Research Papers: Fundamental Issues and Canonical Flows

On the Impulse Produced by Chordwise Flexible Pitching Foils in a Quiescent Fluid

[+] Author and Article Information
Francisco J. Huera-Huarte

Department of Mechanical Engineering,
Universitat Rovira i Virgili,
Tarragona 43007, Spain
e-mail: francisco.huera@urv.cat

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 8, 2017; final manuscript received September 28, 2017; published online December 4, 2017. Assoc. Editor: Pierre E. Sullivan.

J. Fluids Eng 140(4), 041206 (Dec 04, 2017) (10 pages) Paper No: FE-17-1333; doi: 10.1115/1.4038168 History: Received June 08, 2017; Revised September 28, 2017

In this paper, a parametric study showing the impulsive performance of foils with different flexural stiffness pitching in a quiescent fluid is presented. A wide range of Reynolds numbers (different imposed kinematics) and foil rigidities is covered, depicting how flexibility effects on impulse are more important at the largest Reynolds numbers. The impulsive performance of the system is derived from direct thrust force measurements. Passive flexibility alters vortex strength and formation in the wake of the pitching foil. These changes in the wake formation can be used to explain the differences in the measured impulses. The wake dynamics is studied after quantitative analysis of particle image velocimetry data, and it is linked to the momentum transfer generated by the foil.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Mchenry, M. J. , Pell, C. A. , and Long, J. H. , Jr., 1995, “ Mechanical Control of Swimming Speed: Stiffness and Axial Wave Form in Undulating Fish Models,” J. Exp. Biol., 198(11), pp. 2293–2305. http://jeb.biologists.org/content/198/11/2293 [PubMed]
Fish, F. , and Lauder, G. , 2006, “ Passive and Active Flow Control by Swimming Fishes and Mammals,” Annu. Rev. Fluid Mech., 38(1), pp. 193–224. [CrossRef]
Liu, P. , and Bose, N. , 1997, “ Propulsive Performance From Oscillating Propulsors With Spanwise Flexibility Propulsive Performance From Oscillating,” Proc. R. Soc. A, 453(1963), pp. 1763–1770. [CrossRef]
Miao, J.-M. M. , and Ho, M.-H. H. , 2006, “ Effect of Flexure on Aerodynamic Propulsive Efficiency of Flapping Flexible Airfoil,” J. Fluids Struct., 22(3), pp. 401–419. [CrossRef]
Zhao, L. , Huang, Q. , Deng, X. , and Sane, S. P. , 2010, “ Aerodynamic Effects of Flexibility in Flapping Wings,” J. R. Soc., Interface, 7(44), pp. 485–497. [CrossRef]
Barannyk, O. , Buckham, B. J. , and Oshkai, P. , 2012, “ On Performance of an Oscillating Plate Underwater Propulsion System With Variable Chordwise Flexibility at Different Depths of Submergence,” J. Fluids Struct., 28, pp. 152–166. [CrossRef]
Siala, F. F. , Totpal, A. D. , and Liburdy, J. A. , 2016, “ Characterization of Vortex Dynamics in the Near Wake of an Oscillating Flexible Foil,” ASME J. Fluids Eng., 138(10), p. 101202. [CrossRef]
Lucas, K. N. , Thornycroft, P. J. M. , Gemmell, B. J. , Colin, S. P. , Costello, J. H. , and Lauder, G. V. , 2015, “ Effects of Non-Uniform Stiffness on the Swimming Performance of a Passively-Flexing, Fish-Like Foil Model,” Bioinspiration Biomimetics, 10(5), p. 056019. [CrossRef] [PubMed]
Heathcote, S. , Wang, Z. , and Gursul, I. , 2008, “ Effect of Spanwise Flexibility on Flapping Wing Propulsion,” J. Fluids Struct., 24(2), pp. 183–199. [CrossRef]
Marais, C. , Thiria, B. , Wesfreid, J. E. , and Godoy-Diana, R. , 2012, “ Stabilizing Effect of Flexibility in the Wake of a Flapping Foil,” J. Fluid Mech., 710, pp. 659–669. [CrossRef]
Kim, D. , and Gharib, M. , 2011, “ Characteristics of Vortex Formation and Thrust Performance in Drag-Based Paddling Propulsion,” J. Exp. Biol., 214(13), pp. 2283–2291. [CrossRef] [PubMed]
