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Lloyd’s Register services to the energy industryA simplified model for oscillating watercolumn motionRebecca SykesMechanic...
Lloyd’s Register services to the energy industry   Oscillating water column                                               ...
Lloyd’s Register services to the energy industry   Oscillating water column                                               ...
Lloyd’s Register services to the energy industry  Objective     To present a model that furthers our understanding of the ...
Lloyd’s Register services to the energy industry OWC modelling                                Three previous ly us ed mode...
Lloyd’s Register services to the energy industrySimplified OWC model                                                   •  ...
Lloyd’s Register services to the energy industryMathematical model   Initially c ons idering a fixed OWC to examine the di...
Lloyd’s Register services to the energy industry          Mathematical model prediction                                   ...
Lloyd’s Register services to the energy industryStructure for validation – fixed model tovalidate diffraction solution    ...
Lloyd’s Register services to the energy industry ValidationC omparis on of diffraction pres s ure (normalis ed by inc iden...
Lloyd’s Register services to the energy industry  Mathematical model for floating OWCWhen the water c olumn is defined by ...
Lloyd’s Register services to the energy industryMathematical model for floating OWC      Total dynamic pres s ure on the i...
Lloyd’s Register services to the energy industryFloating structure for validation – floating model            Reflective m...
Lloyd’s Register services to the energy industry Validation  Wavedirec tionC omparis on of dynamic pres s ure (normalis ed...
Lloyd’s Register services to the energy industry Validation  Wavedirec tionC omparis on of dynamic pres s ure (normalis ed...
Lloyd’s Register services to the energy industry    What to take away from this…•   Simple model can be used to effectivel...
Lloyd’s Register services to the energy industryAny questions?                ?                   ?                       ...
Lloyd’s Register services to the energy industryFor more information, please contact:Rebecca SykesMechanical Engineer – Re...
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A simplified model for oscillating water column motion

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Rebecca Sykes (Mechanical Engineer) discusses different modelling techniques for understanding the physical process within a floating OWC. Using a simplified OWC model, Rebecca explores ways to get around the limitations of the commonly used "Boundary Element Model".

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A simplified model for oscillating water column motion

