Research Article Mooring Line Damping Estimation …downloads.hindawi.com/journals/tswj/2014/840283.pdfResearch Article Mooring Line Damping Estimation for a Floating Wind Turbine

Research ArticleMooring Line Damping Estimation for a Floating Wind Turbine

Dongsheng Qiao1 and Jinping Ou12

1 Deepwater Engineering Research Center Dalian University of Technology Dalian 116024 China2 State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology Dalian 116024 China

Correspondence should be addressed to Dongsheng Qiao qds903163com

Received 28 May 2014 Revised 10 August 2014 Accepted 13 August 2014 Published 27 August 2014

Academic Editor Pradeep Lancy Menezes

Copyright copy 2014 D Qiao and J Ou This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The dynamic responses ofmooring line serve important functions in the station keeping of a floating wind turbine (FWT)Mooringline damping significantly influences the global motions of a FWTThis study investigates the estimation of mooring line dampingon the basis of the National Renewable Energy Laboratory 5MW offshore wind turbine model that is mounted on the ITI Energybarge A numerical estimation method is derived from the energy absorption of a mooring line resulting from FWT motion Themethod is validated by performing a 180 scale model test Different parameter changes are analyzed for mooring line dampinginduced by horizontal and vertical motionsThese parameters include excitation amplitude excitation period and drag coefficientResults suggest that mooring line damping must be carefully considered in the FWT design

1 Introduction

Renewable wind energy has attracted the attention of manycountries and the development has been from onshore tooffshore Nowadays the occupied proportion of offshorewind energy is growing in the wind energy industry Aswater depth increases the foundations of offshore windturbines change from the traditional bottom-mounted sub-structures to floating support platforms because of economicreasonsThe first operational floating offshore wind turbine isHywind which works at a water depth of 220m in the NorthSea of Norway [1] Then many scholars proposed numeroustypes of floating wind turbine (FWT) mainly referencingfrom the offshore oil and gas industry [2ndash4] Three primaryconcepts are classified according to the means of achievingstatic stability in pitch and roll direction tension leg platform(TLP) spar buoy and barge [5] Some hybrid concepts arealso proposed these concepts include the semi-submersiblefloating platform system [6] and combined tension leg-mooring line system [7] These FWT concepts involve themooring system for station keeping

Linear frequency domain analysis is commonly employedin the preliminary FWT design which is the same as that

in the offshore oil and gas industry However the turbinemass must be added in the global body mass matrix and thecontributions of rotor aerodynamics and gyroscope must beadded in the global restoring and damping matrices Similarstudies investigated different types of FWT such as TLP[8] spar buoy [9] and barge [10] The mooring system issimplified as a linear spring and the stiffness is derived fromthemean offset of a platform in the restoring properties of themooring system Nonlinear dynamic characteristics cannotbe considered in the linear frequency domain analysis

Some scholars studied the global responses of FWT intime domain in which nonlinear dynamic characteristicscan be considered The key issues include the hydrodynamicloading the dynamic coupling between the platform andwind turbine motions and the dynamic coupling betweenthe floating platform and mooring systems However mostscholars focused on the dynamic coupling between the plat-form and wind turbine motions Fulton et al [11] andWithee[12] applied different coupled models between the platformmotion and hydrodynamic loading of TLP designs for 5-MWand 15-MWwind turbines in time domain respectivelyJonkman [13] established a fully coupled time domain aero-hydro-servo-elastic model to analyze the dynamics of FWT

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 840283 10 pageshttpdxdoiorg1011552014840283

2 The Scientific World Journal

including linear hydrostatic restoring nonlinear viscousdrag and the added mass and damping contributions fromlinear wave radiation and quasistatic mooring line module

The mooring lines in these models are treated as static orquasistatic module which ignores the dynamic characteris-tics of a mooring line However the dynamics of a mooringline should not be ignored when the water depth increasesand the reason is that the mooring line damping couldsignificantly affect the motion responses of platform [14 15]

The mooring line damping for a traditional catenarymooring system results from the line hydrodynamic dragwith possible vortex-induced vibration line internal forcesand line friction on the seabed Hydrodynamic drag andfriction damping are significantly affected by the motionof a floating platform aside from the internal dampingcaused by material properties Many studies investigatedthe contribution of mooring line damping to the globalresponses of a deepwater floating platform such as thequasistaticmodel series ofmooring damping calculation [16ndash19]Webster [20] used a time domain finite element approachfor the parametric study of mooring line damping inducedby both horizontal and vertical top end oscillations and theparameters used in this analysis step from a dimensionalanalysis Brown and Mavrakos [21] presented a comparativestudy on mooring line dynamics and damping based on bothtime domain and frequency domain methods Thomas andHearn [22] indicated that the out-of-plane seabed frictioncan be negligible and that in-plane effects can influence thepeak dynamic tension Kitney and Brown [23] presented twodifferent scale experiments to validate the results of otherscholars Qiao andOu [24] calculated the hydrodynamic dragdamping of single-component mooring line and obtainedlinearized damping coefficients

However the mooring system design for FWT is dif-ferent from the deepwater floating platform The typicalinstallation water depth of FWT is substantially shallow (ielt300m) whereas the deepwater floating platform is largerthan 500m The top-end dynamics introduced by turbinerotation provides additional strain to the mooring systemThus the mooring damping estimation for FWT is necessaryto satisfy the requirements for a safe station keeping Theresults contribute to the coupled model between the FWTand itsmooring system such as adding themooring dampingin the linear frequency domain analysis

This study investigates the estimation of mooring linedamping on the basis of National Renewable Energy Labo-ratory 5MW offshore wind turbine model that is mountedon the ITI Energy barge A numerical estimation methodis derived from the energy absorption of a mooring lineresulting from FWTmotion Different parameter changes areanalyzed for mooring line damping induced by horizontaland vertical motions The results of this study could helpimprove the mooring system design of FWT

2 Numerical Model

21 Motion Governing Equation of FWT The FWT is atraditional system with heavy nacelle and rotor on thetop and the whole structural stability finally depends on

Wave Current

Hydrodynamic loads (AQWA program)

Wind loads(Jonkman 2007 [2])

Motion governing equation of FWT Mooring force (ABAQUS program)

Global response

Figure 1 Computational sketch

the mooring system Therefore the hydrodynamic analysiscoupled with wind loads and mooring system should beconsidered

The FWT support platform is simplified as a six rigid-body modes of motion The equations of motion are asfollows

(119872119904+119872119889) (119905) = 119865

119908(119905) + 119865

119888(119905) + 119865sd (119905) + 119865

119898(119905)

+ 119865ℎ(119905) + 119865

119896(119905) + 119865

119889(119905) + 119865

119901(119905)

(1)

where (119905) is the acceleration vector 119872119904is the matrices of

structural massinertia 119872119889is the added massinertia 119865

119908(119905)

is the wind force 119865119888(119905) is the current force 119865sd(119905) is the drift

force 119865119898(119905) is the mooring forces 119865

ℎ(119905) is the hydrostatic

forces119865119896(119905) is thewave Froude-Krylov force119865

119889(119905) is thewave

diffraction force 119865119901(119905) is the damping force

The coupled model is calculated by our program inMATLAB and the simplified computational sketch is shownin Figure 1

The wave loads are calculated through panel methodwhich is based on potential flow theory and the softwareof AQWA Program [25] is used The current loads areconsidered as static force which could be also calculatedby the software of AQWA Program The wind loads mainlydepend on the blade aerodynamic characters and the controlstrategy of the turbine and the wind loads information ischosen from the research results by Jonkman [2]The specificequations for calculating wind wave and current loads areomitted here and these could be referenced by Ren [26]

