Research Article Numerical Simulation of Fluctuating Wind Effects on an Offshore Deck Structure

18 Pages·2017·4.96 MB·English

Hindawi
Shock and Vibration
Volume 2017, Article ID 3210271, 17 pages
https://doi.org/10.1155/2017/3210271
Research Article
Numerical Simulation of Fluctuating Wind Effects on
an Offshore Deck Structure
JinMa,1DaiZhou,1,2,3ZhaolongHan,1KaiZhang,1,4JenniferNguyen,5
JiabaoLu,1andYanBao1
1SchoolofNavalArchitecture,OceanandCivilEngineering,ShanghaiJiaoTongUniversity,Shanghai200240,China
2CollaborativeInnovationCenterforAdvancedShipandDeep-SeaExploration(CISSE),Shanghai200240,China
3StateKeyLaboratoryofOceanEngineering,ShanghaiJiaoTongUniversity,No.800,DongchuanRoad,Shanghai200240,China
4DepartmentofCivilEngineering,GraduateSchoolofUrbanInnovation,YokohamaNationalUniversity,Yokohama2408501,Japan
5CullenCollegeofEngineering,UniversityofHouston,Houston,TX77004,USA
CorrespondenceshouldbeaddressedtoDaiZhou;[email protected]
Received 5 November 2016; Revised 2 February 2017; Accepted 28 February 2017; Published 30 March 2017
AcademicEditor:MarcoBelloli
Copyright©2017JinMaetal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,which
permitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Theoffshorestructuresthatplayavitalroleinoilandgasextractionarealwaysundercomplicatedenvironmentalconditionssuch
astherandomwindloads.Thestructuraldynamicresponseundertheharshwindisstillanimportantissueforthesafetyand
reliabledesignofoffshorestructures.Thisstudyconductsaninvestigationtoanalyzethewind-inducedstructuralresponseofa
typicaloffshoredeckstructure.Anaccurateandefficientmixturesimulationmethodisdevelopedtosimulatethefluctuatingwind
speed,whichisthenintroducedastheboundaryconditionintonumericalwindtunneltests.Largeeddysimulation(LES)isutilized
toobtainthetimeseriesofwindpressuresonthestructuralsurfacesandtodeterminetheworstworkingcondition.Finally,the
wind-inducedstructuralresponsesarecalculatedbyANSYSParametricDesignLanguage(APDL).Thenumericallypredictedwind
pressuresarefoundtobeconsistentwiththeexistingexperimentaldata,demonstratingthefeasibilityoftheproposedmethods.The
wind-induceddisplacementshavethecertainperiodicityandchangesteadily.Thestressesatthetopofthederrickandconnections
betweendeckandderrickarerelativelylarger.Thesemethodsaswellasthenumericalexamplesareexpectedtoprovidereferences
forthewind-resistantdesignoftheoffshorestructures.
1.Introduction tocarryoutthewindfieldanalysesofoffshorestructuresto
guaranteeareasonablesafetydesign.
Numerous offshore structures have been constructed to In general, the wind-induced structural responses are
supply oil and gas all over the world in recent years. The numerically investigated by applying wind pressures on the
offshore structures are designed for resisting random wind structural surfaces by the time-domain analysis method
andwaveloads.Inthecurrentdesignexperience,thelateral [5, 6]. Meanwhile, the numerical simulation in the present
randomwindloadinthedesignoffixedoffshorestructures study could override the two-way fluid-structure interac-
isoforderof10%inthetotallateraldesignloadsand25%in tion with the wind-induced structural response with small
thecaseoffloatingplatforms[1,2].Manyaccidentsinvolving deformation [7]. Wind pressures on structures could be
deck components such as a derrick and crane due to the extracted by the full-scale measurement, wind tunnel test,
random wind loads have already been reported in damage and computational fluid dynamics (CFD) methods. Each
investigation [3]. However, practical estimation and assess- of these methods is complementary with another in view
ment of the fluctuating wind and wind-induced dynamic of their own advantages and limitations [8]. The full-scale
response of the complex offshore deck structures are still measurementcanrecordthefirsthanddataofwindpressures
involved problems [4]. Therefore, with the development of on prototype structures. However, it is generally conducted
theoilexploitationtodeepsea,itisnecessaryandimportant with the limitations of several objective conditions such as
2 ShockandVibration
weatherconditions,highcost,andsiteconditions[9].Wind Table1:Thesizeparametersofthesemisubmersibleplatform.
tunnel test is a relatively mature and effective technique in
wind engineering on scaled models of complex structures Members Dimensions(length×width×height)/m
[10, 11]. However, there are also several limitations in wind Thelowerpartofderrick 17×17×42
tunneltestsforaccurateinvestigationsofwindpressureson Theupperpartof 17×17×22
structuresasfollows:(1)Reynoldsnumbersofscaledmodel derrick(wedge)
tests are smaller than those of prototype structures; (2) the Deck 74.42×74.42×8.6
wind field conditions can hardly be reproduced exactly in Column 17.39×17.39×21.46
windtunneltests[10].
