OTe 7190

Hydrodynamic Aspects of Moored Semisubmersibles and TLP'sJ.A. Pinkster, Delft U. of Technology; Albertus Dercksen, MARIN; and A.K. Dev,Delft U. of Technology

Copyright 1993, Offshore Technology Conference

This paper was presented at the 25th Annual OTC in Houston, Texas, U.S.A., 3-6 May 1993.

This paper was selected for presentation by the OTC Program Committee folloWing review of information contained In an abstract submitted by the author(s). Contents of the paper,as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflectany position of the Offshore Technology Conference or Its officers. Permission to copy Is restricted to an abstract of not more than 300 words. illustratiOns may not be copied. The abstractshould contain conspicuous acknowledgment of where and by whom the paper Is presented.

ABSTRACT

The mean and low~frequency horizon­tal wave drift forces 'on 2 types ofsemi-submersible structures in regu­lar and in irregular waves are de­termined from model tests and calcu­lations. For the measurement of thelow-frequency drift forces in irre­gular waves use is made of a specialdynamic system of restraint.Comparison of measured and computeddrift forces in irregular waves showincreasing divergence betweenpredictions based on 3-dimensionalpotential theory and results of ex­periments with increasing severity ofthe irregular sea conditions.Comparison between computed andmeasured mean drift forces in regularwaves show increasing divergence atlower wave frequencies. A simplemodel for approximating viscouscontributions to the drift forces inirregular waves is applied to sometest results and it is shown that thecorrelation between measurements andpredictions is improved.In order to gain more detailedinsight in the mechanisms of theviscous contribution to the driftforce tests were carried out withsingle fixed vertical cylinder in

601

regular waves. The results of testsconfirm that in conditions of waveswithout current the major part of theviscous contribution to the driftforce is confined to the splash zoneof the cylinder.

INTRODUCTION

The motions and mooring forces ofSemi-Submersibles and TLP' s moored inexposed locations are often dominatedby wave effects. These may be sub­divided in first order wave frequencyforces with frequencies correspondingto the individual waves and mean andlow-frequency second order wave driftforces related to wave groups.From the point of view of the designof mooring systems both first andsecond order wave loads and the mo­tion and mooring load response needto be taken into account. At thedesign stage predictions of thesequantities for a particular designcan be based on computationalmethods, model tests or a rationalcombination of both.Computational methods for wavefrequency loads and motion responsefor semi-submersibles have been indevelopment since the early 70's.See reference [1]. Such methods are

~

-- -~~--~

based on linear hydrodynamic theoryand have proved their worth on manyoccasions.Non-linear, mean wave drift forces onsemi-submersible type structures canbe computed based on the applicationof linear, 3~dimensional diffractiontheory computational methods combinedwith either a far-field method or anear-field method for the evaluationof the second order wave loads on thestructure. In case a far-field methodis applied, generally only the meansecond order horizontal drift forcescan be calculated. See reference [2]and reference [3]. If a near-field orpressure integration method isapplied the mean and low-frequencycomponents of the drift forces can becomputed for 6 degrees of freedom.See reference [4]. This type ofcomputational method assumes the flowto be inviscid thus excluding anyeffects which might arise fromseparated flow around the structure.In the past efforts have been made toverify the computational methods forthe mean and low-frequency or slowlyvarying wave drift forces on semi­submersible type structures. Seereference [5]. It has been surmisedthat the drift forces on semi­submersible type structures, whichconsist of relatively slendersurface-piercing columns and sub­merged floaters, are in some casessignificantly affected by viscouseffects in the flow around thestructural elements. Very little ex­perimental data is available whichcan give insight in such effects. Seereference [10].In order to increase insight in theseeffects MARIN, in co-operation with anumber of offshore operators, design­ers and manufactures, carried outextensive model test programs andcomputations among others of the meanand slowly varying wave forces onslender and full semi-submersibles.In this paper a number of aspects ofthis research including the modeltest programs and the correlationbetween model test results and

602

results of computations arediscussed.The findings of these studies haveconfirmed that significant viscouseffects can be present in the low­frequency wave forces on suchstructures. As a result, a researchprogram has been initiated by theDelft University of Technology intodetermining such effects on structu­ral elements of semi-submersiblessuch as the columns and the pon­toons. The purpose of this researchis to determine for which of theseelements the viscous effects play animportant role and, if possible, todevelop a rational computationalprocedure for taking such effectsinto account when determining themean and slowly varying drift forceson the complete structure. In thispaper some results of recent modeltests carried out on a fixed verti­cal cylinder in waves are presented.