The dynamicmooring forces are considered here and thespecific descriptions are shown in Section 22

22 Governing Equation of the Mooring Line The mooringline is generally presumed to be a completely flexible compo-nent duringmotion response analysisThe followingmotion-governing equation was proposed by Berteaux [27]

119898

120597

120597119905

= Dn + Dt + In + 119865It +120597

1205971199041015840+ (2)

Dn =1

2

120588119908119862Dn119863

10038161003816100381610038161003816Δ119899

10038161003816100381610038161003816Δ119899

(3)

The Scientific World Journal 3

AbsorberLED

Tensionsensor

Water level

Wave maker

60m

2m

Figure 2 A sketch of model setup in wave tank

Dt =1

2

120588119908119862Dt120587119863Δ119905

10038161003816100381610038161003816Δ119905

10038161003816100381610038161003816

(4)

In =1

4

1205881199081205871198632

119862mn (120597 119880119899

120597119905

minus

120597119899

120597119905

) (5)

It =1

4

1205881199081205871198632

119862mt (120597119905

120597119905

minus

120597119905

120597119905

) (6)

where119898 is the mass of the mooring line (per unit length) is the velocity vector of the mooring line Dn is the normaldrag force of the mooring line (per unit length) Dt is thetangential drag force of the mooring line (per unit length)In is the normal inertia force of the mooring line (per unitlength) 119865It is the mooring line tangential inertia forces (perunit length) 1205971205971199041015840 is the partial derivative of mooring linetension per arc length of extended mooring line 1199041015840 and itdescribes the tension change of a mooring line elementarylength 119889119904

1015840 is the net weight of the mooring line 120588119908is the

fluid density119862Dn is the normal drag coefficient119863 is the wirediameter Δ

119899is the relative normal velocity of the fluid 119862Dt

is the tangential drag coefficient Δ119905is the relative tangential

velocity of the fluid119862mn is the normal addedmass coefficient119880119899is the normal fluid velocity vector at the mooring line

direction 119899is the normal velocity vector of the mooring

line 119862mt is the tangential added mass coefficient 119905is the

tangential fluid velocity vector at the mooring line directionand

119905is the tangential velocity vector of the mooring line

As far as (2) is concerned themotion-governing equationis a strong complex time-varying nonlinear equation thatcan be solved using a numerical method In this paper thenonlinear finite element program ABAQUS is used for thesolution In ABAQUS the mooring line is simulated as ahybrid beam element and the Newton-Raphson iterativemethod is used to directly solve the nonlinear problem

23 Mooring Line Damping The energy dissipated 119864 duringone surge oscillation of period 120591 is given by

119864 = int

120591

0

119879119899

119889119902119899

119889119905

119889119905 (7)

where 119879119899is the component of tension in the direction 119899 and

119902119899is the instantaneous displacement in that direction

It is often convenient to express this damping in termsof an equivalent linear damping coefficient 119861

119899 Then the

instantaneous value of 119879119899can be given by

119879119899= 119861119899

119889119902119899

119889119905

(8)

If the oscillation is sinusoidal with an amplitude 1199020 and

a period 120591 the approximate absorbed energy 119864 is given by

119864 = int

120591

0

119879119899

119889119902119899

119889119905

119889119905 = 119861119899int

120591

0

[

119889119902119899

119889119905

]

2

119889119905 =

21205872

1199022

0119861119899

120591

(9)

Consequently the energy dissipated by the mooring lineduring one surge oscillation can be computed and then thelinear damping coefficient is obtained by

119861119899=

119864120591

212058721199022

0

(10)

The dissipated energy 119864 can be obtained by integratingthe work done by the upper tension during one surgeoscillation

Based on the nonlinear finite element dynamic analysisshown in Section 22 the mooring damping is calculated byour program in MATLAB

3 Experiment and Results

The validation of motion governing equation of FWT inSection 21 has been conducted by Ren [26] In his researchthe wind and wave loads are considered and the quasistaticmooring line module is used Due to the fact that the mainaim of the analysis in this paper is to estimate the mooringdamping of FWT the following experiment is designedwhich is only used to validate the numerical calculation ofdynamic mooring forces

31 Experimental Setup A prototype system consisting of acubic floater and two symmetrically arranged lines in 160mwater depth is model tested in the Nonlinear Wave TankState Key Laboratory of Coastal and Offshore EngineeringDalian University of Technology to validate the numericalsimulation method used in this study The wave tank hasa 60m length a 4m width and a 2m operating waterdepth The model scale is 180 by considering the waterdepth of the tank and the capability of the wave maker andother instruments A schematic of the wave tank and thetotal experimental system configuration used in the presentinvestigations are shown in Figure 2

The floater model has a 50 cm length a 50 cm width a20 cm height and a 2 cm thickness The height of the gravitycenter is 6 cm as referred to the underside of the box andthe draft is also 6 cm Two mooring lines are symmetricallyarranged at both sides under the box (Figure 2) The top endof the mooring line is connected to the underside of thebox through a tension sensor whereas the other end is fixedat the bottom of the tank with a horizontal span of 575mThe mooring line is modeled by a wire rope and the mainproperties are shown in Table 1


125 130 135 140 145 150 155 160 165200

250

300

350

400

450

Time (s)

Tens

ion

(kN

)

(a) 14 (s)

150 160 170 180 190200

250

300

350

400

Time (s)

Tens

ion

(kN

)

(b) 18 (s)

230 240 250 260 270260

280

300

320

340

360

Time (s)

Tens

ion

(kN

)

ExperimentNumerical simulation

(c) 25 (s)

270 280 290 300 310 320 330 340 350200

250

300

350

400

Time (s)

Tens

ion

(kN

)


(d) 35 (s)

Figure 3 Tension time series

02 025 03 035 04 045 0540

60

80

100

120

Frequency (rads)

Tens

ion

RAO

(kN

m)


Figure 4 RAO of the mooring line tension

Tension sensors are connected at the top between the linesand floater to measure the tensions acting on the mooringlines The customized FQ-1 type tension sensors each of20 kg capacity with a comprehensive accuracy of 003 FSare equipped with a digital signal recorder box for dataacquisition Three degrees of freedommotions (surge heaveand pitch) of the floater are measured by a CCD camerasystem that uses a high-speed camera sensing two LEDsignals (Figure 2) attached on the model

Table 1 Physical properties of mooring line

Item Prototype ExperimentLength (m) 500 625Diameter (mm) 160 2Submerged weight per unit length (Nm) 778 0122Axial stiffness (N) 151198649 2930

The system was tested at selected regular wave excitationfrequenciesThe wave period was varied from 14 s to 35 s andthe wave height was 6m all referred to the prototype scalebecause of the limited capacity of the wave generator in thelaboratory

32 Experimental Results The tension time series ofmooringlines were obtained on the basis of numerical simulationThe platform was tested at selected regular wave excitationfrequencies and the tension time series of the numericalsimulation and experimental mooring lines were compared(Figure 3) The response amplitude ratio (RAO) of the linetension to the fairlead motion is shown in Figure 4The RAOis defined as the mean double amplitude of the mooring linetension to the mean double amplitude of the fairlead motion

The results shown in Figures 3 and 4 validate thenumerical simulation The time series of the simulated and


(a)

10∘

10∘10∘

10∘

80∘80∘

80∘

y

xBarge

1

23

4

5

6 7

8

(b)

Figure 5 Mooring system configuration of FWT (a) ITI Energy barge (b) Mooring system layout

0

0

Horizontal coordinate (m)

Vert

ical

coor

dina

te (m

)

