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Bottom slamming on heaving point absorber wave energy devices

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Abstract

Oscillating point absorber buoys may rise out of the water and be subjected to bottom slamming upon re-entering the water. Numerical simulations are performed to estimate the power absorption, the impact velocities and the corresponding slamming forces for various slamming constraints. Three buoy shapes are considered: a hemisphere and two conical shapes with deadrise angles of 30° and 45°, with a waterline diameter of 5 m. The simulations indicate that the risk of rising out of the water is largely dependent on the buoy draft and sea state. Although associated with power losses, emergence occurrence probabilities can be significantly reduced by adapting the control parameters. The magnitude of the slamming load is severely influenced by the buoy shape. The ratio between the peak impact load on the hemisphere and that on the 45° cone is approximately 2, whereas the power absorption is only 4–8% higher for the 45° cone. This work illustrates the need to include slamming considerations aside from power absorption criteria in the buoy shape design process and the control strategy.

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Abbreviations

b :

Wet radius at the instantaneous free water surface (m)

b hyd :

Hydrodynamic damping coefficient (kg/s)

b ext :

External damping coefficient (kg/s)

C s :

Slamming force coefficient (–)

C w :

Wetting factor (–)

d :

Draft (m)

f :

Frequency (Hz)

f i :

Frequency component (Hz)

f p :

Peak frequency (Hz)

F :

Force (N)

F ex :

Exciting force (N)

g :

Gravitational acceleration (m/s2)

h :

Drop height (m)

H s :

Significant wave height (m)

k :

Hydrostatic restoring coefficient (kg/s2)

K r :

Radiation impulse response function (kg/s2)

k SS :

Dimensionless value used to describe impact force (Shiffman and Spencer) (–)

m :

Body mass (kg)

m a :

Added mass (kg)

\(m_{\text{a}_{\infty}}\) :

High-frequency limit of the added mass (kg)

m sup :

Supplementary mass (kg)

n f :

Number of frequencies (–)

j :

Imaginary unit

p :

Pressure (bar = 105 Pa)

p abs :

Absorbed power (W)

r :

Radial coordinate (m)

R :

Radius of hemisphere (m)

S :

Spectrum (m2s)

t :

Time (s)

T p :

Peak period (s)

U :

Entry velocity (m/s)

z :

Vertical coordinate (m)

z A,sign :

Significant amplitude of the buoy position (m)

β :

Deadrise angle (° or rad)

ζ :

Water elevation (m)

ρ :

Mass density of fluid (kg/m3)

ω :

Angular frequency (rad/s)

ϕ z :

Phase angle of the buoy position (rad)

σ :

Spectral width parameter (–)

A :

Amplitude

s, sign:

Significant

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Acknowledgments

This research was funded by a Ph.D. grant from the Institute of Promotion of Innovation Through Science and Technology in Flanders (IWT-Vlaanderen), Belgium.

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Authors and Affiliations

  1. Department of Civil Engineering, Ghent University, Technologiepark Zwijnaarde 904, 9050, Zwijnaarde, Belgium

    Griet De Backer, Marc Vantorre, Charlotte Beels & Julien De Rouck

  2. Department of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, 9000, Aalborg, Denmark

    Peter Frigaard

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  1. Griet De Backer
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  2. Marc Vantorre
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  4. Charlotte Beels
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  5. Julien De Rouck
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Corresponding author

Correspondence to Marc Vantorre.

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De Backer, G., Vantorre, M., Frigaard, P. et al. Bottom slamming on heaving point absorber wave energy devices. J Mar Sci Technol 15, 119–130 (2010). https://doi.org/10.1007/s00773-010-0083-0

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  • DOI: https://doi.org/10.1007/s00773-010-0083-0

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