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On the flow generated on the leeward face of a rotating flat plate

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Abstract

We experimentally investigate the flow generated on the leeward face of a rotating trapezoidal flat plate of low-aspect-ratio; the motion is an advancing stroke from rest at 90° angle of attack with Reynolds numbers of O(103). The objectives are to characterize the fluid velocity near the tip of the plate for different plate kinematics. The experiments are conducted in a water tank facility, and digital particle image velocimetry is performed to obtain planar velocity measurements. The flow in the region near the tip is relatively insensitive to Reynolds number over the range studied. The component normal to the plate is unaffected by total rotational amplitude, while the tangential component has dependence on this angle. Also, an estimate of the first tip vortex pinch-off time is obtained from the near-tip velocity data and agrees very well with values estimated using circulation. The angle of incidence of the bulk root-to-tip flow relative to the plate normal becomes more oblique with increasing rotational amplitude. Accordingly, the peak magnitude of the tangential velocity is also increased and as a result advects fluid momentum away from the plate at a higher rate. The more oblique impingement of the root-to-tip flow for increasing rotational amplitude is shown to have a distinct effect on the associated fluid dynamic force normal to the plate. For impulsive plate deceleration the time that a nonnegligible force exists decreases, while for nonimpulsive plate deceleration both this time and the relative force magnitude decrease for larger rotational amplitudes.

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References

  • Ahlborn B, Chapman S, Stafford R, Blake RW, Harper DG (1997) Experimental simulation of the thrust phases of fast-start swimming of fish. J Exp Biol 200:2301–2312

    Google Scholar 

  • Ahlborn D, Harper BG, Blake RW, Ahlborn B, Cam M (1991) Fish without footprints. J Theor Bio 184:521–533

    Article  Google Scholar 

  • Bandyopadhyay PR (2005) Trends in biorobotic autonomous undersea vehicles. IEEE J Oceanic Eng 30:109–139

    Article  Google Scholar 

  • Barrett DS (1996) Propulsive efficiency of a flexible hull underwater vehicle. PhD thesis, MIT

  • Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Borazjani I, Sotiropoulos F (2008) Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J Exp Biol 211:1541–1558

    Article  Google Scholar 

  • Boston Engineering Corporation (2009) http://www.boston-engineering.com. Accessed: 12/10/2012

  • Bozkurttas M, Mittal R, Dong H, Lauder GV, Madden P (2009) Low-dimensional models and performance scaling of a highly deformable fish pectoral fin. J Fluid Mech 631:311–342

    Article  MATH  Google Scholar 

  • Buchholz JHJ, Smits AJ (2006) On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J Fluid Mech 546:433–443

    Article  MATH  Google Scholar 

  • Buchholz JHJ, Smits AJ (2008) The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J Fluid Mech 603:331–365

    Article  MATH  Google Scholar 

  • Carr ZR, Chen C, Ringuette MJ (2013) Finite-span rotating wings: three-dimensional vortex formation and variations with aspect ratio. Exp Fluids 54:1444

    Article  Google Scholar 

  • DeVoria AC, Ringuette MJ (2012) Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins. Exp Fluids 52(2):441–462

    Article  Google Scholar 

  • Domenici P, Blake RW (1997) The kinematics and performance of fish fast-start swimming. J Exp Biol 200:1165–1178

    Google Scholar 

  • Drucker EG, Lauder GV (1999) Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using particle image velocimetry. J Exp Biol 202:2393–2412

    Google Scholar 

  • Drucker EG, Lauder GV (2001) Wake dynamics and fluid forces of turning maneuvers in sunfish. J Exp Biol 203:2379–2393

    Google Scholar 

  • Epps BP, Techet AH (2007) Impulse generated during unsteady manuvering of swimming fish. Exp Fluids 43:691–700

    Article  Google Scholar 

  • Forliti DJ, Strykowski PJ, Debatin K (2000) Bias and precision errors of digital particle image velocimetry. Exp Fluids 28:436–447

    Article  Google Scholar 

  • Gazzola M, Rees WMV, Koumoutsakos P (2012) C-start: optimal start of larval fish. J Fluid Mech 698:5–18

    Article  MathSciNet  MATH  Google Scholar 

  • Graham JMR (1983) The lift on an aerofoil in starting flow. J Fluid Mech 133:413–425

    Article  MATH  Google Scholar 

  • Green MA, Rowley CW, Smits AJ (2011) The unsteady three-dimensional wake produced by trapezoidal pitching panel. J Fluid Mech 685:117–145

    Article  MATH  Google Scholar 

  • Hancock J (1953) The self propulsion of microscopic organisms through liquids. Proc R Soc Lond A 217:96–121

    Google Scholar 

  • Johansson LC, Norberg RA (2003) Delta-wing function of webbed feet gives hydrodynamic lift for swimming propulsion in birds. Nature 424:65–68

    Article  Google Scholar 

  • Jones AR, Babinsky H (2011) Leading edge vortex development on a waving wing at reynolds numbers between 10,000 and 60,000. In: 49th AIAA Aerospace Sciences Meeting and Exhibit, AIAA, pp 1–15

  • Kim D, Gharib M (2011) Characteristics of vortex formation and thrust performance in drag-based paddling propulsion. J Exp Biol 214:2283–2291