152535455565

758595105115125

minus500 minus400 minus300 minus200 minus100minus150

minus100

minus50

T0wH T0wH

Figure 6 Mooring line geometry with nondimensional tension

experimental mooring line tensions agree and the period isequal to thewave excitation periodTheRAOs of themooringtension in the numerical simulation and in the experimentalresults also agree These results suggest that the numericalsimulation method can be directly used in the followingstudy

4 Mooring System of FWT

41 Mooring System Layout TheNational Renewable EnergyLaboratory 5MW offshore wind turbine is used as thebasic model and details on the properties of the model areprovided in [28]The ITI Energy barge which was developed

Table 2 Properties of ITI Energy barge

Item ValueWidth times length (m) 40 times 40Draft (m) 4Water displacement (m3) 6000Mass including ballast (kg) 5452000CM location below still water level (m) 02818Roll inertia about CM (kgsdotm2) 726900000Pitch inertia about CM (kgsdotm2) 726900000Yaw inertia about CM (kgsdotm2) 1454000000Number of mooring lines 8Depth to fairleads anchors (m) 4 150Radius to fairleads anchors (m) 2828 4234Unstretched line length (m) 4733Line diameter (m) 00809Line mass density (kgm) 1304Line extensional stiffness (N) 589000000

by the Department of Naval Architecture and Marine Engi-neering at the Universities of Glasgow and Strathclyde withITI Energy [10] is used for the support structure The mainproperties of the ITI Energy barge are listed in Table 2

The mooring system consists of four (2 times 4) groups(Figure 5) The groups in the mooring system are positioned90∘ apart and the lines in each group are positioned 10∘ apart

42 Baseline of the Mooring System The number 1 mooringline is used as the baseline in this study The differentpretensions (119879

0) are performed in the numerical simulation

to investigate the behavior of the baseline In the nondi-mensional analysis 119879

0119908119867 represents the nondimensional

pretension and 119864119902119900119908119867 represents the nondimensional

damping of the mooring line Here 119908 is the weight perunit length of the line in water 119867 is the water depth 119861

119899


0 2 4 6 8 10 12 140

05

1

15

2

25

001002003

004005006

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)

Nondimensional pretension (T0wH)

(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

000300080015

002500350045

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)

Figure 7 Variation of mooring line damping with excitation amplitude (a) Horizontal motions (b) Vertical motions

Table 3 Mooring line damping estimation under different excitation amplitude

Nondimensionaltension (119879

0119908119867)

Nondimensional damping (119864119902119900119908119867)

Horizontal motion (1199020119867) Vertical motion (119902

0119867)

001 002 003 004 005 006 0003 0008 0015 0025 0035 004515 0002 0004 0008 0012 0018 0025 0019 0095 0266 0606 1053 161825 0006 0016 0033 0057 0086 0123 0027 0153 0477 1184 2144 335435 0014 0044 0092 0158 0246 0358 0035 0204 0648 1632 2970 465945 0025 0084 0177 0311 0492 0736 0043 0249 0796 2010 3662 572955 0039 0135 0299 0546 0905 1396 0050 0296 0951 2415 4434 697865 0057 0211 0484 0891 1398 1935 0062 0374 1213 3109 5682 874275 0078 0296 0656 1111 1594 2080 0078 0475 1553 3962 7005 1022185 0098 0360 0745 1180 1629 2086 0095 0588 1910 4733 7998 1104195 0111 0392 0767 1177 1606 2046 0112 0695 2220 5285 8549 11311105 0117 0396 0752 1145 1561 1992 0125 0779 2435 5570 8706 11228115 0115 0382 0721 1102 1510 1935 0135 0832 2546 5628 8587 10957125 0108 0359 0684 1054 1457 1879 0139 0853 2560 5520 8306 10575

is the mooring damping and 119902119900is the motions amplitude

Figure 6 shows a profile view of the baseline under differentpretensions

5 Parametric Variations

The influences of different parametric variations on themooring line damping are investigated according to thenumerical simulation method mentioned above The param-eters include excitation amplitude (119902

0) excitation period (120591)

and drag coefficient (119862119889)

The nondimensional 1199020119867 and (1205912120587)radic119892119867 are selected

in horizontal and vertical motions on the basis of the motionresponses analysis of ITI Energy barge and the nondimen-sional analysis respectively Only one parameter changes at atime while the other two parameters are kept unchanged

For the baseline (number 1) the initial nondimensionalparameters are 119879

0119908119867 = 25 119902

0119867 = 003 (horizontal

motions) 1199020119867 = 0008 (vertical motions) (1205912120587)radic119892119867 =

24 (horizontal motions) (1205912120587)radic119892119867 = 04 (verticalmotions) and 119862

119889= 12

51 Effects of ExcitationAmplitude Table 3 and Figure 7 showthe effects of excitation amplitude onmooring dampingwhenthe other parameters remain unchanged The characters ofthe curves are similar in the horizontal and vertical motionsThe nondimensional damping initially increases and thendecreases with increasing nondimensional pretension Thenondimensional damping increases with increasing excita-tion amplitude

For the horizontal motions the damping reaches a peakas the nondimensional pretension approaches 8 and the peak


Table 4 Mooring line damping estimation under different excitation period


0119908119867)


Horizontal period ((1205912120587)radic119892119867) Vertical period ((1205912120587)radic119892119867)

12 18 24 3 4 02 04 06 08 10

15 0027 0013 0008 0005 0003 0339 0104 0036 0020 0014

25 0126 0059 0035 0024 0015 0723 0165 0066 0037 0024

35 0356 0165 0097 0065 0039 1103 0220 0088 0049 0033

45 0709 0324 0188 0125 0074 1571 0270 0106 0059 0039

55 1228 0552 0317 0208 0122 2227 0322 0123 0068 0045

65 2044 0907 0513 0334 0192 3441 0406 0152 0083 0054

75 2813 1240 0697 0450 0257 4665 0518 0186 0100 0064

85 3223 1417 0792 0509 0289 5321 0644 0220 0116 0074

95 3349 1464 0815 0522 0294 5396 0765 0246 0129 0082

105 3291 1442 0800 0511 0287 5120 0860 0265 0137 0086

115 3164 1389 0768 0488 0273 4704 0921 0273 0140 0087

125 3019 1321 0728 0462 0257 4259 0947 0273 0138 0086

achieved for small amplitudes is slightly larger than thatfor large amplitudes For the vertical motions the damp-ing reaches a peak when the non-dimensional pretensionapproaches 10 and the peak achieved for small amplitudesis slightly larger than that for large amplitudes

The peak non-dimensional damping of the horizontalmotions is only approximately 10 that of the verticalmotions The reason is that for the baseline the mooringdamping under the horizontal and vertical excitations ismainly focused on the low and wave frequency rangesrespectively This phenomenon indicates that the mooringline damping in the wave frequency range should also beconsidered in the vertical motion prediction of the platform

For small pretension the non-dimensional damping (forboth horizontal and vertical motions) increases as the non-dimensional pretension increases This result corresponds toa nearly constant equivalent linear damping coefficient Forlarge pretension the non-dimensional damping (for bothhorizontal and vertical motions) becomes less dependenton the nondimensional pretension The reason is that themooring line geometry changes from slack to taut withincreasing pretension and themooring line length affects thedamping contributionWhen the nondimensional pretensionreaches 65 the total mooring line is lifted without lyingsegment Thus the damping becomes less dependent on thenondimensional pretension for large pretension

52 Effects of Excitation Period Table 4 and Figure 8 showthe effects of excitation period on mooring damping whenthe other parameters remain unchanged

