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Research Papers: Ocean Engineering

Simultaneous Wake- and Vortex-Induced Vibrations of a Cylinder With Two Degrees of Freedom in Each Direction

[+] Author and Article Information
J. R. Chaplin

Faculty of Engineering and the Environment,
University of Southampton,
Highfield, Southampton SO17 1BJ, UK
e-mail: j.r.chaplin@soton.ac.uk

W. M. J. Batten

Faculty of Engineering and the Environment,
University of Southampton,
Highfield, Southampton SO17 1BJ, UK
e-mail: w.m.batten@soton.ac.uk

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received September 10, 2013; final manuscript received April 22, 2014; published online May 19, 2014. Assoc. Editor: Celso P. Pesce.

J. Offshore Mech. Arct. Eng 136(3), 031101 (May 19, 2014) (9 pages) Paper No: OMAE-13-1086; doi: 10.1115/1.4027523 History: Received September 10, 2013; Revised April 22, 2014

The flow-induced vibration of one cylinder in the wake of another is the subject of continuing interest in connection with interactions between vertical tension risers in deep water. When one riser is downstream of another, it is likely to be subject to wake-induced and vortex-induced excitations at different frequencies simultaneously. Both are complex mechanisms, and it is reasonable to assume that they interact. To begin to understand this complicated process, it is desirable that any modeling should incorporate some features of a multidegree-of-freedom structural response. With this aim, this paper describes experiments in which one cylinder was free to undergo simultaneous wake- and vortex-induced vibrations downstream of a similar but stationary cylinder in a steady flow. The downstream cylinder was mounted on an elastic system that had two natural frequencies in both the in-line and cross-flow directions. Mass ratios were almost the same in all four modes. Measurements are presented of simultaneous wake- and vortex-induced vibrations for cylinder separations of 5 and 10 diameters in the in-line direction, and up to 4 diameters transversely. At a reduced velocity of 83 (based on the cylinder's lower submerged natural frequency) and a separation of 5 diameters, excursions of wake-induced vibrations peaked at almost 5 diameters, when the downstream cylinder was near the edge of the upstream cylinder's wake.

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References

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Figures

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Fig. 1

The concept of an elastic system for mounting a cylinder with two degrees of freedom in each direction in a wake

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Fig. 2

Layout of the elastic system on one side of the tank; m1 is replaced by a rotating mass

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Fig. 3

One side of the elastic support system for the downstream cylinder. The other side was a mirror image of this, on the same shafts and rollers. The stationary upstream cylinder is not shown.

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Fig. 4

The apparatus seen from one side of the tank. The flow is from left to right.

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Fig. 5

The two cylinders in the tank seen from below, with the upstream cylinder on the left

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Fig. 6

Configurations for the two series of initial tests

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Fig. 7

VIV amplitudes (a) and frequencies (b) of an isolated cylinder with two degrees of freedom. In (a), empty symbols refer to Ax, solid symbols to Ay. Trajectories above are plotted on axes one diameter long in each direction.

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Fig. 8

VIV amplitudes of an isolated cylinder with two degrees of freedom. Empty symbols refer to Ax, solid symbols to Ay.

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Fig. 9

Cross-flow amplitudes of a downstream cylinder at L = 5D, B = 0, with one degree of freedom and with four degrees of freedom

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Fig. 10

Spectra of the response of a downstream cylinder with one degree of freedom at L = 5D, B = 0, for (a) V/f0D = 4.5, (b) 9.9, (c) 13.8. Frequencies of the two dominant peaks are plotted in (d) in relation to the natural frequency of the system in air, as functions of the reduced velocity.

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Fig. 11

Time series of displacements of the downstream cylinder with four degrees of freedom at L = 5D, B = D, at V/fn2D = 13.2, V/fn1D = 136. Subscripts L and H denote the low- and high-frequency parts of the response that can be associated with wake- and vortex-induced vibrations. The dashed line in the top plot is the Hilbert transform of yH/D.

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Fig. 12

High (H) and low (L) frequency components of the trajectory of the downstream cylinder at L = 5D, B = D at (a) V/fn2D = 7.6; V/fn1D = 78, (b) 9.0; 93, (c) 11.4; 117, and (d) 13.2; 136. Trajectories of single high-frequency cycles (traversed clockwise) are superimposed in white. The flow is from left to right.

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Fig. 13

Amplitudes of low (left) and high (right) frequency components of displacements at (a) L = 5D, B = 0, (b) L = 5D, B = D, (c) L = 10D, B = 0, and (d) L = 10D, B = 2D. Present results are from the system with four degrees of freedom. Others (plotted on both sides) are from systems with one degree of freedom. Amplitudes in (e) and (f) are √2 times standard deviations. All others are means of the 10% highest peak excursions. Inset plots show relative cylinder positions.

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Fig. 14

Spectra of (a) in-line and (b) cross-flow responses of the downstream cylinder at L = 5D, B = D, V/fn2D = 13.2. For a range of velocities, the dominant frequency in the cross-flow VIV response is plotted in (c) as a proportion of the upper natural frequency, and in (d) as a proportion of the dominant frequency in the in-line WIV response (d). In (e), the dominant frequency in the in-line WIV response is plotted as a function of the Reynolds number.

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Fig. 15

Total trajectories for L = 5 and various B at V/fn2D = 8.0. All tickmarks are at intervals of D.

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Fig. 16

Amplitudes of low (on the left) and high (on the right) frequency motion for the conditions of Fig. 15. Empty symbols refer to Ax, solid symbols to Ay.

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