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Increasing power capture of a wave energy device by inertia adjustment
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  AppliedOceanResearch 34 (2012) 126–134 ContentslistsavailableatSciVerseScienceDirect Applied   Ocean   Research  journalhomepage:www.elsevier.com/locate/apor Increasing   power   capture   of    a   wave   energy   device   by   inertia   adjustment F.   Flocard a , ∗ , T.D.   Finnigan a , b a SchoolofCivilEngineering(J05),TheUniversityofSydney,NSW2006,Sydney,Australia b BioPowerSystemsPty.Ltd.,18BeresfordStreet,NSW2020,Mascot,Australia a   r   t   i   c   l   e   i   n   f   o  Articlehistory: Received4February2011Receivedinrevisedform5August2011Accepted18September2011 Available online 5 October 2011 Keywords: WaveenergyPitchingVerticalcylinderIrregularwavesExperimentalInertiamodification a   b   s   t   r   a   c   t This   paper   presents   results   from   an   experimental   study   on   the   power   capture   of    bottom-hinged   pitchingpoint   absorbers   in   intermediate   water   depth   subjected   to   both   regular   waves   and   irregular   waves.   Pointabsorber   wave   energy   converters   exhibit   high   power   capture   when   the   incoming   wave   frequency   is   closetothe   natural   frequency   of    the   device.   As   average   wave   periods   usually   range   between   5   and   15   sduringtheyear,   a   possible   way   to   improve   power   capture   efficiency   is   to   modify   the   wave   energy   converternatural   frequency   to   match   the   prevailing   wave   frequency.   The   purpose   of    the   work   presented   in   thispaper   is   to   optimize   the   power   capture   of    a   cylindrical   bottom-hinged   point   absorber   bymodifying   theinertia,   which   in   practice   could   be   implemented   by   allowing   some   compartment   of    the   device   to   be   filledwith   water.   The   results   of    our   experiments   showed   that   this   method   of    inertia   modification   could   resultin   an   increase   of    capture   factor   by70–100%   for   the   larger   regular   waves.   Irregular   wave   tests   showed   thattheuse   of    only   two   ballasting   configurations   could   lead   to   an   overall   capture   factor   of    55%   in   Summerand35%   in   Winter,   without   damping   optimization.   The   overall   benefit   of    inertia   modification   is   a   15–25%increase   in   power   capture   when   compared   to   a   constant   inertia   configuration. © 2011 Elsevier Ltd. All rights reserved. 1.Introduction Diminishingfossilfuelreservesandconcernaboutglobalwarm-inghavestimulatedtheadvancementofalternativeenergysourcessuchasoceanwaveenergy.Inordertobesuccessfulintheirdevel-opment,waveenergyconverters(WEC)mustbecommerciallyviable.Thatis,theymustbeabletosurviveoverextendedperiodsandprovideusefulenergyatacompetitiveprice.Waveenergydevicesareusuallyclassifiedaccordingtotheirlocationaseitheroffshore,nearshoreorshoreline[1].   