Research Papers: Ocean Engineering

Dynamic Response of a Sphere Immersed in a Shallow Water Flow

[+] Author and Article Information
D. Mirauda

School of Engineering,
Basilicata University,
viale dell'Ateneo Lucano 10,
Potenza 85100, Italy
e-mail: domenica.mirauda@unibas.it

A. Volpe Plantamura

School of Engineering,
Basilicata University,
viale dell'Ateneo Lucano 10,
Potenza 85100, Italy
e-mail: antonio.volpeplantamura@unibas.it

S. Malavasi

Department of Civil and
Environmental Engineering,
Politecnico di Milano,
piazza Leonardo da Vinci 32,
Milano 20133, Italy
e-mail: stefano.malavasi@polimi.it

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received June 29, 2011; final manuscript received November 17, 2013; published online January 20, 2014. Assoc. Editor: Antonio C. Fernandes.

J. Offshore Mech. Arct. Eng 136(2), 021101 (Jan 20, 2014) (6 pages) Paper No: OMAE-11-1055; doi: 10.1115/1.4026110 History: Received June 29, 2011; Revised November 17, 2013

This work analyzes the dynamic response of a sphere located close to the floor of a hydraulic channel within steady free-surface current flows. The sphere is free to move in transverse (y) and streamwise (x) directions, and it is characterized by a mass ratio m* equal to 1.34. The oscillation amplitudes and the frequencies of the sphere have been measured by means of the image analysis of a charge coupled device (CCD) camera. The experimental data show a significant influence of the free surface on the sphere movement and highlight a different behavior of the dynamic response to the increasing of the water level on the upper part of the body.

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Sarpkaya, T., 1979, “Vortex-Induced Oscillations,” ASME J. Appl. Mech., 46, pp. 241–258. [CrossRef]
Bearman, P. W., 1984, “Vortex Shedding From Oscillating Bluff Bodies,” Annu. Rev. Fluid Mech., 16, pp. 195–222. [CrossRef]
Williamson, C. H. K., and Govardhan, R., 2004, “Vortex-Induced Vibrations,” Annu. Rev. Fluid Mech., 36, pp. 413–455. [CrossRef]
Blevins, R. D., 1990, Flow-Induced Vibrations, Reinhold, New York.
Anagnostopoulos, P., 2002, Flow-Induced Vibrations in Engineering Practice, WIT, Southampton, UK.
Govardhan, R., and Williamson, C. H. K., 1997, “Vortex Induced Motions of a Tethered Sphere,” J. Wind Eng. Ind. Aerodyn., 69–71, pp. 375–385. [CrossRef]
Govardhan, R., and Williamson, C. H. K., 2005, “Vortex Induced Vibration of a Sphere,” J. Fluid Mech., 531, pp. 11–47. [CrossRef]
Williamson, C. H. K., and Govardhan, R., 1997, “Dynamics and Forcing of a Tethered Sphere in a Fluid Flow,” J. Fluids Struct., 11, pp. 293–305. [CrossRef]
Jauvtis, N., Govardhan, R., and Williamson, C. H. K., 2001, “Multiple Modes of Vortex-Induced Vibration of a Sphere,” J. Fluids Struct., 15, pp. 555–563. [CrossRef]
Mirauda, D., Volpe Plantamura, A., and Malavasi, S., 2011, “Boundaries Effects on the Movements of a Sphere Immersed in a Free Surface Flow,” ASME J. Offshore Mech. Arct. Eng, 133, 041301. [CrossRef]
Franzetti, S., Greco, M., Malavasi, S., and Mirauda, D., 2005, “Flow Induced Excitation on Basic Shape Structures,” Vorticity and Turbulence Effects in Fluid Structure Interaction, M.Brocchini and F.Trivellato, eds., WIT, Southampton, UK, pp. 131–156.
Naudascher, E., and Rockwell, D., 1994, Flow-Induced Vibrations: An Engineering Guide, Balkema, Leiden, The Netherlands.
Negri, M., Cozzi, F., and Malavasi, S., 2011, “Self-Synchronized Phase Averaging of PIV Measurements in the Base Region of a Rectangular Cylinder,” Meccanica, 46(2), pp. 423–435. [CrossRef]


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Fig. 1

Normalized amplitude (A*x/A*y) versus m* for different tethered spheres. The ratio is measured for conditions of maximum A*y [7].

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Fig. 2

Transverse amplitude ratio A* in function of U* for spheres with: (a) m*= 0.8, (b) m*= 2.8, and (c) m*= 28 [9]

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Fig. 3

Dynamic response of a sphere with m*= 1.34: (a) transverse amplitude ratio A*y and (b) sphere location [10]. h*= 0 sphere near the free surface; h*= 2 sphere completely immersed; h*= 3.97 sphere near the channel floor.

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Fig. 4

Typical trajectories of the heavy sphere motion (m*= 1.34) at the increasing of the Reynolds number or of the normalized velocity (data from Mirauda et al. [10]) for: (a) h*= 2, (b) h*= 3.97, and (c) h*= 0

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Fig. 5

Sketches of the channel cross section for the seven setups considered with the sphere having mass ratio m*= 1.34 and damping ratio ζ = 0.004

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Fig. 6

Sphere trajectories for the different considered setups in the condition of maximum transverse oscillation amplitude (y): (a) h*= 0, (b) h*= 0.16, (c) h*= 0.31, (d) h*= 0.5, (e) h*= 0.75, (f) h*= 1, and (g) h*= 2

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Fig. 7

Sphere trajectories for different normalized velocity (U*) at: (a) h*= 0; (b) h*= 0.31; (c) h*= 0.75; and (d) h*= 1

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Fig. 8

Normalized amplitudes (A*y and A*x) and transverse frequency ratios (fy*) in function of U*: (a), (c), and (e) at high relative submergences (h*≥0.75); (b), (d), and (f) at low relative submergences (h*≤ 0.5)

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Fig. 9

Evolution in the time of transverse displacements normalized with the diameter of the sphere (D) for high relative submergences (h* ≥ 0.75): (a) mode I and (b) mode II

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Fig. 10

Evolution in the time of transverse displacements normalized with the diameter of the sphere (D) for low relative submergences (0 < h*≤ 0.5) in correspondence of the mode I



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