OTC 5531

Dynamic Aspects of Offshore Riser and Mooring Conceptsby H.J.J. van den Boom, J.N. Dekker, and A.W. van Elsacker,Maritime Research Inst. Netherlands

Copyright 1987 Offshore Technology Conference

This paper was presented at the 19th Annual OTC in Houston, Texas, April 27-30, 1987. The material is subject to correction by the author. Permissionto copy is restricted to an abstract of not more than 300 words.

ABSTRACT

Up to very recently the design of mooring sys-tems and flexible risers lacked an adequate approachto account for dynamic effects in the extreme loadassessment. Usually the design concept was based onthe extreme positions of the floating structure.Recent research has indicated that the dynamicamplification of the tensions in the lines andrisers can be of the same order of magnitude as theco-called quasi static values. Also it has beenconcluded that the dynamic effects in the mooringsystem can affect the low frequency motions of thestructure by the increase of virtual stiffness anddamping.

In this paper newly developed 3D computationalprocedures are presented, describing the motion,tension and bending moment along a flexible pipe ora mooring line. Also correlations with model testdata are discussed.

1. INTRODUCTION

The growth of the number of moored conceptsamongst the offshore structures and the trendstowards cheaper technology as a result of low oilprices, puts high demands on the design of themooring arrangement.

Important parameters in this respect are thelarge displacement of the structure, deep andhostile waters and the required round-the-yearworkability.

The wide variety of mooring systems may be il-lustrated by the existence of shallow and deep watersingle point moorings with temporarily or permanent-ly moored tankers, clump weight systems used forguyed towers and wire moorings of semi-submersiblecrane vessels.

The current design procedures mostly include adynamic motion analysis of the moored object. Thisprovides extreme positions of the structure. Fromthe static load excursion characteristics of themooring system, the mooring line tensions at theseextreme positions can be found.

References and illustrations at end of paper

In this so-called quasi-static mooring analy-sis, all other phenomena having an effect on themaximum line load are taken into account in anoverall safety factor, as required by the certifyingauthorities. Typical values are 3 for operationaland 2 for survival conditions.

Experimental and theoretical research haveshown that high frequency oscillations (in the wavefrequency range) of the upper end of a mooring linecan generate significant dynamic amplification ofthe line loads.

These dynamic effects are depending on:- frequency of oscillation- amplitude of oscillation- specific line mass- pretension- hydromechanic line properties.

Van Sluijs and Blok [5] have found from a sys-tematic series of forced oscillation model tests,that the ratios of maximum dynamic tension and maxi-mum quasi static tension depend strongly on the fre-quency of oscillation. This ratio is enhanced byincreasing oscillation amplitude, increasing pre-tension and reduction of line mass.

Knowing the importance of dynamics for mooringsystems, a similar behaviour is to be expected forrelated "line-type" configurations such as flexiblerisers, pipe bundles etc. The additional parametersconcerning dynamic effects in these cases are thedirect wave forces and the bending stiffness. Thetraditional theoretical approach to solve the dynam-ic behaviour of cable/riser systems is based onsemi-analytical techniques. Geometrical non-lineari-ties are neglected to reduce the equations to dif-ferential equations which could be solved. Perturba-tion techniques were applied with success but arerestricted to certain areas [3].

A more general approach to the problem wasprovided by discretization techniques. The line isassumed to be composed of a limited number of dis-crete elements. These elements can have physicalproperties of their own. The thus formed system ofpartial differential equations describing the vari-ables along the line, could be replaced by equationgof motion in an earth-bound system of coordinates.