Kim, D. , and Gharib, M. , 2011, “ Flexibility Effects on Vortex Formation of Translating Plates,” J. Fluid Mech., 677, pp. 255–271. [CrossRef]
Flammang, B. E. , 2010, “ Functional Morphology of the Radialis Muscle in Shark Tails,” J. Morphol., 271(3), pp. 340–352. [PubMed]
Huera-Huarte, F. , and Gharib, M. , 2017, “ On the Effect of Tip Deflection in Flapping Propulsion,” J. Fluids Struct., 71, pp. 217–233. [CrossRef]
Feilich, K. L. , and Lauder, G. V. , 2015, “ Passive Mechanical Models of Fish Caudal Fins: Effects of Shape and Stiffness on Self-Propulsion,” Bioinspiration Biomimetics, 10(3), p. 036002. [CrossRef] [PubMed]
Alben, S. , Witt, C. , Baker, T. V. , Anderson, E. , and Lauder, G. V. , 2012, “ Dynamics of Freely Swimming Flexible Foils,” Phys. Fluids, 24(5), p. 051901. [CrossRef]
Paraz, F. , Eloy, C. , and Schouveiler, L. , 2014, “ Experimental Study of the Response of a Flexible Plate to a Harmonic Forcing in a Flow,” C. R. Méc., 342(9), pp. 532–538. [CrossRef]
Paraz, F. , Schouveiler, L. , and Eloy, C. , 2016, “ Thrust Generation by a Heaving Flexible Foil: Resonance, Nonlinearities, and Optimality,” Phys. Fluids, 28(1), p. 011903. [CrossRef]
Domenici, P. , and Blake, R. W. , 1997, “ The Kinematics and Performance of Fish Fast-Start Swimming,” J. Exp. Biol., 200, pp. 1165–1178. http://jeb.biologists.org/content/200/8/1165 [PubMed]
Epps, B. P. , and Techet, A. H. , 2007, “ Impulse Generated During Unsteady Maneuvering of Swimming Fish,” Exp. Fluids, 43(5), pp. 691–700. [CrossRef]
Ringuette, M. J. , Milano, M. , and Gharib, M. , 2007, “ Role of the Tip Vortex in the Force Generation of Low-Aspect-Ratio Normal Flat Plates,” J. Fluid Mech., 581, pp. 453–468. [CrossRef]
DeVoria, A. C. , and Ringuette, M. J. , 2013, “ The Force and Impulse of a Flapping Plate Performing Advancing and Returning Strokes in a Quiescent Fluid,” Exp. Fluids, 54(5), p. 1515. [CrossRef]
DeVoria, A. C. , and Ringuette, M. J. , 2012, “ Vortex Formation and Saturation for Low-Aspect-Ratio Rotating Flat-Plate Fins,” Exp. Fluids, 52(2), pp. 441–462. [CrossRef]
Willert, C. , and Gharib, M. , 1991, “ Digital Particle Image Velocimetry,” Exp. Fluids, 10(4), pp. 181–193. [CrossRef]
Huang, H. , Dabiri, D. , and Gharib, M. , 1997, “ On Errors of Digital Particle Image Velocimetry,” Meas. Sci. Technol., 8(12), pp. 1427–1440. [CrossRef]
Wu, J. C. , 1981, “ Theory for Aerodynamic Force and Moment in Viscous Flows,” AIAA J., 19(4), pp. 432–441. [CrossRef]
Saffman, P. , 1992, Vortex Dynamics, Cambridge University Press, Cambridge, UK.
Protas, B. , and Wesfreid, J. E. , 2003, “ On the Relation Between the Global Modes and the Spectra of Drag and Lift in Periodic Wake Flows,” C. R. Méc., 331(1), pp. 49–54. [CrossRef]
Noca, F. , Shiels, D. , and Jeon, D. , 1999, “ A Comparison of Methods for Evaluating Time-Dependent Fluid Dynamic Forces on Bodies, Using Only Velocity Fields and Their Derivatives,” J. Fluids Struct., 13(5), pp. 551–578. [CrossRef]
Hunt, J. C. R. , Wray, A. A. , and Moin, P. , 1988, “ Eddies, Streams, and Convergence Zones in Turbulent Flows,” Center for Turbulence Research Summer Program, Stanford University, Stanford, CA, Report No. CTR - S88, pp. 193–208. https://ntrs.nasa.gov/search.jsp?R=19890015184
Jeong, J. , and Hussain, F. , 1995, “ On the Identification of a Vortex,” J. Fluid Mech., 285(1), pp. 69–94. [CrossRef]
Gharib, M. , Rambod, E. , and Shariff, K. , 1998, “ A Universal Time Scale for Vortex Ring Formation,” J. Fluid Mech., 360, pp. 121–140. [CrossRef]
Raffel, M. , Willert, C. , Wereley, S. T. , and Kompenhans, J. , 2007, Particle Image Velocimetry: A Practical Guide, 2nd ed., Springer-Verlag, Berlin.


