Skip to main content
    • Aa
    • Aa

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

  • A. Andersen (a1), T. Bohr (a1), T. Schnipper (a1) (a2) and J. H. Walther (a2) (a3)

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.

Corresponding author
Email address for correspondence:
Hide All
‡ Present address: Svend Ole Hansen ApS, Sct. Jørgens Allé 5 C, DK-1615 Copenhagen, Denmark.
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

D. G. Bohl  & M. M. Koochesfahani 2009 MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J. Fluid Mech. 620, 6388.

J. H. J. Buchholz  & A. J. Smits 2008 The wake structure and thrust performance of a rigid low-aspect-rato pitching panel. J. Fluid Mech. 603, 331365.

J. Carrier , L. Greengard  & V. Rokhlin 1988 A fast adaptive multipole algorithm for particle simulations. SIAM J. Sci. Stat. Comput. 9 (4), 669686.

J.-M. Chomaz  & B. Cathalau 1990 Soap films as two-dimensional classical fluids. Phys. Rev. A 41, 22432245.

A. J. Chorin 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57 (4), 785796.

Y. Couder  & C. Basdevant 1986 Experimental and numerical study of vortex couples in two-dimensional flows. J. Fluid Mech. 173, 225251.

A. Das , R. K. Shukla  & R. N. Govardhan 2016 Existence of a sharp transition in the peak propulsive efficiency of a low-Re pitching foil. J. Fluid Mech. 800, 307326.

E. G. Drucker  & G. V. Lauder 2002 Experimental hydrodynamics of fish locomotion: functional insights from wake visualization. Intl Comput. Biol. 42, 243257.

M. M. Hejlesen , P. Koumoutsakos , A. Leonard  & J. H. Walther 2015 Iterative Brinkman penalization for remeshed vortex methods. J. Comput. Phys. 280, 547562.

J. W. Jaworski  & R. Gordnier 2015 Thrust augmentation of flapping airfoils in low Reynolds number flow using a flexible membrane. J. Fluids Struct. 52, 199209.

M. M. Koochesfahani 1986 Wake of an oscillating airfoil. Phys. Fluids 29, 2776.

M. M. Koochesfahani 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27, 12001205.

M. J. Lighthill 1969 Hydromechanics of aquatic animal propulsion. Annu. Rev. Fluid Mech. 1, 413446.

A. W. Mackowski  & C. H. K. Williamson 2015 Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching. J. Fluid Mech. 765, 524543.

C. Marais , B. Thiria , J. E. Wesfreid  & R. Godoy-Diana 2012 Stabilizing effect of flexibility in the wake of a flapping foil. J. Fluid Mech. 710, 659669.

J. T. Rasmussen , M. M. Hejlesen , A. Larsen  & J. H. Walther 2010 Discrete vortex method simulations of the aerodynamic admittance in bridge aerodynamics. J. Wind Engng Ind. Aerodyn. 98, 754766.

M. Rivera , P. Vorobieff  & R. E. Ecke 1998 Turbulence in flowing soap films: velocity, vorticity, and thickness fields. Phys. Rev. Lett. 81 (7), 14171420.

M. A. Rutgers , X. L. Wu  & W. B. Daniel 2001 Conducting fluid dynamics experiments with vertically falling soap films. Rev. Sci. Instrum. 72, 30253037.

T. Schnipper , L. Tophøj , A. Andersen  & T. Bohr 2010 Japanese fan flow. Phys. Fluids 22, 091102.

M. Sfakiotakis , D. M. Lane  & J. B. C. Davies 1999 Review of fish swimming modes for aquatic locomotion. IEEE J. Ocean. Engng 24, 237252.

M. S. Triantafyllou , G. S. Triantafyllou  & R. Gopalkrishnan 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids A 3, 28352837.

M. S. Triantafyllou , G. S. Triantafyllou  & D. K. P. Yue 2000 Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32, 3353.

E. D. Tytell  & G. V. Lauder 2004 The hydrodynamics of eel swimming I. Wake structure. J. Expl Biol. 207 (11), 18251841.

C. H. K. Williamson  & A. Roshko 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 335381.

J. C. Wu 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19, 432441.

J. Zhang , S. Childress , A. Libchaber  & M. Shelley 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835839.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Type Description Title

Andersen et al. supplementary movie
Pitching foil with StD = 0.08 and AD = 1.14.

 Video (12.6 MB)
12.6 MB

Andersen et al. supplementary movie
Heaving foil with StD= 0.10 and AD = 1.80.

 Video (10.3 MB)
10.3 MB


Full text views

Total number of HTML views: 22
Total number of PDF views: 345 *
Loading metrics...

Abstract views

Total abstract views: 551 *
Loading metrics...

* Views captured on Cambridge Core between 28th December 2016 - 24th May 2017. This data will be updated every 24 hours.