SECOND ORDER WAVE DRIFT FORCESON A SEMI-SUBMERIBLE

The subj ects of this investigationwere a slender 8-column Semi-Submer­sible I with circular columns and adisplacement of 23,270 tonnes and afull 6-column Semi-Submersible IIwith square columns and a displace­ment of 56,300 tonnes. The body plansof the semi-submersibles are given inFigure 1 and Figure 2. In the follow­ing all results of measurements andcomputations will be given for thefull scale structures.The aims of the study were asfollows:

-To increase insight in the mean andlow-frequency horizontal wave excit­ing forces and motion responses oflarge semi-submersibles

-To check the validity of computa­tional methods for the predictionof first order wave frequency mo­tions and low-frequency wave driftforces based on 3-dimensionalpotential theory.

The total scope of the research doesnot allow all aspects to be treatedhere. In this paper the results ofthe following investigations arepresented:

-Results of model tests in regularwaves to determine the mean hori­zontal wave drift force response.

-Results of tests in irregular wavesto determine the mean and low-fre­quency wave drift force records.

The model tests were carried out at ascale of 1:40 in the Seakeeping Basinof MARIN. This basin measures 100 m x24 m x 2.5 m.

MODEL TEST SET-UP IN THE BASIN

Measurements of the mean horizontalwave drift forces on a model in re­gular waves can be carried out usinga soft-spring restraining or mooringsystem which consists of horizontalwires incorporating soft linearsprings which are connected to forcetransducers mounted on the model. Themooring wires are connected at decklevel. The set-up for tests inregular waves is shown in Figure 3.In order to measure the mean andslowly varying horizontal wave driftforces in irregular waves, ideallythe model should be moored in such away that all low frequency motionresponse is suppressed while leavingthe model completely free to carryout the motions at wave frequencies.The first requirement ensures thatthe measured force is not affected bydynamic magnification effects. Thesecond requirement can be deducedfrom theoretical analysis of thesecond order wave drift forces whichshow that part of the total secondorder excitation forces are directlydependent on the structural motionsat wave frequencies. See reference[4].As a consequence, the model re­straining system must possess thecharacteristics of an ideal DynamicPositioning system. For the model

.....::...=.-.-----=- =-- -

tests a system consisting of hori­zontal restraining wires connected tocontrollable tension winches wasselected. See Figure 4. The wincheswere operated based on an activecontrol system with a feed-back loopsupplemented by a feed-forwardcontrol loop. See Figure 5.The feed-back loop 'acted on the hori­zontal position error and the timederivative of the error (Proportio­nal-Differential control). The feed­forward control loop was based on thereal-time measurement of the re­lative wave elevation on the up-wavecolumns of the semi-submersible. Ithas been shown that a major part ofthe mean and slowly varying secondorder wave drift forces as predictedby potential theory, is due to termsrelated to the square of the instan­taneous relative wave elevationaround the waterline of a floatingstructure. This has been demon­strated, among others, from modeltests on a tanker. See reference [4].Application of feed-back and feed­forward control still does not resultin full suppression of low-frequencymotions however. This due to the factthat the feed-forward loop is supply­ing an imperfect estimate for theinstantaneous low frequency horizon­tal force. As a result, the totalrestraining force is not equal andoppos i te to the low frequency waveexciting force thus resulting inresidual low frequency motions. SeeFigure 6. In order to obtain a bestestimate of the total low frequencywave force on the model, the measuredrestraining force is corrected forthe residual horizontal motions ofthe vessel. This is carried out off­line after a test has been carriedout. The bas ic assump tion behind thisprocess is that the instantaneousdiscrepancy between the true waveforce and the measured restrainingforce results in horizontal motionaccelerations which are described bythe following relationship:

m x(t) = Fd(t) - Fm(t)

603

~-~,~-~- -- ~~-~,=---,--=-------;;;;------=---~ ~

in which m represents the virtualmass of the vessel and x(t) the mo-tion acceleration. Assuming that thevirtual mass is constant, the accele-ration force can be determined in thetime domain by passing a double-differentiating filter over the timerecord of the low frequency horizon-tal motions. The best estimate of thetime record of the horizontal driftforce then follows from:

Fd(t) = Fro(t) + mx(t)

An example of time records ofmeasured restraining force, residualsurge motion, correction force andtotal drift force are shown in Figure7. The results apply to Semi-Submer-sible II.