The nondimensional damping decreases for both thehorizontal and vertical motions as the excitation periodincreases The reason is that the dynamic tension becomeslarger than the quasistatic tension under the high fre-quency (short period) excitation Meanwhile the mooring

line damping increases When the nondimensional periodincreases twice the nondimensional damping becomesapproximately 14 of that for all nondimensional pretensions(both horizontal and vertical motions)

When the nondimensional period is approximately 10the nondimensional damping for the horizontal excitation isapproximately 30 times that for the vertical excitation For thesame value of non-dimensional damping the correspondingnon-dimensional period for the horizontal excitation is inthe low frequency range while the corresponding non-dimensional period for the vertical excitation is in the wavefrequency rangeThis phenomenon further indicates that themooring line damping in the wave frequency range should beconsidered in the vertical motion prediction of the platform

53 Effects of Drag Coefficient Table 5 and Figure 9 show theeffects of drag coefficient on mooring damping when theother parameters remain unchanged The characters of thecurves show some differences in the horizontal and verticalmotions For the horizontal motions the nondimensionaldamping initially increases and then decreases with increas-ing nondimensional pretensionThe damping reaches a peakwhen the nondimensional pretension reaches 95 For thevertical motions the nondimensional damping increases asthe nondimensional pretension increases and reaches 125 inthis paper

With increasing drag coefficient the nondimensionaldamping almost linearly increases This phenomenon indi-cates that the drag coefficient should be prudently selected inthe design

6 Conclusions

Themooring line damping estimation is studied on the basisof the National Renewable Energy Laboratory 5MWoffshore


Table 5 Mooring line damping estimation under different drag coefficient


0119908119867)



119889)

119862119889= 12 119862

119889= 18 119862

119889= 24 119862

119889= 12 119862

119889= 18 119862

119889= 24

15 0008 0010 0012 0095 0122 014625 0033 0046 0058 0153 0212 026735 0092 0128 0165 0204 0286 036345 0177 0252 0326 0249 0351 044755 0299 0431 0563 0296 0420 053365 0484 0707 0929 0374 0531 067975 0656 0964 1271 0475 0676 086585 0745 1100 1453 0588 0833 106095 0767 1136 1501 0695 0979 1233105 0752 1117 1478 0779 1089 1358115 0721 1075 1423 0832 1155 1426125 0684 1022 1355 0853 1176 1441

0 2 4 6 8 10 12 140

1

2

3

4

121824

34

Nondimensional period

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

020406

0810


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)

Figure 8 Variation of mooring line damping with excitation period (a) Horizontal motions (b) Vertical motions

wind turbine model that is mounted on the ITI Energybarge The numerical estimation method is derived from theenergy absorption by a mooring line resulting from the FWTmotion The numerical method is validated by a 180 scalemodel test The following preliminary findings are obtained

(1) The nondimensional damping initially increases andthen decreases with increasing nondimensional pre-tension

(2) The nondimensional damping increases with increas-ing excitation amplitude The peak nondimensionaldamping of the horizontal motions is only approxi-mately 10 that for the vertical motionsThemooringline damping in the wave frequency range should beconsidered in the vertical motion prediction of theplatform

(3) For small pretension the nondimensional dampingincreases with increasing nondimensional preten-sion For large pretension the nondimensional damp-ing becomes less dependent on the nondimensionalpretension

(4) The nondimensional damping decreases for boththe horizontal and vertical motions with increas-ing excitation period When the nondimensionalperiod increases twice the nondimensional dampingbecomes approximately 14 of that for all nondimen-sional pretensions

(5) With increasing drag coefficient the nondimensionaldamping almost linearly increases

The mooring line damping is clearly a complex phe-nomenon that shows some differences in the horizontal andvertical excitations The estimation results for the mooring


0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)

Figure 9 Variation of mooring line damping with drag coefficient (a) Horizontal motions (b) Vertical motions

damping of a FWT can help in the motion prediction andmooring design of the FWT

Conflict of Interests

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

Acknowledgments

This paper was financially supported by National BasicResearch Program of China (Grant nos 2011CB013702 and2011CB013703) National Natural Science Foundation ofChina (Grant nos 51209037 and 51221961) China Post-doctoral Science Foundation Funded Project (Grant no2013T60287) and Fundamental Research Funds for theCentral Universities (Grant no DUT14RC(4)30)

References

[1] F G Nielsen T D Hanson and B Skaare ldquoIntegrated dynamicanalysis of floating offshore wind turbinesrdquo in Proceedings of the25th International Conference on Offshore Mechanics and ArcticEngineering (OMAE 06) Hamburg Germany June 2006

[2] J M Jonkman Dynamics modeling and loads analysis ofan offshore floating wind turbine [PhD thesis] Departmentof Aerospace Engineering Sciences University of ColoradoBoulder Colo USA 2007

[3] D Matha Model development and loads analysis of an offshorewind turbine on a tension leg platform with a comparisonto other floating turbine concepts [MS thesis] University ofStuttgart Stuttgart Germany 2009

[4] J Jonkman Definition of the Floating System for Phase IV ofOC3 NRELTP-500-47535 National Renewable Energy Labo-ratory (NREL) Golden Colo USA 2010

[5] J Jonkman and D Matha ldquoA quantitative comparison of theresponses of three floating platformsrdquo in Proceedings of the

European OffshoreWind Conference and Exhibition StockholmSweden September 2009

[6] D Roddier C Cermelli A Aubault and A Weinstein ldquoWind-Float a floating foundation for offshore wind turbinesrdquo Journalof Renewable and Sustainable Energy vol 2 no 3 Article ID033104 2010

[7] 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

[8] K H Lee Responses of floating wind turbines to wind and waveexcitation [MS thesis] Department of Ocean EngineeringMassachusetts Institute of Technology Cambridge Mass USA2005

[9] EWayman Coupled dynamics and economic analysis of floatingwind turbine systems [MS thesis] Department of Mechani-cal Engineering Massachusetts Institute of Technology Cam-bridge Mass USA 2006

[10] W J M J Vijfhuizen Design of a wind and wave powerbarge [M S thesis] Department of Naval Architecture andMechanical Engineering Universities of Glasgow and Strath-clyde Glasgow Scotland 2006

[11] G R Fulton D J Malcolm H Elwany W Stewart EMoroz and H Dempster ldquoSemi-submersible platform andanchor foundation system for wind turbine supportrdquo NRELSR500ndash40282 National Renewable Energy Laboratory (NREL)Golden Colo USA 2007

[12] J E Withee Fully coupled dynamic analysis of a floating windturbine system [PhD thesis] Department of Ocean Engineer-ing Massachusetts Institute of Technology Cambridge MassUSA 2004

[13] J M Jonkman ldquoDynamics of offshore floating wind turbines-model development and verificationrdquoWind Energy vol 12 no5 pp 459ndash492 2009

[14] M Hall B Buckham and C Crawford ldquoEvaluating the impor-tance of mooring line model fidelity in floating offshore windturbine simulationsrdquoWind Energy 2013

[15] L Sethuraman and V Venugopal ldquoHydrodynamic response ofa stepped-spar floating wind turbine numerical modelling andtank testingrdquo Renewable Energy vol 52 pp 160ndash174 2013


[16] EHuse ldquoInfluence ofmooring line damping upon rigmotionsrdquoin Proceedings of the Offshore Technology Conference HoustonTex USA May 1986

[17] E Huse ldquoNew developments in prediction of mooring systemdampingrdquo in Proceedings of the Offshore Technology ConferenceHouston Tex USA May 1991

[18] Y Liu and L Bergdahl ldquoImprovements on Husersquos model forestimating mooring cable induced dampingrdquo in Proceedings ofthe 17th International Conference on Offshore Mechanics andArctic Engineering (OMAErsquo 98) p 7 July 1998

