Numerical Simulation of Fluctuating Wind Effects on an

Research ArticleNumerical Simulation of Fluctuating Wind Effects onan Offshore Deck Structure

Jin Ma1 Dai Zhou123 Zhaolong Han1 Kai Zhang14 Jennifer Nguyen5

Jiabao Lu1 and Yan Bao1

1School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai 200240 China2Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE) Shanghai 200240 China3State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University No 800 Dongchuan Road Shanghai 200240 China4Department of Civil Engineering Graduate School of Urban Innovation Yokohama National University Yokohama 2408501 Japan5Cullen College of Engineering University of Houston Houston TX 77004 USA

Correspondence should be addressed to Dai Zhou zhoudaisjtueducn

Received 5 November 2016 Revised 2 February 2017 Accepted 28 February 2017 Published 30 March 2017

Academic Editor Marco Belloli

Copyright copy 2017 Jin Ma et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The offshore structures that play a vital role in oil and gas extraction are always under complicated environmental conditions suchas the random wind loads The structural dynamic response under the harsh wind is still an important issue for the safety andreliable design of offshore structures This study conducts an investigation to analyze the wind-induced structural response of atypical offshore deck structure An accurate and efficient mixture simulation method is developed to simulate the fluctuating windspeed which is then introduced as the boundary condition into numerical wind tunnel tests Large eddy simulation (LES) is utilizedto obtain the time series of wind pressures on the structural surfaces and to determine the worst working condition Finally thewind-induced structural responses are calculated byANSYS Parametric Design Language (APDL)The numerically predicted windpressures are found to be consistent with the existing experimental data demonstrating the feasibility of the proposedmethodsThewind-induced displacements have the certain periodicity and change steadilyThe stresses at the top of the derrick and connectionsbetween deck and derrick are relatively larger These methods as well as the numerical examples are expected to provide referencesfor the wind-resistant design of the offshore structures

1 Introduction

Numerous offshore structures have been constructed tosupply oil and gas all over the world in recent years Theoffshore structures are designed for resisting random windand wave loads In the current design experience the lateralrandom wind load in the design of fixed offshore structuresis of order of 10 in the total lateral design loads and 25 inthe case of floating platforms [1 2] Many accidents involvingdeck components such as a derrick and crane due to therandom wind loads have already been reported in damageinvestigation [3] However practical estimation and assess-ment of the fluctuating wind and wind-induced dynamicresponse of the complex offshore deck structures are stillinvolved problems [4] Therefore with the development ofthe oil exploitation to deep sea it is necessary and important

to carry out the wind field analyses of offshore structures toguarantee a reasonable safety design

In general the wind-induced structural responses arenumerically investigated by applying wind pressures on thestructural surfaces by the time-domain analysis method[5 6] Meanwhile the numerical simulation in the presentstudy could override the two-way fluid-structure interac-tion with the wind-induced structural response with smalldeformation [7] Wind pressures on structures could beextracted by the full-scale measurement wind tunnel testand computational fluid dynamics (CFD) methods Eachof these methods is complementary with another in viewof their own advantages and limitations [8] The full-scalemeasurement can record the firsthand data of wind pressureson prototype structures However it is generally conductedwith the limitations of several objective conditions such as

HindawiShock and VibrationVolume 2017 Article ID 3210271 17 pageshttpsdoiorg10115520173210271

2 Shock and Vibration

weather conditions high cost and site conditions [9] Windtunnel test is a relatively mature and effective technique inwind engineering on scaled models of complex structures[10 11] However there are also several limitations in windtunnel tests for accurate investigations of wind pressures onstructures as follows (1) Reynolds numbers of scaled modeltests are smaller than those of prototype structures (2) thewind field conditions can hardly be reproduced exactly inwind tunnel tests [10]

Owing to the rapid developments of computer power andcomputational methods CFD predictions have been widelyused to analyze the wind flows around prototype structuresin engineering practice [12] Large eddy simulation (LES) asone of the main CFD methods has been widely applied inthe simulations of wind fieldsWith powerful CFD tools suchas LES it is possible to conduct full-scale size simulationsof prototype structures in high Reynolds numbers flows andprovide abundant detailed data and information such aspressure distributions on structural surfaces [13]

It is understood that proper generation of the inletboundary conditions for CFD simulations especially for LESin computational wind engineering (CWE) is essential inthe analyses of wind pressure distributions and the dyna-mic responses of prototype structures [14] Therefore theimprovement of simulating fluctuating wind speed in theinlet boundary is provided in the present study Combiningwith the advantages of weighted amplitude wave superposi-tion (WAWS) [15] and autoregression (AR) [16 17] methodswith high accuracy and less time cost respectively a mixturesimulation (MS)method is proposed and demonstrated as anefficient and accurate simulationmethod in the present work

In summary the main objective of this present study isto conduct wind field analyses of the offshore deck structureswhich are carried out by a joint application of CFD techniqueand structural finite element analysis Furthermore timeseries of wind pressures on the structural surfaces at differentwind directions and inclined angles of the platform areextracted in CFD wind tunnel tests and then applied tothe finite element model to investigate the wind-inducedstructural response

This paper is organized as follows the structural modelsin numerical simulation and wind tunnel test are presentedin Section 2 Methods for conducting CFD predictions areprovided in Section 3 An accurate and efficient MS methodfor simulating fluctuatingwind speed as boundary conditionsis proposed in Section 4 Computational procedures for thewhole wind field analyses of the offshore deck structures areincluded in Section 5The validation tests for theMS and LESmethods and numerical cases of wind field investigations arecarried out in Section 6

2 The Model Semisubmersible Platform

The semisubmersible platform in this study is the 6th-generation deepwater drilling platform shown in Figure 1(a)and possesses the function of intelligent drilling technologyattaining the advanced level all over the world The majorstructural components of this platform include derrick deck

Table 1 The size parameters of the semisubmersible platform

Members Dimensions (length times width times height)mThe lower part of derrick 17 times 17 times 42The upper part ofderrick (wedge) 17 times 17 times 22Deck 7442 times 7442 times 86Column 1739 times 1739 times 2146

columns and floating bodies The main parameters of thisplatform are listed in Table 1

The tested model in Figure 1(b) was scaled as 1 100 in[18] The full-scale CFD numerical model of this platformin the present CFD simulations is built based on the testedscaled model [18] and numerical full-scale model [19] Inview of the major consideration of wind field analyses theoffshore platform structures under the water are hidden andthe derrick is totally enclosed as shown in Figure 1(c) which isdemonstrated that the extractedwind pressures are applicablein the wind-induced dynamic response analyses [19 20]However the structural computational model of the derrickin the following time-domain analysis is similar to a realstructure and not enclosed as is plotted in Figure 1(d)

One thing to note is that two types of numerical modelsthe CFD numerical model and the structural computationalmodel are applied in this present study The CFD numericalmodel is a platformmodel used for LES simulations which isestablished by using a combination of Rhino (Robert McNeelamp Assoc USA) and ICEM CFD (ANSYS Inc USA) Thestructural computational model is a finite element model ofthis platform for structural dynamic response analyses intime domain which is built by ANSYS Parametric DesignLanguage (APDL) (ANSYS Inc USA)The finite elements ofthe local components are listed as follows the derrick adoptsbeam element the deck uses shell element and the columnsadopt solid element

3 Numerical Simulation

In this section together with the commercial CFD softwareFluent 145 (ANSYS Inc USA) the unsteady-state analysisof the LES approach is used to predict the time seriesof wind pressures on the surfaces of structures above thewater surface at different working conditions Fluent 145conducts LES simulations based on finite volume method(FVM) [23] Then the wind-induced structural responsesare explored by the extracted wind pressures acting on thestructures using APDL and time-domain analysis methodcooperatively [24] The detailed computational algorithmsand treatments of wind field analyses are addressed in thefollowing subsections

31 CFD Predictions

311 LES Turbulence Model In the present LES study LESseparates flow motions into large and small eddies which iscalculated by using a combination of the direct simulation

Shock and Vibration 3

(a) (b)

(c) (d)

Figure 1 (a) The practical semisubmersible platform (b) The tested model of wind tunnel tests [17] (c) The numerical model used in CFDwind tunnel predictions (d) The derrick model for wind-induced analyses

method and general model theory [25] In view of thesestudies in the LES simulations whose proposed methods areapplied for full-scale CFD numerical model under Reynoldsnumber greater than 108 [10] these methods are adoptedto carry out the present LES simulations under Reynoldsnumber of approximately 6 times 107 It is worth mentioning thatthese methods such as one-equation model are suitable forrelatively coarse grid case and high Reynolds number flows[26] The accuracy and reliability of the proposed numericalframework have been validated by the consensus betweennumerical and experimental results in the previous studies[10 26]

The governing equations of an incompressible flow forLES simulations [26] are expressed as

120597120588V119894120597119905 + 120597120588V119894 V119895120597119909119895 = minus 120597120597119909119894 (119875 +

23120588119896sgs)

+ 120597120597119909119894 [2120588 (120592119904 + 120592) 119878119894119895]

120597V119894120597119909119894 = 0

(1)

where V119894 is the large-scale wind velocity field tensor 119875 theresolved pressure 119878119894119895 the resolved strain-rate tensor 120588 the airdensity 120592 the kinematic viscosity 119896sgs the subgrid scale (SGS)kinematic energy 120592119904 the SGS eddy viscosity and

