ansys aqwa wave

8/10/2019 Ansys Aqwa Wave

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2011ANSYS,Inc. November26,20121

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

ArcticEngineeringOMAE2009,June2009,Honolulu,Hawaii,USA,Vol.4,PaperNo.OMAE200979412,pp.289298.

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