Thedevicespresentedinthispaperbelongtothenearshorecategory(i.e.approximately25mdepth).ThisclassofWEC   devicespresentnumerousadvantagesoveroffshoredevices(i.e.lessexposuretoextremeforcesdevelopedinstormsbynaturalwavebreaking,reducedinstallationandmaintenancecosts)orshorelinedevices(i.e.lowervisualandenvironmentalimpacts,higherannualaver-ageincidentwavepower).Thesystempresentedinthispaperisusuallyreferredtoasbottom-hingedsystem.Itconsistsofacylin-dricalbuoyantsparthatcanpitchaboutahorizontalaxisneartheseafloornormaltotheincidentwavedirection.Thepitchingmotionisdampedbyapowertake-off(PTO)inordertoconvertthewavepowerabsorbedbythecylinderintousefulelectricalormechanicalpower. ∗ Correspondingauthor.Fax:+61293512136. E-mailaddress: francois.flocard@sydney.edu.au(F.Flocard). Theconceptofbottom-hingedwaveenergyconvertershasbeenpreviouslyinvestigated[2–5],oneofthemainadvantagesofthese devicesbeingawideefficiencybandwidth,withoutneedformotionrestriction,asthereisnoinherentend-stopissue.Suchasystemcanbedescribedasaforced-mass-spring-dampersystemanditsmotion,inthefrequencydomain,isdescribedas:( I  + I  a ( ω ))¨   + ( c  r   + c  PTO )˙   + K  = M  wave , (1)where I  ismomentofinertiaofthecylinderand I  a  frequency-dependentaddedmomentofinertia,accountingfortheinertiaof thewatersurroundingthecylinder.Thedampingiscomposedof thedampingfromthePTO( c  PTO )andtheradiation c  r  ,accountingfortheenergytransferredtowavesbeingradiatedaway.Therestoringmomentduetobuoyancycanbemodelledasaspringstiffness K  .OntherightsideofEq.(1),   M  wave  istheexcitationmomentcausedbytheactionofthewavesonthepitchingstructure.Previousstudieshaveproventhatifthedeviceistobeanefficientabsorber,itsown   frequencyofoscillationshouldmatchthefrequencyoftheincomingwaves,andthereforeoperateatnear-resonanceconditions,withincreasedamplitudeandspeedresultinginhigherpowercapture.ControlmethodshavebeenpreviouslyproposedformaintainingtheWEC   nearresonancebyreactivecontrol[6]orthroughlatching[7]onawave-by-wave basis.Whiletheseshort-termcontrolstrategiescanleadtoasubstantialincreaseinpowercapture,theyoftenrequireperfectforeknowledgeoftheincidentwave(whichposescertainchal-lenges)andamorecomplexPTOmechanism.Recentwork[8,9] 0141-1187/$–seefrontmatter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apor.2011.09.003  F.Flocard,T.D.Finnigan/AppliedOceanResearch  34 (2012) 126–134 127 onlatchingofanoscillatingwatercolumn(OWC)usinganon-predictivecontrolmethodhasshownpromisingresultsandcouldbetransposedtopitchingorheavingWECs.Anotherapproach,oftenreferredtoas‘slow-tuning’[10],involvesvaryingthesystem’snaturalfrequencytoapredetermineddominantsea-statefrequencybyadjustingthedevice’sstiffnessorinertia.Theadvantageofthismethodisthatitoperatesonlongertime-framesandreducesdemandsonthePTOsystem[11].This controlmethodhasbeenrecentlyexperimentallytestedonheav-ingpointabsorbersandprovedtoyieldsignificantincreasesinpowercapture[12]butalsoinmaintainingthefloatmotionwithin adesiredrange[13].Forabottom-hingedWEC,thenaturalfrequency( ω n )isafunc-tionoftheratioofthebuoyancytermtothetotalinertia, ω n  =    K I  + I  a , (2)whereitisclearthatanadjustmentof  I  