Research ArticleSpoke Dimension on the Motion Performance of a FloatingWind Turbine with Tension-Leg Platform

H F Wang and Y H Fan

School of Natural Sciences and Humanities Harbin Institute of Technology Shenzhen Graduate School Shenzhen 518055 China

Correspondence should be addressed to H F Wang phdwhf163com

Received 4 August 2015 Revised 13 September 2015 Accepted 15 September 2015

Academic Editor Vadim V Silberschmidt

Copyright copy 2016 H F Wang and Y H Fan This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The tension-leg platform (TLP) supporting structure is a good choice for floating offshore wind turbines because TLP has superiormotion dynamics This study investigates the effects of TLP spoke dimensions on the motion of a floating offshore wind turbinesystem (FOWT) Spoke dimension and offshore floating TLP were subjected to irregular wave and wind excitation to evaluatethe motion of the FOWT This research has been divided into two parts (1) Five models were designed based on different spokedimensions and aerohydroservo-elastic coupled analyses were conducted on the models using the finite element method (2)Considering the coupled effects of the dynamic response of a top wind turbine a supporting-tower structure a mooring systemand two models on a reduced scale of 1 80 were constructed and experimentally tested under different conditions Numerical andexperimental results demonstrate that the spoke dimensions have a significant effect on the motion of FOWT and the experimentalresult that spoke dimension can reduce surge platform movement to improve turbine performance

1 Introduction

Wind energy is one of the most environmentally friendlyrenewable energy sources that are used to generate powerGlobal interest inwind energy has increased because of abun-dant global offshore wind resources Offshore wind resourcesare distributed in areas within 5ndash50 km from coastlines atwater depths greater than 30m Studies show that fixedfoundations such as monopolies jackets and gravity are noteconomic for offshore wind turbines with depths greater than50m To solve this issue floating foundation concepts suchas spar semisubmersible and tension-leg platform (TLP)supporting structures have been used [1 2]

As an active research direction the TLP supportingstructure concept for offshore wind turbines is an appropriatechoice for intermediate water depths because of its superiormotion and dynamic features compared with other floatingconcepts [2ndash6] Withee [7] developed the first TLP windturbine supporting structure in 2004 Wayman et al [8]performed fully coupled time-domain simulations of systemresponses for a 15MW wind turbine mounted on a TLPfloater subject to wind and wave forces Bachynski andMoan

[9] analyzed diverse parametric single-column TLP designsand found that a larger spoke radius had the potential todisplay the best overall behavior under special environmentalconditions however they did not verify the hypothesisCrozier studied the effects of design parameters on per-formance based on a 10MW wind turbine [10] Anotherstudy [11] proposed a new TLP concept by combining thetraditional TLP and spar structure this concept is called theMIT-TLP (Massachusetts Institute of Technology tension-leg platform) model The advantage of this model is thatwithout the moorings this design is stable in calm sea stateswhen the turbine is not operating Matha [12] modified thespoke length of the MIT-TLP model and corrected the faultsto improve motion using the FAST software program thismodifiedmodel is called theNREL-TLP (National RenewableEnergy Laboratory Tension Leg Platform) model On thebasis of a popular 5MW wind turbine designed by NRELMartin built a wind-and-wave-based basin-wide numericalmodel of a 5MWwind turbine on a scale of 1 50 this modelwas intended to assess a commercially viable floating windturbine structure [13] However in the NREL-TLP modelthe effect of the spoke on the motion was not determined

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 8913873 16 pageshttpdxdoiorg10115520168913873

2 Shock and Vibration

Therefore in this work we investigated the spoke effect indetail for the first time

For the model test Goupee et al [14] investigated theunique behavior of various floating wind turbine platformsand conducted model tests at three different floating-typewind turbines on a scale of 1 50 using a wind-and-wave-based basin-wide model at the Maritime Research Instituteof the Netherlands Coulling conducted model tests on asemisubmersible floating wind turbine system on a scale of1 50 They verified the effectiveness of the experimental datafor a floating wind turbine model which was constructed byNREL [15] Ren et al performed a model test on a floating-type wind turbine system on a scale of 1 60 to investigate theinfluence of wind-wave coupling effects on its performanceThey also conducted a numerical simulation and comparedthe results with that of the model output [16] Next theyproposed another TLP system with mooring cables andcompared the model results of both TPL systems [17]

In this research the spoke dimension effect will beinvestigated through numerical simulations and modelingtests Six numerical models were designed with considerationof different spoke dimensions then the addedmass dampingexciting force and response amplitude operators (RAO)were compared Afterwards two models considered for thespoke dimension experiment on a reduced scale of 1 80were demonstrated in the Harbin Institute of TechnologyJoint Laboratory of Wind Tunnel and Water Flume Thedisplacements of these two floating wind turbines in twodifferent directions were compared and analyzed

2 Materials and Methods

21 Numerical Simulation

211 NREL 5MW Offshore Wind Turbine and Environmen-tal Conditions In 2006 the National Renewable EnergyLaboratory (NREL US) provided a detailed design of a5MW offshore wind turbine for the preliminary design ofsupport structures based on a Repower wind turbine whichis produced by Repower System AG in Germany The rotorand hub diameters are 126 and 3m respectively while thehub height is 90mThe cut-in rated and cut-out wind speedsare 3 114 and 25ms respectively The maximum rotorand generator speed are 121 rpm The 1 and 3 p frequencyvalues were between 27 and 35 s [18] This wind turbine waschosen because the required parameters are easily availableand because many studies have already used it as a base windturbine

The environmental conditions considered in this studyare shown in Table 1 These values were adopted from pre-vious studies [6] Similar to other studies the water depthfor this study was fixed at 200m [9 12 14 19] The energydensity of waves was defined byHua et al [20] in the Pierson-Moskowitz wave spectrum

119878 (120596) = 1205873(2119867119904

1198792119911

)

2

1

1205965exp[minus1205873 ( 2

119879119911120596)

4

] (1)

where 120596 is the wave frequency 119867119904is the significant wave

height and 119879119911is the zero-crossing period

Table 1 Environmental conditions

Conditions OperationSignificant wave height119867

1199043

Zero-cross period 119879119911(s) 425

Mean wind speed (ms) 87

212 Initial TLP Model for Numerical Simulation The con-ceptual design for wind turbine TLP structures is an activeresearch field Robertson and Jonkman [11] Zambrano et al[21] and Wayman et al [8] reported the requirements forconceptual design however they did not consider the entirelifecycle from installation scenarios to extreme situationsWang [6] proposed a new design requirement for TLP basedon the NREL-TLP model In this study we considered thenew design requirement which we call the modified NREL-TLP model as the basic requirement for conceptual design

Table 2 shows the four designs used in this study whichwere selected based on the displacement and mass consider-ing cost and research In this study two other models wereconsidered namely TLP-0 and TLP-5 the only differencebetween TLP-1TLP-4 and TLP-0TLP-5 is that the spokeeffect was not considered in the calculations

Computer algorithms were used to simulate the TLPsupporting structure CATIA software was used to generate ageometric model and HyperMesh was used to create a meshmodel Ansys AQWA software was used to calculate hydro-dynamic characteristics An aerohydroservo-elastic coupledanalysis was conducted in the time domain [13 22] Thisanalysis was performed by using the numerical tools of FASTwhich is a publicly available software The matrices for thewind turbines and platform were transferred to the dynamicanalysis module where they were combined to represent thecoupled system To study the spoke dimension effect TLP-0and TLP-5 models and specially designed TLP-2 and TLP-3 models were chosen as examples TLP-0 (TLP-5) has thesame dimensions as TLP-1 (TLP-4)Themass (displacement)of TLP-0 was 1279943 T (741825M3) and that of TLP-5 was2531154 T (618188M3) Compared with TLP-1 and TLP-4the mass increased by 128 (183 displacement) and 4(196 displacement) respectively TLP-2 and TLP-3 weredesigned so that the spoke displacement constitutes up to37 of the entire displacement Furthermore the entiredisplacement of TLP-2 was only 83 of the displacement ofTLP-3 Next the differences in detail are analyzed Figure 2shows the FEMmesh for the different models

213 Response Amplitude Operators (RAO) The equationof motion that governs the rigid body motions of a float-ing structure consists of standard Newtonian equations ofmotion and is summarized in amatrix formbelow describingthe six modes of motion

(119872added (120596) +119872WT +119872structure)120577 (119905)

+ (119861structure (120596) + 119861WT)120577 (119905)

+ (119862WT + 119862structure + 119862mooring) 120577 (119905) = 119883 (120596)

119872total (120596)120577 + 119861total

120577 + 119862total120577 = 119883 (120596)

(2)

Shock and Vibration 3

TLP-1[6]

(a)

TLP-2

(b)

TLP-3

(c)

TLP-4

(d)

Figure 1

Table 2 Dimensions of four modified NREL-TLPs (see also Figure 1)

Parameters TLP-1 [6] TLP-2 TLP-3 TLP-4Column

Diameter-CD (m) 15 12 12 15Length-CL (m) 40 35 45 30

SpokesDiameter-PD (m) 55 6 7 8Length-PL (m) 25 20 18 15

Concrete ballastHeight-CH (m) 2 5 4 5

Gravity point 0 0 minus32988 0 0 minus35426 0 0 minus41681 0 0 minus36857Total mass119879 1468632 186874 1644921 2648716

Displacement1198723 908049 610416 738528 768907

Concrete displacement1198723 35325 56520 45216 88313

where 119872added is the added mass matrix 119872WT is the massmatrix of the wind turbine at a constant wind speed119872structureis the mass matrix of the platform 119861structure is the dampingmatrix of the platform 119861WT is the damping matrix of thewind turbine 119862WT is the stiffness matrix of the wind turbine119862structure is the stiffness matrix of the platform 119862mooring is thestiffness matrix of the mooring system and 120577 120577 and 120577 are theacceleration velocity and displacement of the system

In this study RAO represents the nondimensionalresponse of a system to a unit-amplitude incident wave in adirection along the 119883 coordinate that is the zero incidentangle [13] The motion equations that control the systemrsquoslinear dynamic motion are summarized in (3) [10] as follows

[minus1205962(119872 + 119860 (120596)) + 120596119861 (120596) + 119862] Ξ (120596) = 119883 (120596) (3)

For the translational modes of motion RAO is expressed by[10]

RAOtrans modes (120596) =

1003816100381610038161003816119883119896 (120596)1003816100381610038161003816

119860wave (4)

For the rotational modes of motion RAO is expressed by [10]

RAOrot modes (120596) =

1003816100381610038161003816119883119896 (120596)1003816100381610038161003816

119860wave119871 (5)

where 119860wave represents the wave amplitude and 119871 is thecylinder radius Although RAO are not based on sea state thedamping and stiffness of the wind turbine are based on windspeed

22 Model Test Input

221 Wind Tunnel and Water Flume The Joint Laboratoryof Wind Tunnel and Water Flume at the Harbin Instituteof Technology [17 23] has one of the largest atmosphericboundary layer wind tunnels in China and is used to evaluateexperiments of a water flume on the wind-wave couplingeffect

The displacement and acceleration of a TLP-FOWTalongtwo different directions (ie the surge and the sway) weremeasured and analyzed The following experimental devices

4 Shock and Vibration

X

Y

Z

(a) TLP-0 mesh result

X

Y

Z

(b) TLP-1 mesh result

X

Y

Z

(c) TLP-2 mesh result

X

Y

Z

(d) TLP-3 mesh result

X

Y

Z

(e) TLP-4 mesh result

X

Y

Z

(f) TLP-5 mesh result

Figure 2 Mesh result for different models

Figure 3 A deep groove

were used a high-frequency force balance data acquisitionand its analysis system for receiving dynamic signals a high-precision laser displacement meter an acceleration sensor acurrent meter and a floating body instrument that comprisessix components Figure 4(a) shows the high-frequency forcebalance The forces along the two lateral directions whichare perpendicular to the axial direction of the balance haveranged between 0 and 660N Similarly the lateral bending

moments along the two directions (ie 119872119909and 119872

119910) are

ranged between 0 and 60Nm and the torque (ie 119872119911)

is ranged between 0 and 60Nm The measuring error isusually less than 1 Figure 4(b) shows sensor for measuringdisplacement and acceleration A CCD laser displacementsensor (ie LK-G400 Keyence) and a high-precision accel-eration sensor can be used for the accurate measurement ofthewind-induced structural vibration response It has a gauge