Owingtotherapiddevelopmentsofcomputerpowerand
computationalmethods,CFDpredictionshavebeenwidely columns, and floating bodies. The main parameters of this
usedtoanalyzethewindflowsaroundprototypestructures platformarelistedinTable1.
inengineeringpractice[12].Largeeddysimulation(LES),as The tested model in Figure 1(b) was scaled as 1:100 in
one of the main CFD methods, has been widely applied in [18]. The full-scale CFD numerical model of this platform
thesimulationsofwindfields.WithpowerfulCFDtoolssuch in the present CFD simulations is built based on the tested
as LES, it is possible to conduct full-scale size simulations scaled model [18] and numerical full-scale model [19]. In
ofprototypestructuresinhighReynoldsnumbersflowsand view of the major consideration of wind field analyses, the
provide abundant detailed data and information, such as offshoreplatformstructuresunderthewaterarehiddenand
pressuredistributionsonstructuralsurfaces[13]. thederrickistotallyenclosedasshowninFigure1(c)whichis
It is understood that proper generation of the inlet demonstratedthattheextractedwindpressuresareapplicable
boundaryconditionsforCFDsimulations,especiallyforLES in the wind-induced dynamic response analyses [19, 20].
in computational wind engineering (CWE), is essential in However,thestructuralcomputationalmodelofthederrick
the analyses of wind pressure distributions and the dyna- in the following time-domain analysis is similar to a real
mic responses of prototype structures [14]. Therefore, the structureandnotenclosed,asisplottedinFigure1(d).
improvement of simulating fluctuating wind speed in the Onethingtonoteisthattwotypesofnumericalmodels,
inletboundaryisprovidedinthepresentstudy.Combining theCFDnumericalmodelandthestructuralcomputational
withtheadvantagesofweightedamplitudewavesuperposi- model,areappliedinthispresentstudy.TheCFDnumerical
tion(WAWS)[15]andautoregression(AR)[16,17]methods modelisaplatformmodelusedforLESsimulations,whichis
withhighaccuracyandlesstimecost,respectively,amixture establishedbyusingacombinationofRhino(RobertMcNeel
simulation(MS)methodisproposedanddemonstratedasan & Assoc, USA) and ICEM CFD (ANSYS, Inc., USA). The
efficientandaccuratesimulationmethodinthepresentwork. structuralcomputationalmodelisafiniteelementmodelof
In summary, the main objective of this present study is this platform for structural dynamic response analyses in
toconductwindfieldanalysesoftheoffshoredeckstructures time domain, which is built by ANSYS Parametric Design
whicharecarriedoutbyajointapplicationofCFDtechnique Language(APDL)(ANSYS,Inc.,USA).Thefiniteelementsof
and structural finite element analysis. Furthermore, time thelocalcomponentsarelistedasfollows:thederrickadopts
seriesofwindpressuresonthestructuralsurfacesatdifferent beamelement,thedeckusesshellelement,andthecolumns
wind directions and inclined angles of the platform are adoptsolidelement.
extracted in CFD wind tunnel tests and then applied to
the finite element model to investigate the wind-induced 3.NumericalSimulation
structuralresponse.
Thispaperisorganizedasfollows:thestructuralmodels Inthissection,togetherwiththecommercialCFDsoftware
innumericalsimulationandwindtunneltestarepresented Fluent 14.5 (ANSYS, Inc., USA), the unsteady-state analysis
in Section 2. Methods for conducting CFD predictions are of the LES approach is used to predict the time series
providedinSection3.AnaccurateandefficientMSmethod of wind pressures on the surfaces of structures above the
forsimulatingfluctuatingwindspeedasboundaryconditions water surface at different working conditions. Fluent 14.5
isproposedinSection4.Computationalproceduresforthe conducts LES simulations based on finite volume method
wholewindfieldanalysesoftheoffshoredeckstructuresare (FVM) [23]. Then, the wind-induced structural responses
includedinSection5.ThevalidationtestsfortheMSandLES are explored by the extracted wind pressures acting on the
methodsandnumericalcasesofwindfieldinvestigationsare structures using APDL and time-domain analysis method
carriedoutinSection6. cooperatively [24]. The detailed computational algorithms
and treatments of wind field analyses are addressed in the
2.TheModelSemisubmersiblePlatform followingsubsections.
The semisubmersible platform in this study is the 6th-
3.1.CFDPredictions
generationdeepwaterdrillingplatform,showninFigure1(a),
andpossessesthefunctionofintelligentdrillingtechnology 3.1.1. LES Turbulence Model. In the present LES study, LES
attaining the advanced level all over the world. The major separatesflowmotionsintolargeandsmalleddieswhichis
structuralcomponentsofthisplatformincludederrick,deck, calculated by using a combination of the direct simulation
ShockandVibration 3
(a) (b)
(c) (d)
Figure1:(a)Thepracticalsemisubmersibleplatform.(b)Thetestedmodelofwindtunneltests[17].(c)ThenumericalmodelusedinCFD
windtunnelpredictions.(d)Thederrickmodelforwind-inducedanalyses.
method and general model theory [25]. In view of these where V𝑖 is the large-scale wind velocity field tensor, 𝑃 the
studiesintheLESsimulationswhoseproposedmethodsare resolvedpressure,𝑆𝑖𝑗theresolvedstrain-ratetensor,𝜌 theair
appliedforfull-scaleCFDnumericalmodelunderReynolds density,𝜐thekinematicviscosity,𝑘 thesubgridscale(SGS)
sgs
number greater than 108 [10], these methods are adopted kinematicenergy,𝜐𝑠theSGSeddyviscosity,and
to carry out the present LES simulations under Reynolds
numberofapproximately6×107.Itisworthmentioningthat 𝜐 =𝐶 Δ √𝑘 ,
thesemethods,suchasone-equationmodel,aresuitablefor 𝑠 V V sgs
relativelycoarsegridcaseandhighReynoldsnumberflows
Δ
[26].Theaccuracyandreliabilityoftheproposednumerical Δ = ,
framework have been validated by the consensus between V 1+𝐶 (Δ2𝑆2/𝑘 )
𝑘 sgs
numerical and experimental results in the previous studies
[10,26].