couldbeusedtotunetheresponseofthedevice.Theprocessofinvestigationforthepresentworkwastofirsthavethedeviceoptimallytunedforlowenergywaveclimatesinanunballastedconfiguration;then,formoreenergeticwavecon-ditions,toallowseawatertofillexistingcompartmentslocatedinthecylinderinordertomaintainorincreaseitsperformanceinthemorepowerfulseas.Shorttermcontrolstrategiesareinherentlydifficulttoimple-mentduetotherequiredknowledgeoffutureindividualwaveconditions,bynaturehighlyirregular.Ontheotherhand,slow-tuningcontrolhastheadvantageofbeingbasedaroundlongertimeintervals(i.e.hours)makingitpossibletousereliablepre-dictionsofglobalwavemodels,suchasNOAA’sWAVEWATCHIII.Thephysicalimplementationofthecontrolprocedure,thatisfillingoremptyingvolumesofadozenorsocubicmeters,isafeasi-bleengineeringchallengeandhasbeensuccessfullyemployedforadjustingthefreeboard,andyieldthemaximumovertoppingeffi-ciencyindifferentwaveconditions,ofthefloatingdeviceWaveDragon[14].Finally,itisoftheutmostimportancethatthedeviceisabletosurviveinlargewaveeventsorstorms.Abottomfixedpitchingdeviceoffersthepossibilitytocompletelyfilltheballastcompart-ment,allowingthedevicetobeloweredintoahorizontalpositionparalleltotheseabed,therebyavoidingthepotentiallydestruc-tiveconditionsfoundneartheseasurface.Oncewaveconditionsareconsideredtobesafeagain,pumpingairbackintothecom-partmentwouldallowthedevicetoreturntoaworkingposition.Moreover,thisfeaturecanalsobeusedtofacilitateinstallationormaintenanceoperations.Thispaperpresentsresultsofanexperimentalstudyontheinfluenceofinertiamodificationonpowercapture,inbothreg-ularandirregularwaves.Itbeginswithabriefpresentationoftheexperimentalsetupandofthedifferentwaveconditionsconsid-ered.Theinfluenceofinertiamodificationonpowercaptureandpitchingamplitudeisthenpresentedforregularandirregularwaveconditions. 2.Experimentalsetup ThetestswereconductedintheUniversityofSydneywaveflume.Theflumeis30mlong,1.0mwideandhasameanwaterdepthof0.75m.   Wavesweregeneratedbyadisplacementpistonwave-makerfromEdinburghDesignsLtd.Themodelwasposi-tionedonthecentrallineofthewaveflumeatadistanceof7mfromthewave-maker(seeFig.1).Thewaveelevationswererecorded bythreewavegaugeslocatedaroundthecylinderwitha100Hzsamplingfrequency.Froudescalingwasusedtoinferprototype 3m30m7mWave probe spacing 1.4m0.75mStill Water BeachWavePaddleLevel Fig.1. Layoutoftheexperimentalsetupinthewaveflume(nottoscale). resultsforourexperimentssincegravitationaleffectsarepredom-inantoverfactorssuchasroughness,viscosityandsurfacetension.Aprototypewaterdepthof25mwas   chosen,which,forthewaveflumedepthof0.75m,   givesageometriclengthscalefactorof   =33.UsingFroudescalinghassomelimitations,asitneglectstheinfluenceofviscouseffects,suchasdrag.However,thedampingduetoviscousdragatmodelscaleisexpectedtobegreaterthanatprototypescale,astheReynoldsnumberislowerthanfortheprototype.Thepowercaptureresultsfromthetestscanthereforebeconsideredconservative.TheexperimentalrigshowninFig.2iscomposedofanunder- watershaft,onwhichthebuoyantcylinderisinstalled,mountedonlowfrictionbearings.Asecondrotatingshaftismountedontopofthewavetanksupportingallthesensors.Thetwoshaftsarecoupledthroughthinpre-tensionedstainlesssteelwires.Suchaset-uphastheadvantageofensuringsensorsareaccessibleandoutofthewater.Thesensorsuiteconsistsofa1000pulsesperrevolutionlow-frictionrotaryencoderandareactiontorquesen-sor.Thetorquesensorismountedfloatingontheshaft,suchthatonlythetorqueagainstarotaryviscousdashpotismeasured.Theinstantaneouspowerabsorbedbythecylinderisobtainedthroughthemeasurementsofthereactiontorquesensor( T  )andtheangularencoder(   )andisgivenby: