Excitation Forces on Point Absorbers Exposed to High Order Non-linear Waves

63 Pages·2013·7.75 MB·English

EXCITATION FORCES ON POINT ABSORBERS
EXPOSED TO HIGH ORDER NON-LINEAR WAVES
MASTER THESIS
THOMAS HANSEN VIUFF | MORTEN THØTT ANDERSEN
M.SC., CIVIL ENGINEERING | AALBORG UNIVERSITY | 4. SEMESTER | SPRING 2013

FacultyofEngineeringandScience
SchoolofEngineeringandScience
Sohngårdsholmsvej57
9000Aalborg
Abstract:
Title:
Wave energy devices are often located in inter-
Excitation Forces on Point Absorbers
mediate or shallow water close to the free water
Exposed to High Order Non-linear
surfacewherethewaveexposureisextreme. The
Waves
structures typically consist of large thin curved
plates, spherical shells, or cylindrical structures
which are sensitive to pressure loads. The lack
Projectperiod:
of proper methods to calculate design pressure
distributionshasledtostructuralfailuressuchas
4rd semester,M.Sc. Structuraland bucklingintheshellsinwaveenergyprototypes.
CivilEngineering,Spring2013 As a step towards understanding the complex
loading from high order non-linear waves, this
paper presents a practical approach to estimate
wave excitation forces accounting for both non-
linearity and diffraction effects. The method
is validated by laboratory experiments using a
ThomasHansenViuff hemispherical point absorber with a 6-axis force
transducer, but the technique is believed to be
applicableformosttypesofsubmergedorsemi-
submergedfloatingdevices.
MortenThøttAndersen The applied method is based on calculation of
a peak force coefficient defined as experimen-
tally measured forces on the structure divided
by forces estimated by the chosen theoretical
method. Methods used include an integration of
Supervisor:
the undisturbed wave pressure over the surface
MortenMejlhedeKramer
of the structure, corresponding to the Froude-
Krylov force, and a numerical solution to linear
Circulations: 4
potential diffraction theory. Since the two meth-
Numberofpages: 52
ods have mutual limitations in describing higher
DigitalappendicesonCD
orderwavesanddiffraction,acombinationofthe
CompletedonMondaythe10th ofJune2013
twowillbeintroduced.
Thedissertationisfreelyavailable,butpublication(withreference)maybemadeonlyinagreementwiththeauthors.

Summary in English
The original proposal for this dissertation comes through some of the structural problems
experiencedbyWavestarregardingtheloadsonthefloatingpointabsorber. Duetopriorbuckling
failuresinthefloatshell,thescopeofthisdissertationstartedoutbeinghowtoobtainatimeand
spatially dependent pressure coefficient linking undisturbed pressures to real pressures. During
the progress of the work, the focus have shifted to a better description of peak excitation forces
onthefloat. Thisshiftisdone,basisoftheassumptionthatonceagreaterunderstandingofpeak
forces is achieved, it will later be less complicated to decompose these into pressures since the
theoretical methods all contain a pressure distribution. The final form of the dissertation product
consistsofthreeparts.
• PartII-Thepaper"ExcitationForcesonPointAbsorbersExposedtoHighOrderNon-linear
Waves".
• PartIII-Anappendixfortheconferencepaper.
• PartIII-Twopostersexplainingresearchdonepriortofinalformulationofpaper.
The paper is written by Thomas H. Viuff and Morten T. Andersen under supervision of Morten
M.KramerandwithexperimentalassistancefromMortenM.Jakobsen. Itismeanttobeableto
standalone,butforclarifyingquestionstheappendixcanbeusedtosomeextend. Thepostershave
beenpresentedontheINORE2013symposiuminPembrokeshire,UK,alongwiththepreliminary
resultsavailableatthetime.
The work in the parts mentioned above all revolve around describing the complex loads from
higherorderwavesonthehemisphericalshellbyusingdifferentmethodswithmutuallimitations
and compare these to experimental results. A Froude-Krylov force is obtained by integration
of pressures from an undisturbed wave field on a discretized float shell. This approach is able to
modelthehigherorderwavesandherebyalsodescribethechangingamountofsubmergedvolume
ofthefloat,butneglectallcontributionsfromdiffractionandreflection. Totakethesephenomena
into account the numerical tool WAMIT is used to solve the linear potential diffraction theory,
the trade-off by this is the inability to account for the change in surface elevation. In the paper
a practical method of combining these theories is presented. This method applies a coefficient
of diffraction to the higher order Froude-Krylov force and the combined results are compared to
experimentalmeasurements.
v

