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Wake and thrust of an angularly reciprocating plate

Published online by Cambridge University Press:  27 February 2013

Jeongsu Lee ,
Yong-Jai Park ,
Useok Jeong ,
Kyu-Jin Cho  and
Ho-Young Kim
Jeongsu Lee
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
Yong-Jai Park
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
Useok Jeong
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
Kyu-Jin Cho
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
Ho-Young Kim*
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
*
†Email address for correspondence: [email protected]
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Abstract

As one of the most important force production mechanisms of swimming and flying animals, the fluid dynamics of flapping has been intensively studied. However, these efforts have been mainly directed toward animals in forward motion or locomotive appendages undergoing linear translation. Here we seek to complement the existing knowledge of the flapping mechanism by studying angularly reciprocating flat plates without a free stream velocity, under a so-called ‘bollard pull’ condition. We visualize the flow field around the flat plate to find that two independent vortical structures are formed per half-cycle, resulting in the separation of two distinct vortex pairs at sharp edges rather than a single vortex loop which is typical of a starting–stopping vortex paradigm in flows with free streams. Based on our observations, we derive a scaling law to predict the thrust of the flapping plate; this is the first experimentally validated theoretical model for the thrust of angularly reciprocating plates without a prescribed background flow.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Propulsion Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 720 , 10 April 2013 , pp. 545 - 557
Copyright
©2013 Cambridge University Press

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References

Ahlborn, B., Chapman, S., Stafford, R., Blake, R. W. & Harper, D. G. 1997 Experimental simulation of the thrust phases of fast-start swimming of fish. J. Exp. Biol. 200, 2301–2312.Google Scholar
Birch, J. M. & Dickinson, M. H. 2003 The influence of wing-wake interactions on the production of aerodynamic forces in flapping flight. J. Exp. Biol. 206, 2257–2272.CrossRefGoogle ScholarPubMed
Buchholz, J. H. J. & Smitz, A. J. 2006 On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 546, 433–443.Google Scholar
Buchholz, J. H. J. & Smitz, A. J. 2008 The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331–365.CrossRefGoogle ScholarPubMed
Buckingham, E. 1914 On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4, 345–376.Google Scholar
Chopra, M. G. 1976 Large amplitude lunate-tail theory of fish locomotion. J. Fluid Mech. 74, 161–182.Google Scholar
DeVoria, A. C. & Ringuette, M. J. 2012 Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins. Exp. Fluids 52, 441–462.Google Scholar
Dickinson, M. H. 1996 Unsteady mechanisms of force generation in aquatic and aerial locomotion. Am. Zool. 36, 537–554.Google Scholar
Dickinson, M. H., Lehmann, F.-O. & Sane, S. P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284, 1954–1960.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Drucker, E. G. & Lauder, G. V. 1999 Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using digital particle image velocimetry. J. Exp. Biol. 202, 2393–2412.Google Scholar
Ellington, C. P., Van Den Berg, C., Willmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384, 626–630.Google Scholar
Jardin, T., David, L. & Farcy, A. 2009 Characterization of vortical structures and loads based on time-resolved PIV for asymmetric hovering flapping flight. Exp. Fluids 46, 847–857.Google Scholar
Jones, M. A. 2003 The separated flow of an inviscid fluid around a moving flat plate. J. Fluid Mech. 496, 405–441.Google Scholar
Kim, J. & Chung, W. K. 2006 Accurate and practical thruster modelling for underwater vehicles. Ocean Engng 33, 566–586.Google Scholar
Kim, D. & Gharib, M. 2011 Characteristics of vortex formation and thrust performance in drag-based paddling propulsion. J. Exp. Biol. 214, 2283–2291.Google Scholar
Lang, T. G. 1966 Hydrodynamic analysis of cetacean performance. In Whales, Dolphins and Porpoises (ed. Norris, K. S.). University of California.Google Scholar
Lighthill, M. J. 1970 Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44, 265–301.CrossRefGoogle Scholar
Newman, J. N. 1977 Marine Hydrodynamics. MIT.Google Scholar
Poelma, C., Dickson, W. B. & Dickinson, M. H. 2006 Time-resolved reconstruction of the full velocity field around a dynamically-scaled flapping wing. Exp. Fluids 41, 213–225.Google Scholar
Sonin, A. A. 2004 A generalization of the $\Pi $ -theorem and dimensional analysis. Proc. Natl Acad. Sci. USA 101, 8525–8526.CrossRefGoogle ScholarPubMed
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. K., Nudds, R. L. & Thomas, A. L. R. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425, 707–711.Google Scholar
Techet, A. H. 2008 Propulsive performance of biologically inspired flapping foils at high Reynolds numbers. J. Exp. Biol. 211, 274–279.Google Scholar
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Report 496.Google Scholar
Videler, J. J., Stamhuis, E. J. & Povel, G. D. E. 2004 Leading-edge vortex lifts swifts. Science 306, 1960–1962.Google Scholar
Wang, Z. J. 2004 The role of drag in insect hovering. J. Exp. Biol. 207, 4147–4155.CrossRefGoogle ScholarPubMed
Wu, T. Y. 2006 A nonlinear unsteady flexible wing theory. Structural Control and Health Monitoring 13, 553–560.Google Scholar
Wu, T. Y. 2007 A nonlinear theory for a flexible unsteady wing. J. Engng Maths 58, 279–287.Google Scholar
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2006 Vorticity and Vortex Dynamics. Springer.CrossRefGoogle Scholar
Yu, J., Hu, Y., Huo, J. & Wang, L. 2009 Dolphin-like propulsive mechanism based on an adjustable Scotch yoke. Mechanism and Machine Theory 44, 603–614.Google Scholar
Zdunich, P., Bilyk, D., MacMaster, M., Loewen, D., DeLaurier, J., Kornbluh, R., Low, T., Stanford, S. & Holeman, D. 2007 Development and testing of the Mentor flapping-wing micro air vehicle. J. Aircraft 44, 1701–1711.CrossRefGoogle Scholar