P  ( t  ) = T  ( t  )˙   ( t  ) . (3)Theadjustabledashpotallowsthedampingratetobevaried.Thedampingratewas   fixedforeachexperiment,forwhichthedashpotactedasalineardamper,representativeofatypicalexter-nalpowertake-offmechanism.Mechanicalfrictioninthesystemisconsiderednegligiblewhencomparedtoviscousanddashpotdamping.Thetwodifferentcylinderstestedeachhadahemisphericalcompartmentatthetopthatcouldbefilledwithballastmaterialinordertotesttheeffectofmodifyingcylinderinertiaandthereforesimulatingtheeffect,atprototypescale,ofallowingwatertofillsomeportionofthecylinder(i.e.waterballasting).Themainchar-acteristicsofthecylindersaregiveninTable1f ortheunballasted cylinderandinTable2f orthedifferentballastingconfigurations. Testingtwo   differentgeometriesallowedthecomparisonofthepowercaptureofasurface-piercingdevice(suchascylinderH,forhigh),andadevicehiddenbelowtheoceansurface(cylinderL,forlow).AsrecommendedbyChakrabarti[15],thedimensionsofthe widestshapestesteddidnotexceed1/5thofthetankwidth.Despite  Table1 Geometriccharacteristicsofthedifferentconfigurations(H&L)tested.CylinderHL  D (m)   0.20.2 H    (m) 0.5370.537 H  d  (m)   0.4770.537  z   p  (m)   0.03 − 0.05  128  F.Flocard,T.D.Finnigan/AppliedOceanResearch  34 (2012) 126–134 z  D x θ d  M.W.L.(a) Side view(b) Front viewBallasting Compartment  H  H  d   z  G  z   p Sensor Suiteon Top Shaft Bearings Fig.2. Layoutoftheexperimentalsetupinthewaveflume. followingthisrule,itisclearthatwallreflectionhadaninfluenceontheradiatedwavesandthepowercapturedbythedifferentshapes.Forthesereasons,itcanbeconsideredthattheresultsarerepresen-tativeofthebehaviourandtheperformanceofoneverticalcylinderinaninfinitelineararrayofdevices.Themodificationofinertiaduetotheballastingresultedinachangeofthelocationofthecentreofgravity(  z  G ),pitchingmassmomentofinertia( I  a )andthenaturalfrequency(  f  n )ofthedevice,asdeterminedthroughdecaytestsinstillwater.Modificationof inertiawasachievedbyaddingdifferentmixturesofsandandleadshotintothehollowcompartment.Theadditionalmassvar-iedbetween1.1and4.1kg.Geometricalparameterssuchastotalheightofthecylinder( H  ),thedraft( H  d ),thelocationofthecylin-dertipinrelationtothewatersurface(  z   p )orthediameterareunchangedbythesemodifications.Forascalingratioof   =33,afull-scaleprototypewith6.6mdiameterwouldthenhavearangeofnaturalperiods T  n  between7and15s,whichwouldallowittobenaturallytunedtorealisticwaveperiods,rangingfromlowenergeticwaveconditionstowhatcouldbeexpectedduringastormorheavyswellconditions.  Table2 Inertiacharacteristicsofthedifferentconfigurationstested.Shape# m (kg)  z  G  (m)   I  a  (kgm 2 )  f  n  (Hz)ColorHB0 4.9200.2990.9830.58HB16.0150.2461.4880.54HB27.0200.2111.9560.47HB3 7.8600.1892.3620.44HB4 9.0350.1642.9350.38LB04.8000.3680.7070.72LB15.9400.3161.1000.61LB2 6.9300.2831.4670.54LB3 7.7700.2611.7810.50LB48.9200.2372.2270.42 3.Waveconditions  3.1.Regularwaves Thefirstsetsofexperimentswereconductedinregularwaveswithmodelfrequenciesfrom0.40Hzto1.0Hz,whichcorrespondstofull-scalewaveperiodsfrom5.7sto14.3s.Thewaveamplitudesgeneratedbythepaddlewererangedbetween1.5and6.0cmcor-respondingtofull-scalewavesrangingapproximatelybetween1and4mheights.TheseconditionsspantherangeacrosswhichaWEC   