In order to verify the accuracy ofthis procedure model tests wererepeated using different settings ofthe dynamic restraining system.An-example of the results found forthe spectral density of the slowlyvarying wave drift force on the Semi-Submersible 11 in irregular head seasis shown in Figure 8.The results apply to the system ofrestraint being adjusted to repre-senting a spring system (Proportio-nal control), a spring and dampersystem (Proportional-Differentialcontrol) and a P-D control includingFeed-forward based on the relativewave elevation measurements. Theresults shown in the figure indicatethat the spectral density of thedrift force obtained from tests withsignificantly different characteris-tics of the restraining system arereasonably consistent.

TESTS IN REGULAR WAVES

Tests in regular waves were carriedout for both semi-submersibles for arange of wave frequencies, waveamplitudes and wave directions. Forthe slender Semi-Submersible I testsin head seas were carried out with-out and with bracings. The results

are given in Figure 9 through Figure13 for both structures in head wavesand in beam waves as mean drift forcetransfer functions,In the figures the theoretical valuesfound on the basis of 3-dimensionalpotential theory computations ex-cluding the contribution from thebracings are also given.

Comparison between the results of mo-del tests and computations show thatin the lower wave frequency range themean drift forces tend to be consi-stently underestimated by the compu-tations. The effect of the bracingson the mean drift forces on theslender Semi-Submersible I in headseas is to increase slightly the meandrift forces as can be seen from thecomparison between the measured

results shown in Figure 9 and inFigure 11.

TESTS IN IRREGULAR WAVES

Tests were again carried out for bothsemi-submersibles. The slender Semi-Submersible I was tested with-outbracings.

Results of tests in irregular wavesare given in the form of time tracesof the measured low frequency driftforces compared with time traces ofthe corresponding predicted low fre-quency force based on 3-dimensionalpotential theory. In some cases thespectral density of the computed andmeasured forces are compared. For thetime domain predictions, use was madeof second order impuls response

functions combined with the measuredtime trace of the undisturbed ir-regular wave record in the basin. Seereference [5]. The time domain secondorder impuls response functions forthe drift forces are obtained fromthe complete second order quadratictransfer functions computed in thefrequency domain. The quadratic

transfer functions were computed

based on the pressure integrationmethod, See reference [4].

604

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Tests were carried out in different set-down waves present in the irregu -

irregular sea conditions in order to lar wave field. The troughs of these

determine the dependency of the cor- waves, which have periods comparable

relation between computed and mea- to the wave group periods, are in

sured forces on the sea condition. phase with the peaks of the wave

groups. See Figure 21. The low-

Time traces of the measured and com- frequency wave force components due

puted drift force records for irre- to these waves are in phase with the

gular haed seas are given in Figure horizontal acceleration of the fluid

14 through Figure 17. The spectral which is largest when the slope of

densities of the computed and mea- the set-down waves is greatest. This

sured surge drift forces on Semi- occurs after the peak in the wave

Submersible II are compared in Figure group passes the structure. Due to

18 through Figure 20. comparison this effect the peaks in the computed

between measured and computed data wave drift forces in irregular waves

show that the correlation is good in with longer mean periods tend to lag

low sea conditions with relatively behind the peaks in the wave groups,

short mean periods. In higher sea The measured records, however, stillconditions combined with corres - shown that the peak forces co-incide

pondingly longer mean wave periods with the peaks in the wave groups. A

the correlation worsens. Beside possible explanation is that in “

significant differences in the force longer waves, viscous forces, which

peak values, the phase shift between are dominated by velocity related

peaks in the measured and computed effects, are becoming relatively more

records increases in higher sea con- important. Since the fluid velocities

ditions. The trend is more or less are highest near the peaks in the

the same for both types of semi- wave group, peaks in viscous contri-

submersibles. butions to the drift forces will alsotend to co-incide with the peaks in

DISCUSSION OF RESULTS FROM the wave groups.

