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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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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