Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-29T21:00:28.989Z Has data issue: false hasContentIssue false
  • English
  • Français

Wake structure and thrust generation of a flapping foil in two-dimensional flow

Published online by Cambridge University Press:  28 December 2016

A. Andersen ,
T. Bohr ,
T. Schnipper  and
J. H. Walther
A. Andersen*
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
T. Bohr
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
T. Schnipper
Affiliation:
Department of Physics and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark Department of Mechanical Engineering and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
J. H. Walther
Affiliation:
Department of Mechanical Engineering and Center for Fluid Dynamics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark Swiss Federal Institute of Technology Zürich, Chair of Computational Science, ETH Zentrum, Clausiusstrasse 33, CH-8092 Zürich, Switzerland
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a combined numerical (particle vortex method) and experimental (soap film tunnel) study of a symmetric foil undergoing prescribed oscillations in a two-dimensional free stream. We explore pure pitching and pure heaving, and contrast these two generic types of kinematics. We compare measurements and simulations when the foil is forced with pitching oscillations, and we find a close correspondence between flow visualisations using thickness variations in the soap film and the numerically determined vortex structures. Numerically, we determine wake maps spanned by oscillation frequency and amplitude, and we find qualitatively similar maps for pitching and heaving. We determine the drag–thrust transition for both pitching and heaving numerically, and we discuss it in relation to changes in wake structure. For heaving with low oscillation frequency and high amplitude, we find that the drag–thrust transition occurs in a parameter region with wakes in which two vortex pairs are formed per oscillation period, in contrast to the common transition scenario in regions with inverted von Kármán wakes.

JFM classification

Biological Fluid Dynamics: Propulsion Vortex Flows: Vortex shedding Wakes/Jets: Wakes/Jets
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , R4
Check for updates
Copyright
© 2016 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.)

Footnotes

‡

Present address: Svend Ole Hansen ApS, Sct. Jørgens Allé 5 C, DK-1615 Copenhagen, Denmark.

References

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
Buchholz, J. H. J. & Smits, A. J. 2008 The wake structure and thrust performance of a rigid low-aspect-rato pitching panel. J. Fluid Mech. 603, 331–365.CrossRefGoogle ScholarPubMed
Carrier, J., Greengard, L. & Rokhlin, V. 1988 A fast adaptive multipole algorithm for particle simulations. SIAM J. Sci. Stat. Comput. 9 (4), 669–686.CrossRefGoogle Scholar
Chomaz, J.-M. & Cathalau, B. 1990 Soap films as two-dimensional classical fluids. Phys. Rev. A 41, 2243–2245.CrossRefGoogle ScholarPubMed
Chorin, A. J. 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57 (4), 785–796.Google Scholar
Couder, Y. & Basdevant, C. 1986 Experimental and numerical study of vortex couples in two-dimensional flows. J. Fluid Mech. 173, 225–251.Google Scholar
Couder, Y., Chomaz, J. M. & Rabaud, M. 1989 On the hydrodynamics of soap films. Physica D 37, 384–405.Google Scholar
Das, A., Shukla, R. K. & Govardhan, R. N. 2016 Existence of a sharp transition in the peak propulsive efficiency of a low-Re pitching foil. J. Fluid Mech. 800, 307–326.CrossRefGoogle Scholar
Drucker, E. G. & Lauder, G. V. 2002 Experimental hydrodynamics of fish locomotion: functional insights from wake visualization. Intl Comput. Biol. 42, 243–257.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.Google Scholar
Godoy-Diana, R., Aider, J.-L. & Wesfreid, J. E. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E 77, 016308.Google Scholar
Hejlesen, M. M., Koumoutsakos, P., Leonard, A. & Walther, J. H. 2015 Iterative Brinkman penalization for remeshed vortex methods. J. Comput. Phys. 280, 547–562.Google Scholar
Jaworski, J. W. & Gordnier, R. 2015 Thrust augmentation of flapping airfoils in low Reynolds number flow using a flexible membrane. J. Fluids Struct. 52, 199–209.Google Scholar
von Kármán, T. & Burgers, J. M. 1935 General aerodynamic theory – perfect fluids. In Aerodynamic Theory II (ed. Durand, W. F.). Dover.Google Scholar
Koochesfahani, M. M. 1986 Wake of an oscillating airfoil. Phys. Fluids 29, 2776.Google Scholar
Koochesfahani, M. M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27, 1200–1205.Google Scholar
Larsen, A. & Walther, J. H. 1997 Aeroelastic analysis of bridge girder sections based on discrete vortex simulations. J. Wind Engng Ind. Aerodyn. 67–68, 253–265.Google Scholar
Lighthill, M. J. 1969 Hydromechanics of aquatic animal propulsion. Annu. Rev. Fluid Mech. 1, 413–446.Google Scholar
Mackowski, A. W. & Williamson, C. H. K. 2015 Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching. J. Fluid Mech. 765, 524–543.CrossRefGoogle Scholar
Marais, C., Thiria, B., Wesfreid, J. E. & Godoy-Diana, R. 2012 Stabilizing effect of flexibility in the wake of a flapping foil. J. Fluid Mech. 710, 659–669.Google Scholar
Rasmussen, J. T., Hejlesen, M. M., Larsen, A. & Walther, J. H. 2010 Discrete vortex method simulations of the aerodynamic admittance in bridge aerodynamics. J. Wind Engng Ind. Aerodyn. 98, 754–766.Google Scholar
Rivera, M., Vorobieff, P. & Ecke, R. E. 1998 Turbulence in flowing soap films: velocity, vorticity, and thickness fields. Phys. Rev. Lett. 81 (7), 1417–1420.Google 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.Google Scholar
Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 644, 411–423.CrossRefGoogle Scholar
Schnipper, T., Tophøj, L., Andersen, A. & Bohr, T. 2010 Japanese fan flow. Phys. Fluids 22, 091102.Google Scholar
Sfakiotakis, M., Lane, D. M. & Davies, J. B. C. 1999 Review of fish swimming modes for aquatic locomotion. IEEE J. Ocean. Engng 24, 237–252.Google Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Gopalkrishnan, R. 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids A 3, 2835–2837.Google Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Yue, D. K. P. 2000 Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32, 33–53.Google Scholar
Tytell, E. D. & Lauder, G. V. 2004 The hydrodynamics of eel swimming I. Wake structure. J. Expl Biol. 207 (11), 1825–1841.CrossRefGoogle ScholarPubMed
Walther, J. H. & Larsen, A. 1997 Discrete vortex method for application to bluff body aerodynamics. J. Wind Engng Ind. Aerodyn. 67–68, 183–193.Google Scholar
Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 335–381.CrossRefGoogle Scholar
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19, 432–441.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.Google Scholar

Andersen et al. supplementary movie

Pitching foil with StD = 0.08 and AD = 1.14.

Download Andersen et al. supplementary movie(Video)
Video 21.2 MB

Andersen et al. supplementary movie

Heaving foil with StD= 0.10 and AD = 1.80.

Download Andersen et al. supplementary movie(Video)
Video 27.6 MB