120592119904 = 119862VΔ Vradic119896sgs

Δ V = Δ1 + 119862119896 (Δ21198782119896sgs)

120597119896sgs120597119905 + 120597V119895119896sgs120597119909119895 = minus120591119894119895119878119894119895 minus 119862120576 119896

32sgs

Δ

+ 120597120597119909119895 [(119862119889Δ Vradic119896sgs + 120592) 120597119896sgs120597119909119895 ]

minus 2120592120597119896sgs120597119909119894120597119896sgs120597119909119895

(2)

where 119862V 119862119896 119862120576 and 119862119889 are the constant [27 28] and Δ isthe length scale of filter and can be determined according toHuang and Lirsquos work [26]


(a) (b)

Figure 2 The meshing results (a) Block 1 (b) Block 2

The improved LES approach proposed by Huang and Li[26] has been developed as a Fluent User Defined Function(UDF) library which has been applied in conducting LESsimulations of tall buildings and long-span complex roofstructures in the previous studies [10 12]

312 Numerical Algorithms In the LES predictions allthe discrete equations are solved by the pressure implicitwith splitting of operators (PISO) method The time andspatial discretization are both treated by second-order dis-crete schemes Bounded central differencing is adopted formomentum discretization The LES simulations are per-formed together with ANSYSFluent 145 and the parallelcalculations of 16 central processing unitsThe total time stepsare nearly 41000 with 005 s per time step which are sufficientto reach the statistical convergence for LES simulations [1012]

313 Computational Domain and Mesh Arrangement Thenumerical model of this offshore platform is established infull-scale sizes as sketched in Figure 1(c) The dimensions ofthe computational domain sketched in Figure 2 are 2600m(119871119909)times 600m (119871119910)times 200m (119871119911) as the computational domainis 35 (119871119909) times 8 (119871119910) times 25 (119871119911) [11] The blocking rate of CFDnumerical model in the computational domain is less than3 which is generally acceptable in CWE [9] According tothe multiblock technique in the previous study [12] the flowfield consists of two blocks The small cylindrical flow fieldand CFD numerical model which are combined together bya Boolean operation are defined as ldquoBlock 1rdquo in Figure 2(a)and the remaining part (ie the big rectangular flow field)is defined as ldquoBlock 2rdquo in Figure 2(b) One thing is to notethat theCFDnumericalmodel is nested in ldquoBlock 1rdquo RotatingldquoBlock 1rdquo the specified angle immediately can carry out LESsimulations at the specified wind direction by which LESsimulations can be conducted at multiple wind directionsconveniently Numerous tetrahedral grids are generated inthe neighborhood of the structural surfaces especially in thevicinity of the derrick and the grid stretching ratio is keptto be lt105 The maximum and minimum grid lengths in theneighborhood of the structural surfaces are 08m and 02mrespectively Hexahedron grids are adopted in the regionsfar away from the calculating model and the grid stretchingratio is relatively enlarged for reducing the totalmesh numberfor the sake of saving time cost in computation In view of

the computer performance computing time and engineeringrequirements the minimum maximum and mean values of119910+ are 253308 489245 and 348798 respectively Accordingto the previous study [29] although a recommended value for119910+ is about 1 values lower than 5 are acceptable because thecell stays in the viscous sublayer

The total mesh number is nearly 11 million Accordingto LES theory the mesh quantity should reach Re94 inorder to provide very accurate numerical results And themore the mesh elements in the fluid domain the higherthe computational accuracy that will be reached Howeverit requires much more computing time cost and highercomputer performance which would be a heavy task for CFDsimulation In order to make it feasible to reach moderateaccuracy while simultaneously satisfying the engineeringrequirement (which can allow 10sim30 error for structuresafety design) the grid resolution has to be reduced Forobtaining relative accuracies of the wind pressures forcesand comparing wind coefficients we conducted a grid reso-lution test in the following validation test and found that thepresented mesh balances time cost and numerical accuracysatisfying the engineering requirements

314 Boundary Conditions The boundary conditions aredescribed as the wind velocity profile in accordance withan exponential rule which can satisfy the Navier-Stokesequations in LES simulations [10 18]

119881119911 = 1198810 ( 1198671198670)120572 (3)

where 119881119911 and 1198810 are the average wind velocities at the heightof119867 and1198670 and 120572 is related to geomorphologic features [22]

In unsteady-state analysis of the LES simulations the Flu-ent code provides a direct and convenientmethod to generatea time-dependent turbulent fluctuating wind velocity fieldHowever it is reported that the generated wind field by theFluent code decays rapidly in the inertial range and is not wellapproximated as the marine random wind [26] The powerspectral density (PSD) of the fluctuatingwind is fitted byNPD(Norwegian Petroleum Directorate) spectrum in the presentstudy [22]

119878 (119891) = 320 (119881010)2 (11991110)045(1 + 15119865)356

119865 = 172119891( 11991110)23 (119881010)

minus34 (4)


OutletInlet

Wind

Figure 3 The sketch of the inlet boundary of the fluctuating wind

where 119878(119891) is the PSD function 119891 the wind frequency1198810 theaveragewind speed at the height of1198670 and 119911 the height abovesea level

Given a clear explanation of the wind characteristicsthe fluctuating wind speed of the inlet boundary shown inFigure 3 is simulated by the MS method proposed in thefollowing section This new simulation method MS methodcan generate the time series of wind velocities of a num-ber of spatial nodes accurately and efficiently The pressurefluctuation on structural surfaces can be solved by importingthe inlet boundary conditions in LES simulations in thecommercial software ANSYSFluent 145 Therefore velocityand pressure components together satisfy the Navier-Stokesequations

In order to guarantee the convergence property andefficiency in LES simulations the fluctuating wind velocitiesat each time step at the inlet are modified through the equaltotal flow of the inlet and outlet on the basis of the previousstudies [20 30] The equation is described as

V119894+1 = V119894 minus (sum119899119894=1 V119894119860 119894 minus Ω)119860 (5)

where V119894 is the fluctuating wind speed at time step 119894 119860 119894 thearea of the corresponding grid cell119860 the total area of the inletboundary and Ω the total flow of the outlet boundary at thecorresponding time step

According to the work of Lu et al [20] and Shirani etal [30] the wind velocities at each time step being read andupdated in Fluent 145 are found to be slightly smaller than theinitial wind velocities generated by the self-made MATLABprogram

315 Data Analyses The analyses of wind pressure distribu-tion are carried out in terms of nondimensional coefficients119862119901 and 119862119901rms of a measuring point 119894 defined respectively as

119862119901 = 1198751198940512058811988120

119862119901rms = 119875119894rms0512058811988120 (6)

where 119862119901 and 119862119901rms are the mean and RMS pressure coeffi-cients respectively 119875119894 is the mean pressure 119875119894rms is the RMS

pressure 120588 is the air density and 1198810 is the average of windspeed at the height of 100m

According to China Classification Society common rulesand [19] the equation of the shape coefficient of a structuralmember is expressed as

119904119888119894 = 119862119901 (160119911 )02 119878119862 = sum119894 119904119888119894119878119860 119894119878119860

(7)

where 119894 is ameasuring point on a specified structuralmember119904119888119894 is the shape coefficient 119894 119862119901 the mean pressure coefficient119911 the height of a measuring point 119894 119878119860 119894 the area of thestructural surface which a measuring point 119894 belongs to and119878119860 the total area of multiple structural surfaces The ave-rage pressure coefficients 119878119862 are changing with the winddirections Therefore the shape coefficients vary with winddirections

32 Wind-Induced Structural Response Analyses The timeseries of the extracted wind pressures are applied to theoffshore structures and the wind-induced dynamic responsesare calculated by time-domain analysis method together withAPDL solving the structural dynamic equation as follows

[119872] + [119862] + [119870] 119906 = [119865] (8)

where [119872] [119862] and [119870] are respectively structural massdamping and stiffness matrices and 119906 are respec-tively acceleration velocity and displacement vectors and[119865] are fluctuating wind loads Meanwhile (4) is solved bythe Newmark-120573 approach in this present study [22]

In structural dynamic response analysis the dampingmatrix [119862] is determined by the following equations

[119862] = 120572 [119872] + 120573 [119870] 120585119894 = 120572

2120596119894 +1205731205961198942 (9)

where 120572 and 120573 are the constants in Rayleigh damping whichare calculated by the damping ratio in eachmode shape 120585119894 [20]which is assumed as a constant over a range of frequenciesAnd 120596119894 is the structural frequency in each mode shape


Wavelet method

WAWS method AR method

Time series of fluctuating wind (t) = 1(t) + 2(t)

Parts of energy dispersion S2(휔)Parts of energy concentration S1(휔)

PSD S(휔) = S1(휔)W1(휔) + S2(휔)W2(휔)

1(t)Generate wind speed 2(t)Generate wind speed

Figure 4 The flowchart for simulating the fluctuating using MS method

4 The Method for SimulatingFluctuating Wind

A mixture simulation (MS) method is proposed to generatethe fluctuating wind speed as the boundary conditions inCFD predictions combining with the weighted amplitudewave superposition (WAWS)method [15] and autoregression(AR) methods [16 17] The new approach overcomes thedefects of the abovementioned traditional methods andinherits their own advantages which guarantee the comput-ing accuracy and efficiency simultaneously