𝜕𝑘 𝜕V 𝑘 𝑘3/2
The governing equations of an incompressible flow for sgs + 𝑗 sgs =−𝜏 𝑆 −𝐶 sgs
LESsimulations[26]areexpressedas 𝜕𝑡 𝜕𝑥 𝑖𝑗 𝑖𝑗 𝜀 Δ (2)
𝑗
𝜕 𝜕𝑘
+ [(𝐶 Δ √𝑘 +𝜐) sgs]
𝜕𝜌V𝑖 + 𝜕𝜌V𝑖V𝑗 =− 𝜕 (𝑃+ 2𝜌𝑘 ) 𝜕𝑥𝑗 𝑑 V sgs 𝜕𝑥𝑗
𝜕𝑡 𝜕𝑥 𝜕𝑥 3 sgs
𝑗 𝑖 𝜕𝑘 𝜕𝑘
−2𝜐 sgs sgs,
𝜕 𝜕𝑥 𝜕𝑥
+ [2𝜌(𝜐 +𝜐)𝑆 ], (1) 𝑖 𝑗
𝜕𝑥 𝑠 𝑖𝑗
𝑖
where𝐶V,𝐶𝑘,𝐶𝜀,and𝐶𝑑 aretheconstant[27,28]andΔis
𝜕V
𝑖 =0, thelengthscaleoffilterandcanbedeterminedaccordingto
𝜕𝑥 HuangandLi’swork[26].
𝑖
4 ShockandVibration
(a) (b)
Figure2:Themeshingresults:(a)Block1;(b)Block2.
TheimprovedLESapproachproposedbyHuangandLi thecomputerperformance,computingtime,andengineering
[26]hasbeendevelopedasaFluentUserDefinedFunction requirements,theminimum,maximum,andmeanvaluesof
(UDF) library, which has been applied in conducting LES 𝑦+are2.53308,4.89245,and3.48798,respectively.According
simulations of tall buildings and long-span complex roof tothepreviousstudy[29],althougharecommendedvaluefor
structuresinthepreviousstudies[10,12]. 𝑦+isabout1,valueslowerthan5areacceptablebecausethe
cellstaysintheviscoussublayer.
The total mesh number is nearly 11 million. According
3.1.2. Numerical Algorithms. In the LES predictions, all
9/4
to LES theory, the mesh quantity should reach Re in
the discrete equations are solved by the pressure implicit
order to provide very accurate numerical results. And the
with splitting of operators (PISO) method. The time and
more the mesh elements in the fluid domain, the higher
spatial discretization are both treated by second-order dis-
the computational accuracy that will be reached. However,
crete schemes. Bounded central differencing is adopted for
it requires much more computing time cost and higher
momentum discretization. The LES simulations are per-
computerperformancewhichwouldbeaheavytaskforCFD
formed together with ANSYS/Fluent 14.5 and the parallel
simulation. In order to make it feasible to reach moderate
calculationsof16centralprocessingunits.Thetotaltimesteps
accuracy while simultaneously satisfying the engineering
arenearly41000with0.05spertimestep,whicharesufficient
requirement (which can allow 10∼30% error for structure
toreachthestatisticalconvergenceforLESsimulations[10,
safety design), the grid resolution has to be reduced. For
12].
obtaining relative accuracies of the wind pressures, forces,
andcomparingwindcoefficients,weconductedagridreso-
3.1.3. Computational Domain and Mesh Arrangement. The lutiontestinthefollowingvalidationtestandfoundthatthe
numerical model of this offshore platform is established in presentedmeshbalancestimecostandnumericalaccuracy,
full-scalesizes,assketchedinFigure1(c).Thedimensionsof satisfyingtheengineeringrequirements.
thecomputationaldomain,sketchedinFigure2,are2600m
(𝐿𝑥)×600m(𝐿𝑦)×200m(𝐿𝑧)asthecomputationaldomain 3.1.4. Boundary Conditions. The boundary conditions are
is35(𝐿𝑥)×8(𝐿𝑦)×2.5(𝐿𝑧)[11].TheblockingrateofCFD described as the wind velocity profile in accordance with
numerical model in the computational domain is less than an exponential rule, which can satisfy the Navier-Stokes
3%,whichisgenerallyacceptableinCWE[9].Accordingto equationsinLESsimulations[10,18]:
themultiblocktechniqueinthepreviousstudy[12],theflow 𝐻 𝛼
field consists of two blocks: The small cylindrical flow field 𝑉𝑧 =𝑉0(𝐻 ) , (3)
0
andCFDnumericalmodel,whicharecombinedtogetherby
aBooleanoperation,aredefinedas“Block1”inFigure2(a), where𝑉𝑧and𝑉0aretheaveragewindvelocitiesattheheight
and the remaining part (i.e., the big rectangular flow field) of𝐻and𝐻0and𝛼isrelatedtogeomorphologicfeatures[22].
