Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-19T04:24:48.407Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of fluid flow over a circular flexible plate

Published online by Cambridge University Press:  20 October 2014

Ru-Nan Hua ,
Luoding Zhu  and
Xi-Yun Lu
Ru-Nan Hua
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Luoding Zhu
Affiliation:
Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, 402 North Blackford Street, Indianapolis, IN 46202, USA
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of viscous fluid flow over a circular flexible plate are studied numerically by an immersed boundary–lattice Boltzmann method for the fluid flow and a finite-element method for the plate motion. When the plate is clamped at its centre and placed in a uniform flow, it deforms by the flow-induced forces exerted on its surface. A series of distinct deformation modes of the plate are found in terms of the azimuthal fold number from axial symmetry to multifold deformation patterns. The developing process of deformation modes is analysed and both steady and unsteady states of the fluid–structure system are identified. The drag reduction due to the plate deformation and the elastic potential energy of the flexible plate are investigated. Theoretical analysis is performed to elucidate the deformation characteristics. The results obtained in this study provide physical insight into the understanding of the mechanisms on the dynamics of the fluid–structure system.

JFM classification

Aerodynamics: Aerodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 759 , 25 November 2014 , pp. 56 - 72
Check for updates
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batoz, J. L., Bathe, K. J. & Ho, L. W. 1980 A study of three-node triangular plate bending elements. Intl J. Numer. Meth. Engng 15, 1771–1812.Google Scholar
Cerda, E. & Mahadevan, L. 2003 Geometry and physics of wrinkling. Phys. Rev. Lett. 90, 074302.Google Scholar
Cerda, E., Mahadevan, L. & Pasini, J. M. 2004 The elements of draping. Proc. Natl Acad. Sci. USA 101, 1806–1810.Google Scholar
Cerda, E., Ravi-Chandar, K. & Mahadevan, L. 2002 Wrinkling of an elastic sheet under tension. Nature 419, 579–580.Google Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.CrossRefGoogle Scholar
Connell, B. S. H. & Yue, D. K. P. 2007 Flapping dynamics of a flag in a uniform stream. J. Fluid Mech. 581, 33–67.Google Scholar
Dai, H., Luo, H. & Doyle, J. F. 2012 Dynamic pitching of an elastic rectangular wing in hovering motion. J. Fluid Mech. 693, 473–499.CrossRefGoogle Scholar
Dervaux, J. & Ben Amar, M. 2008 Morphogenesis of growing soft tissues. Phys. Rev. Lett. 101, 068101.Google Scholar
Doyle, J. F. 1991 Static and Dynamic Analysis of Structures. Kluwer.Google Scholar
Doyle, J. F. 2001 Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability. Springer.Google Scholar
Gao, T. & Lu, X.-Y. 2008 Insect normal hovering flight in ground effect. Phys. Fluids 20, 087101.Google Scholar
Goldstein, D., Handler, R. & Sirovich, L. 1993 Modeling a no slip flow boundary with an external force field. J. Comput. Phys. 105, 354–366.Google Scholar
Gosselin, F., de Langre, E. & Machado-Almeida, B. A. 2010 Drag reduction of flexible plates by reconfiguration. J. Fluid Mech. 650, 319–341.Google Scholar
Guo, Z., Zheng, C. & Shi, B. 2002 Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65, 046308.CrossRefGoogle ScholarPubMed
He, X., Luo, L.-S. & Dembo, M. 1996 Some progress in lattice Boltzmann method. Part I. Nonuniform mesh grids. J. Comput. Phys. 129, 357–363.CrossRefGoogle Scholar
Hua, R.-N., Zhu, L. & Lu, X.-Y. 2013 Locomotion of a flapping flexible plate. Phys. Fluids 25, 121901.CrossRefGoogle Scholar
Huang, W.-X., Chang, C. B. & Sung, H. J. 2011 An improved penalty immersed boundary method for fluid–flexible body interaction. J. Comput. Phys. 230, 5061–5079.CrossRefGoogle Scholar
Huang, W.-X., Shin, S. J. & Sung, H. J. 2007 Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226, 2206–2228.CrossRefGoogle Scholar
Huang, W.-X. & Sung, H. J. 2010 Three-dimensional simulation of a flapping flag in a uniform flow. J. Fluid Mech. 653, 301–336.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Kang, C.-K., Aono, H., Cesnik, C. E. S. & Shyy, W. 2011 Effects of flexibility on the aerodynamic performance of flapping wings. J. Fluid Mech. 689, 32–74.CrossRefGoogle Scholar
Kim, D., Cossé, J., Huertas Cerdeira, C. & Gharib, M. 2013 Flapping dynamics of an inverted flag. J. Fluid Mech. 736, R1.Google Scholar
Klein, Y., Efrati, E. & Sharon, E. 2007 Shaping of elastic sheets by prescription of non-Euclidean metrics. Science 315, 1116–1119.Google Scholar
Leissa, A. W.1969 Vibration of plates. NASA Tech. Rep. SP-160.Google Scholar
Li, G.-J. & Lu, X.-Y. 2012 Force and power of flapping plates in a fluid. J. Fluid Mech. 712, 598–613.Google Scholar
Mittal, R., Dong, H., Bozkurttas, M., Najjar, F., Vargas, A. & Vonloebbecke, A. 2008 A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J. Comput. Phys. 227, 4825–4852.CrossRefGoogle ScholarPubMed
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261.Google Scholar
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220–252.Google Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479–517.Google Scholar
Ross, F. W. & Willmarth, W. W. 1971 Some experimental results on sphere and disk drag. AIAA J. 9, 285–291.Google Scholar
Schouveiler, L. & Boudaoud, A. 2006 The rolling up of sheets in a steady flow. J. Fluid Mech. 563, 71–80.Google Scholar
Schouveiler, L. & Eloy, C. 2013 Flow-induced draping. Phys. Rev. Lett. 111, 064301.Google Scholar
Shenoy, A. R. & Kleinstreuer, C. 2008 Flow over a thin circular disk at low to moderate Reynolds numbers. J. Fluid Mech. 605, 253–262.Google Scholar
Tian, F.-B., Luo, H., Zhu, L., Liao, J. C. & Lu, X.-Y. 2011a An efficient immersed boundary–lattice Boltzmann method for the hydrodynamic interaction of elastic filaments. J. Comput. Phys. 230, 7266–7283.Google Scholar
Tian, F.-B., Luo, H., Zhu, L. & Lu, X.-Y. 2011b Coupling modes of three filaments in side-by-side arrangement. Phys. Fluids 23, 111903.Google Scholar
Vogel, S. 1996 Life in Moving Fluids: The Physical Biology of Flow. Princeton University Press.Google Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.Google Scholar