Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-17T19:37:29.143Z Has data issue: false hasContentIssue false
  • English
  • Français

Force and power of flapping plates in a fluid

Published online by Cambridge University Press:  09 October 2012

Gao-Jin Li  and
Xi-Yun Lu
Gao-Jin Li
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
†Email address for correspondence: xlu@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The force and power of flapping plates are studied by vortex dynamic analysis. Based on the dynamic analysis of the numerical results of viscous flow past three-dimensional flapping plates, it is found that the force and power are strongly dominated by the vortical structures close to the body. Further, the dynamics of the flapping plate is investigated in terms of viscous vortex-ring model. It is revealed that the model can reasonably reflect the essential properties of the ring-like vortical structure in the wake, and the energy of the plate transferred to the flow for the formation of each vortical structure possesses a certain relation. Moreover, simplified formulae for the thrust and efficiency are proposed and verified to be reliable by the numerical solutions and experimental measurements of animal locomotion. The results obtained in this study provide physical insight into the understanding of the dynamic mechanisms relevant to flapping locomotion.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Propulsion Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 598 - 613
Copyright
©2012 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

Altshuler, D. L., Princevac, M., Pan, H. & Lozano, J. 2009 Wake patterns of the wings and tail of hovering hummingbirds. Exp. Fluids 46, 835–846.Google Scholar
Blondeaux, P., Fornarelli, F., Guglielmini, L., Triantafyllou, M. S. & Verzicco, R. 2005 Numerical experiments on flapping foils mimicking fish-like locomotion. Phys. Fluids 17, 113601.Google Scholar
Buchholz, J. H. J. & Smits, A. J. 2008 The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331–365.Google Scholar
Chang, C. C. 1992 Potential flow and forces for incompressible viscous flow. Proc. R. Soc. A 437, 517–525.Google Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.Google Scholar
Dabiri, J. O. 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 17–33.Google Scholar
Dai, H., Luo, H. X. & Doyle, J. F. 2012 Dynamic pitching of an elastic rectangular wing in hovering motion. J. Fluid Mech. 693, 473–499.Google Scholar
Dickinson, M. H., Lehmann, F.-O. & Sane, S. P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284, 1954.Google Scholar
Dickson, W. B. & Dickinson, M. H. 2004 The effect of advance ratio on the aerodynamics of revolving wings. J. Expl Biol. 207, 4269–4281.Google Scholar
Dong, H., Mittal, R. & Najjar, F. M. 2006 Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 566, 309–343.Google Scholar
Drucker, E. G. & Lauder, G. V. 1999 Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using particle image velocimetry. J. Expl Biol. 202, 2393–2412.Google Scholar
von Ellenrieder, K. D., Parker, K. & Soria, J. 2003 Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129–138.Google Scholar
Ellington, C. P. 1984a The aerodynamics of hovering insect flight. II. Morphological parameters. Phil. Trans. R. Soc. Lond. B 305, 17–40.Google Scholar
Ellington, C. P. 1984b The aerodynamics of hovering insect flight. III. Kinematics. Phil. Trans. R. Soc. Lond. B 305, 41–78.Google Scholar
Feng, Z.-G. & Michaelides, E. E. 2004 The immersed boundary–lattice Boltzmann method for solving fluid–particles interaction problems. J. Comput. Phys. 195, 602–628.Google Scholar
Filippova, O. & Hänel, D. 1998 Grid refinement for lattice–BGK models. J. Comput. Phys. 147, 219–228.Google Scholar
Fukumoto, Y. & Kaplanski, F. 2008 Global time evolution of an axisymmetric vortex ring at low Reynolds numbers. Phys. Fluids 20, 053103.Google Scholar
Gao, T. & Lu, X.-Y. 2008 Insect normal hovering flight in ground effect. Phys. Fluids 20, 087101.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.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.CrossRefGoogle Scholar
Hedenström, A., Johansson, L. C., Wolf, M., von Busse, R., Winter, Y. & Spedding, G. R. 2007 Bat flight generates complex aerodynamic tracks. Science 316, 894–897.Google Scholar