405

--=--- ~~--'- .---=~_ ~~ .-"'";::::;C_ -0 - ~~_~~.~~_.,=-;::;;_~_-. __~-_~-=.~__~~_~ - __ ~_- ~_~ ~_~=

---=-==----'"',-

- - . -

- ----:--.~=- .'='-~.- -'-.---'-~--

(5)

OTC 5531

(8)

(7)

+ 1/2 ~j(T-2~T) +5/2 X.(T) - 2x (T-~T)-J -j2

+~ it.(THT)2 -J

T (T)= instantaneous length of segment j=~oj(l~)

j

or:

The fluid forces acting on the submerged partof the line originate from line motions (fluid reac-tive forces) and water particle motions due to wavesand current. Dividing the forces into velocity andacceleration dependent parts, the total elementforce may be approximated by the relative motionconcept known as the Morison formulation:

Fluid forces-------------

To derive consistent segment tensions and dis-placements, a Newton-Raphson iteration using theadditional constraint equation for the constitutivestress-strain relation is applied:

T .(T)o/j(T) " I ~xj(T)12 - ~2 {1 + ---L......:....}2 (6)

oj EAj

The element relative velocities and accelera-

Since the inertia part of the fluid reactive forcesis already accounted for in the left hand side ofequation (1) iind the current velocity is assumed tobe constant, u only consists of the water accelera-tion due to waves.

For each time step the system of equations (7)s~ould be solved until acceptable convergence ofT (T+~T) is obtained. The initial tentative tensioncan be taken equal to the tension in the previousstep. Each node j is connected to the adjacent nodesj-1 and j+1, hence equation (7) represents a tridi-agonal (Nx3) system. Such equations may be effi-ciently solved by the so-called Thomas algorithm.

(4)

Assuming that all nodal force contributions areformulated in terms of node positions, velocitiesand accelerations the motions of the nodes may beapproximated by a finite difference method known asthe Houbolt scheme [3]:

ij(T+~T) = 6~T {ll~j(T+~T) - 18~j(T) ++ 9X.(T-~T) - 2X.(T-2~T)}

-J -J

.!j(T+~T) = ~:2 {2~j(T+~T) - 5~(T) + 4~j(T-~T) +- x.(T-2~T)

-J

406

following

RISER, MOORING, DYNAMICS

matrices

(2)

anj " P (CIn - 1) n/4 D~ ~jatj m P (CIt - 1) n/4 D~ ~j[A

nj ], [Atj ] : directional transformationThe nodal force vector F. contains the

-Jinternal and external force components:a. segment tension FT(T)b. shear forces due to bending rigidity Fs(T)c. fluid forces Ff(T)d. sea floor reactive forces Fr(T)e. buoyancy and weight Fwf. buoy forces Fb(T)g. tether forces FTT(T)

Since the tangential stiffness of the line,represented by its modulus of elasticity EA is anorder of magnitude higher than the stiffness innormal direction, the tension is taken into accountin the solution procedure direct [4]

The tension vector on the j-th node resultsfrom the tension and orientation of the adjacentline segments