Grahic Jump Location
Fig. 1

Schematic (top view) of the experimental setup

Grahic Jump Location
Fig. 2

Schematic (side view) of the experimental setup

Grahic Jump Location
Fig. 3

Temporal evolution of the angular position of the shaft (θ), thrust coefficient (CT), and impulse (I) for a typical test conducted. The foil in this case was the infinitely rigid one or reference one, rotating at 277 deg/s (Re = 30,600) with a stroke swept angle of 90 deg.

Grahic Jump Location
Fig. 4

Dimensionless vorticity (ωzc/U) in the wake of the rigid foil (EI0) for the same case of Fig. 3. The sequence starts in the upper left corner to the right. The 12 DPIV instantaneous vorticity snapshots cover approximately three strokes times or 3T. The angular speed imposed in this example case was 277 deg/s (Re = 30,600) with a stroke covering a swept angle of 90 deg.

Grahic Jump Location
Fig. 5

Impulse at t* = 5 (I) as a function of swept angle (2θ0) and angular speed (Ω) or Re) for all the foils investigated withdifferent flexural stiffness. EI symbols appear detailed in Table 1, EI0 is for the rigid foil, and EI1 to EI5 are for the flexible foils with increasing flexibility.

Grahic Jump Location
Fig. 6

Temporal evolution of the impulse for swept angles of 60 deg and 90 deg, for all the cases with the largest Re in Fig. 5. Same symbol convention for stiffness is used as in Fig. 5.

Grahic Jump Location
Fig. 7

Angular position of the actuating shaft (θ), thrust coefficient (CT) and impulse (I) for three experiments with similar imposed kinematics, but different rigidity. Solid dots are for the reference case with EI0 (infinitely rigid), hollow circles for the case with flexural stiffness EI1 and triangles is for the case with EI5 (the most flexible one).

Grahic Jump Location
Fig. 8

Deformation of the foil for the three experiments (from Fig. 7) with similar kinematics and different rigidity. Reference case or infinitely rigid, flexural stiffness EI1 and finally EI5 or the most flexible one.

Grahic Jump Location
Fig. 9

Temporal evolution of dimensionless vorticity in the wake of the flexible foil with highest flexibility (EI5, ▿ in the previous figures)

Grahic Jump Location
Fig. 10

Temporal evolution of dimensionless vorticity in the wake of the flexible foil with the smallest flexibility (EI1, ○ in the previous figures)

Grahic Jump Location
Fig. 11

Evolution of the characteristic size (Δy/c) and the inclination (α) of the vortex structure in the wake of the foils (EI5—▿, EI1—∘, and EI0—•)

Grahic Jump Location
Fig. 12

Evolution of vortex strength (Γ*) in the wake of the foils (EI5—▿, EI1—∘, and EI0—•)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In