Summary in Danish
(Sammendrag)
DenoprindeligeidetilspecialetvardrevetaffirmaetWavestarsproblemstillingmedestimeringen
af bølgelaster i forbindelse med det strukturelle design af flyderen. Med et tidligere
konstruktionsmæssigt kollaps som følge af en underestimering af bølgelasterne var den
oprindelige ide med specialet at finde en tids- og positionsafhængig trykkoefficient som
kombinerede uforstyrede potentialteoretiske trykberegninger med den virkelige trykfordeling på
flyderskallen. Igennemarbejdetmedspecialetændredeprojektetretningtilathavemerefokuspå
enpraktiskbeskrivelseafdemaksimalehorisontaleogvertikalebølgelaster. Overgangentildette
fokus er gjordt ud fra antagelsen om at når en dybere forståelse for de maksimale bølgelasters
parameterafhængighed vil det derefter være lettere at opdele kræfterne i trykfordelinger, da de
teoretiskemetoderalleredemedtagertrykfordelingen. Specialetsendeligeopdelingersomfølger.
1. Del I - Artiklen "Excitation Forces on Point Absorbers Exposed to High Order Non-linear
Waves"
2. DelII-Appendikssomunderstøtterartiklen.
3. DelIII-Toplakaterderforklarerstatusaprojektetforindenudarbejdelsenafartiklen.
Artiklen er skrevet af Thomas H. Viuff og Morten T. Andersen under vejledning af Morten M.
Kramer og Morten M. Jakobsen har assisteret i laboratoriet. Artiklen burde give fyldestgørende
informationer i sig selv, men appendix kan bruges som supplerende info til en hvis grænse.
Plakaterne er brugt i forbindelse med en præsentation af projektet i forbindelse med INORE
2013 symposium konference i Pembrokeshire, UK, sammen med de daværende resultater fra
projektforløbet.
Arbejdet i afsnittene beskrevet ovenfor omhandler alle beskrivelsen af de komplekse laster fra
højere ordens bøljer på en halvkugleformet skal ved at benytte forskellige metoder, som hver
især har forskellige ulemper og sammenligne dem med kraftmålinger foretaget i laboratoriet.
Froude-Krylov kraften findes ved trykintegration for uforstyrret tryk over den discretiserede
flyderskal. Med denne model er det muligt at modelere højere ordens bølger og derved også
atbeskrivedenvarierendemængdeafneddykketvolumenafflyderen. Samtidigundladesbidrag
fra diffraktion og reflektion. For at få disse effekter med i beregningerne benyttes det numeriske
værktøjWAMITtilatløsedenlineærepotentialteoretiskediffraktionsteori. Dogmedvissefejl,da
WAMITikkemedtagerfluktuationerafvandoverfladen. Iartiklenpræsenteresenpraktiskmetode
til at kombinere disse teorier. Metoden anvender en diffraktionskoefficient sammen med den
højereordensFroude-Krylovkraftogdetsamlederesultatsammenlignesmedmålingerforetaget
ilaboratoriet.
vii

Table of contents
I Paper 1
II Appendices 13
AppendixA Listofdigitalappendices 15
AppendixB Experimentalsetup 17
AppendixC Wavetheoriesusedfortheinvestigation 29
AppendixD Undisturbedpressuremodel 33
AppendixE Forcesoncylinder 35
AppendixF Numericalforcesonfloatshell 39
AppendixG Maximumforcevs. waveperiodapproach 41
AppendixH 3x3overviewapproach 45
AppendixI 3x3forcecomparrison 49
Bibliography 53
ix