[mj(T)] " anj[Anj(T)] + atj[Atj(T)]where a j and atj represent the normal and tangen-tial ad!ea mass:

~~~!:~_~J2J2E~~!;The mathematical model for the simulation of

the three dimensional behaviour of flexible lines isan extension of the lumled mass method used formooring chains and wires l2]. The spacewise discret-ization of the line is obtained by lumping the massand all forces to a finite number of nodes.

To derive the governing equations of motionsfor the j-th lumped mass, Newton's law is written inglobal coordinates (Figure 2).

2. THEORY

([ Mj] + [ml T)]) .!j (T) " !. (T) (l)j

The added inertia matrix can be derived from thenormal and tangential fluid inertia coefficients bydirectional transformations:

The most successful methods are well-known as thelumped mass method (LMM) and the finite elementmethod (FEM).

In this paper a LMM-technique and the resultingalgorithm (named DYNFLX) are presented. The valida-tion of this approach has been obtained by use ofthe results of an extensive research program. Thisstudy was carried out by the Maritime ResearchInstitute Netherlands (MARIN), on behalf of theNetherlands Marine Technological Research (MaTS)program (Figure 1).This program was sponsored by the following parties:

Dutch Ministry of Economic AffairsGusto Engineering C.V.Heerema Engineering Service B.V.MARINShell Internationale Petroleum Maatschappij B.V.Van Rietschoten & Houwens B.V.

2

-=-- ~ ~ --=--

~._~..~~__-~~_=c~~=_~~-:~.-~.~~--,.c.:~c--,.. _~-,-_.~.:..._~.~-~_-~g-.-~=-~-~=-,-~~~.'c-..~.=~_.~~-:.;.;._~-:;:-=c-!~-~!-~.~-!~~,~.-!~-g&BE:~--~-=;::_:::::;;---~-~~--~-~-~-~---:,"",!,~-~~-~"-.-=--~~--.-_ ' .__ ~ _-_.. : --=~ __ ~_~""=-_::;~:~~::-_~-O-~-;::'---=-.,-~~-':--- - _~__= __-==--=___~.. =

--,--- -'=0- ..--=--- -.-'-----,---~= =-:::.c:::-=~--....: -:'-~.- -=-.~-~"':..:.~--=--.:::- -~ - _.=-_-,--~.._'-:: ---,--- _~ ~._:;:::_=__ '==~_-=-=."= '"--"--:::0--'-- =', ----e=.-_~= .,..-__-~= ___=_-.-:-.c=::::;; ~ _.;;~~:~~~:~-;,;~ - - -- - - --~- ~,._.~~-:.c,.-==,_ - -~""'- --.;---~ - -=--~~ .,..--- ~~---.==--==----'---;...'---~_=_~~~-~~R7~;_~~_-""=--~'*.~"'~~=:_~~~::;:_- .~.-"~~-=- :=-O"~..:...~ -~C:_ -~"=.:-:.-,-;;--: .- "--.___ _~ ~=-- ~_- ._~~-~."---~ __=__~ _:::=-~~ = ~:_~c:-~-=--.~~ --~~~:~---'-:-:=-.-=~,:;::~. ~""_ -~ _~-~. '= -- o:::c...~_= -- -----==- __ ---,;;c..--=-"-- - - -~ ==---=--:=::-~~-~~-:F:i.~~-~'C~"~~';""C~:~'~-'~=:--c:":'-:5,.-=':;'~"--=-~:::-:'~...:'-_---=:' ~:~T-'-----===-~.:::. :-_'~:-,---.-=,-----=-.-o=-

-C'-=, '::-z- =,,7'---:::::-~ '"~"---:--~','~~===.-~.

OTC 5531 VAN DEN BOOM/DEKKER/VAN ELSACKER 3

moment in the j-th node is acting in the planethrough the elements j-l and j (Figure 3). Accordingto slender beam theory this bending moment can bewritten as a linear function of the angle betweenthe successive elements.

tions are taken equal to the average values of thevalues at the subsequent nodes. The inertia and dragforce shape coefficients for slender cylindricalelements may be formulated in normal and tangentialcomponents. For this reason the fluid forces inDYNFLX are computed in a local system of coordi-nates.

(9)d

4 RISER, MOORING, DYNAMICS O!rc5531

ulated by means of a linear spring system for eachnode. Instabilities due to large impacts are pre-vented by adding a critical damping.

Buoys and Tether.-----.---------

When the line contains large volumes fixed inorientation, the force formulations as presented insubsection Fluid forces cannot be applied. There-fore an additional direction fixed formulation forfluid forces on such components is optional. Toewire or tether application can be applied as linearsprings from any node in arbitrary direction.

Top motions.- ------

The upper-end position of the line is derivedfrom the motions in six degrees of freedom of avessel attached to the line. Phase shifts betweenvessel motions, top motions and direct wave forcesare accounted for.

3. VERIFICATION