canbeexpectedtobeproductivewhendeployedintheocean.Theseregularwavescanallbedescribedasintermediatewaterdepthwavesandrangefromweaklynon-lineartoStoke’sprogressivesecondorderwaveregimes.Fortheintermediatewaterdepthwaveconditionsstudied,inci-dentwavepower[16]isadirectfunctionofwaveamplitude a i  andthewavegroupvelocity c   g  : P  i  = 12 ga 2 i  c   g  . (4)  3.2.Irregularwaves Itisofgreatimportancetostudythebehaviourandthepoweroutputofwaveenergydevicesinirregularwavefieldswhicharerepresentativeofrealoceanconditions.Moreover,itisusefultotestcanonicalstructuresinrealisticwaveclimatesthathavebeenexperiencedbyexistingdevices.ThecombineduseofEuropeanMarineEnergyCentre(EMEC)scattertablesandempiricalspectralshapesallowthegenerationofrealisticwaveconditionsandpowercapturepredictions.TheEMECisaresearchcentrefocusingonwaveandtidalpowerdevelopmentbasedontheislandofOrkney,anarchipelagoinnorthernScotland.WavedatawasrecordedattheBilliaCroowavetestsite,located2kmfromshore,inawaterdepthof50m.   The  F.Flocard,T.D.Finnigan/AppliedOceanResearch  34 (2012) 126–134 129  Table3 Irregularwavescharacteristics(model-scaleandfull-scale)usedfortheexperiments.Zone#Occ.(%)ModelscaleFullscale H  s  (mm)   T  e  (s) H  s  (m)   T  e  (s) P  i  (kW/m)Summer19.8130.980.45.60.52   19.1161.360.57.81.23   14.2561.011.85.89.84 15.1   60 1.1526.613.65 29.4   561.331.97.614.16   5.8801.482.68.532.17   3.6671.862.210.727.48   31091.73.69.867.7Overall–451.221.578.3Winter 1 8.252 1.261.77.211.32 7.4   731.692.49.730.33   12.5961.293.27.439.64   37.11301.474.38.583.55   23.41381.714.69.9109.56 7.1   1492.014.911.6144.77   2.91851.976.111.32188   1.51312.234.312.8119.1Overall–1091.573.79.263 yearlyaveragewavepoweravailableatthesiteisaround30kW/m.Ithasbeenpreviouslydemonstrated[17]thatthewavespectraat theOrkneyTestCentrecanbeexpectedtoyieldasimilarpowercontentonaveragetoBretschneiderspectraofthesamecharacter-istics.Bretschneiderspectraareoftenconsideredinoceanwaveenergystudies[18,19]andareinagoodagreementwiththepreva- lentwaveconditionsfoundintheNorthSeaandSouthPacific.Theyareafunctionofsignificantwaveheight( H  s )andpeakfrequency(  f   p ),definedas: S B (  f  ) = 516 H  2 s  f   p   f   p  f   5 e − 54   f  p f   4 . (5)DataobtainedfromtheEMECconsistedof12scattertablesspanningover2006and2007.Afteranalysisoftheyearlydata,thedecisionwasmadetocreatetwodifferentwaveclimates,oneveryenergetic,calledWinterandconsistingofthethreemostener-geticconsecutivemonths;andanothercalledSummer,fromthelessenergetictrimester.Thetrimestertablescontainednearly4500recordsanditwasnecessarytosimplifythesetablesinordertohaveafeasiblenumberoftests.Thiswasachievedbyconductingazonation,usingasimplifiedversionofthemethoddevelopedby[20],onthescattertabletocreatebiggercells,eachwithitsown H  s andenergyperiod T  e  characteristics.Theselectionofthedifferentzones,8perseason,wasbasedonthepowerlevelsofthecellsandtheirfrequencyofoccurrence.ThissimplificationenabledustostillhaveareasonablerepresentationoftheEMECwaveclimatewhilebeingabletoanalysethebehaviourofthedeviceinverydifferentwaveclimateconditions(seeTable3).Theincidentwavepower[16]containedintheirregularwave fieldisexpressedas: P  i  = g     ∞ 0 c   g  (  f  ) S B (  f  ) df, (6)where  isthewaterdensity,gistheaccelerationduetogravityand c   g   isthewavegroupvelocity. 