Shock and Vibration 5

(a) High-frequency force balance (b) Sensor for measuring displacement and acceleration

(c) System for dynamic signal data acquisition andanalysis

Figure 4 Major devices

(a) Model-TLP-1 (b) Model-TLP-2

Figure 5 Model-TLP-1 and model-TLP-2

length which is ranged between 300 and 500mm Figure 4(c)shows the system for dynamic signal data acquisition andanalysis A system of data acquisition and its analysis of adynamic signal (ie NI-PXI National Instruments America)have been used during the experiments of this paper whichhas (24 + 12) dynamic acquisition channels It can meet therequirements of a dynamic-response data acquisition of alarge and complicated structure which may be subject to theaction of the wind and the wind-wave it can be shown inFigure 3

222 Introduction of Experimental Models In order tocompare the result for two models parameters have beendesigned in detail Table 3 shows the model parameter and

Figure 5 shows the real view for the two models Model-TLP-1 and model-TLP-2 have the same draft diameter anddraft height however in the spoke distance model-TLP-1is 117 times as model-TLP-2rsquos date in the spoke diametermodel-TLP-2 is 3 times as model-TLP-1rsquos date To the spokedisplacement model-TLP-1 is 13 of model-TLP-2 Thepurpose of this design is to distinguish parameter spokedistance and spoke diameter and also is to easily compare thesimulation result with model test result

A tower was installed at the top of both models Theblade of a wind turbine was prepared with a ratio of 1 80The rotating speed of a wind turbine was approximately83 revmin and the facial area of the bladewas approximately1766m2 Under extreme wind speed weather conditions the

6 Shock and Vibration

Table 3 Model-TLP parameters

Parameter Model-TLP-1 Model-TLP-2Draft diameter (m) 023 023Draft height (m) 06 06Spoke distance (m) 0675 0573Spoke diameter (m) 002 006

rotation of the blade of a wind turbine would stop throughthe locking device which was fixed at the top Excluding theballast the weight of the entire structure was approximately101 kg

3 Results

31 Numerical Simulation

311 Hydrodynamic Properties The added mass dampingand exciting force matrices are considered based on themotion and dynamic equations in (2) The calculated waveexcitation force added mass and damping matrices areshown in Figures 6 7 and 8 respectively A portion of theresults have been shown because of symmetry characteristics

The addedmassmatrices in different directions are shownin Figure 6 The difference is evident if spoke dimension isnot considered In A11 (surge-surge direction) TLP-1 andTLP-4rsquos values were larger than those of TLP-0 and TLP-5however this finding is not evident in other directions If weconsider displacement only then TLP-3 is larger than TLP-2and all the values are larger for TLP-3However displacementdoes not only affect A11 because TLP-0 displacement waslower than TLP-4 while the TLP-0 A11 value was larger thanTLP-4 value In A33 (heave-heave direction) and A55 (pitch-pitch direction) the values increase when we considered thespoke dimension effect A comparison between the TLP-2 and TLP-3 results showed that displacement and valuesfor A33 and A55 were larger In A66 (yaw-yaw direction)TLP-0 and TLP-5 results were zero However the magnitudeof A66 was very large in TLP-1 and TLP-4 and cannot beignored Moreover TLP-1rsquos result was four times larger thanTLP-4When the spoke dimension effect was considered theadded mass matrix always increased This effect was mostevident in A66 because the value increased from zero to 1E5and 4E5 in A42 (roll-sway direction) and A15 respectivelybecause the unit was E5 designers should consider thisresult in the near future For the same spoke dimensionratio when the total displacement increases the added massmatrix also increases In the surge-pitch (A15) componentthe absolute value was larger than the others In total thecoefficient of the added mass matrices increases when thespoke dimension effect is considered thereby being usefulfor damping and motion Martin [13] assumed that all off-diagonal translational coefficients are zero The calculationsin this section show that the coefficient ofmassmatrices is notzero because of the spoke effect The size effect on the overallmotion will be analyzed in the next section

The damping effect (Figure 7) approached zero at highand low frequencies however the fourmodels clearly differ at

intermediate frequencies TLP-4 had the maximum dampingmatrix coefficients in the surge directionThe spoke size effectensures that a larger damping coefficient can be obtainedparticularly in B66 (yaw-yaw) where the value for TLP-0 and TLP-5 became zero Thus yaw instability may besevere in the calculation stage A comparison between Figures9(a) 9(b) 9(d) and 9(e) for TLP-0TLP-1 shows that thedamping coefficient decreased by 1 10 10 and 24respectively The decreases were 09 28 25 and 31for TLP-4 and TLP-5 These results indicate that the B55value (pitch-pitch) was more sensitive to the spoke sizeeffect Heave direction displacement was restricted becauseof tension leg therefore B33 (heave-heave direction) was notconsidered in the dampingmatrix and its value was assumedlarge enough in damping In B55 (pitch-pitch direction) themagnitude was E5 therefore the spoke dimension effectshould be considered In fact the spoke dimension effectincreased At the same displacement ratio in TLP-2 and TLP-3 the change was smaller in TLP-2 but TLP-3 was largerthan TLP-2 which indicates that larger displacement leadsto larger damping B66 (yaw-yaw direction) had the samesituation as A66 the damping matrix was limited to zeroif the spoke dimension effect was not considered In theoff-diagonal translational matrices B42 and B15 the effectwas clearly enhanced damping Interestingly in TLP-2 andTLP-3 the off-diagonal matrices did not change When thespoke dimension effect was considered the damping didnot always increase In B66 the spoke dimension effectincreased damping from zero to a larger value In the off-diagonal translational matrices the spoke dimension effectwas enhanced damping At the same displacement ratio theoff-diagonal coefficient did not change at B42 and B51

Obviously the exciting force reduced when the spokeeffect was not considered In this section TLP-2 and TLP-3 had the minimum exciting force For the surge excitingforce TLP-0 andTLP-1 had similar curves thereby indicatingthat the effect was limited The same situation occurred inTLP-4 and TLP-5 For the pitch exciting force the trendwas opposite as shown in Figure 8(c) The exciting force ofTLP-1 and TLP-4 was larger than that of TLP-0 and TLP-5 respectively For TLP-2 and TLP-3 large displacementindicates a large pitch exciting force The yaw exciting forceexhibited the same patterns as the pitch exciting forcehowever the values were the same for the yaw exciting forceTherefore this result can be ignored

Overall the exciting force reduced when we did notconsider the spoke effect in the translation direction whichis the opposite for rotation The same situation occurred inTLP-2 and TLP-3 In this wave direction the pitch excitingforce was the largest whereas the other forces were so smallthat they could be neglected

For B66 (yaw-yaw) TLP-2was the largest in all themodesand could be used to improve yaw damping For the excitingforcematrices the surge exciting forcewas similar clearly thepitch and yaw exciting force of TLP-3 did not change Martin[13] assumed yaw instability in his model because the spokesize effect on the yaw-yaw damping is larger and improvesmotion performance

Shock and Vibration 7

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A11

0

2000

4000

6000

8000

10000

05 1 15 2 250120596 (rads)

(a) A11 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A15

05 1 15 2 250120596 (rads)

times105

minus25

minus2

minus15

minus1

minus05

0

(b) A15 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A33

0

500

1000

1500

2000

2500

3000

05 1 15 2 250120596 (rads)

(c) A33 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A42

times105

0

05

1

15

2

25

05 1 15 2 250120596 (rads)

(d) A42 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A55

times106

0

1

2

3

4

5

6

7

8

05 1 15 2 250120596 (rads)

(e) A55 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A66

times105

05 1 15 2 250120596 (rads)

0

1

2

3

4

(f) A66 added mass

Figure 6 Added mass matrices

8 Shock and Vibration

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B11

05 1 15 2 250120596 (rads)

0

500

1000

1500

2000

2500

3000

(a) B11 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B15

times104

minus3

minus25

minus2

minus15

minus1

minus05

0

05 1 15 2 250120596 (rads)

(b) B15 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B33

minus10

0

10

20

30

40

50

60

70

05 1 15 2 250120596 (rads)

(c) B33 damping matrices

times104

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B42

minus05

0

05

1

15

2

25

3

05 1 15 2 250120596 (rads)

(d) B42 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B55

times105

minus1

0

1

2

3

4

5

05 1 15 2 250120596 (rads)

(e) B55 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B66

05 1 15 2 250120596 (rads)

minus05

0

05

1

15

2

25

(f) B66 damping matrices

Figure 7 Damping matrices

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

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Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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International Journal of

2 Shock and Vibration

Therefore in this work we investigated the spoke effect indetail for the first time

For the model test Goupee et al [14] investigated theunique behavior of various floating wind turbine platformsand conducted model tests at three different floating-typewind turbines on a scale of 1 50 using a wind-and-wave-based basin-wide model at the Maritime Research Instituteof the Netherlands Coulling conducted model tests on asemisubmersible floating wind turbine system on a scale of1 50 They verified the effectiveness of the experimental datafor a floating wind turbine model which was constructed byNREL [15] Ren et al performed a model test on a floating-type wind turbine system on a scale of 1 60 to investigate theinfluence of wind-wave coupling effects on its performanceThey also conducted a numerical simulation and comparedthe results with that of the model output [16] Next theyproposed another TLP system with mooring cables andcompared the model results of both TPL systems [17]

In this research the spoke dimension effect will beinvestigated through numerical simulations and modelingtests Six numerical models were designed with considerationof different spoke dimensions then the addedmass dampingexciting force and response amplitude operators (RAO)were compared Afterwards two models considered for thespoke dimension experiment on a reduced scale of 1 80were demonstrated in the Harbin Institute of TechnologyJoint Laboratory of Wind Tunnel and Water Flume Thedisplacements of these two floating wind turbines in twodifferent directions were compared and analyzed

2 Materials and Methods

21 Numerical Simulation

211 NREL 5MW Offshore Wind Turbine and Environmen-tal Conditions In 2006 the National Renewable EnergyLaboratory (NREL US) provided a detailed design of a5MW offshore wind turbine for the preliminary design ofsupport structures based on a Repower wind turbine whichis produced by Repower System AG in Germany The rotorand hub diameters are 126 and 3m respectively while thehub height is 90mThe cut-in rated and cut-out wind speedsare 3 114 and 25ms respectively The maximum rotorand generator speed are 121 rpm The 1 and 3 p frequencyvalues were between 27 and 35 s [18] This wind turbine waschosen because the required parameters are easily availableand because many studies have already used it as a base windturbine

The environmental conditions considered in this studyare shown in Table 1 These values were adopted from pre-vious studies [6] Similar to other studies the water depthfor this study was fixed at 200m [9 12 14 19] The energydensity of waves was defined byHua et al [20] in the Pierson-Moskowitz wave spectrum

119878 (120596) = 1205873(2119867119904

1198792119911

)

2

1

1205965exp[minus1205873 ( 2

119879119911120596)

4

] (1)

where 120596 is the wave frequency 119867119904is the significant wave

height and 119879119911is the zero-crossing period

Table 1 Environmental conditions

Conditions OperationSignificant wave height119867

1199043

Zero-cross period 119879119911(s) 425

Mean wind speed (ms) 87

212 Initial TLP Model for Numerical Simulation The con-ceptual design for wind turbine TLP structures is an activeresearch field Robertson and Jonkman [11] Zambrano et al[21] and Wayman et al [8] reported the requirements forconceptual design however they did not consider the entirelifecycle from installation scenarios to extreme situationsWang [6] proposed a new design requirement for TLP basedon the NREL-TLP model In this study we considered thenew design requirement which we call the modified NREL-TLP model as the basic requirement for conceptual design

Table 2 shows the four designs used in this study whichwere selected based on the displacement and mass consider-ing cost and research In this study two other models wereconsidered namely TLP-0 and TLP-5 the only differencebetween TLP-1TLP-4 and TLP-0TLP-5 is that the spokeeffect was not considered in the calculations

