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TECHNICAL PAPERS

Experimental Simulation of Fish-Inspired Unsteady Vortex Dynamics on a Rigid Cylinder

[+] Author and Article Information
Promode R. Bandyopadhyay, John M. Castano, William H. Nedderman

Naval Undersea Warfare Center, Newport, RI 02841

Martin J. Donnelly

Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Fluids Eng 122(2), 219-238 (Dec 08, 1999) (20 pages) doi:10.1115/1.483274 History: Received June 29, 1999; Revised December 08, 1999
Copyright © 2000 by ASME
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References

Bandyopadhyay,  P. R., Castano,  J. M., Rice,  J. Q., Philips,  R. B., Nedderman,  W. H., and Macy,  W. K., 1997, “Low-Speed Maneuvering Hydrodynamics of Fish and Small Underwater Vehicles,” ASME J. Fluids Eng., 119, pp. 136–144.
Bandyopadhyay,  P. R., Nedderman,  W. H., and Dick,  J., 1999, “Biologically-Inspired Bodies Under Surface Waves. Part 1: Load Measurements,” ASME J. Fluids Eng., 121, pp. 469–478.
Bandyopadhyay,  P. R., Singh,  S. N., and Chockalingam,  F., 1999, “Biologically-Inspired Bodies Under Surface Waves. Part 2: Theoretical Control of Maneuvering,” ASME J. Fluids Eng., 121, pp. 479–487.
Jones, K. D., Dohring, C. M., and Platzer M. F., 1996, “Wake Structures Behind Plunging Airfoils: A Comparison of Numerical and Experimental Results,” Paper No. AIAA 96-0078.
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Gopalkrishnan,  R., Triantafyllou,  M. S., Triantafyllou,  G. S., and Barrett,  D., 1994, “Active Vorticity Control in a Shear Flow Using a Flapping Foil,” J. Fluid Mech., 274, pp. 1–21.
Hall,  K. C., and Hall,  S. R., 1996, “Minimum Induced Power Requirements for Flapping Flight,” J. Fluid Mech., 323, pp. 285–315.
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Webb, P. W. 1978, “Hydrodynamics: Nonscombroid Fish,” Fish Physiology, Vol. VII, eds., W. S. Hoar and D. I. Randall, Academic Press, pp. 189–237.
Anderson,  J. M., Streitlien,  K., Barrett,  D. S., and Triantafyllou,  M. S., 1998, “Oscillating Foils of High Propulsive Efficiency,” J. Fluid Mech., 360, pp. 41–72.
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Triantafyllou,  M. S., Triantafyllou,  G. S., and Gopalkrishnan,  R., 1991, “Wake Mechanics for Thrust Generation in Oscillating Foils,” Phys. Fluids, 3, No 12, pp. 2835–2837.
Fein, J., 1998, “Dolphin Drag Reduction: Myth or Magic,” Proc. Intl. Sympo. Seawater Drag Reduction, NUWC, Newport, RI. pp. 429–434.
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Rohr, J. J., Hendricks, E. W., Quigley, L., Fish, F. E., Gilpatrick, J. W., Scardina-Ludwig, J., 1998, “Observations of Dolphin Swimming Speed and Strouhal Number,” Tech. Rept. 1769, US Navy Space and Naval Warfare Systems Center, San Diego, CA.
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Bandyopadhyay, P. R., Nedderman, W. H., Castano, J. M., and Donnelly, M. J., 1996, “ A Small Maneuvering Device for Energetic Environment,” NUWC-NPT Video, Naval Undersea Warfare Center Division, Newport, RI.
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Figures