Inunsteady-stateanalysisoftheLESsimulations,theFlu-
is defined as “Block 2” in Figure 2(b). One thing is to note
entcodeprovidesadirectandconvenientmethodtogenerate
thattheCFDnumericalmodelisnestedin“Block1.”Rotating
a time-dependent turbulent fluctuating wind velocity field.
“Block1”thespecifiedangleimmediatelycancarryoutLES
However,itisreportedthatthegeneratedwindfieldbythe
simulations at the specified wind direction, by which LES
Fluentcodedecaysrapidlyintheinertialrangeandisnotwell
simulations can be conducted at multiple wind directions
approximated as the marine random wind [26]. The power
conveniently. Numerous tetrahedral grids are generated in
spectraldensity(PSD)ofthefluctuatingwindisfittedbyNPD
theneighborhoodofthestructuralsurfaces,especiallyinthe
(NorwegianPetroleumDirectorate)spectruminthepresent
vicinity of the derrick, and the grid stretching ratio is kept
study[22]:
tobe<1.05.Themaximumandminimumgridlengthsinthe
neighborhoodofthestructuralsurfacesare0.8mand0.2m, 320(𝑉/10)2(𝑧/10)0.45
𝑆(𝑓)= 0 ,
respectively. Hexahedron grids are adopted in the regions (1+1.5𝐹)3.56
farawayfromthecalculatingmodelandthegridstretching (4)
ratioisrelativelyenlargedforreducingthetotalmeshnumber 𝑧 2/3 𝑉 −3/4
𝐹=172𝑓( ) ( 0) ,
for the sake of saving time cost in computation. In view of 10 10
ShockandVibration 5
Wind
Inlet Outlet
Figure3:Thesketchoftheinletboundaryofthefluctuatingwind.
where𝑆(𝑓)isthePSDfunction,𝑓thewindfrequency,𝑉0the pressure, 𝜌 is the air density, and 𝑉0 is the average of wind
averagewindspeedattheheightof𝐻0,and𝑧 theheightabove speedattheheightof10.0m.
sealevel. AccordingtoChinaClassificationSocietycommonrules
Given a clear explanation of the wind characteristics, and[19],theequationoftheshapecoefficientofastructural
the fluctuating wind speed of the inlet boundary shown in memberisexpressedas
Figure 3 is simulated by the MS method proposed in the
160 0.2
followingsection.Thisnewsimulationmethod,MSmethod,
𝑠𝑐 =𝐶 ( ) ,
can generate the time series of wind velocities of a num- 𝑖 𝑝 𝑧
(7)
ber of spatial nodes accurately and efficiently. The pressure
∑ 𝑠𝑐𝑆𝐴
fluctuationonstructuralsurfacescanbesolvedbyimporting 𝑆𝐶= 𝑖 𝑖 𝑖,
𝑆𝐴
the inlet boundary conditions in LES simulations in the
commercialsoftwareANSYS/Fluent14.5.Therefore,velocity where𝑖isameasuringpointonaspecifiedstructuralmember,
andpressurecomponentstogethersatisfytheNavier-Stokes 𝑠𝑐𝑖istheshapecoefficient𝑖,𝐶𝑝themeanpressurecoefficient,
equations. 𝑧 the height of a measuring point 𝑖, 𝑆𝐴𝑖 the area of the
In order to guarantee the convergence property and structuralsurfacewhichameasuringpoint𝑖belongsto,and
efficiencyinLESsimulations,thefluctuatingwindvelocities 𝑆𝐴 the total area of multiple structural surfaces. The ave-
ateachtimestepattheinletaremodifiedthroughtheequal rage pressure coefficients, 𝑆𝐶, are changing with the wind
totalflowoftheinletandoutletonthebasisoftheprevious
directions. Therefore, the shape coefficients vary with wind
studies[20,30].Theequationisdescribedas
directions.
(∑𝑛 V𝐴 −Ω)
V =V − 𝑖=1 𝑖 𝑖 , (5)
𝑖+1 𝑖 𝐴 3.2. Wind-Induced Structural Response Analyses. The time
series of the extracted wind pressures are applied to the
whereV𝑖 isthefluctuatingwindspeedattimestep𝑖,𝐴𝑖 the offshorestructuresandthewind-induceddynamicresponses
areaofthecorrespondinggridcell,𝐴thetotalareaoftheinlet arecalculatedbytime-domainanalysismethodtogetherwith
boundary,andΩthetotalflowoftheoutletboundaryatthe APDLsolvingthestructuraldynamicequationasfollows:
correspondingtimestep.