The development of the computer algorithms pre-sented in Figure 1 has been undertaken in continuousrelation with extensive model testing programs bothfor module building and integrated validation. Thevalidation has been focussed on specific applica-tions:

- mooring systems and floaters [2]- rigid risers [6]- flexible risers.

Mooring a~ems and floaters---- -- --------

In the 1984 mooring line dynamics study [2]extensive teats have been carried out for determina-tion of fluid reactive force coefficients of chainsand wires.

Model tests utilizing harmonic upper-end forcedoscillations of the line at five frequencies foreleven combinations. The water depths ranged from 75m to 608 m. Chains, steel wires and chain-wirecombi-lines were investigated (Table 1). For thesetests, which were carried out according to Froudetslaw of similitude, use was made of steel atudlesschain and wire. The scale ratios ranged from 19 to76. It should be noted that the chain links of the1.0 and 2.0 mm chain were cut at one side. The EA-valuea were derived from tension-elongation tests(Table 2).

The oscillation tests were carried out in the220mx4mx4mand the 240mx18mx8mbasinsof MARIN. During the tests the forced oscillation,generated by means of a mechanical large stroke os-cillator, was measured by means of a potentiometer.The upper-end line tension and vertical angle weremeasured by means of a two-component force trans-ducer while the tension at the anchor point was mea-sured by means of a ring-type force transducer. Themotions of the line were recorded by underwatervideo. The measured tensions were directly comparedwith the computed results. Moreover comparisons werecarried out on the basis of the Dynamic TensionAmplification (DTA) defined as amplification of themaximum total quasi-static tension, i.e. the statictension at the maximum excursion.

For the 300 m water depth cases typical results

are presented in Figures 4 and 5.

Results of the mentioned study clearly showedthat in practical situations the dynamic behaviourmay contribute to the maximum tension significantly.Important parameters are the non-linear static load-excursion, the low frequency (pre-) tension andthe amplitude and frequency of the exciting upper-end oscillation.

The prime dynamic tension increase originatedfrom the normal drag forces related to large global(first mode) line motions at the middle sections.Long periods of slackness even at low frequencies ofoscillation occurred due to flying of the lineunder the influence of gravity and drag only. Withincreaae frequency the drag and inertia equalledgravity forces resulting in an elevated equilibri-um of the line and normal motions in the uppersection yielding lower DTA-values.

Inertia became of importance at higher wavefrequencies especially for steel wires and multi-component lines.

A good correlation between measured and calcu-lated line tensions was found during the harmonicoscillation tests for the wide range of situationsinvestigated. Because of the non-linear phenomenainvolved, the ultimate validation of the developedcomputer program was carried out by means of modeltests in irregular waves. A model of a floatingstructure was moored by means of two parallel linesand a tensioning weight.

During the tests the motions of the structurewere measured by means of an optical tracking devicewhile the upper-end mooring line tensions and angleswere meazured by means of two-component strain-gauges. The fairlead motions derived from the mea-sured motion at deck level were used as input toDYNFLX. This procedure enabled a deterministicalcomparison between experimental and numeric tensionrecords.

Results for the semi-submersible and the barge(defined in Table 3) in irregular waves with a sig-nificant height of 13.0 m and a mean period of 15.5s are given in Figures 4 and 5. In order to ahow thecontribution of the dynamic behaviour, the computersimulations were repeated for 80 per cent reducedline diameters thus reducing drag (80%) and addedinertia (96%).