4.Results 4.1.Regularwaves ThemostcommonwaytomeasuretheefficiencyofaWEC   isthecapturewidthratio c   f  ,definedastheratioofcapturewidth  c  = P  PTO / P  i ,where P  PTO  isthepowerabsorbedbythedeviceand P  i istheincidentwavepowerperunitwidth,tothephysicalwidthof thedevice( D =0.2m), c   f   = P  PTO P  i D .   (7)Fig.3(a)displaysthevariationofcapturewidthratio,forCylin-derHinitsunballastedconfigurationsubjectedtoregularwaves.Theso-called“pointabsorbereffect”isdemonstratedwithcapturewidthrationeartoorgreaterthanoneclosetothenaturalfre-quency( ω n =0.72Hz).Thegreatestperformanceisfoundforthesmallestseasstates,asviscouslossescanbeexpectedtobelowinsmallamplitudewaves.Thecapturewidththeoreticalmaxi-mumforpitch-surgedeviceshasbeenshowntobeequalto  /  [22];incomparison,duringthetests,thehighestcapturewidthwas   recordedforCylinderHatavalueof   /4  .ThiseffectcanberelatedtotheKeulegan–Carpenternumber(KC)oftheupperpartof thecylinder,whichincreaseswithwaveheightcausingtheviscous 024681012         θ    m   a   x    [          °    ] 0.4   0.5   0.60.70.80.91  f [Hz] i 0.015 0.020.025 0.030.035 0.040.045 0.050.055 0.06 a i  [m]    c     f    [  −   ] 0.20.40.60.811.20 (a)(b) Fig.3. (a) c   f   and(b)maximumpitchingangle   max  forconfigurationHB0subjectedto   regularwaves.  130  F.Flocard,T.D.Finnigan/AppliedOceanResearch  34 (2012) 126–134 024681012         θ    m   a   x    [          °    ] 0.4   0.5   0.6   0.7   0.8   0.9   1  f [Hz] i 0.015 0.020.025 0.030.035 0.040.045 0.050.055 0.06 a i  [m]    c     f    [  −   ] 0.20.40.60.811.20 (a)(b) Fig.4. (a) c   f   and(b)maximumpitchingangle   max  forconfigurationHB3subjectedtoregularwaves. dragdampingtoincreaseaswell,andwasstudiedinananalyti-calworkby[21].Smallerwaveconditionsallowfortheideallinear conditionsofthepointabsorbertheory.Ontheotherhand,itcanbenotedthat c   f   increasesmonotonicallyathigherfrequencyforlargewaveamplitudes.Thisphenomenonwasalsoreportedby[23]f ora bottom-pitchingflapandcanbeexplainedbytherelationbetweenwavesurgeforceandwavefrequency,asshorterwavesexperi-encelargerhorizontalwaterparticleaccelerationandthusinducealargerforceonthestructure.However,suchlargewavesathighfrequencyareunrealistic.Addingasupplementarymassof  m c  =2.9kginthecompartmentlocatedatthetopofthecylinderhasatwo-foldeffect,asitincreasesthemomentofinertia I  a  byafactor2,whiledecreasingsimul-taneouslytherestoringmomentduetonetbuoyancy.As I  a  isindependentoftheinertiamodification,thisresults(seeEq.2)ina decreaseofthenaturalfrequency( ω n =0.44Hz,equivalenttoafull-scale T  n ≈ 13s),shiftingitclosertothatoflargerwaves.AscanbeseeninFig.4(a),whileasignificantdecreasein c   f   canbeobservedforwavesofsmalleramplitudes,withamaximumvaluecloseto0.6, c   f   isalmostdoubledwithwaveswithfrequenciesbelow0.6Hz.Theincreasedinertiaresultsinlargerpitchingangles(seeFig.4(b)), peakingclosetothenaturalfrequencyoftheballastedcylinder,andthereforehigherlossesduetoviscouseffects,relatedtodragcausedbyproductionofturbulence.Ananalysisofthepitchinganglesofthesystemwasperformedinordertoinvestigatenon-linearbehaviourandstudythecouplingofthecylindermotionwiththewaterparticletrajectory.AnRAO(ResponseAmplitudeOperator)wasintroduced,referredtoaspitchasymmetryRAO(RAO   asym )anddefinedas:RAO   asym  = (   max +   