According to the work of Lu et al. [20] and Shirani et [𝑀]{𝑢̈}+[𝐶]{𝑢̇}+[𝐾]{𝑢}=[𝐹], (8)
al.[30],thewindvelocitiesateachtimestepbeingreadand
updatedinFluent14.5arefoundtobeslightlysmallerthanthe where [𝑀], [𝐶], and [𝐾] are, respectively, structural mass,
initialwindvelocitiesgeneratedbytheself-madeMATLAB damping,andstiffnessmatrices,{𝑢̈},{𝑢̇},and{𝑢}are,respec-
program. tively, acceleration, velocity, and displacement vectors, and
[𝐹] are fluctuating wind loads. Meanwhile, (4) is solved by
theNewmark-𝛽approachinthispresentstudy[22].
3.1.5.DataAnalyses. Theanalysesofwindpressuredistribu-
In structural dynamic response analysis, the damping
tionarecarriedoutintermsofnondimensionalcoefficients,
𝐶𝑝and𝐶𝑝rms,ofameasuringpoint𝑖 defined,respectively,as matrix[𝐶]isdeterminedbythefollowingequations:
[𝐶]=𝛼[𝑀]+𝛽[𝐾],
𝑃
𝐶 = 𝑖 ,
𝑝 0.5𝜌𝑉2 𝛼 𝛽𝜔 (9)
0 𝜉 = + 𝑖,
(6) 𝑖 2𝜔 2
𝑃 𝑖
𝐶 = 𝑖,rms ,
𝑝rms 0.5𝜌𝑉02 where𝛼and𝛽aretheconstantsinRayleighdampingwhich
arecalculatedbythedampingratioineachmodeshape𝜉𝑖[20]
where𝐶𝑝 and𝐶𝑝rms arethemeanandRMSpressurecoeffi- whichisassumedasaconstantoverarangeoffrequencies.
cients,respectively,𝑃𝑖isthemeanpressure,𝑃𝑖,rmsistheRMS And𝜔𝑖isthestructuralfrequencyineachmodeshape.
6 ShockandVibration
PSD:S(
휔)=S1(
휔)W1(
휔)+S2(
휔)W2(
휔)
Wavelet method
Parts of energy concentrationS1(
휔) Parts of energy dispersionS2(
휔)
WAWS method AR method
Generate wind speed(cid:2)1(t) Generate wind speed(cid:2)2(t)
Time series of fluctuating wind:(cid:2)(t)=(cid:2)1(t)+(cid:2)2(t)
Figure4:TheflowchartforsimulatingthefluctuatingusingMSmethod.
4.TheMethodfor Simulating TheapplicationoftheWAWSandARmethodsisbriefly
FluctuatingWind presented in the following formula derivation, which has
fullyconsideredtemporalandspatialcorrelationintheself-
Amixturesimulation(MS)methodisproposedtogenerate compiledprograms.
the fluctuating wind speed as the boundary conditions in
CFD predictions, combining with the weighted amplitude (1)TheWAWSMethodintheMSMethod.UsingtheWAWS
wavesuperposition(WAWS)method[15]andautoregression method,thecorrelationfunction𝑅𝑗𝑚isexpressedas
(AR) methods [16, 17]. The new approach overcomes the
defects of the abovementioned traditional methods and
𝑅 (𝜏)=𝐸(V (𝑡)V (𝑡+𝜏))
inheritstheirownadvantageswhichguaranteethecomput- 𝑗𝑚 𝑗 𝑚
ingaccuracyandefficiencysimultaneously.
stocAhasssutimcGinagussthiaantptrhoecesflsu,cthtueasttioncghawstiincdchaisracatesrtiasttiicosncaarny =Δ𝑓∑𝑗 ∑𝑁 󵄨󵄨󵄨󵄨󵄨𝐻𝑗𝑘(𝑓𝑘𝑙)󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨𝐻𝑚𝑘(𝑓𝑘𝑙)󵄨󵄨󵄨󵄨 (11)
𝑘=1𝑙=1
be described by the power spectral density (PSD) function
[31]. Then, the energy distributions of the PSD function of ⋅cos(2𝜋𝑓𝑘𝑙+𝜃𝑗𝑘(𝑓𝑘𝑙)−𝜃𝑚𝑘(𝑓𝑘𝑙)),
thefluctuatingwindareexploredbythewaveletmethod[32]
adopting the Hanning windows [33]. Therefore, the main
thoughts of the MS method are listed as follows: the parts where𝐸isexpectation,Visthetimeseriesofwindspeed,𝐻
of the energy concentration are simulated by the WAWS is obtained by Cholesky decomposition, and 𝜃𝑗𝑘(𝑓𝑘𝑙) is the
method [15] and the parts of the energy dispersion are phaseanglebetweenspatialnodes𝑖and𝑗.
generatedbytheARmethod[16].Thefinalsimulatingresults Assumingthat𝑁→∞andΔ𝑓→0,
ofthefluctuatingwindareobtainedbythesuperpositionof
tshimeusliamtiuolnatipnrgocreesssulitsscboynctlhuedetwdoinmFeitghuordes.4.ThTheescehqeumataiotinc 𝑅𝑗𝑚(𝜏)=∫𝑠ℎ1 ∑𝑗 󵄨󵄨󵄨󵄨󵄨𝐻𝑗𝑘(𝑓𝑘)󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨𝐻𝑚𝑘(𝑓𝑘)󵄨󵄨󵄨󵄨
ofthecalculatingprocessbytheMSmethodisdescribedas 𝑠𝑙1 𝑘=1 (12)
follows:
⋅cos(2𝜋𝑓𝑘+𝜃𝑗𝑘(𝑓𝑘)−𝜃𝑚𝑘(𝑓𝑘))𝑑𝑓.
