Talk outline
description
Transcript of Talk outline
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The Power of Many?.....
Coupled Wave Energy Point Absorbers
Paul YoungMSc candidate, University of Otago
Supervised by Craig Stevens (NIWA), Pat Langhorne & Vernon Squire (Otago)
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Motivation
The big idea
The physics
Results
Where to next?
Talk outline
WECs… WTF?
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World resource
Wave energy flux magnitude (kW per metre of wavefront)
Source: Pelamis Wave Power website
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Source: Smith et al (NIWA), Analysis for Marine Renewable Energy: Wave Energy, 2008
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Source: Smith et al (NIWA), Analysis for Marine Renewable Energy: Wave Energy, 2008
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1. Estimate by UK Carbon Trust
Advantages:
High energy density Low social & environmental impact (?) Reliability & predictability (c.f. wind) Low EROEI (?) Direct desalination
AND...
• Practical worldwide resource ~ 2000-4000 TWh/year1
• (Current global demand~ 17000 TWh/year)
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Motivation
The big idea
The physics
Results
Where to next?
Talk outline
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Point absorbers
Pros:
Suitable for community scale
Less disruption in event of device failure
Cheaper per kW/h?
Cons:
Non-resonant in typical sea conditions
Lower efficiency
Maybe a linked chain of point absorbers will 'see' long
wavelengths better than a lone device?
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Key questions
Is it possible to obtain better power output (per unit) with a linked chain?(Can we improve peak efficiency and/or widen bandwidth?)
How are the mooring forces affected?(Survivability)
What is the interplay between the device spacing and the wavelength?
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My scheme: model device
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1-D (surge only) idealisation
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Motivation
The big idea
The physics
Results
Where to next?
Talk outline
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Further assumptions/simplifications
Small-body approximation
Linear, small amplitude waves
Neglect hydrodynamic interaction between devices
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Forces
Mooring forcesHydrodynamic forces: excitation, drag and radiation
Master equation:
(not including power take-off)
KKKKK RDEM FFFFma
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Technical issues…
Importance of memory effects
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Motivation
The big idea
The physics
Results
Where to next?
Talk outline
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Validating numerical codeFor lone device with zero drag, easy to solve equation of motion analytically.
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Discrepancy between models with and without memory effects noticeable when nonlinear drag introduced, but small.
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HOT OFF THE PRESS:Things get interesting with
multiple devices.
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Some good agreement...
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...some poor agreement...
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Motivation
The big idea
The physics
Results
Where to next?
Talk outline
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Mooring and linkage forces
F M J , K=−S x J−xK , ∣x J−xK∣d0, ∣x J−xK∣d{
Chacterise as tension-only spring
Spring stiffness
(Linkage force on device J from device K)
Device spacing
Position of device K
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Hydrodynamic forces(The tricky part...)
Inline force on small(ish) bodies in oscillatory flow often described by Morison equation:
BUT added mass depends on the oscillation frequency...
F=V s uma u− x −12C d A∣x−u∣ x−u
Dragcoefficient
Area 'seen'by fluidFluid density
Fluid velocity
Added mass
Submergedvolume
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But under nonlinear conditions, device response may be over much broader range of frequencies...
Data from Hulme, A.: The wave forces acting on a floating hemisphere undergoing forced periodic oscillations. 1982.
How big is the effect?
Semi-submerged sphere moving in surge
For device with a ≈ 2m, energy-bearing wavelengths in typical sea state are 0.056ka0.126
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Falnes' formulation
1. Falnes, J.: Ocean Waves and Oscillating Systems: linear interactions including wave-energy extraction. 2002.
Wave forces are decomposed in frequency domain into excitation and radiation forces.
For surge, under small-body approximation, these are1:
F E≈[V sma i] u
F R≈−ma x( + damping term)
F=V s uma u− x −12C d A∣x−u∣ x−u (c.f.
)
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F R=−ma ∞ x−∫0
t
K x t−d
Added mass at infinite frequency
Impulse response function
K t =2∫0
∞
cos t d Added damping
This expression is exact, but added mass and damping depend on body geometry.
Radiation force in time domain
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Thankfully...
...can fit an analytic function that isn't horrible
Data from Hulme, A.: The wave forces acting on a floating hemisphere undergoing forced periodic oscillations. 1982.
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K t =2∫0
∞
cos t dEvaluate integralswith MATLAB symbolic math toolbox to get:
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Master equation
m x J t =F M JF DJF EJF RJ
F M J , K=−S x J− xK , ∣x J− xK∣d0, ∣x J−xK∣d{
F M J=FM J , J−1F M J , J1
F EJ=V sma i u x J , t
F D=−12C d A∣x−u∣ x−u
u=u x J , t n.b.
F R=−ma ∞ x−∫0
t
K x t−d
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Solution method
Solve numerically with 4th order Runge-Kutta procedure on MATLAB
Cast as 1st order vector equation for y=[x1v1x2v2⋮xnvn
](n.b. will be 4n entries with internal mass included)
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Memory integral giving good agreement for linear motion over wavelength range