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Talk outline

The Power of Many? ..... Coupled Wave Energy Point Absorbers Paul Young MSc candidate, University of Otago Supervised by Craig Stevens (NIWA), Pat Langhorne & Vernon Squire (Otago). Talk outline. Motivatio n The big idea The physics Results Where to next?. WECs… WTF?. World resource.

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Talk outline

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  1. The Power of Many?.....Coupled Wave Energy Point AbsorbersPaul YoungMSc candidate, University of OtagoSupervised by Craig Stevens (NIWA), Pat Langhorne & Vernon Squire (Otago)

  2. Talk outline • Motivation • The big idea • The physics • Results • Where to next? WECs… WTF?

  3. World resource Wave energy flux magnitude (kW per metre of wavefront) Source: Pelamis Wave Power website

  4. Source: Smith et al (NIWA), Analysis for Marine Renewable Energy: Wave Energy, 2008

  5. Source: Smith et al (NIWA), Analysis for Marine Renewable Energy: Wave Energy, 2008

  6. 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) 1. Estimate by UK Carbon Trust

  7. Talk outline • Motivation • The big idea • The physics • Results • Where to next?

  8. Maybe a linked chain of point absorbers will 'see' long wavelengths better than a lone device? 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

  9. 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?

  10. My scheme: model device

  11. 1-D (surge only) idealisation

  12. Talk outline • Motivation • The big idea • The physics • Results • Where to next?

  13. Further assumptions/simplifications • Small-body approximation • Linear, small amplitude waves • Neglect hydrodynamic interaction between devices

  14. Master equation: (not including power take-off) Forces Mooring forces Hydrodynamic forces: excitation,drag and radiation

  15. Technical issues… Importance of memory effects

  16. Talk outline • Motivation • The big idea • The physics • Results • Where to next?

  17. Validating numerical code For lone device with zero drag, easy to solve equation of motion analytically.

  18. Discrepancy between models with and without memory effects noticeable when nonlinear drag introduced, but small.

  19. HOT OFF THE PRESS:Things get interesting with multiple devices.

  20. Some good agreement...

  21. ...some poor agreement...

  22. Talk outline • Motivation • The big idea • The physics • Results • Where to next?

  23. { Mooring and linkage forces Chacterise as tension-only spring Spring stiffness Device spacing (Linkage force on device J from device K) Position of device K

  24. Submerged volume Drag coefficient Fluid velocity Area 'seen' by fluid Fluid density Added mass 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...

  25. For device with a ≈ 2m, energy-bearing wavelengths in typical sea state are 0.056ka0.126 Semi-submerged sphere moving in surge But under nonlinear conditions, device response may be over much broader range of frequencies... How big is the effect? Data from Hulme, A.: The wave forces acting on a floating hemisphere undergoing forced periodic oscillations. 1982.

  26. ( + damping term) Falnes' formulation Wave forces are decomposed in frequency domain into excitation and radiation forces. For surge, under small-body approximation, these are1: (c.f. ) 1. Falnes, J.: Ocean Waves and Oscillating Systems: linear interactions including wave-energy extraction. 2002.

  27. Added mass at infinite frequency Impulse response function Radiation force in time domain Added damping This expression is exact, but added mass and damping depend on body geometry.

  28. 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.

  29. Evaluate integrals with MATLAB symbolic math toolbox to get:

  30. { n.b. Master equation

  31. Cast as 1st order vector equation for (n.b. will be 4n entries with internal mass included) Solution method Solve numerically with 4th order Runge-Kutta procedure on MATLAB

  32. Memory integral giving good agreement for linear motion over wavelength range

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