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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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Lloyd’s Register services to the energy industry A simplified model for oscillating water column motion Rebecca Sykes Mechanical Engineer Technical Directorate May 23, 2012
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 shoreline Power is extrac ted from the wave induced vertic al motion of the water free s urface c ompres s ing air in a volume above. This can be us ed to drive an air turbine, s uch as the Wells turbine, whic h is des igned for rec iprocating flows .
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 OWC Majority of propos ed/prototype offs hore OWC have been floating but there is potential to c ombine with other tec hnologies and s o us e their s upport s tructure
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 Column Floating – 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 motion THEREFORE: Increased complexity in predicting the energy capture
Lloyd’s Register services to the energy industry OWC modelling Three previous ly us ed modelling techniques Numerical modelling Analytical modelling Physical modelling Computational time/ Device/geometry specific High time and cost accuracy trade-off Specialist mathematical Scaling Need for verification and skills Increased potential for validation Need for verification and error at small scale Application of OWC validation boundary condition not always easily available
Lloyd’s Register services to the energy industry Simplified 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
Lloyd’s Register services to the energy industry Mathematical model Initially c ons idering a fixed OWC to examine the diffraction pres s ure Time 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 internal Which gives the frequency domain equation volume of water − ω 2 ρ ( L + η 0 )η1 + ρgη1 = p1 ˆ ˆ
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 -0.15 z (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
Lloyd’s Register services to the energy industry Structure for validation – fixed model to validate 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
Lloyd’s Register services to the energy industry Validation C omparis on of diffraction pres s ure (normalis ed by inc ident wave amplitude) in the frequenc y domain
Lloyd’s Register services to the energy industry Mathematical model for floating OWC When 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 ture that 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  d where 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)
Lloyd’s Register services to the energy industry Mathematical 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.
Lloyd’s Register services to the energy industry Floating 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
Lloyd’s Register services to the energy industry Validation Wave direc tion C omparis on of dynamic pres s ure (normalis ed by incident wave amplitude) in the frequenc y domain
Lloyd’s Register services to the energy industry Validation Wave direc tion C omparis on of dynamic pres s ure (normalis ed by incident wave amplitude) in the frequenc y domain Where model has been rotated with res pect to wave direction to as s es s lateral pres s ures
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
Lloyd’s Register services to the energy industry Any questions? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Lloyd’s Register services to the energy industry For more information, please contact: Rebecca Sykes Mechanical Engineer – Renewable Energy, Technology Directorate Lloyd’s Register Group Services Denburn House, 25 Union Terrace Aberdeen, AB10 1NN T +44 (0)1224 267694 E rebecca.sykes@lr.org w www.lr.org/energy Services are provided by members of the Lloyd's Register Group. For further information visit www.lr.org/entities

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A simplified model for oscillating water column motion

  • 1. Lloyd’s Register services to the energy industry A simplified model for oscillating water column motion Rebecca Sykes Mechanical Engineer Technical Directorate May 23, 2012
  • 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 shoreline Power is extrac ted from the wave induced vertic al motion of the water free s urface c ompres s ing air in a volume above. This can be us ed to drive an air turbine, s uch as the Wells turbine, whic h is des igned for rec iprocating flows .
  • 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 OWC Majority of propos ed/prototype offs hore OWC have been floating but there is potential to c ombine with other tec hnologies and s o us e their s upport s tructure
  • 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 Column Floating – 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 motion THEREFORE: Increased complexity in predicting the energy capture
  • 5. Lloyd’s Register services to the energy industry OWC modelling Three previous ly us ed modelling techniques Numerical modelling Analytical modelling Physical modelling Computational time/ Device/geometry specific High time and cost accuracy trade-off Specialist mathematical Scaling Need for verification and skills Increased potential for validation Need for verification and error at small scale Application of OWC validation boundary condition not always easily available
  • 6. Lloyd’s Register services to the energy industry Simplified 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. Lloyd’s Register services to the energy industry Mathematical model Initially c ons idering a fixed OWC to examine the diffraction pres s ure Time 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 internal Which gives the frequency domain equation volume of water − ω 2 ρ ( L + η 0 )η1 + ρgη1 = p1 ˆ ˆ
  • 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 -0.15 z (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. Lloyd’s Register services to the energy industry Structure for validation – fixed model to validate 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. Lloyd’s Register services to the energy industry Validation C omparis on of diffraction pres s ure (normalis ed by inc ident wave amplitude) in the frequenc y domain
  • 11. Lloyd’s Register services to the energy industry Mathematical model for floating OWC When 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 ture that 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  d where 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. Lloyd’s Register services to the energy industry Mathematical 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. Lloyd’s Register services to the energy industry Floating 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. Lloyd’s Register services to the energy industry Validation Wave direc tion C omparis on of dynamic pres s ure (normalis ed by incident wave amplitude) in the frequenc y domain
  • 15. Lloyd’s Register services to the energy industry Validation Wave direc tion C omparis on of dynamic pres s ure (normalis ed by incident wave amplitude) in the frequenc y domain Where model has been rotated with res pect to wave direction to as s es s lateral pres s ures
  • 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. Lloyd’s Register services to the energy industry Any questions? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
  • 18. Lloyd’s Register services to the energy industry For more information, please contact: Rebecca Sykes Mechanical Engineer – Renewable Energy, Technology Directorate Lloyd’s Register Group Services Denburn House, 25 Union Terrace Aberdeen, AB10 1NN T +44 (0)1224 267694 E [email protected] w www.lr.org/energy Services are provided by members of the Lloyd's Register Group. For further information visit www.lr.org/entities