[19] C Bauduin and M Naciri ldquoA contribution on quasi-staticmooring line dampingrdquo Journal of Offshore Mechanics andArctic Engineering vol 122 no 2 pp 125ndash133 2000

[20] W C Webster ldquoMooring-induced dampingrdquo Ocean Engineer-ing vol 22 no 6 pp 571ndash591 1995

[21] D T Brown and S Mavrakos ldquoComparative study on mooringline dynamic loadingrdquoMarine Structures vol 12 no 3 pp 131ndash151 1999

[22] D O Thomas and G E Hearn ldquoDeepwater mooring line dy-namics with emphasis on seabed interference effectsrdquo in Pro-ceedings of the Offshore Technology Conference Houston TexUSA May 1994

[23] N Kitney and D T Brown ldquoExperimental investigation ofmooring line loading using large and small-scale modelsrdquoJournal of Offshore Mechanics and Arctic Engineering vol 123no 1 pp 1ndash9 2001

[24] D Qiao and J Ou ldquoDamping calculation of a deepwatercatenary mooring linerdquo Journal of Vibration and Shock vol 30no 2 pp 24ndash31 2011

[25] AQWA User Manual AQWA-LINE Manual Century Dynam-ics Horsham UK 2006

[26] N X Ren Offshore wind turbine aerodynamic performance andnovel floating system [PhD thesis] Harbin Institute of Technol-ogy Harbin China 2011

[27] H O Berteaux Buoy Engineering Wiley Interscience NewYork NY USA 1976

[28] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-MW reference wind turbine for offshore system devel-opmentrdquo NRELTP 500-38060 National Renewable EnergyLaboratory (NREL) Golden Colo USA 2009

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


including linear hydrostatic restoring nonlinear viscousdrag and the added mass and damping contributions fromlinear wave radiation and quasistatic mooring line module

The mooring lines in these models are treated as static orquasistatic module which ignores the dynamic characteris-tics of a mooring line However the dynamics of a mooringline should not be ignored when the water depth increasesand the reason is that the mooring line damping couldsignificantly affect the motion responses of platform [14 15]

The mooring line damping for a traditional catenarymooring system results from the line hydrodynamic dragwith possible vortex-induced vibration line internal forcesand line friction on the seabed Hydrodynamic drag andfriction damping are significantly affected by the motionof a floating platform aside from the internal dampingcaused by material properties Many studies investigatedthe contribution of mooring line damping to the globalresponses of a deepwater floating platform such as thequasistaticmodel series ofmooring damping calculation [16ndash19]Webster [20] used a time domain finite element approachfor the parametric study of mooring line damping inducedby both horizontal and vertical top end oscillations and theparameters used in this analysis step from a dimensionalanalysis Brown and Mavrakos [21] presented a comparativestudy on mooring line dynamics and damping based on bothtime domain and frequency domain methods Thomas andHearn [22] indicated that the out-of-plane seabed frictioncan be negligible and that in-plane effects can influence thepeak dynamic tension Kitney and Brown [23] presented twodifferent scale experiments to validate the results of otherscholars Qiao andOu [24] calculated the hydrodynamic dragdamping of single-component mooring line and obtainedlinearized damping coefficients

However the mooring system design for FWT is dif-ferent from the deepwater floating platform The typicalinstallation water depth of FWT is substantially shallow (ielt300m) whereas the deepwater floating platform is largerthan 500m The top-end dynamics introduced by turbinerotation provides additional strain to the mooring systemThus the mooring damping estimation for FWT is necessaryto satisfy the requirements for a safe station keeping Theresults contribute to the coupled model between the FWTand itsmooring system such as adding themooring dampingin the linear frequency domain analysis

This study investigates the estimation of mooring linedamping on the basis of National Renewable Energy Labo-ratory 5MW offshore wind turbine model that is mountedon the ITI Energy barge A numerical estimation methodis derived from the energy absorption of a mooring lineresulting from FWTmotion Different parameter changes areanalyzed for mooring line damping induced by horizontaland vertical motions The results of this study could helpimprove the mooring system design of FWT

2 Numerical Model

21 Motion Governing Equation of FWT The FWT is atraditional system with heavy nacelle and rotor on thetop and the whole structural stability finally depends on

Wave Current

Hydrodynamic loads (AQWA program)

Wind loads(Jonkman 2007 [2])

Motion governing equation of FWT Mooring force (ABAQUS program)

Global response

Figure 1 Computational sketch

the mooring system Therefore the hydrodynamic analysiscoupled with wind loads and mooring system should beconsidered

The FWT support platform is simplified as a six rigid-body modes of motion The equations of motion are asfollows

(119872119904+119872119889) (119905) = 119865

119908(119905) + 119865

119888(119905) + 119865sd (119905) + 119865

119898(119905)

+ 119865ℎ(119905) + 119865

119896(119905) + 119865

119889(119905) + 119865

119901(119905)

(1)

where (119905) is the acceleration vector 119872119904is the matrices of

structural massinertia 119872119889is the added massinertia 119865

119908(119905)

is the wind force 119865119888(119905) is the current force 119865sd(119905) is the drift

force 119865119898(119905) is the mooring forces 119865

ℎ(119905) is the hydrostatic

forces119865119896(119905) is thewave Froude-Krylov force119865

119889(119905) is thewave

diffraction force 119865119901(119905) is the damping force

The coupled model is calculated by our program inMATLAB and the simplified computational sketch is shownin Figure 1

The wave loads are calculated through panel methodwhich is based on potential flow theory and the softwareof AQWA Program [25] is used The current loads areconsidered as static force which could be also calculatedby the software of AQWA Program The wind loads mainlydepend on the blade aerodynamic characters and the controlstrategy of the turbine and the wind loads information ischosen from the research results by Jonkman [2]The specificequations for calculating wind wave and current loads areomitted here and these could be referenced by Ren [26]

The dynamicmooring forces are considered here and thespecific descriptions are shown in Section 22

22 Governing Equation of the Mooring Line The mooringline is generally presumed to be a completely flexible compo-nent duringmotion response analysisThe followingmotion-governing equation was proposed by Berteaux [27]

119898

120597

120597119905

= Dn + Dt + In + 119865It +120597

1205971199041015840+ (2)

Dn =1

2

120588119908119862Dn119863

10038161003816100381610038161003816Δ119899

10038161003816100381610038161003816Δ119899

(3)


AbsorberLED

Tensionsensor

Water level

Wave maker

60m

2m


Dt =1

2

120588119908119862Dt120587119863Δ119905

10038161003816100381610038161003816Δ119905

10038161003816100381610038161003816

(4)

In =1

4

1205881199081205871198632

119862mn (120597 119880119899

120597119905

minus

120597119899

120597119905

) (5)

It =1

4

1205881199081205871198632

119862mt (120597119905

120597119905

minus

120597119905

120597119905

) (6)













119864 = int

120591

0

119879119899

119889119902119899

119889119905

119889119905 (7)




119899 Then the


119879119899= 119861119899

119889119902119899

119889119905

(8)



119864 = int

120591

0

119879119899

119889119902119899

119889119905

119889119905 = 119861119899int

120591

0

[

119889119902119899

119889119905

]

2

119889119905 =

21205872

1199022

0119861119899

120591

(9)


119861119899=

119864120591

212058721199022

0

(10)








125 130 135 140 145 150 155 160 165200

250

300

350

400

450

Time (s)

Tens

ion

(kN

)

(a) 14 (s)

150 160 170 180 190200

250

300

350

400

Time (s)

Tens

ion

(kN

)

(b) 18 (s)

230 240 250 260 270260

280

300

320

340

360

Time (s)

Tens

ion

(kN

)


(c) 25 (s)