𝑆(𝑓)=𝑆1(𝑓)𝑊1(𝑓)+𝑆2(𝑓)𝑊2(𝑓), (10)
Thecorrelationfunctionistransformedfromtimedom-
where 𝑆(𝑓) is the PSD function, 𝑓 is the wind frequency, aintofrequencydomainonthebasisofconvolutiontheorem:
𝑊1(𝑓)and𝑊2(𝑓)are,respectively,theHanningwindowsof
athree,erneesrpgeycctiovneclye,nstirmatuiolanteadndbdyistpheersWioAnW,aSndm𝑆e1t(h𝑓o)danadnd𝑆2(A𝑓R) 𝑅𝑗𝑚(𝜏)⊗𝑊1(𝑡)=∫𝑠ℎ1 ∑𝑗 󵄨󵄨󵄨󵄨󵄨𝐻𝑗𝑘(𝑓𝑘)󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨𝐻𝑚𝑘(𝑓𝑘)󵄨󵄨󵄨󵄨
method. 𝑠𝑙1 𝑘=1
The Hanning window number is determined by the
energy distribution of the PSD function in the wind field. ⋅𝑊̂1(𝑓)cos(2𝜋𝑓𝑘+𝜃𝑗𝑘(𝑓𝑘)−𝜃𝑚𝑘(𝑓𝑘))𝑑𝑓 (13)
Accordingtoourexperience,thewindownumberusingthe
WmeAtWhoSd.mIneththoidswisayt,htrheeeMtimSemselathrgoedrctohualndirteduusicnegththeetiAmRe =∫𝑠ℎ1 ∑𝑗 𝑆𝑗𝑘(𝑓)⋅𝑊̂1(𝑓)cos(2𝜋𝑓𝑘)𝑑𝑓,
costincomputationwithnoaccuracylosttosimulateakind 𝑠𝑙1 𝑘=1
ofloadswiththerandomproperties,whichisdemonstrated
inthefollowingvalidationtestsinSection6.1. where⊗representsconvolutionoperation.
ShockandVibration 7
Time series of wind speed simulated by the WAWS Step3. ConstructtheCFDnumericalwindtunnel.
methodV1(𝑡)isobtainedby
Step3.1.CreatethecalculationmodelandmeshfilesbyRhino
andICEMCFD.
V (𝑡)
1
Step 3.2. Set the initial and boundary conditions in
=√2Δ𝑓∑𝑗 ∑𝑁 󵄨󵄨󵄨󵄨󵄨𝐻𝑗𝑘(𝑓𝑙)󵄨󵄨󵄨󵄨󵄨cos(2𝜋𝑓𝑙𝑡+𝜃𝑗𝑘(𝑓𝑙)+𝜑𝑘𝑙), (14) ANSYS/Fluentandstartthecalculation.
Step3.3.Calculatetheresultantforcestodeterminetheworst
𝑘=1𝑙=1
operatingcondition.
𝑗=1,...,𝑚,
Step 3.4. Extract the time series of wind pressure on the
structural surfaces by the UDF program for the following
where𝜑isarandomnumberfrom0to2𝜋. dynamicresponseanalyses.
Step4. Carryoutthewind-induceddynamicresponseanal-
(2)TheARMethodintheMSMethod.Similarly,thecorrela-
ysesbyAPDL.
tionfunctionintheARmethodcanbeexpressedas
Step4.1.Importthefiniteelementmodeloftheplatformand
𝑅𝑖𝑗(𝜏)=∫𝑠ℎ2 𝑆𝑖𝑗(𝑓)𝑊̂2(𝑓)cos(2𝜋𝑓⋅𝜏)𝑑𝑓, (15) deckstructures.
𝑠
𝑙2 Step4.2.Settheinitialandboundaryconditionsandstartthe
calculationbytheNewmark-𝛽methodintimedomainusing
where𝑅isthecorrelationfunction. thesecondarydevelopmentapplicationprograms.
TimeseriesofwindspeedsimulatedbytheARmethod
Step4.3.Extractthecalculationresultssuchasthedeforma-
V2(𝑡)iscalculatedby tionsandstressesofnodesandmembers.
𝑗 𝑝
6.ResultsandDiscussion
V (𝑡)=−∑∑𝑎 V (𝑡−𝑘⋅Δ𝑡)+𝑢(𝑛), (16)
2 𝑖𝑗𝑘 𝑖
𝑖=1𝑘=1
6.1.ValidationTests. Inthissubsection,thenumericalresults
are compared to verify that the methods and self-made
whereΔ𝑡isthetotalsimulatingtimestep,𝑎thecoefficientof programsmentionedinSections3and4areapplicableand
autoregressionmatrix,𝑢(𝑛)theexcitedwhitenoisethrough effectiveinthefollowingnumericalexamples.
all-zerosfilter,and𝑝theorderofARmodel.