Assuming that the fluctuating wind is a stationarystochastic Gaussian process the stochastic characteristics canbe described by the power spectral density (PSD) function[31] Then the energy distributions of the PSD function ofthe fluctuating wind are explored by the wavelet method [32]adopting the Hanning windows [33] Therefore the mainthoughts of the MS method are listed as follows the partsof the energy concentration are simulated by the WAWSmethod [15] and the parts of the energy dispersion aregenerated by the ARmethod [16]The final simulating resultsof the fluctuating wind are obtained by the superposition ofthe simulating results by the two methods The schematicsimulation process is concluded in Figure 4 The equationof the calculating process by the MS method is described asfollows

119878 (119891) = 1198781 (119891)1198821 (119891) + 1198782 (119891)1198822 (119891) (10)

where 119878(119891) is the PSD function 119891 is the wind frequency1198821(119891) and1198822(119891) are respectively the Hanning windows ofthe energy concentration and dispersion and 1198781(119891) and 1198782(119891)are respectively simulated by the WAWS method and ARmethod

The Hanning window number is determined by theenergy distribution of the PSD function in the wind fieldAccording to our experience the window number using theWAWS method is three times larger than it using the ARmethod In this way the MS method could reduce the timecost in computation with no accuracy lost to simulate a kindof loads with the random properties which is demonstratedin the following validation tests in Section 61

The application of the WAWS and AR methods is brieflypresented in the following formula derivation which hasfully considered temporal and spatial correlation in the self-compiled programs

(1) The WAWS Method in the MS Method Using the WAWSmethod the correlation function 119877119895119898 is expressed as

119877119895119898 (120591) = 119864 (V119895 (119905) V119898 (119905 + 120591))= Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119896119897)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896119897)1003816100381610038161003816sdot cos (2120587119891119896119897 + 120579119895119896 (119891119896119897) minus 120579119898119896 (119891119896119897))

(11)

where 119864 is expectation V is the time series of wind speed119867is obtained by Cholesky decomposition and 120579119895119896(119891119896119897) is thephase angle between spatial nodes 119894 and 119895

Assuming that119873 rarrinfin and Δ119891 rarr 0

119877119895119898 (120591) = int119904ℎ1

1199041198971

119895sum119896=1

10038161003816100381610038161003816119867119895119896 (119891119896)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896)1003816100381610038161003816sdot cos (2120587119891119896 + 120579119895119896 (119891119896) minus 120579119898119896 (119891119896)) 119889119891

(12)

The correlation function is transformed from time dom-ain to frequency domain on the basis of convolution theorem

119877119895119898 (120591) otimes 1198821 (119905) = int119904ℎ1

1199041198971

119895sum119896=1

10038161003816100381610038161003816119867119895119896 (119891119896)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896)1003816100381610038161003816sdot 1 (119891) cos (2120587119891119896 + 120579119895119896 (119891119896) minus 120579119898119896 (119891119896)) 119889119891= int119904ℎ11199041198971

119895sum119896=1

119878119895119896 (119891) sdot 1 (119891) cos (2120587119891119896) 119889119891(13)

where otimes represents convolution operation


Time series of wind speed simulated by the WAWSmethod V1(119905) is obtained by

V1 (119905)

= radic2Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119897)10038161003816100381610038161003816 cos (2120587119891119897119905 + 120579119895119896 (119891119897) + 120593119896119897)

119895 = 1 119898

(14)

where 120593 is a random number from 0 to 2120587(2) The AR Method in the MS Method Similarly the correla-tion function in the AR method can be expressed as

119877119894119895 (120591) = int119904ℎ2

1199041198972

119878119894119895 (119891) 2 (119891) cos (2120587119891 sdot 120591) 119889119891 (15)

where 119877 is the correlation functionTime series of wind speed simulated by the AR method

V2(119905) is calculated by

V2 (119905) = minus119895sum119894=1

119901sum119896=1

119886119894119895119896V119894 (119905 minus 119896 sdot Δ119905) + 119906 (119899) (16)

where Δ119905 is the total simulating time step 119886 the coefficient ofautoregression matrix 119906(119899) the excited white noise throughall-zeros filter and 119901 the order of AR model

Overall the total wind speed is obtained by V(119905) = V1(119905) +V2(119905) which is shown in Figure 4

5 The Procedure for the Wind FieldAnalyses of the Platform

In this section the details for conducting LES predictionsand wind-induced dynamic responses analyses of the deckstructures under the action of the fluctuating wind aresummarized as follows

Step 1 Establish the geometric and finite element models byVC++ and APDL

Step 2 Generate the fluctuating wind speed

Step 21 Simulate and correct the time series of thewind speedby using the MATLAB (MathWorks USA) self-compiledprograms

Step 22 Convert these data into data files in the formatthat has a txt extension format These data files are readby ANSYSFluent using the User Defined Functions (UDF)program

Step 3 Construct the CFD numerical wind tunnel

Step 31Create the calculationmodel andmesh files by Rhinoand ICEM CFD

Step 32 Set the initial and boundary conditions inANSYSFluent and start the calculation

Step 33 Calculate the resultant forces to determine the worstoperating condition

Step 34 Extract the time series of wind pressure on thestructural surfaces by the UDF program for the followingdynamic response analyses

Step 4 Carry out the wind-induced dynamic response anal-yses by APDL

Step 41 Import the finite element model of the platform anddeck structures

Step 42 Set the initial and boundary conditions and start thecalculation by the Newmark-120573method in time domain usingthe secondary development application programs

Step 43 Extract the calculation results such as the deforma-tions and stresses of nodes and members

6 Results and Discussion

61 Validation Tests In this subsection the numerical resultsare compared to verify that the methods and self-madeprograms mentioned in Sections 3 and 4 are applicable andeffective in the following numerical examples

611 Validation for the MS Method Tests are constructed todemonstrate the accuracy and efficiency of the MS methodcompared to the traditional simulation methods the WAWSand AR methods The time series of the wind speed at anyspatial point is simulated by the MS WAWS and AR meth-ods respectively The comparison between the simulatedand theoretical results could determine the best simulationmethod

(1) Validation for the Accuracy of the MS Method Thefluctuating wind speed at one single spatial point is simulatedby theMSWAWS andARmethods respectively in the sameinitial condition listed as follows the average wind velocity1198810 = 31654ms the number of the sampling points 119899 =1200 time step Δ119905 = 01 s and the measuring point (inmeters) is located at (0 0 5) The error between the energy[34] of the simulated and theoretical results solved by (17)can assess the accuracy of the simulation method by fastFourier transform (FFT) [35] and frequency-time conversionmethods [36 37]

Ω = 1003817100381710038171003817119883 (119895120596)10038171003817100381710038172119879 =10038171003817100381710038171003817int 119909 (119905) 119890minus119894120596119905100381710038171003817100381710038172119879 (17)


Simulated resultsTarget results

10minus2

100

102

104PS

D

100 10110minus2 10minus110minus3

Frequency (Hz)

(a)

Target resultsSimulated results

10minus2

100

102

104

PSD


Frequency (Hz)

(b)


10minus2

100

102

104


(c)

Figure 5The comparison between simulated and target results byMS AR andWAWSmethods (a) MSmethod (b) ARmethod (c)WAWSmethod

Table 2The comparison of calculating accuracy between the resultsof simulated PSD and theoretical PSD

MS method WAWS method AR methodTheoretical energy 126923 126923 126923Simulating energy 123927 136073 142073Error 236 721 1194

where 119909(119905) is time series of wind velocity 119883(119895120596) the ampli-tude spectrum obtained from 119909(119905) by FFT and 119879 the lastingtime of time series of wind speed The energy Ω is calculatedby the square of the amplitude spectral mode divided by thelasting time 119879

The comparisons between simulated and target results bythe MS AR and WAWS methods are plotted in Figure 5The blue and red curves are target and simulated PSDrespectively As seen from Figure 5 the simulated results bythe MS method are more accurate and closer to the targetresults The numerical accuracy by the AR method in thelower and higher regions is the lowest compared to thoseby the MS and WAWS methods Table 2 conducts furthernumerical accuracy analyses by the energy comparisonsbetween the simulated and theoretical results using the MSWAWS and AR methods Obviously the error of the MSmethod is much lower than the others under the same initialconditions as 236 versus 721 and 1194

These comparisons demonstrate that the MS method isa more accurate simulation method to generate the randomloads compared to the WAWS and AR methods

(2) Validation for the Efficiency of theMSMethod In general anumerical wind tunnel needs the time series of the fluctuating

Table 3 The comparison of the computing time and accuracy at 36and 108 spatial points using the MS WAWS and AR methods

Number of nodes Method Error Computing time (s)

36

WAWS in MS 234 256AR in MS 624 75

MS 479 331WAWS 424 27465AR 2296 75

108


MS 485 7255WAWS 424 647836AR 3285 489

wind of numerous spatial points rather than one singlepoint Time cost in computation becomes an important con-sideration in the numerical examples The comparisons ofthe simulating time using the MS WAWS and AR methodsrespectively are carried out under the same computingconditions mentioned in Validation for the Accuracy of theMS Method

The fluctuating wind velocities of 36 and 108 adjacentgrid nodes in the inlet boundary sketched in Figure 3 aresimulated by three abovementioned simulation methodsTable 3 gives a series of comparisons of computing timeand accuracy of generating the fluctuating wind velocitiesat 36 and 108 adjacent spatial points using three simulationmethods


