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Transcript of Ansys Aqwa Wave
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MultipleWaveSpectra
RichardMay TeamLead,Aqwadevelopment
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1. Introduction
Oceanwaveswithdifferentfrequenciesanddirections
areverydifficulttomodelmathematically
Varioussimplifiedtheories&spectralmodelsofoceanwaves
small
amplitude
linear
Airy
wave
higherorderStokeswave
longcrestedirregularwaves
multipledirectional(shortcrested)irregularwaves
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Wavesinduceforcesonoffshorestructures:
thewaveexcitingforcesatwavefrequency
nonlinearwaveforces:
lowfrequencydriftforce&sumfrequencyforces,
duetotheinstantaneouswettedhullsurfacevarying,
impact,slammingforces.
Longcrestedwavecasedoesnotnecessarilyleadto
conservative
results,
theinteractioneffectbetweenwavesfromdifferent
directionsmaybeimportant(Renaud etal.2008)
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Airywave
SecondorderStokeswave
2. OceanWavesModelinginAqwa
13.0andbefore 14.0andthereafter
same
Formulatedspectrum
Userdefinespectrum
Importedwaveelevation(IWHT)
Main+crossswell
Spreadingwaves
2Dcarpetwaves
same
same
same
SpectralgroupAnycombination
14.0 inLibriumandDrift
14.5 inFer
onesubdirninLine&Naut
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WaveSpectralGroup
SpreadSea
7subdirns
Main+crossswell
2subdirns
2DCarpet
Upto41subdirns
Singlespectrum
1subdirn
ImportedWHT
1subdirn
Up
to
5
IWHTs
Upto20Spectra,41subdirections
Structureofwavespectralgroup
*IWHTs:Importedfilesofwaveelevationtimehistory
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DefinitionofspectralgroupinAqwasuite
Spectralgroup&name
Onecurrent/windsetting
Wavespectrumdefinition
13SPGR
13SGNM UDEF + PSMZ + 2 I WHTs
13CURR 0. 5 50. 0
13I SOW
13WI ND 15. 0 150. 0
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
13NAME 1. UDEF - LONG CRESTED* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
13SEED 1005
13SPDN 0. 000
13UDEF 0. 3142 0. 0000
. . .
13UDEF 1. 8850 0. 4618
13FI NI
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
13NAME 2. LONG CRESTED - FORMULATTED
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
13SEED 1006
13PSMZ 0. 3 2. 5 0. 001 7. 0
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
13NAME 3. I MPORTED WAVE ELEVATI ON
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
13SEED 1007
13I WHT MTWAVE1. WHT
13I WHT MTWAVE2. WHT
13NODR
END13
Seeddefinition(seeAqwa reference4.13.6
fordefaultvalues)
Ignore2nd forceofthis
subdirectionalspectrum
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DefinitionofspectralgroupinAqwaWorkbench
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Waverepresentation: Linearsuperposition nointeraction
3. MultiDirectionalWaveEffectsonLoads
)sincos(
11
),( jmjmmjmmjmwd tYKXKi
jm
N
j
N
m
eatX
1st orderwaveexcitingforce: Linearsuperposition
)()1(
11
1
)(
jmjmwd ti
jmjm
N
j
N
m eFatF
Morisondragforce: Linearsuperpositionoffluid particlevelocities
SC
ti
jmjm
N
j
N
mr
rrdd
UUeXVatU
tUtUCtF
jmjmwd
)(
11
)()(
),()(2
1)(
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Secondorderwaveforces
QuadruplesummationsInteractionbetweenfrequencies(sumanddifference)
andbetweendirections
Driftdamping(Kimetal,1997)
),,;(),;(11111
11 nmjxnmj
N
j
N
n
N
m
FBwdd
)}sin(sin1
)2
()cos(cos{2
1),;(11
n
n
m
m
gjgj
j
j
jnmnmjCC
Kk
,})]()sin[(
)]()cos[()]()sin[(
)]()cos[({)(1 1 11
)2(
knjmknjmjkmn
knjmknjmjkmn
knjmknjmjkmn
N
m
N
n
N
kknjmknjmjkmnknjm
N
j
tQ
tP
tQ
tPaatFd d nm
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MeanDriftforceformultipledirectionalwavecase
MeanDriftforceforsingledirectionalwavecase
Triplesummationsincludingdirectionalcoupling,
Inphaseandoutofphasecomponents,
Sensitivetowaveletrandomphases.
