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Periodically plunging foil near a free surface

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Abstract

Experiments were performed to investigate the effects of amplitude and depth on the drag reduction of a NACA 0012 airfoil plunging near a free surface for a range of frequencies. Beyond the effect of the free surface, at low Strouhal numbers based on amplitude, Sr A, the drag reduction follows a parabolic trend with greater effect for greater amplitude, similar to the Garrick predictions. At Sr A ≈ 0.08, larger amplitudes break from this trend due to leading-edge vortex formation. As a result, smaller amplitudes become preferable for Sr A > 0.12. In addition, for the first time, vortex lock-in is documented experimentally. The effect of depth is twofold; firstly with decreasing depth, there is a general departure from the Garrick trends. Secondly, a reduction in thrust is observed around a constant unsteady parameter of τ = U ∞ 2πf/g ≈ 0.25; around this value significant free-surface waves form that detract from thrust creation. For depths greater than two chord lengths, there is negligible free-surface effect.

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Abbreviations

a :

Amplitude of plunging motion

A :

Peak-to-peak amplitude of plunging motion

C d :

Time-averaged drag coefficient

C d0 :

Time-averaged drag coefficient for the stationary foil

c :

Chord length

d :

Depth

f :

Frequency

h :

Foil position

Fr :

Froude number, \( U_{\infty } /\sqrt {gc} \)

Re :

Reynolds number, ρU ∞ c/μ

Sr c :

Strouhal number based on chord, fc/U ∞

Sr A :

Strouhal number based on amplitude, 2fa/U ∞

t :

Time t = 0 is top of motion

T :

Plunge period

U ∞ :

Freestream velocity

α :

Angle of attack

λ w :

Wavelength of water wave

μ :

Viscosity

ρ :

Density

τ:

Unsteady parameter, U ∞ 2πf/g

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Acknowledgments

The authors would like to acknowledge the support from the Department of the Navy Grant N62909-10-1-7117 issued by the Office of Naval Research Global.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK

    D. J. Cleaver, D. E. Calderon, Z. Wang & I. Gursul

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  1. D. J. Cleaver
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  2. D. E. Calderon
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  3. Z. Wang
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  4. I. Gursul
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Correspondence to I. Gursul.

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Cleaver, D.J., Calderon, D.E., Wang, Z. et al. Periodically plunging foil near a free surface. Exp Fluids 54, 1491 (2013). https://doi.org/10.1007/s00348-013-1491-9

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