and Y. Le Sant, Exp. Fluids 50, 1169 (2011).
Z. Hosseini, J. A. Bourgeois, and R. J. Martinuzzi, Exp. Fluids 54, 1595 (2013).
A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Phys. D-Nonlin. Phenom. 16, 285 (1985).
Y. Z. Liu, and L. Q. Chen, Nonlinear Vibrations (Higher Education Press, Beijing, 2001).
Y. C. Fung, An Introduction to the Theory of Aeroelasticity (Dover Publication, New York, 1993).
J. Zhou, R. J. Adrian, S. Balachandar, and T. M. Kendall, J. Fluid Mech. 387, 353 (1999).
G. A. Rosi, and D. E. Rival, J. Fluid Mech. 811, 37 (2016).
J. S. Wang, Q. Gao, R. J. Wei, and J. J. Wang, Exp. Fluids 58, 126 (2017).
J. Carlier, and M. Stanislas, J. Fluid Mech. 535, 143 (2005).
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Hu, Y., Wang, J., Wang, J. et al. Flow-structure interaction of an inverted flag in a water tunnel. Sci. China Phys. Mech. Astron. 62, 124711 (2019). https://doi.org/10.1007/s11433-019-9405-9
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DOI: https://doi.org/10.1007/s11433-019-9405-9