})sin()cos({1 1 1
)2(
jnjmjjmnjnjmjjmn
N
m
N
n
N
jjnjm QPaaF
d d w
wN
jjjj PaF
1
)2(
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Firstorderwaveexcitingforce
Forcespectrum inFer
)()()(2
)1(
1
)1( mm
N
mF
SFSd
Differencefrequencysecondorder waveforce(v14.5)
222
2
11
),(),(),(
},),()()(8{)()2(
mnmnmn
mnnm
N
n
N
mF
QPD
dDSSSdd
Totalwaveforce
)()()( )2()1( FFF
SSS
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Secondorderforcecoefficients
Waterlineintegral
Bernoulli
Acceleration
Momentum
2nd orderpotentialdSndt
d
F
dSndt
dX
dSn
dlngF
S
S
S
WLrr
0
0
0
)2(
)1()1(
)1()1(
)1()1(
)1()1()2(
][
][2
1
2
1
withoutthe5th termandusingcomplexvaluesforunitwaveamplitude
.][
2
1][
2
1
][4
1
4
1),(
,][21][
21
][4
1
4
1),(
'*''*
'
'*''*'
''
'
'
''''
0
0
0
0
gknsjm
S
knjm
Sknjm
WLrknrjmjkmnjkmn
gknsjmS
knjm
Sknjm
WLrknrjmjkmnjkmn
XdSn
dt
dX
dSndlngQP
XdSndt
dX
dSndlngQP
M
M
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Store database,
Interpolating ofallwaveletsateachtimestep,
Quadruplesummationofall2nd orderforcecomponents
4. ExtendedNewmansApproximation
),,,(
jkmnjkmnjkmnjkmn QPQP
),,,(
jkmnjkmnjkmnjkmn QPQP
isnumericallyprohibitive
Newmansapproximationforsingledirectionalwaves
][2
1' kkjjjk PPP
ExtendedNewmansapproximationformultipledirectionalwaves
].[2
1
],[21
'
'
kknmjjmnjkmn
kknmjjmnjkmn
QQQ
PPP
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4.NewmansApproximation
=1 2 ......... j
1
2
.
.
.
j
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4. ExtendedNewmansApproximation
= 1 2 .................... j
1
2
.
.
.
j
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EmployingextendedNewmansapproximation
})]([){(
]})([){(
1 1 11
1 1 11
)2(
kknmkn
N
m
N
n
N
kkknmknjm
N
j
kknmkn
N
m
N
n
N
kkknmknjm
N
j
QcPss
QsPccF
d d nm
d d nm
)sin(),cos( jmjmjmjmjmjmjmjm tastac where
Requiredirectional couplingmeandriftforcecoefficientsdatabase,
Obtain ofactualrelativedirectionateachtimestep,
Quadruple
summation
reduced
to
triplesummation.