(a)

28 times 106

42 times 1067 times 105

14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

minus3 minus2 minus1 0 1 2 3 4minus4X (m)

(b)

The experimental dataThe simulated results

0minus2 minus1minus3minus4 2 431X (m)

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)


minus2minus4 minus1 0 1 2 3 4minus3X (m)

01

02

03

04RM

S pr

essu

re co

effici

ent

(d)

Figure 6 (a) The sketch of flow field and FB16 model (b) Mesh independent tests (c) The comparison of the wind pressure coefficientsbetween the simulated and experimental results [21] of the roof on the windward side (d) The comparison of the RMS wind pressurecoefficients between the simulated and experimental results [21] of the roof on the windward side

In Table 3 it is obvious to see that the increasing numberof the spatial points could raise the computing difficultyincluding the computing time and accuracy Although thecalculating time by the AR method is always the shortestthe computing error increases rapidly from 1194 of onesingle point to 3285 The simulating accuracy of theWAWS method is acceptable all the time but time cost incomputation of the WAWS method is nearly 100 times morethan those of the MS method Therefore it is concludedthat the MS method is a more efficient simulation methodcompared to the WAWS and AR methods

Based on the two abovementioned validation tests theMS method is an efficient and accurate simulation methodintegrating the advantages of the WAWS and AR methods

612 Validation for the Method of CFD Numerical Wind Tun-nel In order to validate the abovementioned CFD methodsin Section 3 quickly CFD predictions of FB16 in Figure 6(a)[21] whose dimensions are smaller than those of the off-shore platform are conducted as an initial solution of LESsimulations The computational treatment and algorithm aresimilar to Section 3The dimensions of FB16model are 12mtimes67m times 53m The dimensions of the computational domainare defined as 420m times 55m times 15m [12] and the blocking rateof the calculating model is less than 3 The flow field andFB16 are sketched in Figure 6(a)

Through a series of mesh independent tests with the totalgrid number of 70 times 105 14 times 106 28 times 106 and 42 times106 the wind coefficients of the roof on the windward side


(a) (b)

(c)

Figure 7 The sketch of the calculating model with three inclined angles (a) 0∘ (b) 5∘ and (c) 10∘

are displayed in Figure 6(b) Since the total grid numberincreases from 70 times 105 to 42 times 106 the wind coefficientshave little change in value For obtaining relative accuracies ofthe wind pressures forces and comparing wind coefficientsit is found that the presentmesh in the present grid resolutiontest (ie the total grid number 70 times 105) can have a balanceon time cost and numerical accuracy which can satisfy theengineering requirements by and large Therefore the totalgrid number 70 times 105 is adopted in consideration of savingcomputing time while providing accurate results

Figures 6(c) and 6(d) describe the numerical results andexperimental data of the wind pressure coefficients and RMSpressure coefficients Meanwhile the red line represents thepresent CFD results and the dark line is extracted as theexperimental data from [21] The comparison shows thatthe trends of the curves are roughly in agreement and themaximum errors of wind pressure coefficient and RMS windpressure coefficient between the numerical and experimentalresults are respectively less than 15 and 21Therefore theLES method with these standards is available to carry out thefollowing numerical examples

62 Numerical Examples In this section attention is fixedon the wind field analyses of the offshore structures over thewater as plotted in Figure 1 under the action of the harshfluctuatingwind CFDnumerical wind tunnel tests andwind-induced structural response analyses are presented in thefollowing numerical studies

621 CFD Wind Tunnel Predictions The present work inthis subsection is to analyze the wind pressure distributionsand wind resultant forces of this platform with the inclinedangles of 0∘ 5∘ and 10∘ plotted in Figure 7 at differentwind directions As the symmetry of the platform 7 winddirections are defined within the range of 0∘ and 90∘ withintervals of 15∘ Similar to the mesh independent simulationsin the validation tests the total grid number in the presentLES simulations is approximately 11 times 107

According to [10 20 30] CFD simulations adopt thewindspeed updating method by the joint application of MATLABand Fluent The wind speeds of the grid nodes in the inletboundary are simulated by the MS method mentioned inSection 3 using self-compiled MATLAB codes Using the


The transient wind speedThe average wind speedThe theoretical wind speed

0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)

The theoretical dataThe simulated results

0

100

200

300

400

Hei

ght (

m)

0200 03 0401Turbulence intensity

(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)


01 02 03 0400Turbulence intensity

0

100

200

300

400

Hei

ght (

m)

(d)

Figure 8 (a) Boundary layer profile at 1st time step at the inlet obtained to simulate the NPD profile [22] (b) Turbulence intensitymeasurements at 1st time step at the inlet for NPD profile [22] (c) Boundary layer profile at 100th time step at 100m in front of the CFDnumerical model obtained to simulate the NPD profile [22] (d) Turbulence intensity measurements at 100th time step at 100m in front ofthe CFD numerical model for NPD profile [22]

function of UDF the velocity inlet conditions based on(3) and (5) are imported through the CFD interfaces intoFluent software as sketched in Figure 3 Figure 8 gives thecomparisons of the simulated and theoretical results of NPDwind profile and turbulence intensity [22] to validate whetherthe simulated results are in accordance with theoretical datato guarantee the numerical accuracy of CFD simulationsAmong them Figures 8(a) and 8(c) represent the wind profilecomparisons at 1st time step at the inlet and at 100th timestep at 100m in front of the CFD numerical model res-pectively Figures 8(b) and 8(d) show the turbulence intensitycomparisons at 1st time step at the inlet and at 100th time step

at 100m in front of the CFD numerical model respectivelyThe simulated results of wind profile and turbulence intensityare relatively in agreement with the theoretical data Thesimulated results of the average wind speed and turbulenceintensity are especially very close to the target values Further-more the simulated results at 100th time step at 100m in frontof theCFDnumericalmodel are relativelymore accurate thanthose at 1st time step at the inlet by wind speed updatingprocedure in Section 314

Figure 9(a) defines 2 lines used for demonstrating theaccuracy of numerical simulation compared to existingexperimental data and exploring some differences of wind


pressure distributions in different areas on the derrick (Fig-ures 9(b) and 9(c)) Figures 9(b) and 9(c) plot the windpressure distributions of two measuring lines on the wind-ward side at 0∘ and 30∘ wind directions Wind pressure dec-reases with amaximum of nearly 60 as the height increasesThe curves of the present study are relatively close to those ofthe experimental resultsThe statistical results show themax-imum differences of the wind coefficients at 0∘ and 30∘ winddirections between the numerical results and experimentaldata are respectively about 127 and 236 which providespotentially acceptable results for engineering purpose Asseen from Figures 9(d) and 9(e) the simulated RMS windcoefficient curves in Line 1 are closer to the experimentalcurves than those in Line 2 whose curve trends are also inrelative agreement with experimental curves The maximumRMS wind coefficient errors at 0∘ and 30∘ wind directionsin Line 1 are 232 and 239 and those in Line 2 arerelatively larger but less than 30 Furthermore the errorsare speculated to be caused by the limited grid number andcomputational algorithm

Figure 10 plots the shape coefficient and resultant windforces of the platform over the water in 7 wind directionscalculated by using the UDF function Considering thatthe wind area of each local component of this platformchanges at differentwinddirections the variation of the shapecoefficient is irregular in Figure 10(a) The shape coefficientsof the derrick and deck reach their maximum at 0∘ winddirection (ie 150 129 and 117) and the shape coefficientof the column is relatively large at 30∘ and 60∘ wind direction(ie 092 and 096) The curve trends of the numerical andexperimental studies [18 19] are relatively in good agreementThe numerical results are slightly smaller than the windtunnel data and the errors between them are approximately74 or less

As seen fromFigure 10(b) the curves of thewind forces inthe horizontal position and inclination have the same trendThe wind loads of the flat and aslant platforms all increasefrom 0∘ to 45∘ wind direction and decrease from 45∘ to90∘ wind direction The maximum wind load appears at 45∘wind direction in three positions of the platform which is inagreement with the experimental results [18 19] Accordingto China Classification Society common rule and [19] theresultant wind forces are related to the windward area ofthe structural member the wind speed and pressure Thewindward area of the aslant platform is larger than that ofthe flat platform Therefore the wind loads are increasingwith the increasing inclined angles The wind load takes themaximum value under the state of 45∘ wind direction and 10∘inclined angle which is the most adverse survival state andthe error between the simulated and experimental maximumresultant wind forces is about 48 16563 kN versus 17400 kN[18 19]

622 The Wind-Induced Response Analyses In light of thefact that the maximum wind resultant force appears at 45∘wind direction and 10∘ inclined angle in the above subsectionthe wind-induced structural responses of local componentsunder this working condition are investigated in time domainby APDL

Time series of the wind pressure at the top of the derrickand the statistics of wind pressures at different heights alongLine 1 shown in Figure 9(a) are displayed in Figure 11Thus it can be seen that wind pressure decreases with theincreasing height which matches the analyzed results in theLES predictions Meanwhile the change ranges of the meanand intermediate values are relatively larger than the othertwo values

The wind-induced deformations at the top of the derrickat 45∘ wind direction are plotted in Figure 12 The displace-ments in 119909 and 119910 directions are relatively ten times largerthan the deformation in the 119911 direction Due to conductingthe wind-induced analysis at 45∘ wind direction the displace-ments in the 119909 and 119910 directions are quite close listed asfollows the maximum displacements in the 119909 and 119910 direc-tions are respectively 00028m and 00034m the averagedisplacements in two directions are both nearly 95 times 10minus4mThe displacement-time curves in three directions changestably around the average values

