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Vortex structure for flow over a heaving cylinder with a flexible tail

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Abstract

Hydrogen-bubble visualization technique was applied in the investigation of vortex structure for flow over a heaving cylinder attached with a flexible tail along the wake central-line in a water channel. Wake structures have been mapped in the flexible tail length-frequency (L/D, St) phase space with the flexible tail length of L/D = 2–5 and the oscillation Strouhal number of St = 0–0.34. Four wake modes were identified as: (1) 2S_Kármán vortex mode—a Kármán-vortex-like structure with two single vortices formed per cycle in the near wake; (2) 2S_reverse Kármán vortex mode—a reverse Kármán-vortex-like structure with two single vortices per cycle; (3) 2P mode—a bifurcated vortex pair structure with two pairs of vortices per cycle; (4) P + S mode—an unstable vortex structure with three vortices per cycle as a transient mode. Moreover, the typical case of each wake mode was further examined by particle image velocimetry, and the evolutions of vortex structures for the four wake modes were studied in detail.

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Abbreviations

L :

Chord length of flexible tail

D :

Cylinder diameter

St :

Strouhal number defined by the amplitude of the foil’s leading edge or cylinder center

2S:

Two single vortices are shed per cycle of cylinder oscillation

2P:

Two pairs of vortices are shed per cycle of cylinder oscillation

PIV:

Particle image velocimetry

λ*:

Non-dimensional wavelength

St A :

Strouhal number defined by the maximum excursion of the foil’s trailing edge

Re :

Reynolds number

U ∞ :

Free-stream velocity

S :

Displacement of cylinder center

a :

Oscillation amplitude of cylinder center

f :

Oscillation frequency

Π :

Effective stiffness

\(\bar{\rho }\) :

Density ratio

\(\varLambda_{\text{ci}}\) :

Swirling strength

ω z :

Vorticity

ϕ :

Phase angle

l :

Distance between the point on the flexible tail and the leading edge of the tail

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Acknowledgments

The present research is supported by NSFC (10832001 and 11302018).

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Authors and Affiliations

  1. Institute of Fluid Mechanics, Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing, 100191, People’s Republic of China

    Y. Hu, C. Pan & J. J. Wang

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  1. Y. Hu
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  2. C. Pan
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  3. J. J. Wang
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Correspondence to J. J. Wang.

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Hu, Y., Pan, C. & Wang, J.J. Vortex structure for flow over a heaving cylinder with a flexible tail. Exp Fluids 55, 1682 (2014). https://doi.org/10.1007/s00348-014-1682-z

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