),( kknmkknm QP
Lessharddiskandmemoryrequirement,
moreefficient
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ValidationofextendedNewmansapproximation
Rectangularboxindeepwater,Internallid,
No5th term
-6.E+5
-5.E+5
-4.E+5
-3.E+5
-2.E+5
-1.E+5
0.E+0
1.E+5
0.0 0.5 1.0
Full QTF
NewmanApproximation
-8.E+4
-6.E+4
-4.E+4
-2.E+4
0.E+0
2.E+4
4.E+4
6.E+4
0.0 0.2 0.4 0.6 0.8 1.0
'jkmmQ
(
'jkmmP
-6.E+5
-5.E+5
-4.E+5
-3.E+5
-2.E+5
-1.E+5
0.E+0
1.E+5
0.0 0.2 0.4 0.6 0.8 1.0
-1.2E+5
-8.0E+4
-4.0E+4
0.0E+0
4.0E+4
8.0E+4
0.0 0.2 0.4 0.6 0.8 1.0
-5.E+5
-4.E+5
-3.E+5
-2.E+5
-1.E+5
0.E+0
1.E+5
0.0 0.2 0.4 0.6 0.8 1.0
-2.0E+5
-1.6E+5
-1.2E+5
-8.0E+4
-4.0E+4
0.0E+0
4.0E+48.0E+4
0.0 0.2 0.4 0.6 0.8 1.0
m=n:
Newmans
approximation
Goodforsmall
jkmmjkmm QP
Surge
0180 nm
)/(025.0 srad
)/(05.0 srad
)/(1.0 srad
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2nd ordersurgeforce )90,180( 00 nm
-3.0E+5
-2.0E+5
-1.0E+5
0.0E+0
1.0E+5
0.0 0.2 0.4 0.6 0.8 1.0
-2.0E+5
-1.5E+5
-1.0E+5
-5.0E+4
0.0E+0
5.0E+4
1.0E+5
1.5E+5
0.0 0.2 0.4 0.6 0.8 1.0
Full QTF
NewmanApproximation
-3.0E+5
-2.5E+5
-2.0E+5
-1.5E+5
-1.0E+5
-5.0E+4
0.0E+0
5.0E+4
0.0 0.2 0.4 0.6 0.8 1.0
-2.0E+5
-1.5E+5
-1.0E+5
-5.0E+4
0.0E+0
5.0E+4
1.0E+5
0.0 0.2 0.4 0.6 0.8 1.0
-2.0E+5
-1.0E+5
0.0E+0
1.0E+5
0.0 0.2 0.4 0.6 0.8 1.0
-3.0E+5
-2.0E+5
-1.0E+5
0.0E+0
1.0E+5
0.0 0.2 0.4 0.6 0.8 1.0
)/(025.0 srad
)/(05.0 srad
)/(1.0 srad
sameorder
Goodforsmall
'jkmnP
'jkmnQ
'' , jkmnjkmn QP
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Directionalcouplingeffecton2nd ordersurgeforce
0.E+0
1.E+5
2.E+5
3.E+5
4.E+5
5.E+5
6.E+5
0.0 0.2 0.4 0.6 0.8 1.0
Full QTF
Newman
Approximation 0.0E+0
5.0E+4
1.0E+5
1.5E+5
2.0E+5
2.5E+5
3.0E+5
0.0 0.2 0.4 0.6 0.8 1.0
0.0E+0
5.0E+4
1.0E+5
1.5E+5
2.0E+5
2.5E+5
3.0E+5
0.0 0.2 0.4 0.6 0.8 1.0
0.0E+0
5.0E+4
1.0E+5
1.5E+5
2.0E+5
2.5E+5
3.0E+5
0.0 0.2 0.4 0.6 0.8 1.0
00 040
090 0130
2'2' )()( jkmnjkmn QP
)/(05.0
1800
srad
m
Extended Newmansapproximation Enabletoestimate toincludedirectionalcouplingeffect
AsgoodastheoriginalNewmansapproximationformultipledirections
Easyaccomplishment
),(
jkmnjkmn QP
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5. Effectofmultidirectionalspectrum
onamooredLNGcarrier
13500m^3storagecapacityLNGcarrier
(bycourtesyofSBM)
Lengthbetweenperpendiculars:274m
Draft: 11m
Softmooringsystem:
Longitudinalmooringstiffness:281kN/m
Transversemooringstiffness:254kN/m
Rotationalmooringstiffness:4.58E6kNm
Rolldamping:4.0e5kNms/rad
Waterdepth:15m
3.302 180),(cos
Spreadsea:
JONSWAPspectrum:Hs=1m,Tp=10s,
spreadingform:
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Softspringsystemisdefinedbyadditionalstructuralstiffness(SSTF)
39frequenciesand37directionsin[180,180]degrees
Use
MQTFoption
to
calculate
the
directional
coupling
mean
QTF
matrices 25%extraCPUtimeforthedirectionalcouplingmeanQTFcalculation
*.MQTsizeof12mbcomparedto2.3mbof*.RES
AqwaLineCalculation
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Threetreatmentsofspreadingsea:
(1) LongcrestedwavealongmainheadingAB7878P2LONG
(2) Representedby7pointGaussianintegration,nodirectionalcouplingMQTF AB7878P2NOQTF
(3) Representedby7pointGaussianintegration,withdirectionalcouplingMQTF AB7878P2MQTF
Effectsonequilibriumposition
91 DRM1
91FILE AL7878P2M15.MQT
91CSTR 1
END91
Inputdata
Iterativeprocedure
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Timedomainanalysis(AqwaDrift)
5%CPUincrementfor7subdirectioncouplingdriftforcecalculation
Evidentdifferencesbetween3treatmentresults
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Outputtotalforce/responsespectrumcontributedbyallsubspectra
OutputRAOetalinmainsubdirection(withmax.Hs)
OptionallyoutputRAOinspecifiedsubdirection(SSPCindeck18)
Frequencydomainanalysis(AqwaFer 14.5)
Surge (m) Sway (m) Heave (m)
Drift freq. Wave freq. Drift freq. Wave
freq.