    Article  Google Scholar 

  • Koochesfahani MM (1989) Vortical patterns in the wake of an oscillating airfoil. AIAA J 27(9):1200–1205

    Article  Google Scholar 

  • Lighthill MJ (1960) Note on the swimming of slender fish. J Fluid Mech 9:305–317

    Article  MathSciNet  Google Scholar 

  • Lighthill MJ (1969) Hydromechanics of aquatic animal propulsion. Annu Rev Fluid Mech 1:413–446

    Article  Google Scholar 

  • Lighthill MJ (1970) Aquatic animal propulsion of high hydromechanical efficiency. J Fluid Mech 44:265–301

    Article  MATH  Google Scholar 

  • Lighthill MJ (1971) Large-amplitude elongated-body theory of fish locomotion. P Roy Soc Lond B Bio 179(1055):125–138

    Article  Google Scholar 

  • Milano M, Gharib M (2005) Uncovering the physics of flapping flat plates with artificial evolution. J Fluid Mech 534:403–409

    Article  MATH  Google Scholar 

  • Niesterok B, Hanke W (2013) Hydrodynamic patterns from fast-starts in teleost fish and their possible relevance to predator-prey interactions. J Comp Physiol A 199:139–149

    Article  Google Scholar 

  • Noca F, Shiels D, Jeon D (1999) A comparison of methods for evaluating time-dependant fluid dynamic forces on bodies, using only velocity fields and their derivatives. J Fluid Struct 13:551–578

    Article  Google Scholar 

  • Ozen CA, Rockwell D (2012) Three-dimensional vortex structure on a rotating wing. J Fluid Mech 707:541–550

    Article  Google Scholar 

  • Parker K, von Ellenrieder KD, Soria J (2007) Morphology of the forced oscillatory flow past a finite-span wing at low Reynolds number. J Fluid Mech 571:327–357

    Article  MATH  Google Scholar 

  • Poelma C, Dickson WB, Dickinson MH (2006) Time-resolved reconstruction of the full velocity field around a dynamically-scaled flapping wing. Exp Fluids 41:213–225

    Article  Google Scholar 

  • Pullin DI, Wang ZJ (2004) Unsteady forces on an accelerating plate and application to hovering insect flight. J Fluid Mech 509:1–21

    Article  MathSciNet  MATH  Google Scholar 

  • Raffel M, Willert CE, Wereley ST, Kompenhans J (2007) Particle image velocimetry: a practical guide. Springer, Berlin

    Google Scholar 

  • Ringuette MJ, Milano M, Gharib M (2007) Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates. J Fluid Mech 581:453–468

    Article  MATH  Google Scholar 

  • Saffman PG (1992) Vortex dynamics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Sfakiotakis M, Lane DM, Davies BC (1999) Review of fish swimming modes for aquatic locomotion. IEEE J Oceanic Eng 24:237–252

    Article  Google Scholar 

  • Stanley D, Altman A (2009) Experiments in vortex formation on flapping flat plates. In: 47th AIAA Aerospace Sciences Meeting and Exhibit, 2009-389, pp 1–15

  • Suryadi A, Ishii T, Obi S (2010) Stereo piv measurement of a finite, flapping rigid plate in hovering condition. Exp Fluids 49:447–460

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Taylor G (1952a) The action of waving cylindrical tails in propelling microscopic organisms. Proc R Soc Lond A 211:225–239

    Article  MATH  Google Scholar 

  • Taylor GI (1952b) Analysis of the swimming of long and narrow animals. Proc R Soc Lond A 214:158–183

    Google Scholar 

  • Ting SC, Yang JT (2009) Extracting energetically dominant flow features in a complicated fish wake using singular-value decomposition. Physics of Fluids 21:041,901

    Article  Google Scholar 

  • Triantafyllou GS, Triantafyllou MS, Grosenbaugh MA (1993) Optimal thrust development in oscillating foils with application to fish propulsion. J Fluids Struct 7:205–224

    Article  Google Scholar 

  • Tytell ED, Lauder GV (2008) Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus. J Exp Biol 211:3359–3369

    Article  Google Scholar 

  • Westerweel J, Dabiri I, Gharib M (1997) The effect of a discrete window offset on the accuracy of cross-correlation analysis of piv recordings. Exp Fluids 23:20–28

    Article  Google Scholar 

  • Willert CE, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10:181–193

    Article  Google Scholar 

  • Wolfgang MJ, Anderson JM, Grosenbaugh MA, Yue DKP, Triantafyllou MS (1999) Near-body flow dynamics in swimming fish. J Exp Biol 202:2303–2327

    Google Scholar 

  • Wu JC (1981) Theory for aerodynamic force and moment in viscous flows. AIAA J 19(4):432–441

    Article  MATH  Google Scholar 

Download references

Acknowledgments

We would like to thank the reviewers for their insightful comments and suggestions, which have strengthened the manuscript.

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  1. State University of New York at Buffalo, 318 Jarvis Hall, Buffalo, NY, 14260, USA

    Adam C. DeVoria & Matthew J. Ringuette

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  1. Adam C. DeVoria
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  2. Matthew J. Ringuette
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Correspondence to Matthew J. Ringuette.

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DeVoria, A.C., Ringuette, M.J. On the flow generated on the leeward face of a rotating flat plate. Exp Fluids 54, 1495 (2013). https://doi.org/10.1007/s00348-013-1495-5

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