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Numerical calculation method for the optimum wave energy absorption configuration based on the variation of Kochin function

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Abstract

This report is about a numerical calculation method for the wave energy absorption of a floating 2D cylinder. The least condition for the complete energy absorption by making use of an oscillating cylinder in waves is that the floating cylinder has to be wave-free on one side direction when it is forced to oscillate in a given motion mode. The radiated wave amplitude can be expressed by the Kochin function. Based on the relation between the small deformation of the floating body’s profile and the Kochin function, the numerical calculation method which satisfies the complete energy absorption condition by changing the configuration step by step is derived. Some numerical examples are demonstrated.

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Abbreviations

a :

Regular wave amplitude

A 0, A 1 :

Unknown constant values in deformation function

A ± j :

Radiated wave amplitude by j-th mode motion

A R :

Reflected wave amplitude

A T :

Transmitted wave amplitude

B :

Breadth

B 0 :

Initial geometry breadth

C :

Initial geometry configuration

C′:

Deformed geometry configuration

C j :

Restoration force coefficient

d j :

Damping coefficient of the wave power absorption device

E:

Wave power

E Wj :

Wave exciting force for the j-th mode motion

E W0j :

Wave exciting force amplitude for the j-th mode motion

F j :

Hydrodynamic force in the j-th mode

g:

Acceleration of gravity

H ± j :

Kochin function by the j-th mode motion’s velocity potential

K:

Wave number

K 0 :

Target wave number for the maximum wave power absorption efficiency

k j :

Spring constant of the wave power absorption device

m j :

Added mass in the j-th mode motion

M j :

Generalized mass for the j-th mode motion

n:

Normal direction on the floating body’s surface

N j :

Damping force coefficient in the j-th mode motion

Q(x Q, y Q):

A point on the floating body’s surface

R j :

Reaction force by the wave power absorption device for the j-th mode motion

s :

Tangential direction on the floating body’s surface

s 0 :

Total arc length of the floating body’s surface

t :

Time

T :

Wave period

x i :

Coordinate in xy plane

X j :

Motion of the floating body (j = 1: sway; j = 2: heave and j = 3: roll)

X 0j :

Amplitude of the j-th mode motion

η :

Wave power absorption efficiency

ρ :

Density of fluid

ϕ d :

Normalized diffraction velocity potential

ϕ s :

Normalized scattered velocity potential

ϕ 0 :

Normalized incident wave velocity potential

Φ j :

Radiation velocity potential for the j-th mode motion (j = 1, 2, 3) \(\varPhi_{j} = i\omega X_{0j} \phi_{j} e^{i\omega t}\)

Φs :

Scattered velocity potential \(\varPhi_{s} = \frac{iga}{\omega }\phi_{\text{s}} e^{i\omega t}\)

Φ0 :

Incident wave velocity potential \(\varPhi_{0} = \frac{iga}{\omega }\phi_{0} e^{i\omega t}\)

\(\varPhi_{\text{d}} = \varPhi_{\text{s}} + \varPhi_{0}\) :

Diffraction velocity potential \(\phi_{\text{d}} = \phi_{\text{s}} + \phi_{0}\)

Ψ i :

Velocity potential of i-mode radiation

ω :

Circular wave frequency

ω 0 :

Target circular wave frequency for the maximum wave power absorption efficiency

References

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Author information

Authors and Affiliations

  1. Faculdade de Engenharia Naval, DEMEC, Universidade Federal de Pernambuco, Recife, Brazil

    Hiroshi Kawabe & Paula Suemy Arruda Michima

  2. Faculdade de Engenharia Mecânica, DEMEC, Universidade Federal de Pernambuco, Recife, Brazil

    Armando Hideki Shinohara & Cezar Henrique Gonzalez

Authors
  1. Hiroshi Kawabe
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  2. Paula Suemy Arruda Michima
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  3. Armando Hideki Shinohara
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  4. Cezar Henrique Gonzalez
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Corresponding author

Correspondence to Paula Suemy Arruda Michima.

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Kawabe, H., Michima, P.S.A., Shinohara, A.H. et al. Numerical calculation method for the optimum wave energy absorption configuration based on the variation of Kochin function. J Mar Sci Technol 20, 617–628 (2015). https://doi.org/10.1007/s00773-015-0316-3

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  • DOI: https://doi.org/10.1007/s00773-015-0316-3

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