Rebecca Sykes Mechanical Engineer Technical Directorate May 23, 2012

Transcription

1 A simplified model for oscillaing waer column moion Rebecca Sykes Mechanical Engineer Technical Direcorae May 23, 202

2 Oscillaing waer column Convenional OWC have been shoreline devices LIMPET, Scoland Pico, Azores Sanze, Japan Wave shoaling reduces energy o shoreline

3 Oscillaing waer column Jacke Graviy based TLP Floaing OWC Convenional OWC have been shoreline devices LIMPET, Scoland Pico, Azores Sanze, Japan Wave shoaling reduces energy o shoreline Poenial for greaer energy exracion offshore Opions fixed, semi-fixed or floaing

4 Objecive To presen a model ha furhers our undersanding of he physical processes wihin a floaing Oscillaing Waer Column Floaing cheaper CAPEX opion () bu more complex o simulae he diffracion and radiaion problem which exised for he fixed OWC mus be exended when floaing o include radiaion from he device moion THEREFORE: Increased complexiy in predicing he energy capure

5 OWC modelling Numerical modelling Compuaional ime/ accuracy rade-off Need for verificaion and validaion Applicaion of OWC boundary condiion no always easily available Analyical modelling Device/geomery specific Specialis mahemaical skills Need for verificaion and validaion Physical modelling High ime and cos Scaling Increased poenial for error a small scale

6 Simplified OWC model Simple model o highligh fundamenal physics Resonan device, hydrodynamically narrow banded in frequency Verical oscillaion -power producing oscillaion

7 Mahemaical model Time domain pison model from []: S L OW C OW C Sg OW C SP OW C () η OWC and P OWC can be expanded as series in powers of he small parameer OWC and P OWC 0 P 0 P P P Subsiuing ino () and aking hose erms up o firs order S L 0 Sg P S (2) OWC Assuming and P are harmonic such ha Re ˆ e i P Re p e i Which gives he frequency domain equaion 2 L ˆ ˆ 0 g p P OWC

8 z (m) z (m) Lloyd s Regiser services o he energy indusry Mahemaical model predicion y (m) x (m) y (m) x (m) Pressure magniude Pressure phase

9 Srucure for validaion A I x z η OWC p z = -270mm p z = -20mm p z = -44mm Verical cylinder: o o o b = 50.5mm a = 47.0mm d = 300mm o h = m d Tank: 2.65m x 23.27m h Regular waves Measuremens: Wave probe a b o o Free surface elevaion Pressure a hree dephs

10 Validaion

11 Mahemaical model for floaing OWC Sloshing modes naural frequencies for fluid in a cylindrical ank: 2 g n nd n anh a a where κ n =.842, 5.334, ,.706, ,, κ n = κ (n ) +. a d Pressure due o acceleraion and sloshing in surge: Pressure due o acceleraion and sloshing in pich: P 2 cos sin r A P cos sin rz A

12 Mahemaical model for floaing OWC p p p p gz ' g y' x' T Pison model Due o pich Hydrosaic Due o surge where p and p are he complex ampliudes of he acceleraion and 5 sloshing pressures and (x', y', z') are he body fixed coordinaes of a general posiion on he wall.

13 Floaing srucure for validaion Reflecive marker z Wave probe Model dimensions: 2b =35mm 2 a = 04mm d = 300mm A I PTO PTO2 PTO3 PTO4 PTO5 x PTI3 PTI4 PTI5 PTI PTI2 d h h = m Tank: 2.65m x 23.27m Regular waves Measuremens: Model displacemen Free surface elevaion Ballas Spacing maerial a b Pressure a hree dephs

14 Validaion Wave direcion

15 Validaion Wave direcion

16 Wha o ake away from his Simple model can be used o effecively relae he pressure and free surface elevaion for he pison mode of an OWC under cerain condiions Majoriy of losses mus occur around or ouside he column mouh o explain observed losses beween Boundary Elemen Mehod model and physical esing Model can be used o idenify areas which can be modeled using simpler inviscid heory such ha compuaional resources can be focused on areas wih viscous phenomena

17 Any quesions

18 For more informaion, please conac: Rebecca Sykes Mechanical Engineer, Technology Direcorae Lloyd s Regiser Group Services Denburn House, 25 Union Terrace Aberdeen, AB0 NN T +44 (0) E rebecca.sykes@lr.org w Services are provided by members of he Lloyd's Regiser Group. For furher informaion visi