TESTS IN REGULAR AND IRREGULAR In order to investigate this effect,

WAVES a simple model for the viscous con-tributions in the horizontal drift

The results found from tests in forces has been investigated and someregular and irregular waves with further comparisons between the

respect to the drift force seem to measured and computed drift forces,

support each other in that in both including viscous contributions, on

cases the correlation between the slender semi-submersible carried

measurement and computations worsen out .

with an increase in the wave period.The reduction in the correlation VISCOUS COMPONENTS OF THE DRIFTseems to be accompanied by an in- FORCES IN IRREGULAR WAVEScreasing phase shift between measuredand computed forces. The peaks in the The model used to describe the vis-

computed drift forces tend to shift cous contribution to the drift forcesrelative to the wave groups. See is based on the assumption that

Figure 17.This is related to the fact Morison’s equation for the drag forcethat in longer waves diffraction on a vertical cylinder in waves can

effects which make up the major part be applied to the surface-piercing

of the drift forces in shorter waves parts of the columns of a semi-sub-are reduced. In longer waves the mersible. See reference [6] through

low-frequency drift forces are to a reference [10]. For the case of waves

larger extent dominatedby the compo- without current it can be shown that,

nents related to the second order as a first approximation, the viscous

605

~

drag force contribution to the driftforces is confined to the splash zoneon a column. The viscous drag term is—determinedequation:

Fvd(t) = %/J

in which:

v(t) -

D-

C(t) =

from the following

r(t)

cd~ v(L-).lv(t)l.D dz

o

relative horizontalvelocity between thefluid and the column

column diameter

relative wave elevation

Cd = drag coefficient

This contribution to the drift forcecould be evaluated for each column inthe time-domain based on the un-disturbed wave elevation record, thefrequency domain motion characteris-tics of the semi-submersible and anassumption regarding the drag coef-ficient in the above equation. Thesummation of the drag force on eachcolumn results in the estimated vis-cous drag force contribution to thedrift force. The total drift force isfound by adding the viscous andpotential contributions.

The results of thes computations areshown in Figure 22 for the slenderSemi-Submersible I in irregular headseas. In this figure the wave eleva-tion record, the potential part ofthe drift force and the viscous partof the drift force are shown in thetop three traces. The lower traceshows the sum of the viscous forceand the potential force compared withthe total measured force.It is clear that the result of addingthe viscous contribution is a clearlyimproved correlation with themeasured force.overall effectcontribution tobution spectra

In order to show theof adding a viscousthe potential contri-of the low-frequency

surge force in irregular head seasand sway force in beam seas on Semi-Submersible I are given in Figure 23for three different sea conditions.Each figure shows the drag coeffi-cient Cd used for the computations ofthe viscous force contribution. TheCd values used for the computationsof the viscous contribution in somecases had to be adjusted in order toachieve a reasonable fit with themeasured data. This clearly is anunsatisfactory aspect of the simpli-fied model for the viscous effectwhich will need to be refined in thefuture. An important effect notaccounted for is for instance, theshielding effects due to the

I

proximit~ of the columns. However,the above results tend to confirmthat there is a significant viscouseffect in the drift forces on semi-submersible type structures which, inirregular waves without current seemsto be concentrated in the splash zoneof the columns. The analysis has beenbased on a rather simple model forthe viscous contribution which hasnot been verified to any greatextent. In the next section someresults of ongoing detailed researchcarried out at the Delft Universityof Technology into such effects isdescribed.

VISCOUS EFFECTS IN DRIFT FORCESON A FIXED VERTICAL CYLINDER

In the previous section it was indi-cated that the most significant vis-cous contribution to the horizontaldrift force on a semi-submersibleseems to originate from the splashzone of the columns. In order to gainmore insight in such effects, modeltests have been carried out to deter-mine the distribution along the ver-tical of the mean horizontal driftforce on a single vertical cylinderin regular waves. The work is part ofan on-going Ph.D. project.SeeTheNo.