The stress distributions of the local structures are dis-played in Figure 13 It is found that the stresses at the top ofthe derrick and the connections between the derrick and deckat 45∘ wind direction are the largest which reaches 174MPaAccording to the current standards for building and classingoffshore platforms formulated by China Classification Soci-ety the maximum stress value is lower than the allowablestress of 345MPa It is demonstrated that the derrick couldwork well under this survival condition

7 Conclusion

This paper mainly carries out the numerical simulationsof the fluctuating wind effects and wind-induced responseof a derrick on a semisubmersible platform by combiningCFD and structural finite element analysis techniques Thecomputing results lead to the following conclusions

(a) In the first validation test theMSmethod is developedinto an efficient and accurate simulation method whichintegrates the advantages of the WAWS and AR methodsCompared to the two traditional methods the MS methodis more applicable to simulate the fluctuating wind speed ofnumerous spatial nodes in consideration of the time cost andaccuracy in computation Taking the FB16model for an objectin another validation test the simulated results are relativelyclose to the existing experimental data which demonstratedthat LES methods are applicable in analyzing wind effects ona derrick

(b) The curves of wind pressure and RMS pressurecoefficients in the present study are relatively close to thosein the experimental data The errors of the pressure andRMS pressure coefficients 10sim30 are relatively acceptablein consideration of computational efficiency and computerperformances The numerical shape coefficients are slightlysmaller than the wind tunnel results overall and the errorsbetween them are about 74 or less

(c) In accordance with the existing experimental resultswind pressures decrease with a maximum of 60 as theheight increases The worst survival state in LES simulationsand following dynamic response analyses occurs when the


Blue line Line 1Measuring line

Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)

The wind tunnel data The present resultsLine 1Line 2 Line 2

Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)

The wind tunnel data The present results

004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)

Figure 9 (a)Measuring line position (b)Wind pressure coefficient of these lines on thewindward side at 0∘ wind direction (c)Wind pressurecoefficient of these lines on the windward side at 30∘ wind direction (d) RMS wind pressure coefficient of these lines on the windward sideat 0∘ wind direction (e) RMS wind pressure coefficient of these lines on the windward side at 30∘ wind direction


Experimental data Simulated resultsColumnsDeckUpper part of derrickLower part of derrick

ColumnsDeckUpper part of derrickLower part of derrick

30 60 900Wind direction (∘)

04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)

The inclined angle0∘

5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)

Figure 10 (a) The statistical shape coefficients of local components of the platform at different wind directions (b) The statistical resultantwind forces of the platform over the water under different survival conditions

200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)

The wind pressure at different heights

Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)

Figure 11 (a) The time series of the extracted wind pressure at the top of the derrick (b) The wind pressure statistics of measuring pointswith different heights along Line 1

wind resultant force reaches amaximumat 45∘winddirectionand 10∘ inclined angle

(d) The wind-induced dynamic responses are calculatedby the joint application of ANSYS Fluent and APDL Thedisplacements in three directions have certain periodicity andchange steadily around the average value The stresses at the

top of the derrick and the connections between the deck andderrick are the largest which is lower than the allowable stressIt is demonstrated that the offshore deck structures couldwork well in the worst survival condition

In future works the relationship between the wind scalestructural strength and deformations could be investigated


800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)

Figure 12 The displacement-time curves in three directions (a) 119909 direction (b) 119910 direction and (c) 119911 direction


Structural stress (MPa)

Upper part of the derrick Lower part of the derrick

Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07

Figure 13 The stresses of the local structures of the derrick at 45∘ wind direction

further In addition the effects of wind alone wave alone andthe combined actions of both wind and wave on the offshoreplatform could be explored and compared

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Supports fromNational Natural Science Foundation of China(nos 51679139 51278297) the Major Program of the Natio-nal Natural Science Foundation of China (no 51490674)Research Program of Shanghai Leader Talent (no 20) andDoctoral Disciplinary Special Research Project of ChineseMinistry of Education (no 20130073110096) are acknowl-edged

References

[1] E Shehata and A Raheem ldquoNonlinear behaviour of steel fixedoffshore platform under environmental loadsrdquo Ship and Off-shore Structures vol 11 no 1 pp 1ndash15 2014

[2] A A Elshafey M R Haddara and H Marzouk ldquoDynamic res-ponse of offshore jacket structures under random loadsrdquoMarineStructures vol 22 no 3 pp 504ndash521 2009

[3] SGomathinayagamC PVendhan and J ShanmugasundaramldquoDynamic effects of wind loads on offshore deck structures-acritical evaluation of provisions and practicesrdquo Journal of WindEngineering and Industrial Aerodynamics vol 84 no 3 pp 345ndash367 2000

[4] J Jia ldquoInvestigations of a practical wind-induced fatigue cal-culation based on nonlinear time domain dynamic analysisand a full wind-directional scatter diagramrdquo Ships and OffshoreStructures vol 9 no 3 pp 272ndash296 2014

[5] M I Kvittem andTMoan ldquoFrequency versus time domain fati-gue analysis of a semi-submersible wind turbine towerrdquo Journalof Offshore Mechanics and Arctic Engineering vol 137 no 1Article ID 011901 2015

[6] K Wang T Moan and M O L Hansen ldquoStochastic dynamicresponse analysis of a floating vertical-axis wind turbine with asemi-submersible floaterrdquoWind Energy vol 19 no 10 pp 1853ndash1870 2016

[7] C J Lu S N Lu andXDWang ldquoWind-induced dynamic ana-lysis of the arched tensegrity structures in time domainrdquoComputing in Civil and Building Engineering vol 166ndash169 pp140ndash143 2014

[8] C J Baker ldquoWind engineeringmdashpast present and futurerdquo Jour-nal of Wind Engineering and Industrial Aerodynamics vol 95no 9ndash11 pp 843ndash870 2007

[9] Q S Li J R Wu S G Liang Y Q Xiao and C K WongldquoFull-scale measurements and numerical evaluation of wind-induced vibration of a 63-story reinforced concrete tall build-ingrdquo Engineering Structures vol 26 no 12 pp 1779ndash1794 2004

[10] C L Lu Q S Li S H Huang F B Chen and X Y Fu ldquoLargeeddy simulation of wind effects on a long-span complex roofstructurerdquo Journal of Wind Engineering and Industrial Aerody-namics vol 100 no 1 pp 1ndash18 2012

[11] G Diana D Rocchi andM Belloli ldquoWind tunnel a fundamen-tal tool for long-span bridge designrdquo Structure and Infrastruc-ture Engineering vol 11 no 4 pp 533ndash555 2015

[12] B Yan and Q Li ldquoLarge-eddy simulation of wind effects on asuper-tall building in urban environment conditionsrdquo Structureand Infrastructure Engineering vol 12 no 6 pp 765ndash785 2016

[13] S Huang Q S Li and S Xu ldquoNumerical evaluation of windeffects on a tall steel building by CFDrdquo Journal of ConstructionalSteel Research vol 63 no 5 pp 612ndash627 2007

[14] M J Muliawan M Karimirad and T Moan ldquoDynamic respo-nse and power performance of a combined Spar-type floatingwind turbine and coaxial floating wave energy converterrdquoRenewable Energy vol 50 no 3 pp 47ndash57 2013

[15] J Chen R Yang and R Ma ldquoWind field simulation of largehorizontal-axis wind turbine system under different operating


conditionsrdquo Structural Design of Tall and Special Buildings vol24 no 17 pp 973ndash988 2015

[16] C C Zang J M Christian J K Yuan et al ldquoNumerical sim-ulation of wind loads and wind induced dynamic response ofheliostatsrdquo Energy Procedia vol 49 pp 1582ndash1591 2013

[17] D Hill K R Bell D McMillan and D Infield ldquoA vector auto-regressive model for onshore and offshore wind synthesisincorporating meteorological model informationrdquo Advances inScience and Research vol 11 pp 35ndash39 2014

[18] G Zhai ZMa andH Zhu ldquoThewind tunnel tests of wind pres-sure acting on the derrick of deepwater semi-submersibledrilling platformrdquo in Proceedings of the 2011 2nd InternationalConference on Advances in Energy Engineering (ICAEE rsquo11) vol14 pp 1267ndash1272 Bangkok Thailand December 2011

[19] H Zhu ZMaG J Zhai B Xie Y J Fu and J POu ldquoNumericalsimulation andwind tunnel tests of wind loads acting onHYSY-981 semi-submersible platformrdquo Ship amp Ocean Engineering vol38 no 5 pp 149ndash152 2009 (Chinese)

[20] D Lu C M Li and G J Wang ldquoCFD unsteady state numericalsimulation of wind-induced vibration of the Shanghai Jinmaobuildingrdquo China Civil Engineering Journal vol 41 no 8 pp 31ndash35 2008 (Chinese)

[21] R P Hoxey and A P Robertson ldquoPressure coefficients for low-rise building envelopes derived from full-scale experimentsrdquoJournal of Wind Engineering and Industrial Aerodynamics vol53 no 1-2 pp 283ndash297 1994

