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  • Journal of Fluid Mechanics, Volume 675
  • May 2011, pp. 495-517

Optimal frequency for flow energy harvesting of a flapping foil

  • QIANG ZHU (a1)
  • DOI:
  • Published online: 10 March 2011

Inspired by the correlation between the propulsion efficiency of a flapping foil propeller and stability of the wake behind it (which leads to the optimal Strouhal number for propulsion), we numerically simulated a heaving/pitching foil in energy harvesting regime, and investigated the relation between wake stability and the energy harvesting efficiency. The base flow is computed using a Navier–Stokes algorithm and the stability analysis is performed via the Orr–Sommerfeld equation. The wake is found to be convectively unstable and the frequency of the most unstable mode fw is determined. The case when fw ~ f coincides with maximum energy harvesting efficiency of the system (f is the frequency of foil oscillation), suggesting that flow energy extraction is closely related to efficient evolution of the wake. This occurs at a frequency of f ~ 0.15 (f is normalized by the chord length and the flow speed), under the constraint that there is significant vortex shedding from the leading edge at sufficiently large effective angles of attack. Indeed, this ‘foil–wake resonance’ is usually associated with multi-vortex shedding from the leading edge. Furthermore, detailed examination of energy extractions from the heaving and the pitching motions indicates that near the optimal performance point the average energy extraction from the pitching motion is close to zero. This suggests the feasibility of achieving high-efficient energy harvesting through a simple fully passive system we proposed earlier in which no activation is needed.

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A. Barrero-Gil , G. Alonso & A. Sanz-Andres 2010 Energy harvesting from transverse galloping. J. Sound Vib. 329, 28732883.

M. M. Bernistas , K. Raghavan , Y. Ben-Simon & E. M. H. Garsiz 2008 Vivace (vortex induced vibration aquatic clean energy): a new concept in generation of clean and renewable energy from fluid flow. J. Offshore Mech. Arctic Engng 130, 041101.

A. Betz 1966 Introduction to the Theory of Flow Machines. Pergamon.

G. Dumas & T. Kinsey 2006 Eulerian simulations of oscillating airfoils in power extraction regime. In Advances in Fluid Mechanics VI, pp. 245254. WIT.

L. Guglielmini & P. Blondeaux 2004 Propulsive efficiency of oscillating foils. Eur. J. Mech., B/Fluids 23, 255278.

T. Kinsey & G. Dumas 2008 Parametric study of an oscillating airfoil in a power-extraction regime. AIAA J. 46, 13181330.

W. McKinney & J. DeLaurier 1981 The wingmill: an oscillating-wing windmill. J. Energy 5, 109115.

Z. Peng & Q. Zhu 2009 Energy harvesting through flow-induced oscillations of a foil. Phys. Fluids 21, 123602.

E. Shimizu , K. Isogai & S. Obayashi 2008 Multiobjective design study of a flapping wing power generator. J. Fluid Engng 130, 021104.

G. S. Triantafyllou , K. Kupfer & A. Bers 1987 Absolute instabilities and self-sustained oscillations in the wakes of circular-cylinders. Phys. Rev. Lett. 59, 19141917.

G. S. Triantafyllou , M. S. Triantafyllou & M. A. Grosenbaugh 1993 Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7, 205224.

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

Q. Zhu , M. Haase & C. H. Wu 2009 Modeling the capacity of a novel flow-energy harvester. Appl. Math. Model. 33, 22072218.

Q. Zhu & Z. Peng 2009 Mode coupling and flow energy harvesting by a flapping foil. Phys. Fluids 21, 033601.

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