Computer algorithms were used to simulate the TLPsupporting structure CATIA software was used to generate ageometric model and HyperMesh was used to create a meshmodel Ansys AQWA software was used to calculate hydro-dynamic characteristics An aerohydroservo-elastic coupledanalysis was conducted in the time domain [13 22] Thisanalysis was performed by using the numerical tools of FASTwhich is a publicly available software The matrices for thewind turbines and platform were transferred to the dynamicanalysis module where they were combined to represent thecoupled system To study the spoke dimension effect TLP-0and TLP-5 models and specially designed TLP-2 and TLP-3 models were chosen as examples TLP-0 (TLP-5) has thesame dimensions as TLP-1 (TLP-4)Themass (displacement)of TLP-0 was 1279943 T (741825M3) and that of TLP-5 was2531154 T (618188M3) Compared with TLP-1 and TLP-4the mass increased by 128 (183 displacement) and 4(196 displacement) respectively TLP-2 and TLP-3 weredesigned so that the spoke displacement constitutes up to37 of the entire displacement Furthermore the entiredisplacement of TLP-2 was only 83 of the displacement ofTLP-3 Next the differences in detail are analyzed Figure 2shows the FEMmesh for the different models

213 Response Amplitude Operators (RAO) The equationof motion that governs the rigid body motions of a float-ing structure consists of standard Newtonian equations ofmotion and is summarized in amatrix formbelow describingthe six modes of motion

(119872added (120596) +119872WT +119872structure)120577 (119905)

+ (119861structure (120596) + 119861WT)120577 (119905)

+ (119862WT + 119862structure + 119862mooring) 120577 (119905) = 119883 (120596)

119872total (120596)120577 + 119861total

120577 + 119862total120577 = 119883 (120596)

(2)

Shock and Vibration 3

TLP-1[6]

(a)

TLP-2

(b)

TLP-3

(c)

TLP-4

(d)

Figure 1

Table 2 Dimensions of four modified NREL-TLPs (see also Figure 1)

Parameters TLP-1 [6] TLP-2 TLP-3 TLP-4Column

Diameter-CD (m) 15 12 12 15Length-CL (m) 40 35 45 30

SpokesDiameter-PD (m) 55 6 7 8Length-PL (m) 25 20 18 15

Concrete ballastHeight-CH (m) 2 5 4 5

Gravity point 0 0 minus32988 0 0 minus35426 0 0 minus41681 0 0 minus36857Total mass119879 1468632 186874 1644921 2648716

Displacement1198723 908049 610416 738528 768907

Concrete displacement1198723 35325 56520 45216 88313

where 119872added is the added mass matrix 119872WT is the massmatrix of the wind turbine at a constant wind speed119872structureis the mass matrix of the platform 119861structure is the dampingmatrix of the platform 119861WT is the damping matrix of thewind turbine 119862WT is the stiffness matrix of the wind turbine119862structure is the stiffness matrix of the platform 119862mooring is thestiffness matrix of the mooring system and 120577 120577 and 120577 are theacceleration velocity and displacement of the system

In this study RAO represents the nondimensionalresponse of a system to a unit-amplitude incident wave in adirection along the 119883 coordinate that is the zero incidentangle [13] The motion equations that control the systemrsquoslinear dynamic motion are summarized in (3) [10] as follows

[minus1205962(119872 + 119860 (120596)) + 120596119861 (120596) + 119862] Ξ (120596) = 119883 (120596) (3)

For the translational modes of motion RAO is expressed by[10]

RAOtrans modes (120596) =

1003816100381610038161003816119883119896 (120596)1003816100381610038161003816

119860wave (4)

For the rotational modes of motion RAO is expressed by [10]

RAOrot modes (120596) =

1003816100381610038161003816119883119896 (120596)1003816100381610038161003816

119860wave119871 (5)

where 119860wave represents the wave amplitude and 119871 is thecylinder radius Although RAO are not based on sea state thedamping and stiffness of the wind turbine are based on windspeed

22 Model Test Input

221 Wind Tunnel and Water Flume The Joint Laboratoryof Wind Tunnel and Water Flume at the Harbin Instituteof Technology [17 23] has one of the largest atmosphericboundary layer wind tunnels in China and is used to evaluateexperiments of a water flume on the wind-wave couplingeffect

The displacement and acceleration of a TLP-FOWTalongtwo different directions (ie the surge and the sway) weremeasured and analyzed The following experimental devices

4 Shock and Vibration

X

Y

Z

(a) TLP-0 mesh result

X

Y

Z

(b) TLP-1 mesh result

X

Y

Z

(c) TLP-2 mesh result

X

Y

Z

(d) TLP-3 mesh result

X

Y

Z

(e) TLP-4 mesh result

X

Y

Z

(f) TLP-5 mesh result

Figure 2 Mesh result for different models

Figure 3 A deep groove

were used a high-frequency force balance data acquisitionand its analysis system for receiving dynamic signals a high-precision laser displacement meter an acceleration sensor acurrent meter and a floating body instrument that comprisessix components Figure 4(a) shows the high-frequency forcebalance The forces along the two lateral directions whichare perpendicular to the axial direction of the balance haveranged between 0 and 660N Similarly the lateral bending

moments along the two directions (ie 119872119909and 119872

119910) are

ranged between 0 and 60Nm and the torque (ie 119872119911)

is ranged between 0 and 60Nm The measuring error isusually less than 1 Figure 4(b) shows sensor for measuringdisplacement and acceleration A CCD laser displacementsensor (ie LK-G400 Keyence) and a high-precision accel-eration sensor can be used for the accurate measurement ofthewind-induced structural vibration response It has a gauge

Shock and Vibration 5

(a) High-frequency force balance (b) Sensor for measuring displacement and acceleration

(c) System for dynamic signal data acquisition andanalysis

Figure 4 Major devices

(a) Model-TLP-1 (b) Model-TLP-2

Figure 5 Model-TLP-1 and model-TLP-2

length which is ranged between 300 and 500mm Figure 4(c)shows the system for dynamic signal data acquisition andanalysis A system of data acquisition and its analysis of adynamic signal (ie NI-PXI National Instruments America)have been used during the experiments of this paper whichhas (24 + 12) dynamic acquisition channels It can meet therequirements of a dynamic-response data acquisition of alarge and complicated structure which may be subject to theaction of the wind and the wind-wave it can be shown inFigure 3

222 Introduction of Experimental Models In order tocompare the result for two models parameters have beendesigned in detail Table 3 shows the model parameter and

Figure 5 shows the real view for the two models Model-TLP-1 and model-TLP-2 have the same draft diameter anddraft height however in the spoke distance model-TLP-1is 117 times as model-TLP-2rsquos date in the spoke diametermodel-TLP-2 is 3 times as model-TLP-1rsquos date To the spokedisplacement model-TLP-1 is 13 of model-TLP-2 Thepurpose of this design is to distinguish parameter spokedistance and spoke diameter and also is to easily compare thesimulation result with model test result

A tower was installed at the top of both models Theblade of a wind turbine was prepared with a ratio of 1 80The rotating speed of a wind turbine was approximately83 revmin and the facial area of the bladewas approximately1766m2 Under extreme wind speed weather conditions the

6 Shock and Vibration

Table 3 Model-TLP parameters

Parameter Model-TLP-1 Model-TLP-2Draft diameter (m) 023 023Draft height (m) 06 06Spoke distance (m) 0675 0573Spoke diameter (m) 002 006

rotation of the blade of a wind turbine would stop throughthe locking device which was fixed at the top Excluding theballast the weight of the entire structure was approximately101 kg

3 Results

31 Numerical Simulation

311 Hydrodynamic Properties The added mass dampingand exciting force matrices are considered based on themotion and dynamic equations in (2) The calculated waveexcitation force added mass and damping matrices areshown in Figures 6 7 and 8 respectively A portion of theresults have been shown because of symmetry characteristics

The addedmassmatrices in different directions are shownin Figure 6 The difference is evident if spoke dimension isnot considered In A11 (surge-surge direction) TLP-1 andTLP-4rsquos values were larger than those of TLP-0 and TLP-5however this finding is not evident in other directions If weconsider displacement only then TLP-3 is larger than TLP-2and all the values are larger for TLP-3However displacementdoes not only affect A11 because TLP-0 displacement waslower than TLP-4 while the TLP-0 A11 value was larger thanTLP-4 value In A33 (heave-heave direction) and A55 (pitch-pitch direction) the values increase when we considered thespoke dimension effect A comparison between the TLP-2 and TLP-3 results showed that displacement and valuesfor A33 and A55 were larger In A66 (yaw-yaw direction)TLP-0 and TLP-5 results were zero However the magnitudeof A66 was very large in TLP-1 and TLP-4 and cannot beignored Moreover TLP-1rsquos result was four times larger thanTLP-4When the spoke dimension effect was considered theadded mass matrix always increased This effect was mostevident in A66 because the value increased from zero to 1E5and 4E5 in A42 (roll-sway direction) and A15 respectivelybecause the unit was E5 designers should consider thisresult in the near future For the same spoke dimensionratio when the total displacement increases the added massmatrix also increases In the surge-pitch (A15) componentthe absolute value was larger than the others In total thecoefficient of the added mass matrices increases when thespoke dimension effect is considered thereby being usefulfor damping and motion Martin [13] assumed that all off-diagonal translational coefficients are zero The calculationsin this section show that the coefficient ofmassmatrices is notzero because of the spoke effect The size effect on the overallmotion will be analyzed in the next section

The damping effect (Figure 7) approached zero at highand low frequencies however the fourmodels clearly differ at

intermediate frequencies TLP-4 had the maximum dampingmatrix coefficients in the surge directionThe spoke size effectensures that a larger damping coefficient can be obtainedparticularly in B66 (yaw-yaw) where the value for TLP-0 and TLP-5 became zero Thus yaw instability may besevere in the calculation stage A comparison between Figures9(a) 9(b) 9(d) and 9(e) for TLP-0TLP-1 shows that thedamping coefficient decreased by 1 10 10 and 24respectively The decreases were 09 28 25 and 31for TLP-4 and TLP-5 These results indicate that the B55value (pitch-pitch) was more sensitive to the spoke sizeeffect Heave direction displacement was restricted becauseof tension leg therefore B33 (heave-heave direction) was notconsidered in the dampingmatrix and its value was assumedlarge enough in damping In B55 (pitch-pitch direction) themagnitude was E5 therefore the spoke dimension effectshould be considered In fact the spoke dimension effectincreased At the same displacement ratio in TLP-2 and TLP-3 the change was smaller in TLP-2 but TLP-3 was largerthan TLP-2 which indicates that larger displacement leadsto larger damping B66 (yaw-yaw direction) had the samesituation as A66 the damping matrix was limited to zeroif the spoke dimension effect was not considered In theoff-diagonal translational matrices B42 and B15 the effectwas clearly enhanced damping Interestingly in TLP-2 andTLP-3 the off-diagonal matrices did not change When thespoke dimension effect was considered the damping didnot always increase In B66 the spoke dimension effectincreased damping from zero to a larger value In the off-diagonal translational matrices the spoke dimension effectwas enhanced damping At the same displacement ratio theoff-diagonal coefficient did not change at B42 and B51

Obviously the exciting force reduced when the spokeeffect was not considered In this section TLP-2 and TLP-3 had the minimum exciting force For the surge excitingforce TLP-0 andTLP-1 had similar curves thereby indicatingthat the effect was limited The same situation occurred inTLP-4 and TLP-5 For the pitch exciting force the trendwas opposite as shown in Figure 8(c) The exciting force ofTLP-1 and TLP-4 was larger than that of TLP-0 and TLP-5 respectively For TLP-2 and TLP-3 large displacementindicates a large pitch exciting force The yaw exciting forceexhibited the same patterns as the pitch exciting forcehowever the values were the same for the yaw exciting forceTherefore this result can be ignored