Hedenström, A., Rosén, M. & Spedding, G. R. 2006 Vortex wakes generated by robins Erithacus rubecula during free flight in a wind tunnel. J. R. Soc. Interface 3, 263–276.Google Scholar
Hsieh, C. T., Chang, C. C. & Chu, C. C. 2009 Revisiting the aerodynamics of hovering flight using simple models. J. Fluid Mech. 623, 121–148.Google Scholar
Hsieh, C. T., Kung, C. F., Chang, C. C. & Chu, C. C. 2010 Unsteady aerodynamics of dragonfly using a simple wing–wing model from the perspective of a force decomposition. J. Fluid Mech. 663, 233–252.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Center for Turbulence Research, 193-208.Google Scholar
Li, G.-J., Zhu, L. & Lu, X.-Y. 2012 Numerical studies on locomotion performance of fish-like tail fins. J. Hydrodyn. B 24, 488–495.Google Scholar
Lighthill, M. J. 1986 An Informal Introduction of Theoretical Fluid Mechanics. Clarendon.Google Scholar
Müller, U. K., Van den Heuvel, B. L. E., Stamhuis, E. J. & Videler, J. J. 1997 Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet (Chelon labrosus Risso). J. Expl Biol. 200, 2893–2906.Google Scholar
Narasimhan, M., Dong, H. B., Mittal, R. & Singh, S. N. 2006 Optimal yaw regulation and trajectory control of biorobotic AUV using mechanical fins based on CFD parametrization. Trans. ASME: J. Fluids Engng 128, 687–698.Google Scholar
Nauen, J. C. & Lauder, G. V. 2002 Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber japonicus (Scombridae). J. Expl Biol. 205, 1709–1724.Google Scholar
Norbury, J. 1973 A family of steady vortex rings. J. Fluid Mech. 57, 417–431.Google Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479–517.Google Scholar
Richard, B. 1958 The speed of swimming of fish as related to size and to the frequency and amplitude of the tail beat. J. Expl Biol. 35, 109–133.Google Scholar
Saffman, P. G. 1970 The velocity of viscous vortex rings. SIAM J. 49, 371–380.Google Scholar
Sambilay, V. C. 1990 Interrelationships between swimming speed, caudal fin aspect ratio and body length of fishes. ICLARM Fishbyte 8, 16–20.Google Scholar
Shi, X. & Lim, S. P. 2007 A LBM-DLM/FD method for 3D fluid–structure interactions. J. Comput. Phys. 226, 2028–2043.Google Scholar
Sullivan, I. S., Niemela, J. J., Hershberger, R. E., Bolster, D. & Donnelly, R. J. 2008 Dynamics of thin vortex rings. J. Fluid Mech. 609, 319–347.Google Scholar
Taira, K. & Colonius, T. 2009 Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers. J. Fluid Mech. 623, 187–207.Google Scholar
Taylor, G. I. 1953 Formation of a vortex ring by giving an impulse to a circular disk and then dissolving it away. J. Appl. Phys. 24, 104.CrossRefGoogle Scholar
Taylor, G., Nudds, R. & Thomas, A. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425, 707–711.Google Scholar
Wang, X. X. & Wu, Z. N. 2010 Stroke-averaged lift forces due to vortex rings and their mutual interactions for a flapping flight model. J. Fluid Mech. 654, 453–472.Google Scholar
Willmott, A. P., Ellington, C. P. & Thomas, A. L. R. 1997 Flow visualization and unsteady aerodynamics in the flight of the hawkmoth, Manduca sexta . Phil. Trans. R. Soc. Lond. B 352, 303–316.Google Scholar
Withers, P. C. 1981 An aerodynamic analysis of bird wings as fixed aerofoils. J. Expl Biol. 90, 143–162.CrossRefGoogle Scholar
Wu, J.-C. 1981 Theory for aerodynamic force and moment in viscous flow. AIAA J. 19, 432–441.Google Scholar
Wu, J.-Z., Lu, X.-Y. & Zhuang, L.-X. 2007 Integral force acting on a body due to local flow structures. J. Fluid Mech. 576, 265–286.Google Scholar
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2006 Vorticity and Vortex Dynamics. Springer.Google Scholar
Wu, T. Y. 2011 Fish swimming and bird/insect flight. Annu. Rev. Fluid Mech. 43, 25–58.Google Scholar
Xu, C.-Y., Chen, L.-W. & Lu, X.-Y. 2010 Large-eddy simulation of the compressible flow past a wavy cylinder. J. Fluid Mech. 665, 238–273.Google Scholar
Yu, D. Z., Mei, R. W. & Shyy, W. 2002 A multi-block lattice Boltzmann method for viscous fluid flows. Intl J. Numer. Meth. Fluids 39, 99–120.Google Scholar
Zhang, J., Liu, N.-S. & Lu, X.-Y. 2010 Locomotion of a passively flapping flat plate. J. Fluid Mech. 659, 43–68.Google Scholar