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Ocean Engineering

# Effect of Bottom Boundary on VIV for Energy Harnessing at $8×103

[+] Author and Article Information
K. Raghavan1

Department of Naval Architecture and Marine Engineering, University of Michigan, 2600 Draper Road, Ann Arbor, MI 48109-2145

Michael M. Bernitsas

Department of Naval Architecture and Marine Engineering, University of Michigan, 2600 Draper Road, Ann Arbor, MI 48109-2145 and Director of Ocean Renewable Energy Laboratory, University of Michigan, 2600 Draper Road, Ann Arbor, MI 48109-2145michaelb@umich.edu

D. E. Maroulis

Department of Naval Architecture and Marine Engineering, University of Michigan, 2600 Draper Road, Ann Arbor, MI 48109-2145

1

Present address: Chevron Energy Technology Company.

J. Offshore Mech. Arct. Eng 131(3), 031102 (May 28, 2009) (13 pages) doi:10.1115/1.2979798 History: Received June 19, 2007; Revised July 02, 2008; Published May 28, 2009

## Abstract

The concept of extracting energy from ocean/river currents using vortex induced vibration was introduced at the OMAE2006 Conference. The vortex induced vibration aquatic clean energy (VIVACE) converter, implementing this concept, was designed and model tested; VIV amplitudes of two diameters were achieved for Reynolds numbers around $105$ even for currents as slow as 1.6 kn. To harness energy using VIV, high damping was added. VIV amplitude of 1.3 diameters was maintained while extracting energy at a rate of $PVIVACE=0.22×0.5×pU3DL$ at 1.6 kn. Strong dependence of VIV on Reynolds number was proven for the first time due to the range of Reynolds numbers achieved at the Low-Turbulence Free Surface Water (LTFSW) Channel of the University of Michigan. In this paper, proximity of VIVACE cylinders in VIV to a bottom boundary is studied in consideration of its impact on VIV, potential loss of harnessable energy, and effect on soft sediments. VIV tests are performed in the LTFSW Channel spanning the following ranges of parameters: $Re∊[8×103–1.5×105]$, $m∗∊[1.0–3.14]$, $U∊[0.35–1.15 m/s]$, $L/D∊[6–36]$, closest distance to bottom boundary $(G/D)∊[4−0.1]$, and $m∗ζ∊[0.14–0.26]$. Test results show strong impact for gap to diameter ratio of $G/D<3$ on VIV, amplitude of VIV, range of synchronization, onset of synchronization, frequency of oscillation, hysteresis at the onset of synchronization, and hysteresis at the end of synchronization.

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## Figures

Figure 1

Simple schematic of a VIVACE module with coordinate system

Figure 2

VIVACE model in the Low-Turbulence Free Surface Water Channel

Figure 3

Schematic representation of the shift in the timing of vortex shedding, with the body at the extreme of its vertical motion in VIV

Figure 4

Amplitude ratio versus reduced velocity for 0.157<G/D<3.207

Figure 5

Amplitude ratio as a function of reduced velocity for gap ratios 0.157, 0.268, 1.837, and 3.207A

Figure 9

Positive and negative maximum amplitude ratio versus reduced velocity: G/D=1.84

Figure 16

Hysteresis persists through most of the synchronization range: G/D=0.157

Figure 17

Frequency spectrum and time series plot of A/D: U=1.25 m/s(U∗=13.8), G/D=0.157, and D=2.5 in.

Figure 18

Ratio of frequency of oscillation to natural frequency in water:G/D=0.405

Figure 19

Positive and negative maximum amplitude ratio: G/D=0.405

Figure 20

Ratio of frequency of oscillation to natural frequency in water: G/D=0.63

Figure 21

Positive and negative maximum amplitude ratios:G/D=0.63

Figure 22

Positive and negative maximum amplitude ratio: G/D=0.268

Figure 23

Ratio of frequency of oscillation to natural frequency in water: G/D=0.268

Figure 6

Amplitude ratio as a function of reduced velocity for gap ratios 0.405, 0.630, 1.837, and 3.207

Figure 7

Amplitude ratio for gap ratios 0.157, 0.268, 0.405, and 0.630

Figure 8

Frequency spectrum and time series plot of A/D: U=0.76 m/s (U∗=9, maximum amplitude achieved), G/D=4.18, and D=2.5 in.

Figure 10

Frequency spectrum and time series plot of A/D: U=0.76 m/s (U∗=9, maximum amplitude achieved), G/D=1.84, and D=3.0 in.

Figure 24

Ratio of frequency of oscillation to the natural frequency in water with increasing and decreasing velocity: G/D=0.157

Figure 25

Boundary layer thickness of a plane bottom boundary at 0.65 m. At U=0.75 m/s transition occurs from laminar to turbulent flow.

Figure 26

Our test results shown on the modified Skop–Griffin plot (5)

Figure 11

Frequency spectrum and time series plot of A/D: U=0.76 m/s (U∗=9, maximum amplitude achieved), G/D=0.268, and D=2.5 in.

Figure 12

Frequency spectrum and time series for displacement: sin(2πt) for sin(2πt)>−0.9 and zero for sin(2πt)≤−0.9

Figure 13

Frequency spectrum and time series for displacement: sin(2πt)+0.1 sin(4πt) for sin(2πt)>−0.9 and zero for sin(2πt)≤−0.9

Figure 14

Ratio of frequency of oscillation to natural frequency in water

Figure 15

Ratio of frequency of oscillation to natural frequency in water: G/D=1.87

## Errata

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