Overall the exciting force reduced when we did notconsider the spoke effect in the translation direction whichis the opposite for rotation The same situation occurred inTLP-2 and TLP-3 In this wave direction the pitch excitingforce was the largest whereas the other forces were so smallthat they could be neglected

For B66 (yaw-yaw) TLP-2was the largest in all themodesand could be used to improve yaw damping For the excitingforcematrices the surge exciting forcewas similar clearly thepitch and yaw exciting force of TLP-3 did not change Martin[13] assumed yaw instability in his model because the spokesize effect on the yaw-yaw damping is larger and improvesmotion performance

Shock and Vibration 7

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A11

0

2000

4000

6000

8000

10000

05 1 15 2 250120596 (rads)

(a) A11 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A15

05 1 15 2 250120596 (rads)

times105

minus25

minus2

minus15

minus1

minus05

0

(b) A15 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A33

0

500

1000

1500

2000

2500

3000

05 1 15 2 250120596 (rads)

(c) A33 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A42

times105

0

05

1

15

2

25

05 1 15 2 250120596 (rads)

(d) A42 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A55

times106

0

1

2

3

4

5

6

7

8

05 1 15 2 250120596 (rads)

(e) A55 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A66

times105

05 1 15 2 250120596 (rads)

0

1

2

3

4

(f) A66 added mass

Figure 6 Added mass matrices

8 Shock and Vibration

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B11

05 1 15 2 250120596 (rads)

0

500

1000

1500

2000

2500

3000

(a) B11 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B15

times104

minus3

minus25

minus2

minus15

minus1

minus05

0

05 1 15 2 250120596 (rads)

(b) B15 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B33

minus10

0

10

20

30

40

50

60

70

05 1 15 2 250120596 (rads)

(c) B33 damping matrices

times104

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B42

minus05

0

05

1

15

2

25

3

05 1 15 2 250120596 (rads)

(d) B42 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B55

times105

minus1

0

1

2

3

4

5

05 1 15 2 250120596 (rads)

(e) B55 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B66

05 1 15 2 250120596 (rads)

minus05

0

05

1

15

2

25

(f) B66 damping matrices

Figure 7 Damping matrices

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

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Shock and Vibration

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Shock and Vibration 3

TLP-1[6]

(a)

TLP-2

(b)

TLP-3

(c)

TLP-4

(d)

Figure 1

Table 2 Dimensions of four modified NREL-TLPs (see also Figure 1)

Parameters TLP-1 [6] TLP-2 TLP-3 TLP-4Column

Diameter-CD (m) 15 12 12 15Length-CL (m) 40 35 45 30

SpokesDiameter-PD (m) 55 6 7 8Length-PL (m) 25 20 18 15

Concrete ballastHeight-CH (m) 2 5 4 5

Gravity point 0 0 minus32988 0 0 minus35426 0 0 minus41681 0 0 minus36857Total mass119879 1468632 186874 1644921 2648716

Displacement1198723 908049 610416 738528 768907

Concrete displacement1198723 35325 56520 45216 88313

where 119872added is the added mass matrix 119872WT is the massmatrix of the wind turbine at a constant wind speed119872structureis the mass matrix of the platform 119861structure is the dampingmatrix of the platform 119861WT is the damping matrix of thewind turbine 119862WT is the stiffness matrix of the wind turbine119862structure is the stiffness matrix of the platform 119862mooring is thestiffness matrix of the mooring system and 120577 120577 and 120577 are theacceleration velocity and displacement of the system

In this study RAO represents the nondimensionalresponse of a system to a unit-amplitude incident wave in adirection along the 119883 coordinate that is the zero incidentangle [13] The motion equations that control the systemrsquoslinear dynamic motion are summarized in (3) [10] as follows

[minus1205962(119872 + 119860 (120596)) + 120596119861 (120596) + 119862] Ξ (120596) = 119883 (120596) (3)

For the translational modes of motion RAO is expressed by[10]

RAOtrans modes (120596) =

1003816100381610038161003816119883119896 (120596)1003816100381610038161003816

119860wave (4)

For the rotational modes of motion RAO is expressed by [10]

RAOrot modes (120596) =

1003816100381610038161003816119883119896 (120596)1003816100381610038161003816

119860wave119871 (5)

where 119860wave represents the wave amplitude and 119871 is thecylinder radius Although RAO are not based on sea state thedamping and stiffness of the wind turbine are based on windspeed

22 Model Test Input

221 Wind Tunnel and Water Flume The Joint Laboratoryof Wind Tunnel and Water Flume at the Harbin Instituteof Technology [17 23] has one of the largest atmosphericboundary layer wind tunnels in China and is used to evaluateexperiments of a water flume on the wind-wave couplingeffect

The displacement and acceleration of a TLP-FOWTalongtwo different directions (ie the surge and the sway) weremeasured and analyzed The following experimental devices

4 Shock and Vibration

X

Y

Z

(a) TLP-0 mesh result

X

Y

Z

(b) TLP-1 mesh result

X

Y

Z

(c) TLP-2 mesh result

X

Y

Z

(d) TLP-3 mesh result

X

Y

Z

(e) TLP-4 mesh result

X

Y

Z

(f) TLP-5 mesh result

Figure 2 Mesh result for different models

Figure 3 A deep groove

were used a high-frequency force balance data acquisitionand its analysis system for receiving dynamic signals a high-precision laser displacement meter an acceleration sensor acurrent meter and a floating body instrument that comprisessix components Figure 4(a) shows the high-frequency forcebalance The forces along the two lateral directions whichare perpendicular to the axial direction of the balance haveranged between 0 and 660N Similarly the lateral bending

moments along the two directions (ie 119872119909and 119872

119910) are

ranged between 0 and 60Nm and the torque (ie 119872119911)

is ranged between 0 and 60Nm The measuring error isusually less than 1 Figure 4(b) shows sensor for measuringdisplacement and acceleration A CCD laser displacementsensor (ie LK-G400 Keyence) and a high-precision accel-eration sensor can be used for the accurate measurement ofthewind-induced structural vibration response It has a gauge

Shock and Vibration 5

(a) High-frequency force balance (b) Sensor for measuring displacement and acceleration

(c) System for dynamic signal data acquisition andanalysis

Figure 4 Major devices

(a) Model-TLP-1 (b) Model-TLP-2

Figure 5 Model-TLP-1 and model-TLP-2

length which is ranged between 300 and 500mm Figure 4(c)shows the system for dynamic signal data acquisition andanalysis A system of data acquisition and its analysis of adynamic signal (ie NI-PXI National Instruments America)have been used during the experiments of this paper whichhas (24 + 12) dynamic acquisition channels It can meet therequirements of a dynamic-response data acquisition of alarge and complicated structure which may be subject to theaction of the wind and the wind-wave it can be shown inFigure 3

222 Introduction of Experimental Models In order tocompare the result for two models parameters have beendesigned in detail Table 3 shows the model parameter and

Figure 5 shows the real view for the two models Model-TLP-1 and model-TLP-2 have the same draft diameter anddraft height however in the spoke distance model-TLP-1is 117 times as model-TLP-2rsquos date in the spoke diametermodel-TLP-2 is 3 times as model-TLP-1rsquos date To the spokedisplacement model-TLP-1 is 13 of model-TLP-2 Thepurpose of this design is to distinguish parameter spokedistance and spoke diameter and also is to easily compare thesimulation result with model test result

A tower was installed at the top of both models Theblade of a wind turbine was prepared with a ratio of 1 80The rotating speed of a wind turbine was approximately83 revmin and the facial area of the bladewas approximately1766m2 Under extreme wind speed weather conditions the

6 Shock and Vibration

Table 3 Model-TLP parameters

Parameter Model-TLP-1 Model-TLP-2Draft diameter (m) 023 023Draft height (m) 06 06Spoke distance (m) 0675 0573Spoke diameter (m) 002 006

rotation of the blade of a wind turbine would stop throughthe locking device which was fixed at the top Excluding theballast the weight of the entire structure was approximately101 kg

3 Results

31 Numerical Simulation

311 Hydrodynamic Properties The added mass dampingand exciting force matrices are considered based on themotion and dynamic equations in (2) The calculated waveexcitation force added mass and damping matrices areshown in Figures 6 7 and 8 respectively A portion of theresults have been shown because of symmetry characteristics

The addedmassmatrices in different directions are shownin Figure 6 The difference is evident if spoke dimension isnot considered In A11 (surge-surge direction) TLP-1 andTLP-4rsquos values were larger than those of TLP-0 and TLP-5however this finding is not evident in other directions If weconsider displacement only then TLP-3 is larger than TLP-2and all the values are larger for TLP-3However displacementdoes not only affect A11 because TLP-0 displacement waslower than TLP-4 while the TLP-0 A11 value was larger thanTLP-4 value In A33 (heave-heave direction) and A55 (pitch-pitch direction) the values increase when we considered thespoke dimension effect A comparison between the TLP-2 and TLP-3 results showed that displacement and valuesfor A33 and A55 were larger In A66 (yaw-yaw direction)TLP-0 and TLP-5 results were zero However the magnitudeof A66 was very large in TLP-1 and TLP-4 and cannot beignored Moreover TLP-1rsquos result was four times larger thanTLP-4When the spoke dimension effect was considered theadded mass matrix always increased This effect was mostevident in A66 because the value increased from zero to 1E5and 4E5 in A42 (roll-sway direction) and A15 respectivelybecause the unit was E5 designers should consider thisresult in the near future For the same spoke dimensionratio when the total displacement increases the added massmatrix also increases In the surge-pitch (A15) componentthe absolute value was larger than the others In total thecoefficient of the added mass matrices increases when thespoke dimension effect is considered thereby being usefulfor damping and motion Martin [13] assumed that all off-diagonal translational coefficients are zero The calculationsin this section show that the coefficient ofmassmatrices is notzero because of the spoke effect The size effect on the overallmotion will be analyzed in the next section

The damping effect (Figure 7) approached zero at highand low frequencies however the fourmodels clearly differ at

intermediate frequencies TLP-4 had the maximum dampingmatrix coefficients in the surge directionThe spoke size effectensures that a larger damping coefficient can be obtainedparticularly in B66 (yaw-yaw) where the value for TLP-0 and TLP-5 became zero Thus yaw instability may besevere in the calculation stage A comparison between Figures9(a) 9(b) 9(d) and 9(e) for TLP-0TLP-1 shows that thedamping coefficient decreased by 1 10 10 and 24respectively The decreases were 09 28 25 and 31for TLP-4 and TLP-5 These results indicate that the B55value (pitch-pitch) was more sensitive to the spoke sizeeffect Heave direction displacement was restricted becauseof tension leg therefore B33 (heave-heave direction) was notconsidered in the dampingmatrix and its value was assumedlarge enough in damping In B55 (pitch-pitch direction) themagnitude was E5 therefore the spoke dimension effectshould be considered In fact the spoke dimension effectincreased At the same displacement ratio in TLP-2 and TLP-3 the change was smaller in TLP-2 but TLP-3 was largerthan TLP-2 which indicates that larger displacement leadsto larger damping B66 (yaw-yaw direction) had the samesituation as A66 the damping matrix was limited to zeroif the spoke dimension effect was not considered In theoff-diagonal translational matrices B42 and B15 the effectwas clearly enhanced damping Interestingly in TLP-2 andTLP-3 the off-diagonal matrices did not change When thespoke dimension effect was considered the damping didnot always increase In B66 the spoke dimension effectincreased damping from zero to a larger value In the off-diagonal translational matrices the spoke dimension effectwas enhanced damping At the same displacement ratio theoff-diagonal coefficient did not change at B42 and B51

Obviously the exciting force reduced when the spokeeffect was not considered In this section TLP-2 and TLP-3 had the minimum exciting force For the surge excitingforce TLP-0 andTLP-1 had similar curves thereby indicatingthat the effect was limited The same situation occurred inTLP-4 and TLP-5 For the pitch exciting force the trendwas opposite as shown in Figure 8(c) The exciting force ofTLP-1 and TLP-4 was larger than that of TLP-0 and TLP-5 respectively For TLP-2 and TLP-3 large displacementindicates a large pitch exciting force The yaw exciting forceexhibited the same patterns as the pitch exciting forcehowever the values were the same for the yaw exciting forceTherefore this result can be ignored

