Steps in the development of a wave energy converter:

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• Steps in the development of a wave energy
  converter
• Basic conception
• Theoretical/numerical modelling
• Model testing in wave basin/flume
• Engineering prototype testing in real sea

• Theoretical/numerical modelling
• First step to assess a given concept/invention
• Essential to optimize size, geometry of device
• Optimize/specifiy PTO
• Establish control procedures/strategies/algorithm
  s

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• Theoretical/numerical hydrodynamic modelling
• Frequency-domain
• Time-domain
• Stochastic

• In all cases, linear water wave theory is
  assumed
• small amplitude waves and body-motions
• real viscous fluid effects neglected

Non-linear water wave theory may be used at a
later stage to investigate some water flow
details.
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Frequency domain model

• Basic assumptions
• Monochromatic (sinusoidal) waves
• The system (input?output) is linear

• Historically the first model
• The starting point for the other models

• Advantages
• Easy to model and to run
• First step in optimization process
• Provides insight into devices behaviour
• Disadvantages
• Poor representation of real waves
• Only a few WECs are approximately linear systems
  (OWC
• with Wells turbine)

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Bsic
Time-domain model

• Basic assumptions
• In a given sea state, the waves are represented
  by a
• spectral distribution

• Advantages
• Fairly good representation of real waves
• Applicable to all systems (linear and
  non-linear)
• Yields time-series of variables
• Adequate for control studies
• Disadvantages
• Computationally demanding and slow to run

Essential at an advanced stage of theoretical
modelling
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Bsic
Stochastic model

• Basic assumptions
• In a given sea state, the waves are represented
  by a
• spectral distribution
• The waves are a Gaussian process
• The system is linear (restriction may be partly
  removed)

• Advantages
• Fairly good representation of real waves
• Very fast to run in computer
• Yields directly probability density
  distributions
• Disadvantages
• Restricted to approximately linear systems (e.g.
  OWCs with Wells turbines)
• Does not yield time-series of variables

Extensively used in the optimization,
specifications and design of the breakwter-OWC at
Porto, Portugal
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Most wave energy converters are complex (possibly
multi-body) mechanical systems with several
degrees of freedom.
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OSCILLATING BODY
Basic equation (Newton)
m
PTO force
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• Frequency domain
• Sinusoidal waves
• Linear system

Linear spring
Linear damper
Solution
A and B to be computed (AQUADYN, WAMIT,...)
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buoyancy
added mass
mass
PTO damping
PTO spring
Excitation force
radiation damping
Power force ? velocity Time-averaged power
absorbed from the waves
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Note for given body and given wave frequency ?,
B and are fixed. Then, the absorbed
power will be maximum when
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Capture width L measures the power absorbing
capability of device (like power coefficient of
wind turbines)
absorbed power
E energy flux of incident wve per unit crest
length
For an axisymmetric body oscillating in heave
(vertical oscillations), it can be shown (1976)
that
or
For wind turbines, Betzs limit is
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Example hemi-spherical floater of radius a
for
If T 9 s
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Oscillating body Time-domain analysis
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Time domain
(1)
external
added mass
radiation
diffraction
hydrostatic
forces
memory function
from ?(?) and spectral distribution
(Pierson-Moskowitz)
Equation (1) to be numerically integrated
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Phase control of oscillating bodies Time-domain
analysis
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Phase-control by latching
Whenever the body velocity comes down to zero,
keep the body fixed for an appropriate perid of
time. This is an artificial way of reducing the
frequency of the body free-oscillations, and
achieving resonance.
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PHASE CONTROL
How to achieve phase-control by latching in a
floating body with a hydraulic power-take-off
mechanism?
Introduce a delay in the release of the latched
body.
How?
Increase the resisting force the hydrodynamic
forces have to overcome to restart the body
motion.
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REGULAR WAVES Period T 9 s Amplitude 0,667
m
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velocity
Diffr. force
Phase-control
No phase-control
displacement
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IRREGULAR WAVES Period Te 9 s Height Hs
2 m
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THANK YOU FOR YOUR ATTENTION