  1. 1. Lloyd’s Register services to the energy industryA simplified model for oscillating watercolumn motionRebecca SykesMechanical EngineerTechnical DirectorateMay 23, 2012
  2. 2. Lloyd’s Register services to the energy industry Oscillating water column • Conventional OWC have been shoreline devices • LIMPET, Scotland • Pico, Azores • Sanze, Japan… • Wave shoaling reduces energy to shorelinePower is extrac ted from the wave induced vertic al motion of the water free s urface c ompres s ing airin a volume above. This can be us ed to drive an air turbine, s uch as the Wells turbine, whic h isdes igned for rec iprocating flows .
  3. 3. Lloyd’s Register services to the energy industry Oscillating water column • Conventional OWC have been shoreline devices J ac ket • LIMPET, Scotland • Pico, Azores • Sanze, Japan… G ravity bas ed • Wave shoaling reduces energy to shoreline TLP • Potential for greater energy extraction offshore • Options – fixed, semi-fixed or floating Floating OWCMajority of propos ed/prototype offs hore OWC have been floating but there is potential to c ombinewith other tec hnologies and s o us e their s upport s tructure
  4. 4. Lloyd’s Register services to the energy industry Objective To present a model that furthers our understanding of the physical processes within a floating Oscillating Water ColumnFloating – cheaper CAPEX option (?)… The diffraction and radiation problem which existed for the fixed OWC must be …but more complex to simulate extended when floating to include radiation from the device motionTHEREFORE: Increased complexity in predicting the energy capture
  5. 5. Lloyd’s Register services to the energy industry OWC modelling Three previous ly us ed modelling techniquesNumerical modelling Analytical modelling Physical modellingComputational time/ Device/geometry specific High time and costaccuracy trade-off Specialist mathematical ScalingNeed for verification and skills Increased potential forvalidation Need for verification and error at small scaleApplication of OWC validationboundary condition notalways easily available
  6. 6. Lloyd’s Register services to the energy industrySimplified OWC model • A simple geometrical model was used to highlight the fundamental physics avoiding proprietary device specific particularities • An OWC is a highly resonant device when undamped, and is hydrodynamically narrow banded in frequency • Vertical oscillation -power G eometry examined producing oscillation
  7. 7. Lloyd’s Register services to the energy industryMathematical model Initially c ons idering a fixed OWC to examine the diffraction pres s ureTime domain piston model from [1]: ρS ( L + ηOWC )ηOWC + ρSgηOWC = SPOWC  (1) ηOWC and POWC can be expanded as series in powers of the small parameter ε η OWC ( t ) = η0 + εη1( t ) + ε 2η2 ( t ) + ε 3η3 ( t ) + ... and P OWC ( t ) = P0 + εP1( t ) + ε 2 P2 ( t ) + ε 3P3 ( t ) + ... Substituting into (1) and taking those terms up to first order ηOWC (  0 1 ) ρS L + η η + ρSgη = P S 1 1 (2)Assuming η1 and P1 are harmonic such that η = Reη eiωt   ˆ1  P = Re p eiωt   1  POWC 1   1   C ons idered internalWhich gives the frequency domain equation volume of water − ω 2 ρ ( L + η 0 )η1 + ρgη1 = p1 ˆ ˆ
  8. 8. Lloyd’s Register services to the energy industry Mathematical model prediction 3 45 0 40 0 2.5 -0.05 -0.05 35 -0.1 -0.1 2 30 -0.15 -0.15z (m) z (m) -0.2 25 -0.2 1.5 -0.25 20 -0.25 -0.3 -0.3 15 1 -0.35 -0.35 0.1 0.1 10 0.05 0.1 0.05 0.1 0.5 0 0.05 5 0 0.05 0 0 -0.05 -0.05 -0.05 -0.05 0 y (m) -0.1 -0.1 y (m) -0.1 -0.1 x (m) x (m) Pressure magnitude Pressure phase
  9. 9. Lloyd’s Register services to the energy industryStructure for validation – fixed model tovalidate diffraction solution z pz = -270mm • Vertical cylinder: pz = -201mm ηOWC o b = 50.5mm pz = -144mm x o a = 47.0mm AI o d = 300mm o h = 1m d • Tank: 2.65m x 23.27m h • Regular waves • Measurements: a o Free surface elevation Wave probe b o Pressure at three depths S c hematic of model us ed in wave flume experimental tes ting
  10. 10. Lloyd’s Register services to the energy industry ValidationC omparis on of diffraction pres s ure (normalis ed by inc ident wave amplitude) in the frequenc y domain
  11. 11. Lloyd’s Register services to the energy industry Mathematical model for floating OWCWhen the water c olumn is defined by a floating s tructure, radiation effects mus t als o be c ons idered; for a s truc turethat is axis ymmetric about a vertical axis in unidirec tional waves , the dominant lateral modes are s urge and pitc h.Sloshing modes natural frequencies for fluid in a cylindrical tank: gκ1n κ d  a ω1n = 2 tanh 1n  a  a  dwhere κ1n = 1.8412, 5.3314, 8.5363, 11.706, 14.8636,…, κ1n = κ1(n –1) + π. Pressure due to acceleration and Pressure due to acceleration and sloshing in surge: sloshing in pitch: Pξ1 ( t ) = ρ ξ1 ω 2 cos θ sin ( ωt )( r + A) Pξ5 ( t ) = ρ ξ5 ω 2 cos θ sin ( ωt )( rz + A)
  12. 12. Lloyd’s Register services to the energy industryMathematical model for floating OWC Total dynamic pres s ure on the internal s urface of a floating OWC : { pT = p1 + pξ1 + pξ5 − ρ gz +  g ( ξ3 + ξ 4 y − ξ5 x )    } Pis ton model Due to pitc h Hydros tatic Due to s urge where pξ and pξ are the complex amplitudes of the acceleration and 1 5 sloshing pressures and (x, y, z) are the body fixed coordinates of a general position on the wall.
  13. 13. Lloyd’s Register services to the energy industryFloating structure for validation – floating model Reflective marker Wave probe z • Model dimensions: • 2b =315mm • 2 a = 104mm • d = 300mm AI • h = 1m x • Tank: 2.65m x 23.27m PTO1 PTI1 • Regular waves PTO2 PTI2 d • Measurements: PTO3 PTI3 PTO4 PTI4 • Model displacement h PTO5 PTI5 • Free surface elevation a • Pressure at three Ballast b depths Spacing material S c hematic of model us ed in wave flume experimental tes ting
  14. 14. Lloyd’s Register services to the energy industry Validation Wavedirec tionC omparis on of dynamic pres s ure (normalis ed by incident wave amplitude) in the frequenc y domain
  15. 15. Lloyd’s Register services to the energy industry Validation Wavedirec tionC omparis on of dynamic pres s ure (normalis ed by incident wave amplitude) in the frequenc y domainWhere model has been rotated with res pect to wave direction to as s es s lateral pres s ures
  16. 16. Lloyd’s Register services to the energy industry What to take away from this…• Simple model can be used to effectively relate the pressure and free surface elevation for the piston mode of an OWC under certain conditions• Majority of losses must occur around or outside the column mouth to explain observed losses between Boundary Element Method model and physical testing• Model can be used to identify areas which can be modeled using simpler inviscid theory such that computational resources can be focused on areas with viscous phenomena
  17. 17. Lloyd’s Register services to the energy industryAny questions? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
  18. 18. Lloyd’s Register services to the energy industryFor more information, please contact:Rebecca SykesMechanical Engineer – Renewable Energy,Technology DirectorateLloyd’s Register Group ServicesDenburn House, 25 Union TerraceAberdeen, AB10 1NNT +44 (0)1224 267694E rebecca.sykes@lr.orgw www.lr.org/energyServices are provided by members of the Lloyds Register Group.For further information visit www.lr.org/entities

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