Overall the exciting force reduced when we did notconsider the spoke effect in the translation direction whichis the opposite for rotation The same situation occurred inTLP-2 and TLP-3 In this wave direction the pitch excitingforce was the largest whereas the other forces were so smallthat they could be neglected

For B66 (yaw-yaw) TLP-2was the largest in all themodesand could be used to improve yaw damping For the excitingforcematrices the surge exciting forcewas similar clearly thepitch and yaw exciting force of TLP-3 did not change Martin[13] assumed yaw instability in his model because the spokesize effect on the yaw-yaw damping is larger and improvesmotion performance

Shock and Vibration 7

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A11

0

2000

4000

6000

8000

10000

05 1 15 2 250120596 (rads)

(a) A11 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A15

05 1 15 2 250120596 (rads)

times105

minus25

minus2

minus15

minus1

minus05

0

(b) A15 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A33

0

500

1000

1500

2000

2500

3000

05 1 15 2 250120596 (rads)

(c) A33 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A42

times105

0

05

1

15

2

25

05 1 15 2 250120596 (rads)

(d) A42 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A55

times106

0

1

2

3

4

5

6

7

8

05 1 15 2 250120596 (rads)

(e) A55 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A66

times105

05 1 15 2 250120596 (rads)

0

1

2

3

4

(f) A66 added mass

Figure 6 Added mass matrices

8 Shock and Vibration

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B11

05 1 15 2 250120596 (rads)

0

500

1000

1500

2000

2500

3000

(a) B11 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B15

times104

minus3

minus25

minus2

minus15

minus1

minus05

0

05 1 15 2 250120596 (rads)

(b) B15 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B33

minus10

0

10

20

30

40

50

60

70

05 1 15 2 250120596 (rads)

(c) B33 damping matrices

times104

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B42

minus05

0

05

1

15

2

25

3

05 1 15 2 250120596 (rads)

(d) B42 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B55

times105

minus1

0

1

2

3

4

5

05 1 15 2 250120596 (rads)

(e) B55 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B66

05 1 15 2 250120596 (rads)

minus05

0

05

1

15

2

25

(f) B66 damping matrices

Figure 7 Damping matrices

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

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Shock and Vibration

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International Journal of

4 Shock and Vibration

X

Y

Z

(a) TLP-0 mesh result

X

Y

Z

(b) TLP-1 mesh result

X

Y

Z

(c) TLP-2 mesh result

X

Y

Z

(d) TLP-3 mesh result

X

Y

Z

(e) TLP-4 mesh result

X

Y

Z

(f) TLP-5 mesh result

Figure 2 Mesh result for different models

Figure 3 A deep groove

were used a high-frequency force balance data acquisitionand its analysis system for receiving dynamic signals a high-precision laser displacement meter an acceleration sensor acurrent meter and a floating body instrument that comprisessix components Figure 4(a) shows the high-frequency forcebalance The forces along the two lateral directions whichare perpendicular to the axial direction of the balance haveranged between 0 and 660N Similarly the lateral bending

moments along the two directions (ie 119872119909and 119872

119910) are

ranged between 0 and 60Nm and the torque (ie 119872119911)

is ranged between 0 and 60Nm The measuring error isusually less than 1 Figure 4(b) shows sensor for measuringdisplacement and acceleration A CCD laser displacementsensor (ie LK-G400 Keyence) and a high-precision accel-eration sensor can be used for the accurate measurement ofthewind-induced structural vibration response It has a gauge

Shock and Vibration 5

(a) High-frequency force balance (b) Sensor for measuring displacement and acceleration

(c) System for dynamic signal data acquisition andanalysis

Figure 4 Major devices

(a) Model-TLP-1 (b) Model-TLP-2

Figure 5 Model-TLP-1 and model-TLP-2

length which is ranged between 300 and 500mm Figure 4(c)shows the system for dynamic signal data acquisition andanalysis A system of data acquisition and its analysis of adynamic signal (ie NI-PXI National Instruments America)have been used during the experiments of this paper whichhas (24 + 12) dynamic acquisition channels It can meet therequirements of a dynamic-response data acquisition of alarge and complicated structure which may be subject to theaction of the wind and the wind-wave it can be shown inFigure 3

222 Introduction of Experimental Models In order tocompare the result for two models parameters have beendesigned in detail Table 3 shows the model parameter and

Figure 5 shows the real view for the two models Model-TLP-1 and model-TLP-2 have the same draft diameter anddraft height however in the spoke distance model-TLP-1is 117 times as model-TLP-2rsquos date in the spoke diametermodel-TLP-2 is 3 times as model-TLP-1rsquos date To the spokedisplacement model-TLP-1 is 13 of model-TLP-2 Thepurpose of this design is to distinguish parameter spokedistance and spoke diameter and also is to easily compare thesimulation result with model test result

A tower was installed at the top of both models Theblade of a wind turbine was prepared with a ratio of 1 80The rotating speed of a wind turbine was approximately83 revmin and the facial area of the bladewas approximately1766m2 Under extreme wind speed weather conditions the

6 Shock and Vibration

Table 3 Model-TLP parameters

Parameter Model-TLP-1 Model-TLP-2Draft diameter (m) 023 023Draft height (m) 06 06Spoke distance (m) 0675 0573Spoke diameter (m) 002 006

rotation of the blade of a wind turbine would stop throughthe locking device which was fixed at the top Excluding theballast the weight of the entire structure was approximately101 kg

3 Results

31 Numerical Simulation

311 Hydrodynamic Properties The added mass dampingand exciting force matrices are considered based on themotion and dynamic equations in (2) The calculated waveexcitation force added mass and damping matrices areshown in Figures 6 7 and 8 respectively A portion of theresults have been shown because of symmetry characteristics

The addedmassmatrices in different directions are shownin Figure 6 The difference is evident if spoke dimension isnot considered In A11 (surge-surge direction) TLP-1 andTLP-4rsquos values were larger than those of TLP-0 and TLP-5however this finding is not evident in other directions If weconsider displacement only then TLP-3 is larger than TLP-2and all the values are larger for TLP-3However displacementdoes not only affect A11 because TLP-0 displacement waslower than TLP-4 while the TLP-0 A11 value was larger thanTLP-4 value In A33 (heave-heave direction) and A55 (pitch-pitch direction) the values increase when we considered thespoke dimension effect A comparison between the TLP-2 and TLP-3 results showed that displacement and valuesfor A33 and A55 were larger In A66 (yaw-yaw direction)TLP-0 and TLP-5 results were zero However the magnitudeof A66 was very large in TLP-1 and TLP-4 and cannot beignored Moreover TLP-1rsquos result was four times larger thanTLP-4When the spoke dimension effect was considered theadded mass matrix always increased This effect was mostevident in A66 because the value increased from zero to 1E5and 4E5 in A42 (roll-sway direction) and A15 respectivelybecause the unit was E5 designers should consider thisresult in the near future For the same spoke dimensionratio when the total displacement increases the added massmatrix also increases In the surge-pitch (A15) componentthe absolute value was larger than the others In total thecoefficient of the added mass matrices increases when thespoke dimension effect is considered thereby being usefulfor damping and motion Martin [13] assumed that all off-diagonal translational coefficients are zero The calculationsin this section show that the coefficient ofmassmatrices is notzero because of the spoke effect The size effect on the overallmotion will be analyzed in the next section

The damping effect (Figure 7) approached zero at highand low frequencies however the fourmodels clearly differ at

intermediate frequencies TLP-4 had the maximum dampingmatrix coefficients in the surge directionThe spoke size effectensures that a larger damping coefficient can be obtainedparticularly in B66 (yaw-yaw) where the value for TLP-0 and TLP-5 became zero Thus yaw instability may besevere in the calculation stage A comparison between Figures9(a) 9(b) 9(d) and 9(e) for TLP-0TLP-1 shows that thedamping coefficient decreased by 1 10 10 and 24respectively The decreases were 09 28 25 and 31for TLP-4 and TLP-5 These results indicate that the B55value (pitch-pitch) was more sensitive to the spoke sizeeffect Heave direction displacement was restricted becauseof tension leg therefore B33 (heave-heave direction) was notconsidered in the dampingmatrix and its value was assumedlarge enough in damping In B55 (pitch-pitch direction) themagnitude was E5 therefore the spoke dimension effectshould be considered In fact the spoke dimension effectincreased At the same displacement ratio in TLP-2 and TLP-3 the change was smaller in TLP-2 but TLP-3 was largerthan TLP-2 which indicates that larger displacement leadsto larger damping B66 (yaw-yaw direction) had the samesituation as A66 the damping matrix was limited to zeroif the spoke dimension effect was not considered In theoff-diagonal translational matrices B42 and B15 the effectwas clearly enhanced damping Interestingly in TLP-2 andTLP-3 the off-diagonal matrices did not change When thespoke dimension effect was considered the damping didnot always increase In B66 the spoke dimension effectincreased damping from zero to a larger value In the off-diagonal translational matrices the spoke dimension effectwas enhanced damping At the same displacement ratio theoff-diagonal coefficient did not change at B42 and B51

Obviously the exciting force reduced when the spokeeffect was not considered In this section TLP-2 and TLP-3 had the minimum exciting force For the surge excitingforce TLP-0 andTLP-1 had similar curves thereby indicatingthat the effect was limited The same situation occurred inTLP-4 and TLP-5 For the pitch exciting force the trendwas opposite as shown in Figure 8(c) The exciting force ofTLP-1 and TLP-4 was larger than that of TLP-0 and TLP-5 respectively For TLP-2 and TLP-3 large displacementindicates a large pitch exciting force The yaw exciting forceexhibited the same patterns as the pitch exciting forcehowever the values were the same for the yaw exciting forceTherefore this result can be ignored

Overall the exciting force reduced when we did notconsider the spoke effect in the translation direction whichis the opposite for rotation The same situation occurred inTLP-2 and TLP-3 In this wave direction the pitch excitingforce was the largest whereas the other forces were so smallthat they could be neglected

For B66 (yaw-yaw) TLP-2was the largest in all themodesand could be used to improve yaw damping For the excitingforcematrices the surge exciting forcewas similar clearly thepitch and yaw exciting force of TLP-3 did not change Martin[13] assumed yaw instability in his model because the spokesize effect on the yaw-yaw damping is larger and improvesmotion performance

Shock and Vibration 7

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A11

0

2000

4000

6000

8000

10000

05 1 15 2 250120596 (rads)

(a) A11 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A15

05 1 15 2 250120596 (rads)

times105

minus25

minus2

minus15

minus1

minus05

0

(b) A15 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A33

0

500

1000

1500

2000

2500

3000

05 1 15 2 250120596 (rads)

(c) A33 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A42

times105

0

05

1

15

2

25

05 1 15 2 250120596 (rads)

(d) A42 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A55

times106

0

1

2

3

4

5

6

7

8

05 1 15 2 250120596 (rads)

(e) A55 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A66

times105

05 1 15 2 250120596 (rads)

0

1

2

3

4

(f) A66 added mass

Figure 6 Added mass matrices

8 Shock and Vibration

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B11

05 1 15 2 250120596 (rads)

0

500

1000

1500

2000

2500

3000

(a) B11 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B15

times104

minus3

minus25

minus2

minus15

minus1

minus05

0

05 1 15 2 250120596 (rads)

(b) B15 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B33

minus10

0

10

20

30

40

50

60

70

05 1 15 2 250120596 (rads)

(c) B33 damping matrices

times104

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B42

minus05

0

05

1

15

2

25

3

05 1 15 2 250120596 (rads)

(d) B42 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B55

times105

minus1

0

1

2

3

4

5

05 1 15 2 250120596 (rads)

(e) B55 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B66

05 1 15 2 250120596 (rads)

minus05

0

05

1

15

2

25

(f) B66 damping matrices

Figure 7 Damping matrices

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

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Shock and Vibration

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DistributedSensor Networks

International Journal of

Shock and Vibration 5

(a) High-frequency force balance (b) Sensor for measuring displacement and acceleration