[22] A J Coulling A J Goupee A N Robertson J M Jonkmanand H J Dagher ldquoValidation of a FAST semi-submersiblefloating wind turbine numerical model with DeepCwind testdatardquo Journal of Renewable and Sustainable Energy vol 5 no2 Article ID 023116 2013

[23] ANSYS Inc ANSYS FLUENT Tutorial Guide ANSYS IncCanonsburg Pa USA 2012

[24] Y Quan S Wang M Gu and J Kuang ldquoField measurementof wind speeds and wind-induced responses atop the shanghaiworld financial center under normal climate conditionsrdquoMath-ematical Problems in Engineering vol 2013 Article ID 90264314 pages 2013

[25] B W Yan and Q S Li ldquoInflow turbulence generation methodswith large eddy simulation for wind effects on tall buildingsrdquoComputers and Fluids vol 116 pp 158ndash175 2015

[26] S Huang and Q S Li ldquoA new dynamic one-equation subgrid-scalemodel for large eddy simulationsrdquo International Journal forNumerical Methods in Engineering vol 81 no 7 pp 835ndash8652010

[27] T Kajishima and T Nomachi ldquoOne-equation subgrid scalemodel using dynamic procedure for the energy productionrdquoJournal of Applied Mechanics Transactions ASME vol 73 no3 pp 368ndash373 2006

[28] M Okamoto and N Shima ldquoInvestigation for the one-equa-tion-type subgridmodel with eddy-viscosity expression includ-ing the shear-dumping effectrdquo JSME International JournalSeries B Fluids andThermal Engineering vol 42 no 2 pp 154ndash161 1999

[29] C PeyrardM Belloli P Bousseau et al ldquoCFDmodeling of flowinduced vibration on amobile cylinder fro a 30 kndash60 kReynoldsnumber comparison between simulation and experimentalresultsrdquo in Proceedings of the ASME 2009 Pressure Vessels andPiping Division Conference (PVP rsquo09) pp 301ndash308 PragueCzech Republic July 2009

[30] E Shirani J H Ferziger andW C Reynolds ldquoMixing of a pas-sive scalar in isotropic and sheared homogeneous turbulencerdquoNASA STIRecon Technical Report N TF-15 1981

[31] J Hu and J Wang ldquoShort-term wind speed prediction usingempirical wavelet transform and Gaussian process regressionrdquoEnergy vol 93 pp 1456ndash1466 2015

[32] H Liu H-Q Tian D-F Pan and Y-F Li ldquoForecasting modelsfor wind speed using wavelet wavelet packet time series andArtificial Neural Networksrdquo Applied Energy vol 107 pp 191ndash208 2013

[33] W Cui L Liu X Yang Y Wang L Feng and V Springel ldquoAnideal mass assignment scheme for measuring the power spec-trum with fast fourier transformsrdquo Astrophysical Journal vol687 no 2 pp 738ndash744 2008

[34] J Ma The research of wind field and fluid-structure-interactionand fine identification for space structure [PhD thesis] ShanghaiJiao Tong University 2008

[35] A Testa D Gallo and R Langella ldquoOn the processing of har-monics and interharmonics using hanningwindow in standardframeworkrdquo IEEE Transactions on Power Delivery vol 19 no 1pp 28ndash34 2004

[36] J Nunn L JWright C Soller L Zhang I AWalmsley and B JSmith ldquoLarge-alphabet time-frequency entangled quantum keydistribution by means of time-to-frequency conversionrdquo OpticsExpress vol 21 no 13 pp 15959ndash15973 2013

[37] Y-H Liu Q H Liu and Z-P Nie ldquoA new efficient FDTDtime-to-frequency-domain conversion algorithmrdquo Progress inElectromagnetics Research vol 92 pp 33ndash46 2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


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Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



weather conditions high cost and site conditions [9] Windtunnel test is a relatively mature and effective technique inwind engineering on scaled models of complex structures[10 11] However there are also several limitations in windtunnel tests for accurate investigations of wind pressures onstructures as follows (1) Reynolds numbers of scaled modeltests are smaller than those of prototype structures (2) thewind field conditions can hardly be reproduced exactly inwind tunnel tests [10]

Owing to the rapid developments of computer power andcomputational methods CFD predictions have been widelyused to analyze the wind flows around prototype structuresin engineering practice [12] Large eddy simulation (LES) asone of the main CFD methods has been widely applied inthe simulations of wind fieldsWith powerful CFD tools suchas LES it is possible to conduct full-scale size simulationsof prototype structures in high Reynolds numbers flows andprovide abundant detailed data and information such aspressure distributions on structural surfaces [13]

It is understood that proper generation of the inletboundary conditions for CFD simulations especially for LESin computational wind engineering (CWE) is essential inthe analyses of wind pressure distributions and the dyna-mic responses of prototype structures [14] Therefore theimprovement of simulating fluctuating wind speed in theinlet boundary is provided in the present study Combiningwith the advantages of weighted amplitude wave superposi-tion (WAWS) [15] and autoregression (AR) [16 17] methodswith high accuracy and less time cost respectively a mixturesimulation (MS)method is proposed and demonstrated as anefficient and accurate simulationmethod in the present work

In summary the main objective of this present study isto conduct wind field analyses of the offshore deck structureswhich are carried out by a joint application of CFD techniqueand structural finite element analysis Furthermore timeseries of wind pressures on the structural surfaces at differentwind directions and inclined angles of the platform areextracted in CFD wind tunnel tests and then applied tothe finite element model to investigate the wind-inducedstructural response

This paper is organized as follows the structural modelsin numerical simulation and wind tunnel test are presentedin Section 2 Methods for conducting CFD predictions areprovided in Section 3 An accurate and efficient MS methodfor simulating fluctuatingwind speed as boundary conditionsis proposed in Section 4 Computational procedures for thewhole wind field analyses of the offshore deck structures areincluded in Section 5The validation tests for theMS and LESmethods and numerical cases of wind field investigations arecarried out in Section 6

2 The Model Semisubmersible Platform

The semisubmersible platform in this study is the 6th-generation deepwater drilling platform shown in Figure 1(a)and possesses the function of intelligent drilling technologyattaining the advanced level all over the world The majorstructural components of this platform include derrick deck

Table 1 The size parameters of the semisubmersible platform

Members Dimensions (length times width times height)mThe lower part of derrick 17 times 17 times 42The upper part ofderrick (wedge) 17 times 17 times 22Deck 7442 times 7442 times 86Column 1739 times 1739 times 2146

columns and floating bodies The main parameters of thisplatform are listed in Table 1

The tested model in Figure 1(b) was scaled as 1 100 in[18] The full-scale CFD numerical model of this platformin the present CFD simulations is built based on the testedscaled model [18] and numerical full-scale model [19] Inview of the major consideration of wind field analyses theoffshore platform structures under the water are hidden andthe derrick is totally enclosed as shown in Figure 1(c) which isdemonstrated that the extractedwind pressures are applicablein the wind-induced dynamic response analyses [19 20]However the structural computational model of the derrickin the following time-domain analysis is similar to a realstructure and not enclosed as is plotted in Figure 1(d)

One thing to note is that two types of numerical modelsthe CFD numerical model and the structural computationalmodel are applied in this present study The CFD numericalmodel is a platformmodel used for LES simulations which isestablished by using a combination of Rhino (Robert McNeelamp Assoc USA) and ICEM CFD (ANSYS Inc USA) Thestructural computational model is a finite element model ofthis platform for structural dynamic response analyses intime domain which is built by ANSYS Parametric DesignLanguage (APDL) (ANSYS Inc USA)The finite elements ofthe local components are listed as follows the derrick adoptsbeam element the deck uses shell element and the columnsadopt solid element

3 Numerical Simulation

In this section together with the commercial CFD softwareFluent 145 (ANSYS Inc USA) the unsteady-state analysisof the LES approach is used to predict the time seriesof wind pressures on the surfaces of structures above thewater surface at different working conditions Fluent 145conducts LES simulations based on finite volume method(FVM) [23] Then the wind-induced structural responsesare explored by the extracted wind pressures acting on thestructures using APDL and time-domain analysis methodcooperatively [24] The detailed computational algorithmsand treatments of wind field analyses are addressed in thefollowing subsections

31 CFD Predictions

311 LES Turbulence Model In the present LES study LESseparates flow motions into large and small eddies which iscalculated by using a combination of the direct simulation


(a) (b)

(c) (d)




120597120588V119894120597119905 + 120597120588V119894 V119895120597119909119895 = minus 120597120597119909119894 (119875 +

23120588119896sgs)

+ 120597120597119909119894 [2120588 (120592119904 + 120592) 119878119894119895]

120597V119894120597119909119894 = 0

(1)


120592119904 = 119862VΔ Vradic119896sgs

Δ V = Δ1 + 119862119896 (Δ21198782119896sgs)


32sgs

Δ

+ 120597120597119909119895 [(119862119889Δ Vradic119896sgs + 120592) 120597119896sgs120597119909119895 ]

minus 2120592120597119896sgs120597119909119894120597119896sgs120597119909119895

(2)



(a) (b)








119881119911 = 1198810 ( 1198671198670)120572 (3)



119878 (119891) = 320 (119881010)2 (11991110)045(1 + 15119865)356

119865 = 172119891( 11991110)23 (119881010)

minus34 (4)


OutletInlet

Wind









119862119901 = 1198751198940512058811988120

119862119901rms = 119875119894rms0512058811988120 (6)