min ) Da i , (8)wheremaximumpositivepitchangle(   max )referstothedown-wavedirection(i.e.towardsthebeach),minimumnegativepitchangle(   min )referstotheup-wavedirection(i.e.towardsthepad-dle).Fig.5showsthevariationofthepitchasymmetryRAOwith wavefrequencyinregularwavesofincreasingamplitudeforthreedifferentcases.Fig.5(a)and(b)presenttheresultsforcylinderH D0fortwosettingsoftheviscousdashpots( c  D 1 ≈ 4.0Nms/rad& c  D 2 ≈ 10.0Nms/rad),whileFig.5(c)showstheresultsforcylinder −0.3−0.2−0.100.10.20.30.4   0.60.81  f [Hz] i 0.40.60.81  f [Hz] i 0.4   0.6   0.8   1  f [Hz] i −0.3−0.2−0.100.10.20.3(b) H B0 D2   (a) H B0 D1(c) L B0 D2    R   A   O         θ    a   s   s   y   m     [  -   ] 0.015 0.020.025 0.030.035 0.040.045 0.050.055 0.06 a i  [m] Fig.5. RAO   asym  forconfiguration(a)HB0underdampingcoefficient c  D 1 ,(b)HB0underdampingcoefficient c  D 2  and(c)LB0underdampingcoefficient c  D 2 . LD0dampedat c  D 2 .TheyalldisplaythesametrendofageneralpositivegradientforthepitchasymmetryRAO,startingnegativeandcrossingthezeropointclosetothenaturalfrequencyofthesystem.ItcanalsobeobservedthatRAO   asym  doesnotseemtovaryexcessivelywithwaveheight,dampersettingandthereforepitchangle.Thus,thepitchasymmetrycanbeassociatedwiththephaserelationshipbetweenthewaveandmotionofthedevice.Anexplanationforthisbehaviouristheincreaseofforcingmomentontothestructureinshorterwaves.Fig.6displaystheperformanceoffourdifferentballastconfigu-rations(B0,B1,B2andB3)ofthecylinderHsubjectedtofourregularwaveconditionsofincreasingamplitudeattheconstantdampingcoefficient c  D 2 .Analysisofoceanwavedatashowsthat,generally,increasingwaveheightisaccompaniedbyincreasingwaveperiod.Therefore,thewhitebackgroundineachofthefoursubplotshigh-lightsthefrequencyrangeoverwhichawaveofthisamplitudewouldbeexpectedtooccurintheocean.Thisfiguredemonstratesthebenefitofadaptiveinertiamodification,aseachofthedifferentconfigurationsperformsbestforoneoftheregularwavecondition.TheHB0configuration,takenasareference,reachesthehighest c   f  ( ≈ 0.90)intheapplicablefrequencyrange(periodrangeequivalentto6.5–7.5satfull-scale)forthesmallestwave(0.015mequiva-lenttoa1mheightatfull-scale).Oneprobableexplanationfortheverysharpdecreaseatthehighestfrequenciesisasub-optimaldampersetting,astheviscousdashpotmay   notbeadequateforsuchpitchingfrequencies.TheadditionalinertiaforB1leadstoanincreasein c   f   of17%for a i =0.030mfor  f  i  lowerthan0.55Hz.Forthelargestwave( a i =0.030mequivalentto4mfull-scale),HB3improvestheefficiencysubstantially,withanincreasein c   f   of 75%.Thecomparisonofdifferentinertiaconfigurationsforcylin-derLgavethesameresults,withLB0exhibitingthehighestpowercapture( c   f  =0.90)inthesmallerandshorterwavesandLB3out-performingtheotherinertiasettingsathighperiodsandlargerwaves.However,thelowerpositioninthewatercolumnresultedinadecreaseofapproximately15%inefficiency. 4.2.Irregularwaves CylinderconfigurationsHandL,eachwithfivedifferentinertiasettings(seeTable2),weretestedinthe18irregularwavecondi- tionsdescribedinTable3.Figs.7and8presentthepowercapture comparisonforboththeSummerandWinterwaveconditions,forcylinderLandH,respectively.Itwasobservedthatthecapturefactorishighestforthesmallestsea-states,withsmallsignificant
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