reference [11].model tests were2 towing tank of

I

carried out inthe Ship Hydro-

606

I

mechanics Department. This facility given for the model scale.measures 80 m x 2.75 m x 1,25 m and The model tests were carried out foris equiped with a single flap a range of wave frequencies corres-hydraulically operated wave-maker pending to the longer waves for acapable of generating regular and semi-submersible. At scale 1:100 theirregular waves. The basin is fitted wave frequencies tested in the modelout with a towing carriage with a correspond to 0.3 r/s to 0.8 r/s atspecial low speed carriage control full scale. This is a range offor the simulationof current effects frequencies relevant for extreme seaby towing. conditions.The model cylinder which had a dia- The results shown in Figure 25 andmeter of 0.075 m is shown in Figure Figure 26 confirm that the greatest24. Afiscale 1:100 this could be re- discrepancies between the potentialpreventative of a column with a 7.5 m computations and the measurements ofdiameter. The splash zone and the the mean forces are found for thesub-surface part are independently splash zone of the cylinder. Theattached to a central core through measured mean forces are consistentlyforce transducers measuring the significantly larger than the com-horizontal force on each of the two puted values, For the sub-surfacesections. part of the cylinder, differences

Model tests were carried out in regu- also occur between measurements andlar waves with and without current. computations. In a relative senseFor each test the vertical position they appear to be of the same orderof the cylinder was adjusted so that as for the splash zone part. However,the through of the wave passing the the absolute value of the forces iscylinder passed just above the sepa- considerable lower and the differen-ration between the splash zone part ces between measurements and compu-of the cylinder and the sub-surface tations are less consistent.part of the cylinder. This ensured It can be concluded that these modelthat the sub-surface part of the tests poit to the splash zone contri-cylinder was fully submerged at all bution to the viscous part of thetimes. Results of measurements in mean drift force as being the mostregular waves without current of the important one.mean horizontal drift force on thesplash zone and the sub-surface zone FINAL REMARKSare compared with results of calcula-tions of the relevant contributions In this paper we have shown someto the drift forces based on 3-dimen- results of an extensive series ofsional potential theory and the ap- model tests on two semi-submersiblesplication of the pressure integration which confirm differences betweenor near-field method in Figure 25 and computed and measured mean and low-Figure 26 respectively. frequency horizontal wave driftAccording to the near-field theory forces in regular and irregularfor drift forces, the splash zone waves.contribution is dependent on the Application of a simple model for thesquare of the relative wave elevation viscous contribution to the driftaround the cylinder while the drift forces indicated that irregular wavesforce on the subsurface element is without current the major source ofdue to the non-linear pressure con- the viscous contribution was to betribution in the Bernoulli pressure found at the splash zone part of theequation. For this reason the results columns of a semi-submersible.of mean force measurements have been Model test in regular waves with adivided by the square of the undis- fixed vertical cylinder representingturbed wave amplitude. Results are a single column of a semi-submersible

607

or a TLF confirm that the largestdiscrepancies between computed andmeasured drift forces are indeed tobe found in the splash zone.Further experimental investigationsare required in order to be able toformulate a more detailed model forthe viscous effects which can alsotake into account such aspects as theinteraction effects due to the proxi-mity of the columns of a semi-submer-sible.

REFERENCES

[1]

[2]

[3]

[4

[5]

[6]

Haoft, J.P.: ‘HydrodynamicAspects of Semi-SubmersiblePlatforms’ , Publication No.400, Netherlands Ship ModelBasin, 1972

Newman, J.N,: ‘The Drift Forceand Moment on Ships in Waves’ ,Journal of Ship Research, 1966

Faltinsen, O.M. and Michelsen,F,C,: ‘Motions of Large Struc-tures in Waves at Zero FroudeNumber’ , Symposium on MarineVehicles, London, 1974

Pinkster, J.A.: ‘Low-FrequencySecond Order Wave ExcitingForces on Floating Structu-res’ , Publication No, 650,Netherlands Ship Model Basin,Wageningen, 1980

Pinkster, .J.A. and Huijsmans,R.H.M, : ‘The Low Frequency Mo-tions of a ‘Semi-Submersible inWaves’ , Boss’82, Boston, 1982

Pijfers, J.G.L. and Brink,

[7]

[8]

[9]

[10]

[11]

Huse, E.: ‘Wave induced Mean

Force on Platforms in Direc-tion Opposite to Wave Propa-gation’, Norwegian Maritime