270 280 290 300 310 320 330 340 350200

250

300

350

400

Time (s)

Tens

ion

(kN

)


(d) 35 (s)


02 025 03 035 04 045 0540

60

80

100

120

Frequency (rads)

Tens

ion

RAO

(kN

m)










(a)

10∘

10∘10∘

10∘

80∘80∘

80∘

y

xBarge

1

23

4

5

6 7

8

(b)


0

0


Vert

ical

coor

dina

te (m

)

152535455565

758595105115125


minus100

minus50

T0wH T0wH















119899


0 2 4 6 8 10 12 140

05

1

15

2

25

001002003

004005006

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

000300080015

002500350045

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)




0119908119867)



0119867)

001 002 003 004 005 006 0003 0008 0015 0025 0035 004515 0002 0004 0008 0012 0018 0025 0019 0095 0266 0606 1053 161825 0006 0016 0033 0057 0086 0123 0027 0153 0477 1184 2144 335435 0014 0044 0092 0158 0246 0358 0035 0204 0648 1632 2970 465945 0025 0084 0177 0311 0492 0736 0043 0249 0796 2010 3662 572955 0039 0135 0299 0546 0905 1396 0050 0296 0951 2415 4434 697865 0057 0211 0484 0891 1398 1935 0062 0374 1213 3109 5682 874275 0078 0296 0656 1111 1594 2080 0078 0475 1553 3962 7005 1022185 0098 0360 0745 1180 1629 2086 0095 0588 1910 4733 7998 1104195 0111 0392 0767 1177 1606 2046 0112 0695 2220 5285 8549 11311105 0117 0396 0752 1145 1561 1992 0125 0779 2435 5570 8706 11228115 0115 0382 0721 1102 1510 1935 0135 0832 2546 5628 8587 10957125 0108 0359 0684 1054 1457 1879 0139 0853 2560 5520 8306 10575










0119908119867 = 25 119902




119889= 12






0119908119867)



12 18 24 3 4 02 04 06 08 10

15 0027 0013 0008 0005 0003 0339 0104 0036 0020 0014

25 0126 0059 0035 0024 0015 0723 0165 0066 0037 0024

35 0356 0165 0097 0065 0039 1103 0220 0088 0049 0033

45 0709 0324 0188 0125 0074 1571 0270 0106 0059 0039

55 1228 0552 0317 0208 0122 2227 0322 0123 0068 0045

65 2044 0907 0513 0334 0192 3441 0406 0152 0083 0054

75 2813 1240 0697 0450 0257 4665 0518 0186 0100 0064

85 3223 1417 0792 0509 0289 5321 0644 0220 0116 0074

95 3349 1464 0815 0522 0294 5396 0765 0246 0129 0082

105 3291 1442 0800 0511 0287 5120 0860 0265 0137 0086

115 3164 1389 0768 0488 0273 4704 0921 0273 0140 0087

125 3019 1321 0728 0462 0257 4259 0947 0273 0138 0086










6 Conclusions





0119908119867)



119889)

119862119889= 12 119862

119889= 18 119862

119889= 24 119862

119889= 12 119862

119889= 18 119862

119889= 24

15 0008 0010 0012 0095 0122 014625 0033 0046 0058 0153 0212 026735 0092 0128 0165 0204 0286 036345 0177 0252 0326 0249 0351 044755 0299 0431 0563 0296 0420 053365 0484 0707 0929 0374 0531 067975 0656 0964 1271 0475 0676 086585 0745 1100 1453 0588 0833 106095 0767 1136 1501 0695 0979 1233105 0752 1117 1478 0779 1089 1358115 0721 1075 1423 0832 1155 1426125 0684 1022 1355 0853 1176 1441

0 2 4 6 8 10 12 140

1

2

3

4

121824

34


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

020406

0810


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)










0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)





Acknowledgments


References



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















AbsorberLED

Tensionsensor

Water level

Wave maker

60m

2m


Dt =1

2

120588119908119862Dt120587119863Δ119905

10038161003816100381610038161003816Δ119905

10038161003816100381610038161003816

(4)

In =1

4

1205881199081205871198632

119862mn (120597 119880119899

120597119905

minus

120597119899

120597119905

) (5)

It =1

4

1205881199081205871198632

119862mt (120597119905

120597119905

minus

120597119905

120597119905

) (6)













119864 = int

120591

0

119879119899

119889119902119899

119889119905

119889119905 (7)




119899 Then the


119879119899= 119861119899

119889119902119899

119889119905

(8)



119864 = int

120591

0

119879119899

119889119902119899

119889119905

119889119905 = 119861119899int

120591

0

[

119889119902119899

119889119905

]

2

119889119905 =

21205872

1199022

0119861119899

120591

(9)


119861119899=

119864120591

212058721199022

0

(10)








125 130 135 140 145 150 155 160 165200

250

300

350

400

450

Time (s)

Tens

ion

(kN

)

(a) 14 (s)

150 160 170 180 190200

250

300

350

400

Time (s)

Tens

ion

(kN

)

(b) 18 (s)

230 240 250 260 270260

280

300

320

340

360

Time (s)

Tens

ion

(kN

)


(c) 25 (s)

270 280 290 300 310 320 330 340 350200

250

300

350

400

Time (s)

Tens

ion

(kN

)


(d) 35 (s)


02 025 03 035 04 045 0540

60

80

100

120

Frequency (rads)

Tens

ion

RAO

(kN

m)










(a)

10∘

10∘10∘

10∘

80∘80∘

80∘

y

xBarge

1

23

4

5

6 7

8

(b)


0

0


Vert

ical

coor

dina

te (m

)

152535455565

758595105115125


minus100

minus50

T0wH T0wH















119899


0 2 4 6 8 10 12 140

05

1

15

2

25

001002003

004005006

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

000300080015

002500350045

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)




0119908119867)



0119867)

001 002 003 004 005 006 0003 0008 0015 0025 0035 004515 0002 0004 0008 0012 0018 0025 0019 0095 0266 0606 1053 161825 0006 0016 0033 0057 0086 0123 0027 0153 0477 1184 2144 335435 0014 0044 0092 0158 0246 0358 0035 0204 0648 1632 2970 465945 0025 0084 0177 0311 0492 0736 0043 0249 0796 2010 3662 572955 0039 0135 0299 0546 0905 1396 0050 0296 0951 2415 4434 697865 0057 0211 0484 0891 1398 1935 0062 0374 1213 3109 5682 874275 0078 0296 0656 1111 1594 2080 0078 0475 1553 3962 7005 1022185 0098 0360 0745 1180 1629 2086 0095 0588 1910 4733 7998 1104195 0111 0392 0767 1177 1606 2046 0112 0695 2220 5285 8549 11311105 0117 0396 0752 1145 1561 1992 0125 0779 2435 5570 8706 11228115 0115 0382 0721 1102 1510 1935 0135 0832 2546 5628 8587 10957125 0108 0359 0684 1054 1457 1879 0139 0853 2560 5520 8306 10575










0119908119867 = 25 119902




119889= 12






0119908119867)



12 18 24 3 4 02 04 06 08 10

15 0027 0013 0008 0005 0003 0339 0104 0036 0020 0014

25 0126 0059 0035 0024 0015 0723 0165 0066 0037 0024

35 0356 0165 0097 0065 0039 1103 0220 0088 0049 0033

45 0709 0324 0188 0125 0074 1571 0270 0106 0059 0039

55 1228 0552 0317 0208 0122 2227 0322 0123 0068 0045

65 2044 0907 0513 0334 0192 3441 0406 0152 0083 0054

75 2813 1240 0697 0450 0257 4665 0518 0186 0100 0064

85 3223 1417 0792 0509 0289 5321 0644 0220 0116 0074

95 3349 1464 0815 0522 0294 5396 0765 0246 0129 0082

105 3291 1442 0800 0511 0287 5120 0860 0265 0137 0086

115 3164 1389 0768 0488 0273 4704 0921 0273 0140 0087

125 3019 1321 0728 0462 0257 4259 0947 0273 0138 0086










6 Conclusions





0119908119867)