Overall,thetotalwindspeedisobtainedbyV(𝑡)=V1(𝑡)+ 6.1.1.ValidationfortheMSMethod. Testsareconstructedto
V2(𝑡),whichisshowninFigure4. demonstrate the accuracy and efficiency of the MS method
comparedtothetraditionalsimulationmethods:theWAWS
5.TheProcedurefor theWindField and AR methods. The time series of the wind speed at any
spatialpointissimulatedbytheMS,WAWS,andARmeth-
AnalysesofthePlatform
ods, respectively. The comparison between the simulated
and theoretical results could determine the best simulation
In this section, the details for conducting LES predictions
method.
and wind-induced dynamic responses analyses of the deck
structures under the action of the fluctuating wind are
(1) Validation for the Accuracy of the MS Method. The
summarizedasfollows.
fluctuatingwindspeedatonesinglespatialpointissimulated
bytheMS,WAWS,andARmethods,respectively,inthesame
Step1. Establishthegeometricandfiniteelementmodelsby
initial condition listed as follows: the average wind velocity
VC++andAPDL.
𝑉0 = 31.654m/s, the number of the sampling points 𝑛 =
Step2. Generatethefluctuatingwindspeed. 1200, time stepΔ𝑡 = 0.1 s, and the measuring point (in
meters)islocatedat(0,0,5).Theerrorbetweentheenergy
Step2.1.Simulateandcorrectthetimeseriesofthewindspeed [34] of the simulated and theoretical results solved by (17)
by using the MATLAB (MathWorks, USA) self-compiled can assess the accuracy of the simulation method by fast
programs. Fouriertransform(FFT)[35]andfrequency-timeconversion
methods[36,37]:
Step 2.2. Convert these data into data files in the format
tbhyaAt NhaSsYSa/.FtxluteenxttuensisniognthfeorUmsaetr.DThefienseeddaFtuanfictlieosnasr(eUrDeaFd) Ω= 󵄩󵄩󵄩󵄩𝑋(𝑗𝜔)󵄩󵄩󵄩󵄩2 = 󵄩󵄩󵄩󵄩󵄩∫𝑥(𝑡)𝑒−𝑖𝜔𝑡󵄩󵄩󵄩󵄩󵄩2, (17)
program. 𝑇 𝑇
8 ShockandVibration
104 104
102 102
D D
S S
P 100 P 100
10−2 10−2
10−3 10−2 10−1 100 101 10−3 10−2 10−1 100 101
Frequency (Hz) Frequency (Hz)
Simulated results Simulated results
Target results Target results
(a) (b)
104
102
100
10−2
10−3 10−2 10−1 100 101
Simulated results
Target results
(c)
Figure5:ThecomparisonbetweensimulatedandtargetresultsbyMS,AR,andWAWSmethods:(a)MSmethod;(b)ARmethod;(c)WAWS
method.
Table2:Thecomparisonofcalculatingaccuracybetweentheresults Table3:Thecomparisonofthecomputingtimeandaccuracyat36
ofsimulatedPSDandtheoreticalPSD. and108spatialpointsusingtheMS,WAWS,andARmethods.
MSmethod WAWSmethod ARmethod Numberofnodes Method Error Computingtime(s)
Theoreticalenergy 12.6923 12.6923 12.6923 WAWSinMS 2.34% 256
Simulatingenergy 12.3927 13.6073 14.2073 ARinMS 6.24% 75
Error 2.36% 7.21% 11.94% 36 MS 4.79% 331
WAWS 4.24% 27465
AR 22.96% 75
where𝑥(𝑡)istimeseriesofwindvelocity,𝑋(𝑗𝜔)theampli-
tudespectrumobtainedfrom𝑥(𝑡)byFFT,and𝑇thelasting WAWSinMS 2.07% 6766
timeoftimeseriesofwindspeed.TheenergyΩiscalculated ARinMS 9.40% 489
bythesquareoftheamplitudespectralmodedividedbythe 108 MS 4.85% 7255
lastingtime𝑇. WAWS 4.24% 647836
Thecomparisonsbetweensimulatedandtargetresultsby AR 32.85% 489
the MS, AR, and WAWS methods are plotted in Figure 5.
The blue and red curves are target and simulated PSD,
respectively.AsseenfromFigure5,thesimulatedresultsby
the MS method are more accurate and closer to the target
wind of numerous spatial points rather than one single
results. The numerical accuracy by the AR method in the
point.Timecostincomputationbecomesanimportantcon-
lower and higher regions is the lowest compared to those
sideration in the numerical examples. The comparisons of
by the MS and WAWS methods. Table 2 conducts further
thesimulatingtimeusingtheMS,WAWS,andARmethods,
numerical accuracy analyses by the energy comparisons
respectively, are carried out under the same computing
betweenthesimulatedandtheoreticalresultsusingtheMS,
conditionsmentionedinValidationfortheAccuracyofthe
WAWS, and AR methods. Obviously, the error of the MS
methodismuchlowerthantheothersunderthesameinitial MSMethod.
conditionsas2.36%versus7.21%and11.94%. The fluctuating wind velocities of 36 and 108 adjacent
These comparisons demonstrate that the MS method is grid nodes in the inlet boundary sketched in Figure 3 are
amoreaccuratesimulationmethodtogeneratetherandom simulated by three abovementioned simulation methods.
loadscomparedtotheWAWSandARmethods. Table 3 gives a series of comparisons of computing time
and accuracy of generating the fluctuating wind velocities
(2)ValidationfortheEfficiencyoftheMSMethod.Ingeneral,a at36and108adjacentspatialpointsusingthreesimulation
numericalwindtunnelneedsthetimeseriesofthefluctuating methods.