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Manifestations, namely natural and forced, of momentum transfer from flapping foils. (a) Unsteady and continuous distribution of vorticity in wake; (b) discretization (or wrapping) of unsteady vorticity layer in wake via a natural instability process; (c) forced discretization (or wrapping) of vorticity via salient edge separation at flap trailing edge, “bypassing” natural instability process.
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Estimated steady state drag on the basic cylinder model shown in Fig. 6. Horizontal axis: speed of water (cm/s).
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Ensemble averaged time trace of axial force on the model shown in Fig. 6. Positive axial force indicates thrust.
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Measurements of dolphin tail beat frequency, reproduced from Rohr et al. 17. Legend: Fish 15: □-Tursiops Truncatus; Rohr et al. 17 ▴-Tursiops Truncatus, X-Pseudorca Crassidens; Lang and Daybell 18: ▪ - Lagenorhyncus Obliquidens. This data is modeled in the present work as a family of parallel lines each being for a characteristic dolphin length.
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Reproduced from Rohr et al. 17. Data in Fig. 4 is replotted expressing swimming speed as body lengths traveled per second. Legend: Fish 15: □-Tursiops Truncatus; Rohr et al. 17: ▴-Tursiops Truncatus, X-Pseudorca Crassidens; Lang and Daybell 18: ▪-Lagenorhyncus Obliquidens; Kayan and Pyatetskiy 19: — Tursips.
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Schematic diagram of the dual flapping foil device mounted at the end of the tail cone of a rigid cylinder. Axis z is along span of flap.
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Photograph of water tunnel model of the dual flapping foil device. Dual flapping foils and divider plate are shown at the right end; to the left of foils lie the actuators, two phase transducers, and actuator control circuits. The six-component load cell is located at the junction of the strut and cylinder.
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The caudal fins of seals and sea lions are examples of dual-flapping foils which make them wonderful swimmers
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Schematic of second model. A software operated digital controller is used to select the phase lag of the nose slider actuator relative to the two flap actuators which operate in phase, called waving mode here (as opposed to clapping mode where they operate in anti-phase).
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Photograph of second model and digital controller of actuators
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Variation of nose slider depth with actuator voltage and frequency
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(a) Flow visualization tests of clapping mode: flaps closing (top, graphic depiction; bottom, photograph) (b) Flow visualization tests of clapping mode: flaps opening (top, graphic depiction; bottom, photograph) (c) Flow visualization tests of waving mode: flaps toward port (top, graphic depiction; bottom, photograph) (d) Flow visualization tests of waving mode: flaps toward starboard (top, graphic depiction; bottom, photograph).
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Ensemble-averaged coefficient of axial force (ca) due to a single flapping foil; positive values indicate thrust (ct) and negative values indicate drag (cd);U=20 cm/s: (a) 2.6 Hz, (b) 4.24 Hz, and (c) 6.2 Hz. LVDT signature indicates flap phase≡highest values: flap fully open; lowest values, flap fully closed.
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Ensemble-averaged axial force and flap opening due to dual-flapping foils in clapping mode. High LVDT values≡flap fully open; low LVDT values≡flap fully closed. The flaps are actually in opposite phase. (a) 2.6 Hz; (b) 4.24 Hz; (c) 6.2 Hz.
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Ensemble-averaged (a) axial force, (b) yawing moment, and (c) flap phase in waving mode; U=20 cm/s/s;f=6.2 Hz. The flaps are actually in phase.
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Comparison of measurements of axial force (thrust) coefficient
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Phased-average measurements of axial jet speed due to dual-flapping foil. Axial velocities shown are relative to U of 20 cm/s. Measurements in two different planes are compared.
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Measurements of the axial force efficiency of the dual-flapping foils
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Estimated efficiency of dual-flapping foils. Estimated values of bare body drag (viscous+form) removed from measurements of total efficiency (rigid body+flapping foils) shown in Fig. 18.
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Summary of all single- and dual-flap axial force coefficients. Solid line: Two-dimensional discrete Vortex Shedding Model of Bandyopadhyay 26. Both thrust- and drag-producing cases are shown. Note that body drag is included in axial force.
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(a) The variation of time-averaged axial force with Strouhal number in the single foil-rigid body cases; (b) the variation of time-averaged yawing moment with Strouhal number in the single foil-rigid body case
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(a) Sensitivity of unsteady axial force in single flapping foils to flapping frequency at St=0.3; (b) sensitivity of unsteady yawing moment in single flapping foils to flapping frequency at St=0.3
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Vorticity-velocity vector plots in the axial plane for clapping. The velocity perturbations are with respect to freestream velocity. Filled squares on the y-axis indicate the location of flap trailing edge in this and succeeding figures. Note that, when the flap is at outboard extremity, the outer-most vortex trajectory is at 70 deg to the x-axis which is much larger than the flap trailing edge angle of 30 deg.
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Vorticity-velocity vector maps in the axial plane in the waving mode.
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Vorticity-velocity vector maps in the axial plane in the clapping mode
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Vorticity-velocity vector maps in the cross-stream plane in the waving mode; x/D=0.066. Filled square markers at z/D=0.5 within each frame indicate flap location.
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Vorticity-velocity vector maps in the cross-stream plane in the clapping mode; x/D=0.066. Filled square markers at z/D=0.5 within each frame indicate flap location.
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Vortex circulation versus flap phase; starboard flap x/D=0.0656, (a) waving and (b) clapping
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Circulation distribution at a downstream station (x/D=0.5577) compared to that in Fig. 28, (a) waving and (b) clapping
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Schematic diagram showing the inward trajectory of the inner shed axial vortex (a) as opposed to the outer shed axial vortex (b) in both modes of flap oscillation
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Schematic of production of drag (momentum deficit) and yaw force due to a Kármán vortex train
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Schematic of production of thrust (momentum excess) and yaw force due to a negative Kármán vortex train
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Schematic of vortex train in clapping mode showing the origin of axial and crossstream force vectors
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Schematic of vortex train in waving mode showing the origin of axial and crossstream force vectors
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Ensemble averaged trace of axial force on the model. Tail flap St=0.25–0.35. Nose slider: (a) off, (b) on.
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Effect of phase lag of nose slider on axial force. Tail flap St=0.13. Lag: (a) 120 deg, (b) 300 deg.
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Ensemble averaged time trace of axial force on the model. (a) Nose slider phase lag: 0 deg; (b) 60 deg; (c) 120 deg; (d) 180 deg; (e) 240 deg; (f ) 300 deg.
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Variation of time-averaged axial thrust with phase lag of nose slider. Speed, frequency and tail flap St: (a) 16.2–21.0 cm/s, 3.77 Hz and 0.6–0.46; (b) 27.4–30.5 cm/s; 3.64 Hz and 0.375–0.337; (c) 36–38 cm/s; 3.65 Hz and 0.276–0.263.
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Schematics of mechanism of vortex interaction: (a) effect of unsteadiness of a vorticity source on vortex trajectory and (b) mechanism of thrust modulation

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