Active Water-Wave Absorber

 Active Water-Wave Absorber Composition

Active Water-Wave Absorber

Matt Carney

ME236: Control & Optimization of Distributed Parameters Professor Alex Bayen University of California, Berkeley '04. 30. 3 years ago UC Berkeley, Spring 3 years ago 1

Articles

• • • • • • Motivation Primary Idea Books Search Target Current Function Future Job www.emec.org.uk

UC Berkeley, Spring 2007

two

Motivation

• Significant amounts of energy is stored in the ocean

• Significant potential for taking out energy by waves

• Control is the key to customizing energy removal and economic feasibility.

www.epri.com/oceanenergy

UC Berkeley, Spring 2007

3

Preliminary Idea

• 1-Degree of Freedom Point Absorber • Direct Travel Linear Electrical generator • Enhance Hydrodynamic Guidelines – Added Mass – Added Diffusing

• Boost Phase Control

UC Berkeley, Spring 3 years ago 4

Books Search

• Eriksson, Meters., Isber, T., Leijon, Meters. " Hydrodynamic Modeling of any Direct-Drive Wave Energy Convsersion app. ” Worldwide Journal of Engineering Scientific research, vol. 43, pages 1377-1387, 2005. Falnes, Johannes " Ocean Surf and Oscillating Systems: Thready Interactions Which includes Wave-energy Removal. ” Cambridge University Press, Cambridge. 2002. Havelock, T. H., " Forced Surface-Waves on Water. ” Philosophic Magazine of Science, vol. 8, no . 51, March. 1929. Milgram, Jerome H., " Energetic Water-Wave Absorbers. ” Log Fluid Technicians, vol. 43, part 5, pages 845-859, 1970. Yeung, Ronald T. " Added Mass and Damping of the Vertical Cylinder in Finite-depth Waters. ” Applied Ocean Research, volume. 3, number 3, webpages 119-133. 1981.

•

• • •

UC Berkeley, Spring 2007

5

Concentrate

• Make simpler the Problem!

• " To absorb a wave means to create a say or, basically: To eliminate a influx is to produce a wave. ” – Johannes Falnes UC Berkeley, Springtime 2007 six

(2D Wave-Maker) -1

Active Water-Wave Absorbers Jerome They would. Milgram Log of Liquid Mechanics (1970), vol. 43, pp. 845-859 S

back button y Оё

C

D p

-в€ћ

h

d

UC Berkeley, Spring 3 years ago

7

Formulation

пѓ‘ 2пЃ† пЂЅ zero

Boundary Circumstances Assume: little amplitude waves allowing linearization of equations, simple harmonic oscillations, in the beginning irrotational liquid, neglect viscosity and surface tension. about on on on at

пЃ†tt пЂ« gпЃ† y пЂЅ 0

пЃ† sumado a пЂЅ пЃЋt пЃ†y пЂЅ 0

yпЂЅ0 yпЂЅ0

sumado a пЂЅ пЂ­h

• Dynamic free surface • Kinematic free area • Insobornable floor • Termination (Flapper) wall • Condition by infinity almost 8

пЃ† x пЂЅ пЃ™t

xпЂЅ0

пѓ‘пЃ† пЂј п‚Ґ

x пЂЅ пЂ­п‚Ґ

UC Berkeley, Planting season 2007

Derivations

• Separating of Variables used to solve Laplacian

пЃ† пЂЅ пЃ†( x, y, t ) пЂЅ

Fk ( x) пЂЅ eif k times Gk ( y ) пЂЅ cosh f k ( sumado a пЂ« h)

k пЂЅ пЂ­п‚Ґ

C k Fk ( x)Gk ( y)e it 

п‚Ґ

• Free Surface area BC leads to the dispersion relation

пЃ¬2 h

fh пЂЅ g tanh( fh )

UC Berkeley, Early spring 2007 9

Calculations

• Due to boundedness of the border condition for negative infinity the potential function leads to

пЃ†( x, y ) пЂЅ A cosh f zero ( con пЂ« h)e

' 0

пЂ­if zero x

  A great cosh farreneheit n ( y  h)eif n x

in пЂЅ0

п‚Ґ

•

where, the A'0 term identifies the trend reflected from your flapper wall membrane. Channel termination (Flapper - active absorber) where, пЃ™( y, t ) пЂЅ BпЃ№ ( y)e пЂ­iпЃ¬t

•

con п‚і пЂ­p пѓ¬y пЂ« p sumado a пЂј пЂ­p пѓ®0 The channel end of contract boundary condition then needs the following:

пЃ№ ( y) пЂЅ пѓ­

пЃ† times пЂЅ пЃ™t

( A0  A ) cosh f 0 ( sumado a  h)   An n n cosh f n ( sumado a  h)   B ( y) ' 0 n 1

п‚Ґ

UC Berkeley, Spring 3 years ago

10

Orthogonality

• The condition of orthogonality has to be satisfied on the moving end of contract.

пѓІ

•

0

пЂ­h

Gk ( y)Gn ( y)dy пЂЅ 0

pertaining to

kп‚№n

This condition applies to the results in the previous webpage and permits the definition in the following integrals, 0 пѓ№ 1 пѓ© 1 (1) I d пЂЅ пѓІ cosh 2 f n ( con пЂ« h)dy пЂЅ h пѓЄ1 пЂ« sinh two f d hпѓє пЂ­h 2 пѓ« 2 fnh пѓ» zero p you (2) We n пЂЅ пѓІ пЃ№ ( sumado a ) cosh f in ( y пЂ« h)dy пЂЅ sinh f n h пЂ« 2 пЃ›cosh f n (h пЂ­ p) пЂ­ cosh farreneheit n hпЃќ пЂ­h fn fn These kinds of integrals can then be used to specify the ratio of coefficient values ' ( pertaining to n пЂЅ 0, A 0 пЂ­ A0 пѓј пЃ¬ I n2 ) пѓЅ пЂЅ пЂ­ B ( 2), for in п‚№ zero, fn In An пѓѕ

•

UC Berkeley, Spring...