119889)

119862119889= 12 119862

119889= 18 119862

119889= 24 119862

119889= 12 119862

119889= 18 119862

119889= 24

15 0008 0010 0012 0095 0122 014625 0033 0046 0058 0153 0212 026735 0092 0128 0165 0204 0286 036345 0177 0252 0326 0249 0351 044755 0299 0431 0563 0296 0420 053365 0484 0707 0929 0374 0531 067975 0656 0964 1271 0475 0676 086585 0745 1100 1453 0588 0833 106095 0767 1136 1501 0695 0979 1233105 0752 1117 1478 0779 1089 1358115 0721 1075 1423 0832 1155 1426125 0684 1022 1355 0853 1176 1441

0 2 4 6 8 10 12 140

1

2

3

4

121824

34


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

020406

0810


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)










0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)





Acknowledgments


References



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















125 130 135 140 145 150 155 160 165200

250

300

350

400

450

Time (s)

Tens

ion

(kN

)

(a) 14 (s)

150 160 170 180 190200

250

300

350

400

Time (s)

Tens

ion

(kN

)

(b) 18 (s)

230 240 250 260 270260

280

300

320

340

360

Time (s)

Tens

ion

(kN

)


(c) 25 (s)

270 280 290 300 310 320 330 340 350200

250

300

350

400

Time (s)

Tens

ion

(kN

)


(d) 35 (s)


02 025 03 035 04 045 0540

60

80

100

120

Frequency (rads)

Tens

ion

RAO

(kN

m)










(a)

10∘

10∘10∘

10∘

80∘80∘

80∘

y

xBarge

1

23

4

5

6 7

8

(b)


0

0


Vert

ical

coor

dina

te (m

)

152535455565

758595105115125


minus100

minus50

T0wH T0wH















119899


0 2 4 6 8 10 12 140

05

1

15

2

25

001002003

004005006

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

000300080015

002500350045

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)




0119908119867)



0119867)

001 002 003 004 005 006 0003 0008 0015 0025 0035 004515 0002 0004 0008 0012 0018 0025 0019 0095 0266 0606 1053 161825 0006 0016 0033 0057 0086 0123 0027 0153 0477 1184 2144 335435 0014 0044 0092 0158 0246 0358 0035 0204 0648 1632 2970 465945 0025 0084 0177 0311 0492 0736 0043 0249 0796 2010 3662 572955 0039 0135 0299 0546 0905 1396 0050 0296 0951 2415 4434 697865 0057 0211 0484 0891 1398 1935 0062 0374 1213 3109 5682 874275 0078 0296 0656 1111 1594 2080 0078 0475 1553 3962 7005 1022185 0098 0360 0745 1180 1629 2086 0095 0588 1910 4733 7998 1104195 0111 0392 0767 1177 1606 2046 0112 0695 2220 5285 8549 11311105 0117 0396 0752 1145 1561 1992 0125 0779 2435 5570 8706 11228115 0115 0382 0721 1102 1510 1935 0135 0832 2546 5628 8587 10957125 0108 0359 0684 1054 1457 1879 0139 0853 2560 5520 8306 10575










0119908119867 = 25 119902




119889= 12






0119908119867)



12 18 24 3 4 02 04 06 08 10

15 0027 0013 0008 0005 0003 0339 0104 0036 0020 0014

25 0126 0059 0035 0024 0015 0723 0165 0066 0037 0024

35 0356 0165 0097 0065 0039 1103 0220 0088 0049 0033

45 0709 0324 0188 0125 0074 1571 0270 0106 0059 0039

55 1228 0552 0317 0208 0122 2227 0322 0123 0068 0045

65 2044 0907 0513 0334 0192 3441 0406 0152 0083 0054

75 2813 1240 0697 0450 0257 4665 0518 0186 0100 0064

85 3223 1417 0792 0509 0289 5321 0644 0220 0116 0074

95 3349 1464 0815 0522 0294 5396 0765 0246 0129 0082

105 3291 1442 0800 0511 0287 5120 0860 0265 0137 0086

115 3164 1389 0768 0488 0273 4704 0921 0273 0140 0087

125 3019 1321 0728 0462 0257 4259 0947 0273 0138 0086










6 Conclusions





0119908119867)



119889)

119862119889= 12 119862

119889= 18 119862

119889= 24 119862

119889= 12 119862

119889= 18 119862

119889= 24

15 0008 0010 0012 0095 0122 014625 0033 0046 0058 0153 0212 026735 0092 0128 0165 0204 0286 036345 0177 0252 0326 0249 0351 044755 0299 0431 0563 0296 0420 053365 0484 0707 0929 0374 0531 067975 0656 0964 1271 0475 0676 086585 0745 1100 1453 0588 0833 106095 0767 1136 1501 0695 0979 1233105 0752 1117 1478 0779 1089 1358115 0721 1075 1423 0832 1155 1426125 0684 1022 1355 0853 1176 1441

0 2 4 6 8 10 12 140

1

2

3

4

121824

34


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

020406

0810


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)










0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)





Acknowledgments


References



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















(a)

10∘

10∘10∘

10∘

80∘80∘

80∘

y

xBarge

1

23

4

5

6 7

8

(b)


0

0


Vert

ical

coor

dina

te (m

)

152535455565

758595105115125


minus100

minus50

T0wH T0wH















119899


0 2 4 6 8 10 12 140

05

1

15

2

25

001002003

004005006

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

000300080015

002500350045

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)




0119908119867)



0119867)

001 002 003 004 005 006 0003 0008 0015 0025 0035 004515 0002 0004 0008 0012 0018 0025 0019 0095 0266 0606 1053 161825 0006 0016 0033 0057 0086 0123 0027 0153 0477 1184 2144 335435 0014 0044 0092 0158 0246 0358 0035 0204 0648 1632 2970 465945 0025 0084 0177 0311 0492 0736 0043 0249 0796 2010 3662 572955 0039 0135 0299 0546 0905 1396 0050 0296 0951 2415 4434 697865 0057 0211 0484 0891 1398 1935 0062 0374 1213 3109 5682 874275 0078 0296 0656 1111 1594 2080 0078 0475 1553 3962 7005 1022185 0098 0360 0745 1180 1629 2086 0095 0588 1910 4733 7998 1104195 0111 0392 0767 1177 1606 2046 0112 0695 2220 5285 8549 11311105 0117 0396 0752 1145 1561 1992 0125 0779 2435 5570 8706 11228115 0115 0382 0721 1102 1510 1935 0135 0832 2546 5628 8587 10957125 0108 0359 0684 1054 1457 1879 0139 0853 2560 5520 8306 10575










0119908119867 = 25 119902




119889= 12






0119908119867)



12 18 24 3 4 02 04 06 08 10

15 0027 0013 0008 0005 0003 0339 0104 0036 0020 0014

25 0126 0059 0035 0024 0015 0723 0165 0066 0037 0024

35 0356 0165 0097 0065 0039 1103 0220 0088 0049 0033

45 0709 0324 0188 0125 0074 1571 0270 0106 0059 0039

55 1228 0552 0317 0208 0122 2227 0322 0123 0068 0045

65 2044 0907 0513 0334 0192 3441 0406 0152 0083 0054

75 2813 1240 0697 0450 0257 4665 0518 0186 0100 0064

85 3223 1417 0792 0509 0289 5321 0644 0220 0116 0074

95 3349 1464 0815 0522 0294 5396 0765 0246 0129 0082

105 3291 1442 0800 0511 0287 5120 0860 0265 0137 0086

115 3164 1389 0768 0488 0273 4704 0921 0273 0140 0087

125 3019 1321 0728 0462 0257 4259 0947 0273 0138 0086










6 Conclusions





0119908119867)