119904119888119894 = 119862119901 (160119911 )02 119878119862 = sum119894 119904119888119894119878119860 119894119878119860

(7)



[119872] + [119862] + [119870] 119906 = [119865] (8)



[119862] = 120572 [119872] + 120573 [119870] 120585119894 = 120572

2120596119894 +1205731205961198942 (9)



Wavelet method




PSD S(휔) = S1(휔)W1(휔) + S2(휔)W2(휔)






119878 (119891) = 1198781 (119891)1198821 (119891) + 1198782 (119891)1198822 (119891) (10)





119877119895119898 (120591) = 119864 (V119895 (119905) V119898 (119905 + 120591))= Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119896119897)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896119897)1003816100381610038161003816sdot cos (2120587119891119896119897 + 120579119895119896 (119891119896119897) minus 120579119898119896 (119891119896119897))

(11)



119877119895119898 (120591) = int119904ℎ1

1199041198971

119895sum119896=1

10038161003816100381610038161003816119867119895119896 (119891119896)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896)1003816100381610038161003816sdot cos (2120587119891119896 + 120579119895119896 (119891119896) minus 120579119898119896 (119891119896)) 119889119891

(12)


119877119895119898 (120591) otimes 1198821 (119905) = int119904ℎ1

1199041198971

119895sum119896=1


119895sum119896=1

119878119895119896 (119891) sdot 1 (119891) cos (2120587119891119896) 119889119891(13)




V1 (119905)

= radic2Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119897)10038161003816100381610038161003816 cos (2120587119891119897119905 + 120579119895119896 (119891119897) + 120593119896119897)

119895 = 1 119898

(14)


119877119894119895 (120591) = int119904ℎ2

1199041198972

119878119894119895 (119891) 2 (119891) cos (2120587119891 sdot 120591) 119889119891 (15)



V2 (119905) = minus119895sum119894=1

119901sum119896=1

119886119894119895119896V119894 (119905 minus 119896 sdot Δ119905) + 119906 (119899) (16)






















Ω = 1003817100381710038171003817119883 (119895120596)10038171003817100381710038172119879 =10038171003817100381710038171003817int 119909 (119905) 119890minus119894120596119905100381710038171003817100381710038172119879 (17)



10minus2

100

102

104PS

D


Frequency (Hz)

(a)


10minus2

100

102

104

PSD


Frequency (Hz)

(b)


10minus2

100

102

104


(c)










36


MS 479 331WAWS 424 27465AR 2296 75

108


MS 485 7255WAWS 424 647836AR 3285 489




(a)

28 times 106


14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent


(b)



minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)



01

02

03

04RM

S pr

essu

re co

effici

ent

(d)







(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)




120597120588V119894120597119905 + 120597120588V119894 V119895120597119909119895 = minus 120597120597119909119894 (119875 +

23120588119896sgs)

+ 120597120597119909119894 [2120588 (120592119904 + 120592) 119878119894119895]

120597V119894120597119909119894 = 0

(1)


120592119904 = 119862VΔ Vradic119896sgs

Δ V = Δ1 + 119862119896 (Δ21198782119896sgs)


32sgs

Δ

+ 120597120597119909119895 [(119862119889Δ Vradic119896sgs + 120592) 120597119896sgs120597119909119895 ]

minus 2120592120597119896sgs120597119909119894120597119896sgs120597119909119895

(2)



(a) (b)








119881119911 = 1198810 ( 1198671198670)120572 (3)



119878 (119891) = 320 (119881010)2 (11991110)045(1 + 15119865)356

119865 = 172119891( 11991110)23 (119881010)

minus34 (4)


OutletInlet

Wind









119862119901 = 1198751198940512058811988120

119862119901rms = 119875119894rms0512058811988120 (6)




119904119888119894 = 119862119901 (160119911 )02 119878119862 = sum119894 119904119888119894119878119860 119894119878119860

(7)



[119872] + [119862] + [119870] 119906 = [119865] (8)



[119862] = 120572 [119872] + 120573 [119870] 120585119894 = 120572

2120596119894 +1205731205961198942 (9)



Wavelet method




PSD S(휔) = S1(휔)W1(휔) + S2(휔)W2(휔)






119878 (119891) = 1198781 (119891)1198821 (119891) + 1198782 (119891)1198822 (119891) (10)





119877119895119898 (120591) = 119864 (V119895 (119905) V119898 (119905 + 120591))= Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119896119897)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896119897)1003816100381610038161003816sdot cos (2120587119891119896119897 + 120579119895119896 (119891119896119897) minus 120579119898119896 (119891119896119897))

(11)



119877119895119898 (120591) = int119904ℎ1

1199041198971

119895sum119896=1

10038161003816100381610038161003816119867119895119896 (119891119896)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896)1003816100381610038161003816sdot cos (2120587119891119896 + 120579119895119896 (119891119896) minus 120579119898119896 (119891119896)) 119889119891

(12)


119877119895119898 (120591) otimes 1198821 (119905) = int119904ℎ1

1199041198971

119895sum119896=1


119895sum119896=1

119878119895119896 (119891) sdot 1 (119891) cos (2120587119891119896) 119889119891(13)




V1 (119905)

= radic2Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119897)10038161003816100381610038161003816 cos (2120587119891119897119905 + 120579119895119896 (119891119897) + 120593119896119897)

119895 = 1 119898

(14)


119877119894119895 (120591) = int119904ℎ2

1199041198972

119878119894119895 (119891) 2 (119891) cos (2120587119891 sdot 120591) 119889119891 (15)



V2 (119905) = minus119895sum119894=1

119901sum119896=1

119886119894119895119896V119894 (119905 minus 119896 sdot Δ119905) + 119906 (119899) (16)






















Ω = 1003817100381710038171003817119883 (119895120596)10038171003817100381710038172119879 =10038171003817100381710038171003817int 119909 (119905) 119890minus119894120596119905100381710038171003817100381710038172119879 (17)



10minus2

100

102

104PS

D


Frequency (Hz)

(a)


10minus2

100

102

104

PSD


Frequency (Hz)

(b)


10minus2

100

102

104


(c)










36


MS 479 331WAWS 424 27465AR 2296 75

108


MS 485 7255WAWS 424 647836AR 3285 489




(a)

28 times 106


14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent


(b)



minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)



01

02

03

04RM

S pr

essu

re co

effici

ent

(d)







(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)








119881119911 = 1198810 ( 1198671198670)120572 (3)



119878 (119891) = 320 (119881010)2 (11991110)045(1 + 15119865)356

119865 = 172119891( 11991110)23 (119881010)

minus34 (4)


OutletInlet

Wind









119862119901 = 1198751198940512058811988120

119862119901rms = 119875119894rms0512058811988120 (6)




119904119888119894 = 119862119901 (160119911 )02 119878119862 = sum119894 119904119888119894119878119860 119894119878119860

(7)



[119872] + [119862] + [119870] 119906 = [119865] (8)



[119862] = 120572 [119872] + 120573 [119870] 120585119894 = 120572

2120596119894 +1205731205961198942 (9)



Wavelet method




PSD S(휔) = S1(휔)W1(휔) + S2(휔)W2(휔)






119878 (119891) = 1198781 (119891)1198821 (119891) + 1198782 (119891)1198822 (119891) (10)





119877119895119898 (120591) = 119864 (V119895 (119905) V119898 (119905 + 120591))= Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119896119897)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896119897)1003816100381610038161003816sdot cos (2120587119891119896119897 + 120579119895119896 (119891119896119897) minus 120579119898119896 (119891119896119897))

(11)



119877119895119898 (120591) = int119904ℎ1

1199041198971

119895sum119896=1

10038161003816100381610038161003816119867119895119896 (119891119896)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896)1003816100381610038161003816sdot cos (2120587119891119896 + 120579119895119896 (119891119896) minus 120579119898119896 (119891119896)) 119889119891

(12)


119877119895119898 (120591) otimes 1198821 (119905) = int119904ℎ1

1199041198971

119895sum119896=1


119895sum119896=1

119878119895119896 (119891) sdot 1 (119891) cos (2120587119891119896) 119889119891(13)




V1 (119905)

= radic2Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119897)10038161003816100381610038161003816 cos (2120587119891119897119905 + 120579119895119896 (119891119897) + 120593119896119897)

119895 = 1 119898

(14)


119877119894119895 (120591) = int119904ℎ2

1199041198972

119878119894119895 (119891) 2 (119891) cos (2120587119891 sdot 120591) 119889119891 (15)



V2 (119905) = minus119895sum119894=1

119901sum119896=1

119886119894119895119896V119894 (119905 minus 119896 sdot Δ119905) + 119906 (119899) (16)






















Ω = 1003817100381710038171003817119883 (119895120596)10038171003817100381710038172119879 =10038171003817100381710038171003817int 119909 (119905) 119890minus119894120596119905100381710038171003817100381710038172119879 (17)



10minus2

100

102

104PS

D


Frequency (Hz)

(a)


10minus2

100

102

104

PSD


Frequency (Hz)

(b)


10minus2

100

102

104


(c)










36


MS 479 331WAWS 424 27465AR 2296 75

108


MS 485 7255WAWS 424 647836AR 3285 489




(a)

28 times 106


14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent


(b)



minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)



01

02

03

04RM

S pr

essu

re co

effici

ent

(d)







(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










OutletInlet

Wind









119862119901 = 1198751198940512058811988120

119862119901rms = 119875119894rms0512058811988120 (6)




