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The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

Published online by Cambridge University Press:  30 April 2008

JAMES H. J. BUCHHOLZ  and
ALEXANDER J. SMITS
JAMES H. J. BUCHHOLZ
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
ALEXANDER J. SMITS
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
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Abstract

Thrust performance and wake structure were investigated for a rigid rectangular panel pitching about its leading edge in a free stream. For ReC = O(104), thrust coefficient was found to depend primarily on Strouhal number St and the aspect ratio of the panel AR. Propulsive efficiency was sensitive to aspect ratio only for AR less than 0.83; however, the magnitude of the peak efficiency of a given panel with variation in Strouhal number varied inversely with the amplitude to span ratio A/S, while the Strouhal number of optimum efficiency increased with increasing A/S. Peak efficiencies between 9% and 21% were measured. Wake structures corresponding to a subset of the thrust measurements were investigated using dye visualization and digital particle image velocimetry. In general, the wakes divided into two oblique jets; however, when operating at or near peak efficiency, the near wake in many cases represented a Kármán vortex street with the signs of the vortices reversed. The three-dimensional structure of the wakes was investigated in detail for AR = 0.54, A/S = 0.31 and ReC = 640. Three distinct wake structures were observed with variation in Strouhal number. For approximately 0.20 < St < 0.25, the main constituent of the wake was a horseshoe vortex shed by the tips and trailing edge of the panel. Streamwise variation in the circulation of the streamwise horseshoe legs was consistent with a spanwise shear layer bridging them. For St > 0.25, a reorganization of some of the spanwise vorticity yielded a bifurcating wake formed by trains of vortex rings connected to the tips of the horseshoes. For St > 0.5, an additional structure formed from a perturbation of the streamwise leg which caused a spanwise expansion. The wake model paradigm established here is robust with variation in Reynolds number and is consistent with structures observed for a wide variety of unsteady flows. Movies are available with the online version of the paper.

JFM classification

Wakes/Jets: Wakes Wakes/Jets: Vortex streets Biological Fluid Dynamics: Propulsion
Type
Papers
Information
Journal of Fluid Mechanics , Volume 603 , 25 May 2008 , pp. 331 - 365
Copyright
Copyright © Cambridge University Press 2008

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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
Buchholz, J. H. J. & Smits, A. J. 2005 Gallery of fluid motion: the wake of a low aspect ratio pitching plate. Phys. Fluids 17, 091102-1.CrossRefGoogle Scholar
Buchholz, J. H. J. & Smits, A. J. 2006 On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 546, 433–443.CrossRefGoogle Scholar
Buchholz, J. H. J., Jiménez, J. M., Allen, J. J. & Smits, A. J. 2003 Hydrodynamics of thrust production in a fish-like flapping membrane. In 13th Intl. Symp. on Unmanned Untethered Submersible Technology. University of New Hampshire, Durham, NH.Google Scholar
Buchholz, J. H. J., Clark, R. P. & Smits, A. J. 2008 Thrust performance of unsteady propulsors using a novel measurement system, and concurrent wake patterns. Exps. Fluids (in press).CrossRefGoogle Scholar
Clark, R. P. & Smits, A. J. 2006 Thrust production and wake structure of a batoid-inspired oscillating fin. J. Fluid Mech. 562, 415–429.CrossRefGoogle ScholarPubMed
Dabiri, J. O. & Gharib, M. 2005 Starting flow through nozzles with temporally variable exit diameter. J. Fluid Mech. 538, 111–136.CrossRefGoogle Scholar
Delo, C. J., Kelso, R. M. & Smits, A. J. 2004 Three-dimensional structure of a low-Reynolds-number turbulent boundary layer. J. Fluid Mech. 512, 47–83.CrossRefGoogle Scholar
Dong, H., Mittal, R., Bozkurttas, M. & Najjar, F. 2005 Wake structure and performance of finite aspect-ratio flapping foils. AIAA Paper 2005-0081.CrossRefGoogle Scholar
Drucker, E. G. & Lauder, G. V. 1999 Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using particle image velocimetry. J. Exp. Biol. 202, 2393–2412.CrossRefGoogle ScholarPubMed
von Ellenrieder, K. D., Parker, K. & Soria, J. 2003 Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129–138.CrossRefGoogle Scholar
Freymuth, P. 1988 Propulsive vortical signature of plunging and pitching airfoils. AIAA J. 27 (9), 1200–1205.Google Scholar
Gharib, M., Rambod, E. & Shariff, K 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Govardhan, R. & Williamson, C. H. K. 2005 Vortex-induced vibrations of a sphere. J. Fluid Mech. 531, 11–47.CrossRefGoogle Scholar
Guglielmini, L. 2004 Modeling of thrust generating foils. PhD thesis, University of Genoa.Google Scholar
Jiménez, J. M. 2002 Low Reynolds number studies in the wake of a submarine model using particle image velocimetry. Master's thesis, Princeton University.Google Scholar
Jiménez, J. M., Buchholz, J. H. J., Staples, A. E., Allen, J. J. & Smits, A. J. 2003 Flapping membranes for thrust production. In IUTAM Symp. on Integrated Modeling of Fully Coupled Fluid–Structure Interactions Using Analysis, Computations, and Experiments, Rutgers University, New Brunswick, NJ (ed. Benaroya, H. & Wei, T.), pp. 115–24. Kluwer.CrossRefGoogle Scholar
Jones, K. D., Dohring, C. M. & Platzer, M. F. 1998 Experimental and computational investigation of the Knoller–Betz effect. AIAA J. 36, 1240–1246.CrossRefGoogle Scholar
Koochesfahani, M. M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27, 1200–1205.CrossRefGoogle Scholar
Lighthill, M. J. 1963 Introduction. Boundary layer theory. In Laminar boundary Layers (ed. Rosenhead, L.), pp. 46–113. Oxford University Press.Google Scholar
Lim, T. T. 2000 Dye and smoke visualization. In Flow Visualization: Techniques and Examples (ed. Smits, A. J. & Lim, T. T.), pp. 43–72. Imperial College Press, London.CrossRefGoogle Scholar
Milano, M. & Gharib, M. 2005 Uncovering the physics of flapping flat plates with artificial evolution. J. Fluid Mech. 534, 403–409.CrossRefGoogle Scholar
Ohmi, K., Coutanceau, M., Loc, T. P. & Dulieu, A. 1990 Vortex formation around an oscillating and translating airfoil at large incidences. J. Fluid Mech. 211, 37–60.CrossRefGoogle Scholar
Ohmi, K., Coutanceau, M., Daube, O. & Loc, T. P. 1991 Further experiments on vortex formation around an oscillating and translating airfoil at large incidences. J. Fluid Mech. 225, 607–630.CrossRefGoogle Scholar
Oshima, Y. & Natsume, A. 1980 Flow field around an oscillating airfoil. In Flow Visualization II. Proc. Second Intl Symp. on Flow Visualization, Bochum, W. Germany (ed. Merzkirch, W.). Hemisphere.Google Scholar
Oshima, Y. & Oshima, K. 1980 Vortical flow behind an oscillating airfoil. In Proc. 15th Congress, Intl. Union of Theoretical and Applied Mechanics Amsterdam: North Holland.Google Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.CrossRefGoogle Scholar
Raffel, M., Willert, C. & Kompenhans, J. 1998 Particle Image Velocimetry. Springer.CrossRefGoogle Scholar
Triantafyllou, G. S., Triantafyllou, M. S. & Grosenbaugh, M. A. 1993 Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluid Struct. 7, 205–224.CrossRefGoogle Scholar
Triantafyllou, M. S. & Triantafyllou, G. S. 1995 An efficient swimming machine. Sci. Am. 272, pp. 64–70.CrossRefGoogle Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Gopalkrishnan, R. 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids A 3 (12), 2835–2837.CrossRefGoogle Scholar
Tytell, E. D. & Lauder, G. V. 2004 The hydrodynamics of eel swimming–I. Wake structure. J. Exp. Biol. 207, 1825–1841.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
Wu, J. Z. & Wu, J. M. 1996 Vorticity dynamics on boundaries. In Adv. Appl. Mech. (ed. Hutchison, J. W. & Wu, T. Y.), vol. 32, pp. 119–275. Academic.Google Scholar