ShockandVibration 9
0.0
−0.5
nt
e
ci
ffi
e −1.0
o
c
e
ur
ess −1.5
pr
d
n
Wi
−2.0
−2.5
−4 −3 −2 −1 0 1 2 3 4
X (m)
Total grid number
7×105 2.8×106
1.4×106 4.2×106
(a) (b)
0.0 0.4
−0.5
nt nt
fficie fficie 0.3
oe −1.0 oe
ure c ure c
d press −1.5 S press 0.2
n M
Wi R
−2.0
−2.5 0.1
−4 −3 −2 −1 0 1 2 3 4 −4 −3 −2 −1 0 1 2 3 4
X (m) X (m)
The experimental data The experimental data
The simulated results The simulated results
(c) (d)
Figure6:(a)ThesketchofflowfieldandFB16model.(b)Meshindependenttests.(c)Thecomparisonofthewindpressurecoefficients
between the simulated and experimental results [21] of the roof on the windward side. (d) The comparison of the RMS wind pressure
coefficientsbetweenthesimulatedandexperimentalresults[21]oftheroofonthewindwardside.
InTable3,itisobvioustoseethattheincreasingnumber 6.1.2.ValidationfortheMethodofCFDNumericalWindTun-
of the spatial points could raise the computing difficulty nel. InordertovalidatetheabovementionedCFDmethods
including the computing time and accuracy. Although the inSection3quickly,CFDpredictionsofFB16inFigure6(a)
calculating time by the AR method is always the shortest, [21], whose dimensions are smaller than those of the off-
the computing error increases rapidly from 11.94% of one shore platform, are conducted as an initial solution of LES
single point to 32.85%. The simulating accuracy of the simulations.Thecomputationaltreatmentandalgorithmare
WAWS method is acceptable all the time, but time cost in similartoSection3.ThedimensionsofFB16modelare12m×
computationoftheWAWSmethodisnearly100timesmore 6.7m×5.3m.Thedimensionsofthecomputationaldomain
than those of the MS method. Therefore, it is concluded aredefinedas420m×55m×15m[12]andtheblockingrate
that the MS method is a more efficient simulation method of the calculating model is less than 3%. The flow field and
comparedtotheWAWSandARmethods. FB16aresketchedinFigure6(a).
Based on the two abovementioned validation tests, the Throughaseriesofmeshindependenttestswiththetotal
MS method is an efficient and accurate simulation method grid number of 7.0 × 105, 1.4 × 106, 2.8× 106, and 4.2×
6
integratingtheadvantagesoftheWAWSandARmethods. 10 , the wind coefficients of the roof on the windward side
10 ShockandVibration
(a) (b)
(c)
∘ ∘ ∘
Figure7:Thesketchofthecalculatingmodelwiththreeinclinedangles:(a)0,(b)5,and(c)10.
are displayed in Figure 6(b). Since the total grid number 6.2. Numerical Examples. In this section, attention is fixed
increases from 7.0 × 105 to 4.2 × 106, the wind coefficients onthewindfieldanalysesoftheoffshorestructuresoverthe
havelittlechangeinvalue.Forobtainingrelativeaccuraciesof water as plotted in Figure 1 under the action of the harsh
thewindpressures,forces,andcomparingwindcoefficients, fluctuatingwind.CFDnumericalwindtunneltestsandwind-
itisfoundthatthepresentmeshinthepresentgridresolution induced structural response analyses are presented in the
test(i.e.,thetotalgridnumber7.0×105)canhaveabalance followingnumericalstudies.
on time cost and numerical accuracy, which can satisfy the
engineering requirements by and large. Therefore, the total 6.2.1. CFD Wind Tunnel Predictions. The present work in
gridnumber7.0×105 isadoptedinconsiderationofsaving thissubsectionistoanalyzethewindpressuredistributions
computingtimewhileprovidingaccurateresults. andwindresultantforcesofthisplatformwiththeinclined
Figures6(c)and6(d)describethenumericalresultsand angles of 0∘, 5∘, and 10∘ plotted in Figure 7 at different
experimentaldataofthewindpressurecoefficientsandRMS wind directions. As the symmetry of the platform, 7 wind
∘ ∘
pressurecoefficients.Meanwhile,theredlinerepresentsthe directions are defined within the range of 0 and 90 with
∘
present CFD results and the dark line is extracted as the intervalsof15 .Similartothemeshindependentsimulations
experimental data from [21]. The comparison shows that in the validation tests, the total grid number in the present
the trends of the curves are roughly in agreement and the LESsimulationsisapproximately1.1×107.
maximumerrorsofwindpressurecoefficientandRMSwind Accordingto[10,20,30],CFDsimulationsadoptthewind
pressurecoefficientbetweenthenumericalandexperimental speedupdatingmethodbythejointapplicationofMATLAB
resultsare,respectively,lessthan15%and21%.Therefore,the and Fluent. The wind speeds of the grid nodes in the inlet
LESmethodwiththesestandardsisavailabletocarryoutthe boundary are simulated by the MS method mentioned in
followingnumericalexamples. Section 3 using self-compiled MATLAB codes. Using the