(c) System for dynamic signal data acquisition andanalysis

Figure 4 Major devices

(a) Model-TLP-1 (b) Model-TLP-2

Figure 5 Model-TLP-1 and model-TLP-2

length which is ranged between 300 and 500mm Figure 4(c)shows the system for dynamic signal data acquisition andanalysis A system of data acquisition and its analysis of adynamic signal (ie NI-PXI National Instruments America)have been used during the experiments of this paper whichhas (24 + 12) dynamic acquisition channels It can meet therequirements of a dynamic-response data acquisition of alarge and complicated structure which may be subject to theaction of the wind and the wind-wave it can be shown inFigure 3

222 Introduction of Experimental Models In order tocompare the result for two models parameters have beendesigned in detail Table 3 shows the model parameter and

Figure 5 shows the real view for the two models Model-TLP-1 and model-TLP-2 have the same draft diameter anddraft height however in the spoke distance model-TLP-1is 117 times as model-TLP-2rsquos date in the spoke diametermodel-TLP-2 is 3 times as model-TLP-1rsquos date To the spokedisplacement model-TLP-1 is 13 of model-TLP-2 Thepurpose of this design is to distinguish parameter spokedistance and spoke diameter and also is to easily compare thesimulation result with model test result

A tower was installed at the top of both models Theblade of a wind turbine was prepared with a ratio of 1 80The rotating speed of a wind turbine was approximately83 revmin and the facial area of the bladewas approximately1766m2 Under extreme wind speed weather conditions the

6 Shock and Vibration

Table 3 Model-TLP parameters

Parameter Model-TLP-1 Model-TLP-2Draft diameter (m) 023 023Draft height (m) 06 06Spoke distance (m) 0675 0573Spoke diameter (m) 002 006

rotation of the blade of a wind turbine would stop throughthe locking device which was fixed at the top Excluding theballast the weight of the entire structure was approximately101 kg

3 Results

31 Numerical Simulation

311 Hydrodynamic Properties The added mass dampingand exciting force matrices are considered based on themotion and dynamic equations in (2) The calculated waveexcitation force added mass and damping matrices areshown in Figures 6 7 and 8 respectively A portion of theresults have been shown because of symmetry characteristics

The addedmassmatrices in different directions are shownin Figure 6 The difference is evident if spoke dimension isnot considered In A11 (surge-surge direction) TLP-1 andTLP-4rsquos values were larger than those of TLP-0 and TLP-5however this finding is not evident in other directions If weconsider displacement only then TLP-3 is larger than TLP-2and all the values are larger for TLP-3However displacementdoes not only affect A11 because TLP-0 displacement waslower than TLP-4 while the TLP-0 A11 value was larger thanTLP-4 value In A33 (heave-heave direction) and A55 (pitch-pitch direction) the values increase when we considered thespoke dimension effect A comparison between the TLP-2 and TLP-3 results showed that displacement and valuesfor A33 and A55 were larger In A66 (yaw-yaw direction)TLP-0 and TLP-5 results were zero However the magnitudeof A66 was very large in TLP-1 and TLP-4 and cannot beignored Moreover TLP-1rsquos result was four times larger thanTLP-4When the spoke dimension effect was considered theadded mass matrix always increased This effect was mostevident in A66 because the value increased from zero to 1E5and 4E5 in A42 (roll-sway direction) and A15 respectivelybecause the unit was E5 designers should consider thisresult in the near future For the same spoke dimensionratio when the total displacement increases the added massmatrix also increases In the surge-pitch (A15) componentthe absolute value was larger than the others In total thecoefficient of the added mass matrices increases when thespoke dimension effect is considered thereby being usefulfor damping and motion Martin [13] assumed that all off-diagonal translational coefficients are zero The calculationsin this section show that the coefficient ofmassmatrices is notzero because of the spoke effect The size effect on the overallmotion will be analyzed in the next section

The damping effect (Figure 7) approached zero at highand low frequencies however the fourmodels clearly differ at

intermediate frequencies TLP-4 had the maximum dampingmatrix coefficients in the surge directionThe spoke size effectensures that a larger damping coefficient can be obtainedparticularly in B66 (yaw-yaw) where the value for TLP-0 and TLP-5 became zero Thus yaw instability may besevere in the calculation stage A comparison between Figures9(a) 9(b) 9(d) and 9(e) for TLP-0TLP-1 shows that thedamping coefficient decreased by 1 10 10 and 24respectively The decreases were 09 28 25 and 31for TLP-4 and TLP-5 These results indicate that the B55value (pitch-pitch) was more sensitive to the spoke sizeeffect Heave direction displacement was restricted becauseof tension leg therefore B33 (heave-heave direction) was notconsidered in the dampingmatrix and its value was assumedlarge enough in damping In B55 (pitch-pitch direction) themagnitude was E5 therefore the spoke dimension effectshould be considered In fact the spoke dimension effectincreased At the same displacement ratio in TLP-2 and TLP-3 the change was smaller in TLP-2 but TLP-3 was largerthan TLP-2 which indicates that larger displacement leadsto larger damping B66 (yaw-yaw direction) had the samesituation as A66 the damping matrix was limited to zeroif the spoke dimension effect was not considered In theoff-diagonal translational matrices B42 and B15 the effectwas clearly enhanced damping Interestingly in TLP-2 andTLP-3 the off-diagonal matrices did not change When thespoke dimension effect was considered the damping didnot always increase In B66 the spoke dimension effectincreased damping from zero to a larger value In the off-diagonal translational matrices the spoke dimension effectwas enhanced damping At the same displacement ratio theoff-diagonal coefficient did not change at B42 and B51

Obviously the exciting force reduced when the spokeeffect was not considered In this section TLP-2 and TLP-3 had the minimum exciting force For the surge excitingforce TLP-0 andTLP-1 had similar curves thereby indicatingthat the effect was limited The same situation occurred inTLP-4 and TLP-5 For the pitch exciting force the trendwas opposite as shown in Figure 8(c) The exciting force ofTLP-1 and TLP-4 was larger than that of TLP-0 and TLP-5 respectively For TLP-2 and TLP-3 large displacementindicates a large pitch exciting force The yaw exciting forceexhibited the same patterns as the pitch exciting forcehowever the values were the same for the yaw exciting forceTherefore this result can be ignored

Overall the exciting force reduced when we did notconsider the spoke effect in the translation direction whichis the opposite for rotation The same situation occurred inTLP-2 and TLP-3 In this wave direction the pitch excitingforce was the largest whereas the other forces were so smallthat they could be neglected

For B66 (yaw-yaw) TLP-2was the largest in all themodesand could be used to improve yaw damping For the excitingforcematrices the surge exciting forcewas similar clearly thepitch and yaw exciting force of TLP-3 did not change Martin[13] assumed yaw instability in his model because the spokesize effect on the yaw-yaw damping is larger and improvesmotion performance

Shock and Vibration 7

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A11

0

2000

4000

6000

8000

10000

05 1 15 2 250120596 (rads)

(a) A11 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A15

05 1 15 2 250120596 (rads)

times105

minus25

minus2

minus15

minus1

minus05

0

(b) A15 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A33

0

500

1000

1500

2000

2500

3000

05 1 15 2 250120596 (rads)

(c) A33 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A42

times105

0

05

1

15

2

25

05 1 15 2 250120596 (rads)

(d) A42 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A55

times106

0

1

2

3

4

5

6

7

8

05 1 15 2 250120596 (rads)

(e) A55 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A66

times105

05 1 15 2 250120596 (rads)

0

1

2

3

4

(f) A66 added mass

Figure 6 Added mass matrices

8 Shock and Vibration

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B11

05 1 15 2 250120596 (rads)

0

500

1000

1500

2000

2500

3000

(a) B11 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B15

times104

minus3

minus25

minus2

minus15

minus1

minus05

0

05 1 15 2 250120596 (rads)

(b) B15 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B33

minus10

0

10

20

30

40

50

60

70

05 1 15 2 250120596 (rads)

(c) B33 damping matrices

times104

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B42

minus05

0

05

1

15

2

25

3

05 1 15 2 250120596 (rads)

(d) B42 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B55

times105

minus1

0

1

2

3

4

5

05 1 15 2 250120596 (rads)

(e) B55 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B66

05 1 15 2 250120596 (rads)

minus05

0

05

1

15

2

25

(f) B66 damping matrices

Figure 7 Damping matrices

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

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6 Shock and Vibration

Table 3 Model-TLP parameters

Parameter Model-TLP-1 Model-TLP-2Draft diameter (m) 023 023Draft height (m) 06 06Spoke distance (m) 0675 0573Spoke diameter (m) 002 006

rotation of the blade of a wind turbine would stop throughthe locking device which was fixed at the top Excluding theballast the weight of the entire structure was approximately101 kg

3 Results

31 Numerical Simulation

311 Hydrodynamic Properties The added mass dampingand exciting force matrices are considered based on themotion and dynamic equations in (2) The calculated waveexcitation force added mass and damping matrices areshown in Figures 6 7 and 8 respectively A portion of theresults have been shown because of symmetry characteristics

The addedmassmatrices in different directions are shownin Figure 6 The difference is evident if spoke dimension isnot considered In A11 (surge-surge direction) TLP-1 andTLP-4rsquos values were larger than those of TLP-0 and TLP-5however this finding is not evident in other directions If weconsider displacement only then TLP-3 is larger than TLP-2and all the values are larger for TLP-3However displacementdoes not only affect A11 because TLP-0 displacement waslower than TLP-4 while the TLP-0 A11 value was larger thanTLP-4 value In A33 (heave-heave direction) and A55 (pitch-pitch direction) the values increase when we considered thespoke dimension effect A comparison between the TLP-2 and TLP-3 results showed that displacement and valuesfor A33 and A55 were larger In A66 (yaw-yaw direction)TLP-0 and TLP-5 results were zero However the magnitudeof A66 was very large in TLP-1 and TLP-4 and cannot beignored Moreover TLP-1rsquos result was four times larger thanTLP-4When the spoke dimension effect was considered theadded mass matrix always increased This effect was mostevident in A66 because the value increased from zero to 1E5and 4E5 in A42 (roll-sway direction) and A15 respectivelybecause the unit was E5 designers should consider thisresult in the near future For the same spoke dimensionratio when the total displacement increases the added massmatrix also increases In the surge-pitch (A15) componentthe absolute value was larger than the others In total thecoefficient of the added mass matrices increases when thespoke dimension effect is considered thereby being usefulfor damping and motion Martin [13] assumed that all off-diagonal translational coefficients are zero The calculationsin this section show that the coefficient ofmassmatrices is notzero because of the spoke effect The size effect on the overallmotion will be analyzed in the next section

The damping effect (Figure 7) approached zero at highand low frequencies however the fourmodels clearly differ at

intermediate frequencies TLP-4 had the maximum dampingmatrix coefficients in the surge directionThe spoke size effectensures that a larger damping coefficient can be obtainedparticularly in B66 (yaw-yaw) where the value for TLP-0 and TLP-5 became zero Thus yaw instability may besevere in the calculation stage A comparison between Figures9(a) 9(b) 9(d) and 9(e) for TLP-0TLP-1 shows that thedamping coefficient decreased by 1 10 10 and 24respectively The decreases were 09 28 25 and 31for TLP-4 and TLP-5 These results indicate that the B55value (pitch-pitch) was more sensitive to the spoke sizeeffect Heave direction displacement was restricted becauseof tension leg therefore B33 (heave-heave direction) was notconsidered in the dampingmatrix and its value was assumedlarge enough in damping In B55 (pitch-pitch direction) themagnitude was E5 therefore the spoke dimension effectshould be considered In fact the spoke dimension effectincreased At the same displacement ratio in TLP-2 and TLP-3 the change was smaller in TLP-2 but TLP-3 was largerthan TLP-2 which indicates that larger displacement leadsto larger damping B66 (yaw-yaw direction) had the samesituation as A66 the damping matrix was limited to zeroif the spoke dimension effect was not considered In theoff-diagonal translational matrices B42 and B15 the effectwas clearly enhanced damping Interestingly in TLP-2 andTLP-3 the off-diagonal matrices did not change When thespoke dimension effect was considered the damping didnot always increase In B66 the spoke dimension effectincreased damping from zero to a larger value In the off-diagonal translational matrices the spoke dimension effectwas enhanced damping At the same displacement ratio theoff-diagonal coefficient did not change at B42 and B51