Drift freq. Wave
freq.
Long crested 1.073 0.018 0.000 0.000 0.011 0.036
Spread,
no coupling
0.558 0.025 0.563 0.040 0.007 0.055
Spread, coupling 0.620 0.025 0.618 0.040 0.007 0.055
Comparisonofthesignificanttranslationalmotions
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Spectralgroupisintroducedtomodelmultidirectionalwaves
ThedirectionalcouplingmeanQTFsarecalculatedandusedinAqwa
ExtendedNewmansapproximationprovidesafast&relativelyaccurateapproachwithacceptableharddisk/memoryrequirements
MultipledirectionalwavesanddirectionalcouplingQTFshouldbeconsideredformooredoffshorestructurehydrodynamicanalysis.
6. Conclusions
Thanks!
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Azzalini A,DuS.,MayR.(2012) ExtendedNewmansapproximationforthesecondorderdriftforceinshortcrestedwaves,preparedforNAV2012.
ChenX.J.,MoanT.,FuS.X.andCuiW.C.(2006)"SecondOrderHydroelastic AnalysisofaFloatingPlateinMultidirectionalIrregularWaves",International
JournalofNonLinearMechanics,Vol.16,pp.12061218.
KimS.,Sclavounos P.D.andNielsenF.G.(1997)"SlowDriftResponsesofMooredPlatforms",Proc.ofthe8thInt.Conf.ontheBehaviourofOffshore
StructuresBOSS1997,July1997,Delft,TheNetherland,Vol.2,pp.161176.
NewmanJ.N.(1974)"SecondOrder,SlowlyVaryingForcesonVesselsinIrregularWaves", Proc.ofInt.Symp.DynamicsofMarineVehiclesand
StructuresinWaves,Ed.BishopREDandPriceWG,Mech.Eng.PublicationsLtd,London,UK,pp.193197.
PinksterJ.A.(1980)"LowFrequencySecondOrderWaveExcitingForcesonFloatingStructures", PhDThesis,DelftUniversity of Technology.
Renaud M.,Rezende F.C.,ChenX.B.andParigi C.J.(2008)"SecondOrderWaveLoadsonaLNGCarrierinMultiDirectionalIrregularWaves",Proc.of8th
Int.Conf.onHydrodynamics ICHD,October2008,Nantes,France,pp.373380.
Renaud M.,Rezende F.,WaalsO.,ChenX.B.andvanDijk R.(2008)"SecondOrderWaveLoadsonaLNGCarrierinMultiDirectionalWaves",Proc.ofthe
27thInt.Conf.onOcean,offshoreandArcticEngineeringOMAE2008,June2008,Estoril,Portugal,Vol.1,PaperNo.OMAE20085740979,pp.363370.
Rezende F.C.andChenX.B.(2010)"ApproximationofSecondorderLowFrequencyWaveLoadinginMultiDirectionalWaves",Proc.oftheASME 29th
Int.Conf.onOceanandArcticEngineering,June2010,Shanghai,China,Vol.3,PaperNo.OMAE201021099,pp.855861.
Sergent E.andNaciri M.(2010)"WaveSpreadingandWaveDriftLoadsforaStandardLNGCarrierinShallowWater",Proc.oftheASME 29thInt.Conf.
onOceanandArcticEngineering,June2010,Shanghai,China,Vol.1,PaperNo.OMAE201020580,pp.355362.
WaalsO.J.(2009)"TheEffectofWaveDirectionalityonLowFrequencyMotionsandMooringForces",Proc.ofthe28thInt.Conf.onOcean,offshoreand
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