Research, VO1.5, No.1, 1977

Standing, R.G., Brendling,W.J. and Jackson, G.E.: ‘Full-scale Measured and PredictedLow-Frequency Motions of theSemi-Submersible Support Ves-sel ‘Uncle John”, First In-ternational Offshore and PolarEngineering Conference ,Edinburgh, 1991

Ferretti, C. and Berta, M.:‘Viscous Effect Contributionto the Drift Forces on Float-ing Structures’ , InternationalSymposium on Ocean EngineeringShip Handling, Gothenburg, ’80

Chakrabarti, S.K.: ‘Steady

Drift Force on Vertical Cylin-der - Viscous vs. Potential’,Applied Ocean Research, VO1.6,No.2, 1984

Dev, A.K.: ‘Experimental In-vestigations of Viscous Mean

Drift Forces on a Fixed Verti-cal Circular Cylinder in Wavesand Currents Part I’ , Report

No. 928-M, Ship HydrodynamicsDepartment, Delft University

of Technology, 1992

A.W. : ‘Calculated Drift Forcesof Two Semi-Submersible Plat-form Types in Regular and Ir-regular Waves’ , Paper No. OTC2977, Offshore Technology

Conference, Houston, 1977

608

— — —— — — — — ———

9.14 20.57 aI

! 1 I I

iI I I5,49 5.49 3.14

I 1 !

I I

3.051 19.i41 I 3.05

59.44

Dimensionsin

22.86 t 22.86 ! 22.86

1.52 68.58I

Fig. 1–General arrangement of Semisubmersible 1.

Dimensionsaregiveninmetres

---1

~----, +_-

1I I I

%: )3 1s.51~J -———

—. —------—-—

~! ‘,,

II II,1 IIII II,1 {1

73.5 ,—. —. _.__._[.lil II,1 ,1

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-a-l—--

-:.-r

14.0

w

I \ !---- ---- *-- :

L

! I

#- I25.0

——I

I !5.0

55.’3 I

Fig. Z–General arrangement of Semisubmersible Il.

609

Fig.3—Test setup for tests in regular waves.

—. .- — — . .—— .— —

—

1wave s

Drift forces

1’ Feed.f cmwasd ~Q1ativecontrol

Wzlve dev.system

Ffg. 4—Tast srrtup for tests in Irregular waves.

2“’0=’=)

Fig. 5—Block diagram of control system for tests in irregular waves.

IFB (Forcefrom control system)

Fig,6—Block diagram of forces acting on the structure.

‘~r BSSM..I Surge motions .m ~L-----., -. .

->, ~ .=

Fig. S—Spectra of drift forces obtained for different restralnhrg system characteristics for the Fig. 7-Exemple of (a) measured restraining form, (b) correction force for motions,scme sea conditions, and (8+ b) total drift force record.

610

I I.20 - — calculation

A 0 a Rqularwaves,

b aA

-lo —

oA

o , A I—o 0.5 1.0 1.3

w In rad.sec.-~

Fig. 9 - Mean Surge drift force on Semi-SubmersibleI in regularheadwaves

20- — Calculati.A o 0 I+- -VU.

A

10 -

9

AA

o 1. A I I

o 0.5 1.0 1.3

0 in rad.sec.-l

Fig. 10 - Mean sway drift force on Semi-SubmersibleI in regularbeamwaves

0 0.s 1.0 1.5e in rad..s,c..l

Fig 11 - Mean surge drift force on Semi-SubmersibleI in regularheadwaves includingeffectof br-ing=

611

—. .- — — . .—— .— —

—

07

5

t5000

0 0.25 0.50

Fig. 18-Spectral density on surge drift force of Fig. 1S onSemisubmersible II.

1— Measu]

i#

.-.. calculiII,1

20000 -t ‘,1,1,11:,1

III

~:

lsooo +;

, I III 1};]! It, , ,I q, t; t,l ~I ~1

t1 II

t10000 t

9!

It1

1 1I I

: ,

: !1

5000 +-(I

0. I

0 0.25

Fig. 20-Spectral deneity of surge drlff force of Fig. 17 onSemlsubmereible Il.

*

!I — Measured

.. .. Cslculskd

l(W)OO

m

5

t

&II

~

~b?’i,I

o ‘.

o 0.2.s 0.50

@ ~ radla

Fig, 19–Spectral density of surge drift force of Fig. 16 onSemisubmersible W.