Since in the basic approach to the extremeloading assessment it was assumed that motions fothe floating structure are not affected by thedynamic mooring forces some additional analyses wereperformed. To this end the dynamic tension recordsresulting from hi-harmonic top oscillations, combin-ing a typical low frequency oscillation with a wavefrequency response, were investigated.

The low frequency energy in the hi-harmonicresult was studied by removing the high frequencytension components by means of low-pass filtering.This result was compared with the tension due to thelow frequency oscillation are given in Figure 6.

The change of restoring forces experienced bythe floating structure is illustrated by an increasein amplitude of low frequency tension and a phaaeshift. Dividing the tension record in an in-phaseand quadrature phase component, it is clear that thedynamic behaviour of the mooring line may increaseboth the effective mooring stiffness and the low

408

. . . . . . . . . . .

J-u //2 , .-. ,JJ-!., x.., -U. u.u..( . . . . -4-. ..-.. ,

frequency damping. The latter can be of the sameorder of magnitude as the potential and viscous

variations performed:

fluid damping acting on the vessels hull directly - Results for location 2 and 3 are sensitive forand is therefore important for the low frequency changes in inertia coefficients cIn and Cit.behaviour of the mooring structure. Apparently, the effect of increasing cIn/cIt

increases for higher frequencies.Flexible risers - Results for locations 2 and 3 are sensitive for-----.-----

changes in the normal drag coefficient of theThe newly developed DYNFLX program was sub- arch, ~n. The effect of a ~n modification seems

jetted to several verification tests based on com- to be reduced for higher frequencies.parison with well-known analytical solutions. In - Results for locations 2 and 3 prove to be insensi-addition to this, it was decided to carry out a tive to changes in the tangential drag coefficientcorrelation study between calculations and model cDt.tests for a so-called lazy-wave flexible riserpresented in Figure 7.

4. CONCLUSIONSThe riser was manufactured at MARIN to scale 1

to 30.5 having the correct weight, mass and outer The following major conclusions were drawn fromdimensions. The bending stiffness was approximated the research programs presented in this paper:through a proper choice of the material and was

. Dynamic behaviour of mooring lines occurs in manychecked by a bending test. practical offshore mooring situations and strongly

Furthermore, buoyancy rings were fitted in increases the maximum line tensions.order to reach the appropriate shape of the lazy- . Dynamic components of mooring line tension maywave configuration. affect the low frequency motions of the moored

The riser top was subjected to forced harmonic structure by increase of the virtual stiffness anddamping of the system.oscillations in x, y and z direction with constant l The hydromechanic properties of both mooring linesamplitude for a number of frequencies.

and riser systems are of prime Importance forTo establish meaningful correlation results, it motion, tension and bending behaviour.

was essential that the DYNFLX model discretization . The presented Lumped Mass Method does provide aclosely approximated the tank model. This was easily cost effective and accurate approach to predictingachieved for mass and flexibility, while for the the motions and internal loads of 3-D mooring andhydrodynamic coefficients of smooth cylindrical riser systems under random top excitation, wavesparts of the riser well-known values were taken from and current.literature.

