Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-02-05T17:39:43.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex wakes of a flapping foil

Published online by Cambridge University Press:  25 August 2009

TEIS SCHNIPPER ,
ANDERS ANDERSEN  and
TOMAS BOHR
TEIS SCHNIPPER
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
ANDERS ANDERSEN*
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
TOMAS BOHR
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an experimental study of a symmetric foil performing pitching oscillations in a vertically flowing soap film. By varying the frequency and amplitude of the oscillation we visualize a variety of wakes with up to 16 vortices per oscillation period, including von Kármán vortex street, inverted von Kármán vortex street, 2P wake, 2P+2S wake and novel wakes ranging from 4P to 8P. We map out the wake types in a phase diagram spanned by the width-based Strouhal number and the dimensionless amplitude. We follow the time evolution of the vortex formation near the round leading edge and the shedding process at the sharp trailing edge in detail. This allows us to identify the origins of the vortices in the 2P wake, to understand that two distinct 2P regions are present in the phase diagram due to the timing of the vortex shedding at the leading edge and the trailing edge and to propose a simple model for the vorticity generation. We use the model to describe the transition from 2P wake to 2S wake with increasing oscillation frequency and the transition from the von Kármán wake, typically associated with drag, to the inverted von Kármán wake, typically associated with thrust generation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 411 - 423
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72.CrossRefGoogle Scholar
Aref, H., Stremler, M. A. & Ponta, F. L. 2006 Exotic vortex wakes – point vortex solutions. J. Fluids Struct. 22, 929–940.CrossRefGoogle Scholar
Bohl, D. G. & Koochesfahani, M. M. 2009 MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J. Fluid Mech. 620, 63–88.CrossRefGoogle Scholar
Bratt, J. B. 1953 Flow patterns in the wake of an oscillating aerofoil. Aero. Res. Counc. R. M. 2773, 1–28.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.CrossRefGoogle ScholarPubMed
Chomaz, J.-M. & Cathalau, B. 1990 Soap films as two-dimensional classical fluids. Phys. Rev. A 41, 2243–2245.CrossRefGoogle ScholarPubMed
Couder, Y. & Basdevant, C. 1986 Experimental and numerical study of vortex couples in two-dimensional flows. J. Fluid Mech. 173, 225–251.CrossRefGoogle Scholar
Couder, Y., Chomaz, J.-M. & Rabaud, M. 1989 On the hydrodynamics of soap films. Physica D 37, 384–405.CrossRefGoogle Scholar
Garrick, I. E. 1936 Propulsion of a flapping and oscillating airfoil. Rep. No. 567. NACA.Google Scholar
Gharib, M. & Derango, P. 1989 A liquid film (soap film) tunnel to study two-dimensional laminar and turbulent shear flows. Physica D 37, 406–416.CrossRefGoogle Scholar
Godoy-Diana, R., Aider, J.-L. & Wesfreid, J. E. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E 77, 016308.CrossRefGoogle ScholarPubMed
Godoy-Diana, R., Marais, C., Aider, J.-L. & Wesfreid, J. E. 2009 A model for the symmetry breaking of the reverse Benard–von Kármán vortex street produced by a flapping foil. J. Fluid Mech. 622, 23–32.CrossRefGoogle Scholar
von Kármán, T. & Burgers, J. M. 1935 General aerodynamic theory – perfect fluids. In Aerodynamic Theory II, pp. 280–310 (ed. by Durand, W. F.). Dover Publications, 1963.Google Scholar
Koochesfahani, M. M. 1986 Wake of an oscillating airfoil. Phys. Fluids 29, 2776.CrossRefGoogle Scholar
Koochesfahani, M. M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27, 1200–1205.CrossRefGoogle Scholar
Lai, J. C. S. & Platzer, M. F. 1999 Jet characteristics of a plunging airfoil. AIAA J. 37, 1529–1537.CrossRefGoogle Scholar
Lentink, D., Muijres, F. T., Donker-Duyvis, F. J. & van Leeuwen, J. L. 2008 Vortex–wake interactions of a flapping foil that models animal swimming and flight. J. Exp. Biol. 211, 267–273.CrossRefGoogle ScholarPubMed
Lighthill, M. J. 1969 Hydromechanics of aquatic animal propulsion. Annu. Rev. Fluid Mech. 1, 413–446.CrossRefGoogle Scholar
Müller, U. K., van den Boogaart, J. G. M. & van Leeuwen, J. L. 2008 Flow patterns of larval fish: undulatory swimming in the intermediate flow regime. J. Exp. Biol. 211, 196–205.CrossRefGoogle ScholarPubMed
Müller, U. K., Smit, J., Stamhuis, E. J. & Videler, J. J. 2001 How the body contributes to the wake in undulatory fish swimming: flow fields of a swimming eel (Anguilla anguilla). J. Exp. Biol. 204, 2751–2762.CrossRefGoogle Scholar
Ponta, F. L. & Aref, H. 2005 Vortex synchronization regions in shedding from an oscillating cylinder. Phys. Fluids 17, 011703.CrossRefGoogle Scholar
Prandtl, L. & Tietjens, O. G. 1934 Fundamentals of Hydro- and Aeromechanics. Dover Publications.Google Scholar
Rivera, M., Vorobieff, P. & Ecke, R. E. 1998 Turbulence in flowing soap films: velocity, vorticity, and thickness fields. Phys. Rev. Lett. 81, 1417–1420.CrossRefGoogle Scholar
Rutgers, M. A., Wu, X. L. & Daniel, W. B. 2001 Conducting fluid dynamics experiments with vertically falling soap films. Rev. Sci. Instrum. 72, 3025–3037.CrossRefGoogle Scholar
Sfakiotakis, M., Lane, D. M. & Davies, J. B. C. 1999 Review of fish swimming modes for aquatic locomotion. IEEE J. Oceanic Engng 24, 237–252.CrossRefGoogle Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Yue, D. K. P. 2000 Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32, 33–53.CrossRefGoogle Scholar
Vorobieff, P. & Ecke, R. E. 1999 Cylinder wakes in flowing soap films. Phys. Rev. E 60, 2953–2956.CrossRefGoogle ScholarPubMed
Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355–381.CrossRefGoogle Scholar
Zhang, J., Childress, S., Libchaber, A. & Shelley, M. 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835–839.CrossRefGoogle Scholar