Fig. 21 –Wave eet.down in irregular wave8.

CD = 0.80

25.02Calculated (potential part) a

tf o

-25,CQJ2S.W ---Measured

1 Force Calculated (viscouspart) btfo,

—---.~-” -’..%-—--------

t~’:k-=--~.<~:=’c”lat”--25,1YI

r-’fwT0 50 100

tin,

Fig. 22-Low-frequency surge drift force on Semlsubmersibla I in irregular head seas,

—. .- — . ——— .— ———— —

— Heammd durimq.Od.l t.st

—— til.mlamd, *t*nt ial cmcributim only

-——-— Calc.lat.d, visccus .ff.cc kncltiad

mad seas beam Se6S

160- 160H, . 3,0S; T1 . 1.1 , K, . 3.09;T1 . 7.1 s

‘\CD . 0.60 C3 = 9.5$

m“ .m: : ‘\

\80

2n IJO

\

.

# $~

\

.\

0 0400 800

% . 5.85; T1 . 11.3 s H= . 5.0S: T1 - 11.3 ,

\\ CD = 0.30 \\\

CD = 0.75\

: ; \

2 .

200

\

a 4005 .

# ~b~t \ ,

---\

0

400%

4000. 11.14.TL . 14,1 , H, . 11,24: T> . 1*,1 s

CD . !.00

.M .m

2 H

200

!

H 20005 .

$Fkb

\ m\\\\

00 0.1 0.4 0 0.2 0,4

u in radls u 1. ..6/*

Fig. 23-Spectra of low-frequency drift forces on Semisubmemible 1.

r“.-—A—.. . . . . .

.W-.

1

~] Eliwt., - C, L,.”E,

/

““” m,. “!!?.”

/‘k -.,

.—.——

!-, TM, c,,, w

/,- w-.

w, m “! ,MD.,

/

Fig. 24-Arrangement and model setup of fixed verticalcylinder.

MEAN DRIFT FORCE lN/M_21100 --- - .

[H]. HlOHE$T 8ET OF WE AMP,(o . INTERIASO,ATEs,, 0, WE AMP,(L) . LOWESTSET OF WE AMP,

80 -

80 -

40

20 -

0

0

A

o

ol-.---.-.-~l0123458 78

OMEGA lR/Sl

o Measured $ MEASURED

— POTENTIAL THEORY : MEASURED(L)

Fig. 25-Mean drift forces on the splaeh zone part of thecylinder.

MEAN DRIFT FORCE lN/M-21so ----

[

——[H) . H!OHES7 SET Or VLWEAMP, ;01. lNTERMEOtATESST OF ww N4P, ,

~ IL] . LOWESTSET OF VMVEAhlP,

80

40

20 0

0

t“---—T-TT=”O

6 b

-20L..——.~01234.56 78

OME@A IRISI

o MEASURED(1) @ MEAsURE

— POTENTIAL THEoRY u MEASURED(L)

fig. 26-Mean drift forces on the subsurface part of thecylinder.

613

—._. _

=.. .:–—–-=..— .-————=————-———-— —— -..— ..-— -.___=__~= ._..== .,==— .=a —_—. -, __= -—

—.—=—

. .—-..— -- —.=... _+

s——==.=——-—–. ——_ . . .: .—= . > ~_ .,- —-—

.— —— — .—_ ___ ~ ~ ? ,— - -—=.—=__——.—_ ._:—_ :— .:= : ~- =

. —— .- _- & ..s.=a.=—–.— —

_.—_== ._=__ .=—. _—_ = .=, —.==—,-____:.-— ___ -—:_.-. :___—___—. —__ ~. -.. .. —= .-=— ..—.—..—=. -..—

.==e.= .--— ——_——- ,—= =——. .-:—.

— —.— —. — _=. = -__= _— =...=< v—. .__—= _- _-_: ___ ____= ------ —:.-== .. =._ ——_.- .

— _.—-——.