The arch, however, including the buoyancy beads 5. ACKNOWLEDGEMENTas well as two transducers, was ldentifLed as mainarea of uncertainty. The authors are indebted to the mentionedSince this part of the riser is also represented in sponsors of the research programs of the Netherlandsthe mathematical model by means of cylindrical mem- Marine Technological Research (MaTS) for their kindhers with an equivalent diameter, it is implicitly permission to make use of the results from theseassumed that the influence of the buoyancy beads on programs.drag and inertia in normal and tangential directioncan be descrLbed by a single parameter. Therefore itwas felt appropriate to investigate the sensitivity NOMENCLATUREof calculation results for separate variations inthe individual hydrodynamic coefficients ~n, ~t, A = amplitude, material area cross-section

cIn and Cit. a = added inertia, vectorBFor the correlation study the oscillations in z b

= buoyancy per unit length

direction were chosen as representative for the test ~M= vector= bending moment

model behaviour, since this component introducessignificant tension and bend radius variations at CD

= hydrodynamic drag coefficientC1

the instrumented locations.= hydrodynamic inertia coefficient= current

In Figure 8 some calculated and measured mean ; = line diametervalues for bending and tension are presented. On the d = water depth, vectorbasis of the fair agreement found, it was concluded dc = volumetric diameterthat the geometry and material properties of the E = Youngs modulusdiscretization correspond with the tank model. = subscript; element, vector

The results; = force in global co-ordinates

of the parameter variations arealso presented in Fig. 8. Apart from the complex ~j = nodal force vector

= force in local coordinatesnature of the problem, interpretation was hampered gby:

= gravitational accelerationH = water depth, frequency domain transfer

- Standard deviations for signals at locations 2 and function3 are small compared to the mean values. h = impulse response function

- The rate of change in bending moments at the in- I = second moment of sectional areastrumented locations is large. Hence, approxfma- j = subscript: node numbertion by a discretized model may lead to noticeable k = iteration indexdifferences. L = length

.LNevertheless, some trends

= line segment lengthwere deduced from the ~

= line mass (matrix)

409

6 RISER, MOORING,DYNAMICS OTC 5531

Hj =1inertia matrix + = segment length errorj = time dependent added inertia matrix k = Segment errOr vector ($1, .... $j, .... *N)~ = node [A*] =length error derivative matrix [aY/aT]n = subscript: normal directionR = radius obtained from equations (5) and (6)

c- = horizontal distance in wave direction, w = angular frequency of oscillation, wave

bending radius frequency

sQ

= shear force = transformation matrix

r = tension, period of oscillationrT = tether tensiont = subscript: tangential direction, time REFERENCES

u = relative fluid velocity in local co-ordinates 1. Bathe, K. and Wilson, E.L.: Numerical methods

u = relative fluid velocity in global co- in finite element analysis, Prentice Hall,

ordinates Englewood Cliffs, 1976.

v = velocity 2. Boom, H.J.J. van den: Dynamic behaviour of

w = subscript: weight, wave mooring lines, BOSS-Conference, Delft 1985.

x = displacement, input record 3. Polderdijk, S.H.: Response of Anchor Lines to

;j = excursion vector (x,y,z)Excitation at the Top, BOSS Conference, Delft,

= output record 1985.

X,y,z = 3-D system of coordinates 4. Ractliffe, A.T.: Dynamic response of catenaryrisers, RINA Int. Symposium on Floating Pro-

U = angle duction Systems, London, 1984.

6 = angle 5. SI.uijs,M.F. van and Blok, J.J.: The Dynamicbehaviour of mooring lines, OTC paper 2881,E = element strainc = wave elevation

Houston, 1977.

A = transformation matrix 6. Sun Yi-Qing and Boom, H.J.J. van den: DynamicA = scale factor behaviour of marine risers, Offshore China

85, Guangzhou, 1985.!J = angleP = fluid density

7. Wheeler, J.D.: Method for calculating forces

u = standard deviation produced by irregular waves, Journal of

T = time Petroleum Technology, March 1970.

4 = line angle

TABLE lTEST SITUATIONS FOR MOORING STUDIES PERFORMED

Water depth Water depth Water depth Water depth75 m 150 m 300 m 608 m

a=19 A=38 i=76 A=76

Chain Situation Situation SituationD=O.076 m 1 4 7/12/15