119889)

119862119889= 12 119862

119889= 18 119862

119889= 24 119862

119889= 12 119862

119889= 18 119862

119889= 24

15 0008 0010 0012 0095 0122 014625 0033 0046 0058 0153 0212 026735 0092 0128 0165 0204 0286 036345 0177 0252 0326 0249 0351 044755 0299 0431 0563 0296 0420 053365 0484 0707 0929 0374 0531 067975 0656 0964 1271 0475 0676 086585 0745 1100 1453 0588 0833 106095 0767 1136 1501 0695 0979 1233105 0752 1117 1478 0779 1089 1358115 0721 1075 1423 0832 1155 1426125 0684 1022 1355 0853 1176 1441

0 2 4 6 8 10 12 140

1

2

3

4

121824

34


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

020406

0810


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)










0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)





Acknowledgments


References



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 2 4 6 8 10 12 140

05

1

15

2

25

001002003

004005006

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

2

4

6

8

10

12

000300080015

002500350045

q0Hq0H

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)




0119908119867)



0119867)

001 002 003 004 005 006 0003 0008 0015 0025 0035 004515 0002 0004 0008 0012 0018 0025 0019 0095 0266 0606 1053 161825 0006 0016 0033 0057 0086 0123 0027 0153 0477 1184 2144 335435 0014 0044 0092 0158 0246 0358 0035 0204 0648 1632 2970 465945 0025 0084 0177 0311 0492 0736 0043 0249 0796 2010 3662 572955 0039 0135 0299 0546 0905 1396 0050 0296 0951 2415 4434 697865 0057 0211 0484 0891 1398 1935 0062 0374 1213 3109 5682 874275 0078 0296 0656 1111 1594 2080 0078 0475 1553 3962 7005 1022185 0098 0360 0745 1180 1629 2086 0095 0588 1910 4733 7998 1104195 0111 0392 0767 1177 1606 2046 0112 0695 2220 5285 8549 11311105 0117 0396 0752 1145 1561 1992 0125 0779 2435 5570 8706 11228115 0115 0382 0721 1102 1510 1935 0135 0832 2546 5628 8587 10957125 0108 0359 0684 1054 1457 1879 0139 0853 2560 5520 8306 10575










0119908119867 = 25 119902




119889= 12






0119908119867)



12 18 24 3 4 02 04 06 08 10

15 0027 0013 0008 0005 0003 0339 0104 0036 0020 0014

25 0126 0059 0035 0024 0015 0723 0165 0066 0037 0024

35 0356 0165 0097 0065 0039 1103 0220 0088 0049 0033

45 0709 0324 0188 0125 0074 1571 0270 0106 0059 0039

55 1228 0552 0317 0208 0122 2227 0322 0123 0068 0045

65 2044 0907 0513 0334 0192 3441 0406 0152 0083 0054

75 2813 1240 0697 0450 0257 4665 0518 0186 0100 0064

85 3223 1417 0792 0509 0289 5321 0644 0220 0116 0074

95 3349 1464 0815 0522 0294 5396 0765 0246 0129 0082

105 3291 1442 0800 0511 0287 5120 0860 0265 0137 0086

115 3164 1389 0768 0488 0273 4704 0921 0273 0140 0087

125 3019 1321 0728 0462 0257 4259 0947 0273 0138 0086










6 Conclusions





0119908119867)



119889)

119862119889= 12 119862

119889= 18 119862

119889= 24 119862

119889= 12 119862

119889= 18 119862

119889= 24

15 0008 0010 0012 0095 0122 014625 0033 0046 0058 0153 0212 026735 0092 0128 0165 0204 0286 036345 0177 0252 0326 0249 0351 044755 0299 0431 0563 0296 0420 053365 0484 0707 0929 0374 0531 067975 0656 0964 1271 0475 0676 086585 0745 1100 1453 0588 0833 106095 0767 1136 1501 0695 0979 1233105 0752 1117 1478 0779 1089 1358115 0721 1075 1423 0832 1155 1426125 0684 1022 1355 0853 1176 1441

0 2 4 6 8 10 12 140

1

2

3

4

121824

34


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

020406

0810


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)










0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)





Acknowledgments


References



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















0119908119867)



12 18 24 3 4 02 04 06 08 10

15 0027 0013 0008 0005 0003 0339 0104 0036 0020 0014

25 0126 0059 0035 0024 0015 0723 0165 0066 0037 0024

35 0356 0165 0097 0065 0039 1103 0220 0088 0049 0033

45 0709 0324 0188 0125 0074 1571 0270 0106 0059 0039

55 1228 0552 0317 0208 0122 2227 0322 0123 0068 0045

65 2044 0907 0513 0334 0192 3441 0406 0152 0083 0054

75 2813 1240 0697 0450 0257 4665 0518 0186 0100 0064

85 3223 1417 0792 0509 0289 5321 0644 0220 0116 0074

95 3349 1464 0815 0522 0294 5396 0765 0246 0129 0082

105 3291 1442 0800 0511 0287 5120 0860 0265 0137 0086

115 3164 1389 0768 0488 0273 4704 0921 0273 0140 0087

125 3019 1321 0728 0462 0257 4259 0947 0273 0138 0086










6 Conclusions





0119908119867)



119889)

119862119889= 12 119862

119889= 18 119862

119889= 24 119862

119889= 12 119862

119889= 18 119862

119889= 24

15 0008 0010 0012 0095 0122 014625 0033 0046 0058 0153 0212 026735 0092 0128 0165 0204 0286 036345 0177 0252 0326 0249 0351 044755 0299 0431 0563 0296 0420 053365 0484 0707 0929 0374 0531 067975 0656 0964 1271 0475 0676 086585 0745 1100 1453 0588 0833 106095 0767 1136 1501 0695 0979 1233105 0752 1117 1478 0779 1089 1358115 0721 1075 1423 0832 1155 1426125 0684 1022 1355 0853 1176 1441

0 2 4 6 8 10 12 140

1

2

3

4

121824

34


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

020406

0810


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)










0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)





Acknowledgments


References



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















0119908119867)



119889)

119862119889= 12 119862

119889= 18 119862

119889= 24 119862

119889= 12 119862

119889= 18 119862

119889= 24

15 0008 0010 0012 0095 0122 014625 0033 0046 0058 0153 0212 026735 0092 0128 0165 0204 0286 036345 0177 0252 0326 0249 0351 044755 0299 0431 0563 0296 0420 053365 0484 0707 0929 0374 0531 067975 0656 0964 1271 0475 0676 086585 0745 1100 1453 0588 0833 106095 0767 1136 1501 0695 0979 1233105 0752 1117 1478 0779 1089 1358115 0721 1075 1423 0832 1155 1426125 0684 1022 1355 0853 1176 1441

0 2 4 6 8 10 12 140

1

2

3

4

121824

34


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

1

2

3

4

5

6

020406

0810


Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(b)










0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)





Acknowledgments


References



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 2 4 6 8 10 12 140

05

1

15

2

121824

Cd

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


(a)

0 2 4 6 8 10 12 140

05

1

15

121824

Non

dim

ensio

nal d

ampi

ng (E

q0w

H)


Cd

(b)





Acknowledgments


References



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















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