Buchholz and Smits supplementary movie

Movie 1. This movie corresponds to figure 12(b) in the paper. Panel 2 (S/C=0.83) is shown, pitching in water, with St=0.21, A/S=0.31, ReC=36 000 (St=fA/U, S being the panel span, C the panel chord, A the peak-to-peak transverse amplitude of the trailing edge, f the pitching frequency, and U the free-stream velocity). This is the optimal Strouhal number for this combination of S/C and A/S with a propulsive efficiency of 21%. The temporal evolution of the structures is illustrated using rhodamine B (red) and fluorescein (green) dyes injected from spanwise arrays of dye ports on each side of a stationary fairing supporting the panel by its leading edge. From the perspective shown here, rhodamine B dye is injected from the top side of the fairing and fluorescein dye is injected from the bottom side. In the near wake, the vortices have an approximately axisymmetric shape forming a wake with the appearance of a reverse von Karman vortex street (note that the green vortices are on top whereas the red ones are below). However, as the structures convect downstream, they spread in the transverse direction, eventually losing their coherence.

Download Buchholz and Smits supplementary movie(Video)
Video 4.1 MB

Buchholz and Smits supplementary movie

Movie 2. This movie corresponds to figure 12(c) in the paper. Panel 2 is shown (S/C=0.83) with St=0.41, A/S=0.31, ReC=18 000. The dye patterns suggest the creation of two distinct vortices in each pitching cycle as at St=0.21; however, in this case, they break down within a fraction of a cycle. Portions of the vortices can be seen migrating to the opposite side, forming a bifurcating wake with two jet-like structures.

Download Buchholz and Smits supplementary movie(Video)
Video 4.2 MB

Buchholz and Smits supplementary movie

Movie 3. This movie corresponds to figure 26 in the paper. Panel 1 is shown (S/C=0.54) with St=0.64, A/S=0.31, ReC=640, illuminated with halogen light. The movie clarifies the development of the perturbations in the streamwise vortices with respect to the phase of the panel motion. Green structures are shed as the panel pitches down and red structures are shed as the panel pitches up. Growth of the hairpin is initiated one half-cycle after the creation of the structure during the generation of the opposite-signed structure.

Download Buchholz and Smits supplementary movie(Video)
Video 5.9 MB