Obviously the exciting force reduced when the spokeeffect was not considered In this section TLP-2 and TLP-3 had the minimum exciting force For the surge excitingforce TLP-0 andTLP-1 had similar curves thereby indicatingthat the effect was limited The same situation occurred inTLP-4 and TLP-5 For the pitch exciting force the trendwas opposite as shown in Figure 8(c) The exciting force ofTLP-1 and TLP-4 was larger than that of TLP-0 and TLP-5 respectively For TLP-2 and TLP-3 large displacementindicates a large pitch exciting force The yaw exciting forceexhibited the same patterns as the pitch exciting forcehowever the values were the same for the yaw exciting forceTherefore this result can be ignored

Overall the exciting force reduced when we did notconsider the spoke effect in the translation direction whichis the opposite for rotation The same situation occurred inTLP-2 and TLP-3 In this wave direction the pitch excitingforce was the largest whereas the other forces were so smallthat they could be neglected

For B66 (yaw-yaw) TLP-2was the largest in all themodesand could be used to improve yaw damping For the excitingforcematrices the surge exciting forcewas similar clearly thepitch and yaw exciting force of TLP-3 did not change Martin[13] assumed yaw instability in his model because the spokesize effect on the yaw-yaw damping is larger and improvesmotion performance

Shock and Vibration 7

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A11

0

2000

4000

6000

8000

10000

05 1 15 2 250120596 (rads)

(a) A11 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A15

05 1 15 2 250120596 (rads)

times105

minus25

minus2

minus15

minus1

minus05

0

(b) A15 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A33

0

500

1000

1500

2000

2500

3000

05 1 15 2 250120596 (rads)

(c) A33 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A42

times105

0

05

1

15

2

25

05 1 15 2 250120596 (rads)

(d) A42 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A55

times106

0

1

2

3

4

5

6

7

8

05 1 15 2 250120596 (rads)

(e) A55 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A66

times105

05 1 15 2 250120596 (rads)

0

1

2

3

4

(f) A66 added mass

Figure 6 Added mass matrices

8 Shock and Vibration

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B11

05 1 15 2 250120596 (rads)

0

500

1000

1500

2000

2500

3000

(a) B11 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B15

times104

minus3

minus25

minus2

minus15

minus1

minus05

0

05 1 15 2 250120596 (rads)

(b) B15 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B33

minus10

0

10

20

30

40

50

60

70

05 1 15 2 250120596 (rads)

(c) B33 damping matrices

times104

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B42

minus05

0

05

1

15

2

25

3

05 1 15 2 250120596 (rads)

(d) B42 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B55

times105

minus1

0

1

2

3

4

5

05 1 15 2 250120596 (rads)

(e) B55 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B66

05 1 15 2 250120596 (rads)

minus05

0

05

1

15

2

25

(f) B66 damping matrices

Figure 7 Damping matrices

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

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Shock and Vibration 7

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A11

0

2000

4000

6000

8000

10000

05 1 15 2 250120596 (rads)

(a) A11 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A15

05 1 15 2 250120596 (rads)

times105

minus25

minus2

minus15

minus1

minus05

0

(b) A15 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A33

0

500

1000

1500

2000

2500

3000

05 1 15 2 250120596 (rads)

(c) A33 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A42

times105

0

05

1

15

2

25

05 1 15 2 250120596 (rads)

(d) A42 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A55

times106

0

1

2

3

4

5

6

7

8

05 1 15 2 250120596 (rads)

(e) A55 added mass

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

A66

times105

05 1 15 2 250120596 (rads)

0

1

2

3

4

(f) A66 added mass

Figure 6 Added mass matrices

8 Shock and Vibration

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B11

05 1 15 2 250120596 (rads)

0

500

1000

1500

2000

2500

3000

(a) B11 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B15

times104

minus3

minus25

minus2

minus15

minus1

minus05

0

05 1 15 2 250120596 (rads)

(b) B15 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B33

minus10

0

10

20

30

40

50

60

70

05 1 15 2 250120596 (rads)

(c) B33 damping matrices

times104

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B42

minus05

0

05

1

15

2

25

3

05 1 15 2 250120596 (rads)

(d) B42 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B55

times105

minus1

0

1

2

3

4

5

05 1 15 2 250120596 (rads)

(e) B55 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B66

05 1 15 2 250120596 (rads)

minus05

0

05

1

15

2

25

(f) B66 damping matrices

Figure 7 Damping matrices

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

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International Journal of

8 Shock and Vibration

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B11

05 1 15 2 250120596 (rads)

0

500

1000

1500

2000

2500

3000

(a) B11 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B15

times104

minus3

minus25

minus2

minus15

minus1

minus05

0

05 1 15 2 250120596 (rads)

(b) B15 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B33

minus10

0

10

20

30

40

50

60

70

05 1 15 2 250120596 (rads)

(c) B33 damping matrices

times104

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B42

minus05

0

05

1

15

2

25

3

05 1 15 2 250120596 (rads)

(d) B42 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B55

times105

minus1

0

1

2

3

4

5

05 1 15 2 250120596 (rads)

(e) B55 damping matrices

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

B66

05 1 15 2 250120596 (rads)

minus05

0

05

1

15

2

25

(f) B66 damping matrices

Figure 7 Damping matrices

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

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Shock and Vibration

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DistributedSensor Networks

International Journal of

Shock and Vibration 9

0

50

100

150

200

250

300

350

400Su

rge e

xciti

ng fo

rces

(0∘)

05 1 15 2 250120596 (rads)

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

(a) Surge exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

2

4

6

8

10

12

14

Roll

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(b) Roll exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

1000

2000

3000

4000

5000

6000

7000

Pitc

h ex

citin

g fo

rces

(0∘)

05 1 15 2 250120596 (rads)

(c) Pitch exciting force

TLP-0TLP-1TLP-2

TLP-3TLP-4TLP-5

0

01

02

03

04

05

06

07

08

Yaw

exci

ting

forc

es (0

∘)

05 1 15 2 250120596 (rads)

(d) Yaw exciting force

Figure 8 Exciting force matrices

312 RAO Result The RAO of TLP models with varyingdimensions were obtained from FAST (Figures 9 10 and11) We first considered the spoke dimension effect on TLP-0TLP-1 and TLP-4TLP-5 A comparison between the TLP-0and TLP-1 results shows that the trend and curve are almostthe same The spoke dimension effect on the surge RAO at ahigh frequency is insignificant In the lower frequency rangethe results of TLP-0 and TLP-5 were larger than those of TLP-1 and TLP-4 In the higher frequency range the trend was theopposite in fact we focused on the higher frequency rangeonly In this portion TLP-0 had the maximum RAO valueand TLP-5 was larger than TLP-1 and TLP-4 This findingindicates that considering the spoke dimension effect couldenhance RAO values In the roll direction the result of TLP-0was smaller than that of TLP-1 thereby indicating that whenthe spoke dimension effect is not considered the result islower than the real value In the lower frequency range the

sway RAO values of TLP-0 and TLP-5 were larger than thoseof TLP-1 and TLP-4 At high frequencies the trend was theopposite At the same time the frequency range of TLP-5 andTLP-4 was smaller than that of TLP-0 and TLP-1 this resultwas possible because of the larger displacement for TLP-0 andTLP-1 In the higher frequency range themaximum value forTLP-0 was 50 of TLP-1 For the pitch RAO value TLP-1 andTLP-4 were larger than TLP-0 and TLP-5 at low frequenciesAt higher frequencies TLP-1 and TLP-4 were larger thanTLP-0 and TLP-5 The same situation for frequency rangeoccurred in the pitch RAO where the maximum frequencypoints for TLP-1 and TLP-4 were larger than those for TLP-0 and TLP-5 In the heave RAO value their trends weresimilar The gradient for TLP-1 was larger than that for TLP-0 and the same situation occurred for the TLP-4 and TLP-5 models A smaller displacement had a smaller yaw RAOvalue The TLP-1 value was smaller than the TLP-0 value

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

10 Shock and Vibration

TLP-0TLP-1

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-0 and TLP-1

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(b) Roll TLP-0 and TLP-1

0

002

004

006

008

01

RAO

of s

way

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(c) Sway TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of p

itch

TLP-0TLP-1

(d) Pitch TLP-0 and TLP-1

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-0TLP-1

(e) Heave TLP-0 and TLP-1

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-0TLP-1

(f) Yaw TLP-0 and TLP-1

Figure 9 TLP-0 and TLP-1 RAO

thereby indicating that a considerable dimensional effect isbetter for yaw response

In a similar displacement ratio for TLP-2 and TLP-3 thedisplacement of TLP-3 was larger than that of TLP-2 Themaximum surge RAO value for TLP-3 was larger than thatfor TLP-2 For the sway RAO values at higher frequenciesthe value of TLP-3 was higher than that of TLP-2 reaching60 Heave RAO were similar during 04 radss to 12 radsthe TLP-1rsquos value is smallest and TLP-2rsquos value is biggestand TLP-2rsquos displacement for spoke part is biggest The rollRAO values were similar at lower frequency but at higher

frequency the maximum of TLP-2 was larger than that ofTLP-3 For the pitch the RAOof TLP-3was larger than that ofTLP-2 regardless of frequency For sway and pitch RAO theresult of TLP-3 is larger than that for TLP-2 at any frequencyFor the heave the TLP-1rsquos value is smallest and TLP-2rsquos valueis biggest for the yaw RAO TLP-4rsquos value is smallest for theroll RAO the result of TLP-3 is smaller than that of TLP-2

32 Model Test Result The mooring system is not thepoint of this research The mooring system is assumedto be undamaged under various operating conditions and

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

TLP-4TLP-5

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

0005

001

0015

RAO

of r

oll

TLP-4TLP-5

(b) Roll TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

002

004

006

008

01

RAO

of s

way

TLP-4TLP-5

(c) Sway TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

0

002

004

006

008

01

RAO

of p

itch

(d) Pitch TLP-4 and TLP-5

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-4TLP-5

(e) Heave TLP-4 and TLP-5

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-4TLP-5

(f) Yaw TLP-4 and TLP-5

Figure 10 TLP-5 and TLP-4 RAO

may be permanently fixed to a system In reality con-sidering that a large external tension is applied on thetension legs the floating structure can be fixed tightly ina floating sea Thus the vertical rigidity of a structure isapproximately equal to infinity that is the experimentalresults of a vertical fixed system can be treated as accept-able however it can be movement in surge sway androtation direction Wind turbine was rotated at a presetspeed which remained unchanged just before the maximumwind speed Figure 12 shows the process for the modeltest

321 Combining a Typical Wind and a Regular Wave Threedifferent wind speeds were used in the experiments a ratedwind speed a maximum wind speed and an extreme windspeed The wind turbine operated normally on the first twowind speeds However the wind turbine ceased to operate atthe extreme wind speed Table 4 shows the used parametersof a wind speed and an external wave

Figure 13(a) shows the surge displacement result underthe rated wind speed coupled wave loads The maximumsurge displacement results for model-TLP-1 and model-TLP-2 were 25 and 1mm respectively Considering the whole

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

TLP-1TLP-2

TLP-3TLP-4

0

02

04

06

08

1RA

O o

f sur

ge

02 04 06 08 1 12 14 16 18 20120596 (rads)

(a) Surge

0

0005

001

0015

RAO

of r

oll

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(b) Roll

0 02 04 06 08 1 12 14 16 18 20

002

004

006

008

01

RAO

of s

way

120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(c) Sway

0

002

004

006

008

01

RAO

of p

itch

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(d) Pitch

02 04 06 08 1 12 14 16 18 20120596 (rads)

0

001

002

003

RAO

of h

eave

TLP-1TLP-2

TLP-3TLP-4

(e) Heave

0

002

004

006

RAO

of y

aw

02 04 06 08 1 12 14 16 18 20120596 (rads)