—

-.<—>__. = _=_. =—_= =._——-Q —.-

____ —-. -.——_ ..s. =—— ._—_— _:_—_. ———. —-=4. e.._—: —___ ___~ __—___ ~yu_= -T+ ,_= ~=_ ___ ~ . . . ..

~— .= >—~:.=- +—=—- .=. _ _–——=.-——___ -.:, .===– _ __ ~= _–_ _– ._, .=..= ____ =____ .— , -.=— .==. =. ,-=. . s.–.=i=<_==<_==,. ~ ––==—=....._=_...—, ._ ~—=—..—” _ _ : —-: = : _. :-=-_ _— ._ —-__.=,—_.—–—._. ~. : —_.. . .=_ ~=—. ~- -=—. .

. =_ G .—.--= ——=: -- ..— ——___.__— ~.= ~__ ~=__—.= _= .—= a.-: —..:~ .-.=.—=—==.—v._m %._~ ..==T=_==_...=.-.=...

—=., , .%:—_ ~%=,==.=. ..a~~ —___ .—..-==. —=_~= _=---- .= ....—— -—.. --– ==. .—=+ -. ~.>< -. a—:-e—.z-=~. .Ta.=%::a: 2*. –.=..-_--=:=g:*~_:~-- ?.=-::=:.=—l—- - -.:-==— ...——-=...——::.-=... . , - .<—.., .. >___ -<-; -%-=. +=- . —-,=:—. ==..– .. . ___. ~. .—~..., .=.. —.<——.-;..=.- m.—=. - _.—==~.— . s=—~_L_.. _

. .—._ .=—. .. . .—= +~=~ .—= ~ +. .—-= --.— + .—=—-e_-_=._._ ~ .=—==.. .- ,_z _.-.~* . ..–== ~..—: _. ____ .;_. ~—_.- ___~= .._ ~ ~..—= = - .. —- _—, __ .– .~,

-=----- . e==.—=. .=. .- >__ . . . . -...>- —.--=— .— —__.. .=. ——=. _——. _____ ___ ---- ——— ._.— _ .—. - ——— ——-—. —___ —= ...--

-50— Czlmlaticm Io u A R&ax waves. (Ucexii.mg W-aVdheight)

> 8u

0

A

P-

E 8

-25 - 9 A

,d 0.L. 8>

0 -0.5 1.0 1.5

u — radls

Fig. 12- Mean surge drift force on Semi-Submersible 1(in regular head waves,

50.— —Ci. [O ❑ A W’3UMZ==s . [UC- W-V* Might)

❑

Q.

25 - 0

0

0 0.5 1.0 3

. — rad/s

Fig. 13-Mean sway efriff force on Samisubmersible II In regular beamwaves.

— Measured 4E0 = 3.lm

— Calcufakd %, - 7.1 *

dir - 180.

m-rm0 50 100

tir. ,

Fig. 15-Low.frequency surge driff force on Semisubmersible II inirregular head aeaa-Ha = 3.1 m, T, -7.1 ●.

5.03 I1

Wave

mO

. Mtaturcd— C4kuhted

Wo -5.5 m

*1 - 11.3 s

diz - 130-

m0 50 100

tic!,

Fig. 16–Low.frequency surge drlff force on Samiaubmeraible II Inirregular head aeaa-Hs x 5.5 m, T, =11,3 a.

614

S.@.l ~ Wave 4W - 3.09; $= - 7.12 s

m o .’,’!3‘. -’. -“ !ti’.. -’ ‘“;‘,,?’.;”:’’’’.’...:;’. . :.”’..; .’.!j:.., ,’,-...”. .“ ;’

-5.@I J— Measured.. . . Cahdared

10.03,1 Force

tf o------- ,,=---.~” -

-Io,lx J ~

-~...--------- /=

.._ ,,

4m -5-85 =; $1 = 11.30 =

10.027 Force

! 4-. 13..24 M; %1 = 14.25 s10.C4-

Forceto*- . .......

---

‘=--./-----ks “...--...’{”--+----- ;7%;,:,:-10.W-

7,1 L’

‘\ ;\,‘u’

1, I , t I I 10 50 100

t in seconds

Fig. 14-Low.frequency eurge driff force on Samiaubmemible I inIrragular head aeaa.

4=0 - Io.3 =— Mu.rurtd %1 - 14.5 ●. . Catculatrd

dir - 180.

‘. ‘

Fmmmo 50 100

tins

Fig. 17—Low.frequency surge driff force on Semisubmaralble II InIrregular head seasHa = 10.3 m, T, x 14.5 s.