Chain Situation Situation SituationD=O.152 m 2 5 8/13/16

Wire Situation Situation SituationD=O.076 m 3 6 9/14/17

Combi-line Situation SituationD=O.076 m 10 11

TABLE2MOORING LINES PROPERTIES AS MODELLED

[

Model chains Prototype chain

D (mm) B (mm) L (mm) M (kg/m) W (N/m) dc (m) EA (N*105) A M (kg/m) W (N/m) dc (m) EA (N*109)

1.0 4.2 7.9 0.021 0.177 0.0019 0.03 76 124 1048 0.144 1.19

2.0 6.8 12.0 0.080 0.690 0.0036 0.11 38 119 1021 0.137 0.60

4.0 14.2 22.8 0.338 2.874 0.0076 7.00 19 125 1063 0.144 4.90

8.0 26.9 40.1 1.383 11.801 0.0151 22.00 9.5 128 1092 0.144 1.93

410

. . . . . . . . . . .

TABLE 3MOORED FLOATER CHARACTERISTICS

Designation

LengthBeamDepthDraftDisplacementweightCentreof gravityabove baseTransversemetacentricheightTransversegyradiusin airLongitudinalgyradiusin airNaturalperiods:

Surge (sit. 12/15)(sit. 13/16)

Wave

Roll (free-floating)(sit. 12/15)(sit. 13/16)

Pitch (free-floating)(sit. 12/15)(sit. 13/16)

Symbol

LBDT

T=

T=

%

e

Unit

n

m

n

Illtm

Illm

m

s

s

s

s

Magnitude

Seni-subl Bag.

117.0 230.o85.0 57.564.7 26.522.8 7.646,360 87,75021.54.436.038.0

217.0 357.0lok.o 173.0

23.0

50.9 10.446.9 10.447.9 10.339.938.435.1

RESPONSIBILITYYear

MaTS (lRO] MP.RIN INDUSTRYI I

1983

L

1984

1985

DYNLINE (vM-v-5) I

* 2D mathematicalmodel

* oscillating tests* Harmonic testsl Irregular testsl PublicationBOSS 1985

Delivery tosponsors:S1Pf4/KSEPLGusto/SBM

DYNPIPE 51eerema/B1uewaterR&H

* Bending

: ;::;;c:g: ess ~

China 1985

DYNRIS

stiffness I I MARIN I

I I 4 v .waveforces* Preprocessing andpostprocessing!I I I/r I*cRAYver.ion [

DYNFLX (VM-VII-8)

l 3D ma+h.=-.+ic.l,... Inde 1

....-..-----

I ,.. . I I* Bi;ka stiffness IDYNAFA

I

L- -1l Wave f~rces IaW--L-Fatigueanalysisl Flexiblerisermodel+--+-* Publi. .-ication cmC87 I I Delivery toI

sponsorsI I

Y

1987 uExmivs10t4 DYNFLX(VM-1x-8)- Torsionl Advanced accessand application* systematicmodeltests* validationI

Fig. lR&Dpr~rsms onmoc.dng and riser dynamics,

I.n /x x7 gA k\\\

* El

N

. . . .. .. .. .. .. . . .

I

6).-U

412

II

WAVE[Ml

x[Ml

z[Ml

5

20

10

T 2000[kNl

2000T(reduceddynamics)

T2000

[kNl

10;i;15

10Z-N15[Ml

,

0 400Time [s]

Irregular wave results for barge(situation 15)

10

10

5

5

, I I

o~400

Time [s]

Irregular wave results for semi-sub(situation 12)

I

200

u

N15

1Oc)

Line discretization [M]

0 .

0

Y

/

o 0.5 1.0 1.5u [rad/s]

Harmonic oscillation results

Fig. 4Discretization, DTA-values, and irregular wave results for Situations 7/12/1 5.

III

I

1 I

10 lo-WAVE[Ml

20-x A.+[Ml w-

1

1 I I1

z[Ml

T 500[kNl

T 5.10

(reducedynamic

5.10T[kN]

1X-N15[M]

1Z-N15[MJ

5000

-1

5.105~11 1 I I

5.105-

~ o~0

Time [s] Time [s]

II

Line discretization [M]

m0

Irl -

./ l

] ;I ,

0 0.5 1.0 1.5u [rad/s]

Irregular wave results for barge Irregular wave results for semi-sub Harmonic oscillation results(situation 16) (situation 13)

Fig. 5Discretization, DTA-values, and irregular wave results for Situation 8/10/13/1 6.

2 = 0.50 rad/s U2 = 0.75 rad/s w~ = 1.00 rad/s

5

X-TOP[Ml O

-5

1000T[kN]

o

~oo ~ 1~,o 200 0 100 Time[s] 200

Results for w, + W2 after low pass filtering Results for q

Fig. 6Bi-harmonic simulation raaults.

. . .

.

.

.

.

.

.

.

.

.

. . . .

1

Force transducers location 1

0Mom. transducer

I

location 2Force transducer

I Mom. transducerN. 1Force transducer 10catiOn 3m! 1,.,....,,,,,..:.,..,.,..::.. ..,,.:,,.,..,;,::..,...:,...:. ,,.,.,,:,,,....:,... ,..,.. .,.

54.24

Fig. 7General test arrangement flexible riser.

415

Em

1.6

OBM

0.8

c

MEAN VALUES BENDING MOMENT

Experiment

-- DYNFLX

x

0.4 0.8

2

8

? c

MEAN VALUES TENSION

Experiment_----DyNFLx

-w----i i

0.4 0.8

FLEXIBLE RISER PARAMETER VARIATIONS

Experiment........ Base case...................... Increased CTn

----- Increased Increased- Increased

. . .

.

.

.

.

.

.

.

.

.

. . . .

aT

o~. . 1.2

.

c IncIncIn

ItcIt cDncIt cDt /

1.6

BM

O.E

o

1.6

T3

0.$

.u

/

2

Fig. 8-Flexible riser correlation results.

416