119904119888119894 = 119862119901 (160119911 )02 119878119862 = sum119894 119904119888119894119878119860 119894119878119860

(7)



[119872] + [119862] + [119870] 119906 = [119865] (8)



[119862] = 120572 [119872] + 120573 [119870] 120585119894 = 120572

2120596119894 +1205731205961198942 (9)



Wavelet method




PSD S(휔) = S1(휔)W1(휔) + S2(휔)W2(휔)






119878 (119891) = 1198781 (119891)1198821 (119891) + 1198782 (119891)1198822 (119891) (10)





119877119895119898 (120591) = 119864 (V119895 (119905) V119898 (119905 + 120591))= Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119896119897)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896119897)1003816100381610038161003816sdot cos (2120587119891119896119897 + 120579119895119896 (119891119896119897) minus 120579119898119896 (119891119896119897))

(11)



119877119895119898 (120591) = int119904ℎ1

1199041198971

119895sum119896=1

10038161003816100381610038161003816119867119895119896 (119891119896)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896)1003816100381610038161003816sdot cos (2120587119891119896 + 120579119895119896 (119891119896) minus 120579119898119896 (119891119896)) 119889119891

(12)


119877119895119898 (120591) otimes 1198821 (119905) = int119904ℎ1

1199041198971

119895sum119896=1


119895sum119896=1

119878119895119896 (119891) sdot 1 (119891) cos (2120587119891119896) 119889119891(13)




V1 (119905)

= radic2Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119897)10038161003816100381610038161003816 cos (2120587119891119897119905 + 120579119895119896 (119891119897) + 120593119896119897)

119895 = 1 119898

(14)


119877119894119895 (120591) = int119904ℎ2

1199041198972

119878119894119895 (119891) 2 (119891) cos (2120587119891 sdot 120591) 119889119891 (15)



V2 (119905) = minus119895sum119894=1

119901sum119896=1

119886119894119895119896V119894 (119905 minus 119896 sdot Δ119905) + 119906 (119899) (16)






















Ω = 1003817100381710038171003817119883 (119895120596)10038171003817100381710038172119879 =10038171003817100381710038171003817int 119909 (119905) 119890minus119894120596119905100381710038171003817100381710038172119879 (17)



10minus2

100

102

104PS

D


Frequency (Hz)

(a)


10minus2

100

102

104

PSD


Frequency (Hz)

(b)


10minus2

100

102

104


(c)










36


MS 479 331WAWS 424 27465AR 2296 75

108


MS 485 7255WAWS 424 647836AR 3285 489




(a)

28 times 106


14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent


(b)



minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)



01

02

03

04RM

S pr

essu

re co

effici

ent

(d)







(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Wavelet method




PSD S(휔) = S1(휔)W1(휔) + S2(휔)W2(휔)






119878 (119891) = 1198781 (119891)1198821 (119891) + 1198782 (119891)1198822 (119891) (10)





119877119895119898 (120591) = 119864 (V119895 (119905) V119898 (119905 + 120591))= Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119896119897)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896119897)1003816100381610038161003816sdot cos (2120587119891119896119897 + 120579119895119896 (119891119896119897) minus 120579119898119896 (119891119896119897))

(11)



119877119895119898 (120591) = int119904ℎ1

1199041198971

119895sum119896=1

10038161003816100381610038161003816119867119895119896 (119891119896)10038161003816100381610038161003816 1003816100381610038161003816119867119898119896 (119891119896)1003816100381610038161003816sdot cos (2120587119891119896 + 120579119895119896 (119891119896) minus 120579119898119896 (119891119896)) 119889119891

(12)


119877119895119898 (120591) otimes 1198821 (119905) = int119904ℎ1

1199041198971

119895sum119896=1


119895sum119896=1

119878119895119896 (119891) sdot 1 (119891) cos (2120587119891119896) 119889119891(13)




V1 (119905)

= radic2Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119897)10038161003816100381610038161003816 cos (2120587119891119897119905 + 120579119895119896 (119891119897) + 120593119896119897)

119895 = 1 119898

(14)


119877119894119895 (120591) = int119904ℎ2

1199041198972

119878119894119895 (119891) 2 (119891) cos (2120587119891 sdot 120591) 119889119891 (15)



V2 (119905) = minus119895sum119894=1

119901sum119896=1

119886119894119895119896V119894 (119905 minus 119896 sdot Δ119905) + 119906 (119899) (16)






















Ω = 1003817100381710038171003817119883 (119895120596)10038171003817100381710038172119879 =10038171003817100381710038171003817int 119909 (119905) 119890minus119894120596119905100381710038171003817100381710038172119879 (17)



10minus2

100

102

104PS

D


Frequency (Hz)

(a)


10minus2

100

102

104

PSD


Frequency (Hz)

(b)


10minus2

100

102

104


(c)










36


MS 479 331WAWS 424 27465AR 2296 75

108


MS 485 7255WAWS 424 647836AR 3285 489




(a)

28 times 106


14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent


(b)



minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)



01

02

03

04RM

S pr

essu

re co

effici

ent

(d)







(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











V1 (119905)

= radic2Δ119891 119895sum119896=1

119873sum119897=1

10038161003816100381610038161003816119867119895119896 (119891119897)10038161003816100381610038161003816 cos (2120587119891119897119905 + 120579119895119896 (119891119897) + 120593119896119897)

119895 = 1 119898

(14)


119877119894119895 (120591) = int119904ℎ2

1199041198972

119878119894119895 (119891) 2 (119891) cos (2120587119891 sdot 120591) 119889119891 (15)



V2 (119905) = minus119895sum119894=1

119901sum119896=1

119886119894119895119896V119894 (119905 minus 119896 sdot Δ119905) + 119906 (119899) (16)






















Ω = 1003817100381710038171003817119883 (119895120596)10038171003817100381710038172119879 =10038171003817100381710038171003817int 119909 (119905) 119890minus119894120596119905100381710038171003817100381710038172119879 (17)



10minus2

100

102

104PS

D


Frequency (Hz)

(a)


10minus2

100

102

104

PSD


Frequency (Hz)

(b)


10minus2

100

102

104


(c)










36


MS 479 331WAWS 424 27465AR 2296 75

108


MS 485 7255WAWS 424 647836AR 3285 489




(a)

28 times 106


14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent


(b)



minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)



01

02

03

04RM

S pr

essu

re co

effici

ent

(d)







(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











10minus2

100

102

104PS

D


Frequency (Hz)

(a)


10minus2

100

102

104

PSD


Frequency (Hz)

(b)


10minus2

100

102

104


(c)










36


MS 479 331WAWS 424 27465AR 2296 75

108


MS 485 7255WAWS 424 647836AR 3285 489




(a)

28 times 106


14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent


(b)



minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)



01

02

03

04RM

S pr

essu

re co

effici

ent

(d)







(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

28 times 106


14 times 106

Total grid number

minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent


(b)



minus25

minus20

minus15

minus10

minus05

00

Win

d pr

essu

re co

effici

ent

(c)



01

02

03

04RM

S pr

essu

re co

effici

ent

(d)







(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c)









0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

100

200

300

400H

eigh

t (m

)

30 40 50 6020Wind speed (ms)

(a)


0

100

200

300

400

Hei

ght (

m)


(b)


0

100

200

300

400

Hei

ght (

m)

30 40 50 6020Wind speed (ms)

(c)



0

100

200

300

400

Hei

ght (

m)

(d)













7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















7 Conclusion







Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Red line Line 2(a)

04

08

12

16

Win

d pr

essu

re co

effici

ent

20 500 4010 6030

Height (m)


Line 1

(b)

04

08

12

16

20

Win

d pr

essu

re co

effici

ent

200 30 40 50 6010

Height (m)


Line 1

(c)


004

008

012

016RM

S pr

essu

re co

effici

ent

10 20 30 40 50 600

Height (m)

Line 1Line 2 Line 2

Line 1

(d)

10 20 30 40 50 600

Height (m)

02

04

06

RMS

pres

sure

coeffi

cien

t


Line 1

(e)






04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













04

06

08

10

12

14

16Sh

ape c

oeffi

cien

t

(a)


5∘

10∘

8000

10000

12000

14000

16000

18000

The r

esul

tant

win

d fo

rce (

kN)

15 30 45 60 75 900Wind direction (∘)

(b)


200 400 600 800 10000Time step

09

12

15

18

21

The w

ind

pres

sure

(kPa

)

(a)


Meanvalue

Maximumvalue

Minimumvalue

Intermediatevalue

10m30m

50m60m

0

1000

2000

3000

4000

Win

d pr

essu

re (P

a)

(b)







800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

The d

ispla

cem

ent i

n x

dire

ctio

n (m

)

(a)

800 1000200 400 6000Time step

minus00010

minus00005

00000

00005

00010

00015

00020

00025

The d

ispla

cem

ent i

n y

dire

ctio

n (m

)

(b)

minus000010

minus000008

minus000006

minus000004

minus000002

000000

000002

The d

ispla

cem

ent i

n z

dire

ctio

n (m

)

800 1000200 400 6000Time step

(c)





Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Nodal solution

SMN = 681344

SMX = 0174E + 08

681237193E + 06

386E + 06579E + 06772E + 06

154E + 07135E + 07116E + 07956E + 06

174E + 07





Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Numerical Simulation of Fluctuating Wind Effects on an