TLP-1TLP-2

TLP-3TLP-4

(f) Yaw

Figure 11 TLP-1 TLP-2 TLP-3 and TLP-4 RAO

displacement response in 90 s for the two models the resultof model-TLP-1 was significantly higher than that of model-TLP-2 Figure 13(b) shows the surge displacement responseunder the maximum wind speed coupled wave loads within40 s the result of model-TLP-2 was significantly lower thanthat of model-TLP-1 while in the remaining 50 s intervalthe results of model-TLP-2 were greater than those formodel-TLP-1 In Figure 13(c) the results of model-TLP-2were less than model-TLP-1 maximum displacement Theresult in Figure 13 indicates that spoke dimension affectssurge displacement in rated and extreme load conditions and

themaximumdisplacement ofmodel-TLP-2was less than theresults of model-TLP-1

322 Combining a Typical Wind and an Irregular WaveThis section examines the dynamic response of a normaloperating wind turbine under an irregular wave An irregularwave referred to as a ldquoPierson-Moskowitz sea spectrumrdquo (iea fully developed spectrum which is abbreviated as ldquoPMspectrardquo) was selected for these testing scenarios [22] PMspectrum was derived based on the measured data of theNorth Atlantic Ocean the data can be applied to simulate

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 13

(a) Combining wind and wave (b) Wave

Figure 12 Model test process

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

025

02

015

01

005

0

minus005

minus01

minus015

minus02

minus025

1

2

Model-TLP-Model-TLP-

(a) Rated wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

03

02

01

0

Model-TLP-1Model-TLP-2

(b) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

minus01

minus02

minus03

minus04

03

04

02

01

0

Model-TLP-1Model-TLP-2

(c) Extreme wind load condition

Figure 13 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Shock and Vibration

0 10 20 30 40 50 60 70 80

Time (s)

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

15

1

05

0

minus05

minus1

minus15

(a) Maximum wind load condition

0 10 20 30 40 50 60 70 80

Time (s)

08

06

02

04

0

minus02

minus04

minus06

minus08

Surg

e disp

lace

men

t (10

mm

)

Model-TLP-1Model-TLP-2

(b) Extreme wind load condition

Figure 14 Model-TLP-1 and model-TLP-2 surge displacement for different load conditions

Table 4 Combining a typical wind and a regular wave

Load Rated wind Maximum wind Extreme windWave height (m) 0038 0075 015Period (s) 3162 2672 25Wind speed(ms) 126 276 552

Wind turbineoperationsituation

Operation Operation Parked

fully developed waves in an infinite-wave region of the seaPM spectrum has been widely applied in oceanographicengineering because of several advantages such as the empir-ical spectra sufficient references the method of reasonableanalysis and convenience When we compared this situationwith the aforementioned coupled operating conditions theconditions of wind-wave coupled operation fit well withtheir practical conditionsTheir related parameters are shownin Table 5

The results after the use of the irregular wave PMspectrum are shown in Figure 14 For maximum surge dis-placement the result of model-TLP-2 was less than that ofmodel-TLP-1 undermaximumwind speed coupling irregularwave conditions as shown in Figure 14(a) In Figure 14(b)the extremewind speed coupling results under irregular waveconditions in model-TLP-2 were significantly lower than theresults of model-TLP-1 According to the previous modeldata the spoke length of model-TLP-1 increased by 15compared with that of model-TLP-2 but the spoke diametermodel-TLP-2 was three times that of model-TLP-1 A com-prehensive comparison of the surge displacement load com-bination for the two responses under typical wind conditionsand regular wave coupling conditions showed that model-TLP-1 surge displacement was significantly higher than thatof model-TLP-2 Under typical wind conditions and irregular

Table 5 Combination of a typical wind and an irregular wave

Wind Maximum wind Extreme windWave height (m) 006 015Period (s) 103 134Wind speed (ms) 276 552Operation situation Operation Parked

wave coupling conditions model-TLP-1 surge displacementwas significantly higher than that of model-TLP-2 in ratedwind speeds and extreme wind speeds However at maxi-mum wind speed the result of model-TLP-1 was less thanthat of model-TLP-2 at an interval Data show that the scaleeffect of spoke helps to reduce surge displacement responsewhile surge displacement response is sensitive to the spokediameter

33 Model Test and Numerical Result Comparison As seenformerly in Table 3 and Figure 5 model-TLP-1 and model-TLP-2 have the same draft diameter and draft height in thespoke distance model-TLP-1 is 117 times as model-TLP-2rsquosdate in the spoke diameter model-TLP-2 is 3 times as model-TLP-1rsquos date To the spoke displacement model-TLP-1 is 13of model-TLP-2 Based on the model test result in a typicalwind and an irregular wave condition regardless of extremewind (wave period is 103 s) andmaximumwind (wave periodis 134 s) it is obvious that model-TLP-2 surge displacementis smaller thanmodel-TLP-1rsquos result In particular in extremewind load case model-TLP-2 surge displacement reduces33 comparing with model-TLP-1 In a typical wind and aregular wave condition model-TLP-1 surge displacement issmaller than model-TLP-2 in extreme wind (wave period is2672 s) and maximum wind (wave period is 25 s) conditionbecause in the model test spoke part cannot be deletedabsolutely but only can beminimized Back to the surge RAOresult of simulation in the lower frequency range the result

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 15

for TLP model considering spoke dimension is bigger thanmodel result without considering spoke dimension In thehigher frequency range the trend was the opposite Com-paring the simulation and model test result this conclusionhas been verified And model test shows spoke dimensionincrease to reduce platform movement to improve turbineperformance

4 Conclusions

In this study the spoke dimension effect in TLP models wasevaluated and tested for the first time Results indicate thatdynamic characteristics improve when spoke dimension isconsideredThis finding verifies the predictions of Bachynskiand Moan [9] and Matha [12] in which spokes or pontoonsenhance motion behavior The primary effect of spoke onthe dynamic characteristics is that the spoke dimensioneffect increases the added mass matrices This effect wasmost evident in the yaw-yaw direction where the M66value increased from zero to E5 Moreover A42 and A15values were not neglected For the same spoke dimensionratio when the total displacement increases the added massmatrices also increase Damping did not always increaseand became constant at some point For the off-diagonaltranslation matrices the effect of the spoke dimension ondampingwas positive At the samedisplacement ratio the off-diagonal coefficient did not change at any point The excitingforce reduced when the spoke effect was not considered inthe translation direction and the trend was opposite to therotation directionWhen considering spoke dimension to thesurge RAO and sway RAO in the lower frequency rangethe result for model considering spoken dimension is smallerthan those model without consider spoken dimension in thehigher frequency range the trend was the opposite and themodel test has been done to verify surge RAO conclusion Forthe pitch and heave RAO value at low frequencies the resultfor model considering spoke dimension is larger than modelwithout considering spoke dimension in the higher fre-quency range the trend was the opposite A smaller displace-ment had a smaller yaw RAO value thereby indicating thata considerable dimensional effect is better for yaw responseAt the same displacement ratio sway pitch and roll RAOweremore sensitive to displacementModel tests showed thatthe scale spoke increase helps reduce platform movementto improve turbine performance In the specific conditionsthe surge displacement was more sensitive to the spokediameter

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research is supported by the Shen Zhen StrategicDevelopment for New Industry Foundation (Grant no JCYJ-20150513151706576)The financial support is greatly acknowl-edged

References

[1] A Athanasia and A B Genachte ldquoDeep offshore and newfoundation conceptsrdquo Energy Procedia vol 35 no 41 pp 198ndash209 2013

[2] C M Wang T Utsunomiya S C Wee and Y S ChooldquoResearch on floating wind turbines a literature surveyrdquo IESJournal Part A Civil amp Structural Engineering vol 3 no 4 pp267ndash277 2010

[3] K Suzuki H Yamaguchi M Akase et al ldquoInitial design oftension leg platform for offshore wind farmrdquo Journal of FluidScience amp Technology vol 6 no 3 pp 372ndash381 2011

[4] K ShimadaMMiyakawa T Ohyama et al ldquoPreliminary studyon the optimum design of a tension leg platform for offshorewind turbine systemsrdquo Journal of Fluid Science amp Technologyvol 6 no 3 pp 382ndash391 2011

[5] S Butterfield W Musial J Jonkman P Sclavounos and LWayman ldquoEngineering challenges for floating offshore windturbinesrdquo in Proceedings of the Copenhagen Offshore WindConference amp Expedition vol 13 pp 25ndash28 CopenhagenDenmark 2005

[6] H-FWang and Y-H Fan ldquoPreliminary design of offshore windturbine tension leg platform in the south china seardquo Journal ofEngineering Science and Technology Review vol 6 no 3 pp 88ndash92 2013

[7] J E Withee Fully coupled dynamic analysis of a floatingwind turbine system [PhD thesis] Massachusetts Institute ofTechnology Cambridge Mass USA 2004

[8] E N Wayman P D Sclavounos S Butterfield J Jonkmanand W Musial ldquoCoupled dynamic modeling of floating windturbine systemsrdquoWear vol 302 pp 1583ndash1591 2006

[9] E E Bachynski and T Moan ldquoDesign considerations fortension leg platform wind turbinesrdquoMarine Structures vol 29no 1 pp 89ndash114 2012

[10] A Crozier Design and Dynamic Modeling of the Support Struc-ture for a 10mw Offshore Wind Turbine Institutt for Energi- ogProsessteknikk 2011

[11] A N Robertson and J M Jonkman ldquoLoads analysis of severaloffshore floating wind turbine conceptsrdquo in Proceedings of the21st International Offshore and Polar Engineering Conference(ISOPE rsquo11) pp 443ndash450 Maui Hawaii USA June 2011

[12] DMathaModel Development and Loads Analysis of an OffshoreWind Turbine on a Tension Leg Platform with a Comparison toOther Floating Turbine Concepts April 2009 National Renew-able Energy Laboratory (NREL) Golden Colo USA 2010

[13] H R Martin Development of a Scale Model Wind Turbinefor Testing of Offshore Floating Wind Turbine Systems MaineMaritime Academy 2011

[14] A J Goupee B Koo R W Kimball K F Lambrakos and HJ Dagher ldquoExperimental comparison of three floating windturbine conceptsrdquo Journal of Offshore Mechanics and ArcticEngineering vol 136 no 2 Article ID 020906 pp 467ndash4762012

[15] 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 amp Sustainable Energy vol 5 no 2Article ID 023116 2013

[16] N Ren Y Li and J Ou ldquoThewind-wave tunnel test of a tension-leg platform type floating offshore wind turbinerdquo Journal ofRenewable amp Sustainable Energy vol 4 no 6 Article ID 0631172012

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

16 Shock and Vibration

[17] N Ren Y Li and J Ou ldquoThe effect of additionalmooring chainson the motion performance of a floating wind turbine with atension leg platformrdquo Energies vol 5 no 4 pp 1135ndash1149 2012

[18] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-mw reference wind turbine for offshore system devel-opmentrdquo Tech Rep National Renewable Energy LaboratoryGolden Colo USA 2009

[19] H-F Wang Y-H Fan and Y Liu ldquoDynamic analysis of onetype of tension leg platform for offshore wind turbinerdquo Journalof Power Technologies vol 94 no 1 pp 42ndash49 2014

[20] F Hua B Fan L U Yan and J Q Wang ldquoAn empirical relationbetween sea wave spectrum peak period and zero-crossingperiodrdquo Advances in Marine Science vol 22 no 1 pp 16ndash222004

[21] T Zambrano T Maccready T Kiceniuk D G Roddier and CA Cermelli ldquoDynamic modeling of deepwater offshore windturbine structures in Gulf of Mexico storm conditionsrdquo inProceedings of the 25th International Conference on OffshoreMechanics and Arctic Engineering pp 629ndash634 AmericanSociety of Mechanical Engineers Hamburg Germany June2006

[22] J Jonkman and D Matha ldquoQuantitative comparison of theresponses of three floating platformsrdquo Australian HistoricalStudies vol 86 no 41 p 8 2010

[23] httpcivilhiteducnshowphpid=679

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of