THE EFFECTS OF MOORING LINE DAMPING AND · PDF fileTHE EFFECTS OF MOORING LINE DAMPING AND ... - the Gxyz axis fixed on the ship with origin at the ship center of gravity. ... (ITTC).

THE EFFECTS OF MOORING LINE DAMPING AND

WAVE DRIFT DAMPING ON MOORED TANKER

DYNAMICS

Hernani L. Brinati*, Kazuo Nishimoto*, Carlos Hakio Fucatu*,Isaias Q. Maseti**, Martin Fuljahn*

""University of Sao Paulo** CENPES, Research Center, Petrobras

Abstract- This paper is concerned with the analysis of the dynamic behaviorof a tanker, acting as a FPSO, moored through a differentiated complianceanchoring system (DICAS). It is presented, initially, the mathematical modelsof the moored tanker dynamics, with special consideration on the descriptionof the interaction between waves and current, and the mooring line dampingThe mathematical formulation is used to simulate the performance of a130kDWT tanker in the DICAS configuration. The simulation results arecompared with model test data in order to evaluate the accuracy of themodels proposed to represent the wave drift and mooring line damping.

INTRODUCTION

Tankers have been commonly used as floating production storage andoffloading (FPSO) systems. Different mooring line configurations have beenproposed to keep the ship stationed: the single point mooring system (SPM),the spread mooring system (SMS) and the turret system. Although Petrobrashave some SPM systems operating in deep waters, it seems that the two lastconfigurations are today the best candidates for future FPSO. Compared tothe SMS system, the turret configuration has the advantage of allowing thevessel to keep aligned with the resultant of the environmental forces. Avariation of the SMS system - the Differentiated Compliance AnchoringSystem (DICAS) - which presents as a main feature lines with differentstiffness, was proposed by Petrobras. The objective of this configuration is togive the ship, like in the turret one, some freedom to get aligned with the

Transactions on the Built Environment vol 29, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509

12 Offshore Engineering

environmental forces. Full scale trials and model tests have been carried outto evaluate the expected favorable performance of DIG AS system. The scopeof the present paper is to analyze the system behavior with basis onsimulation results obtained with a proposed mathematical model.

The dynamic behavior of moored vessels have been investigated by severalauthors. It may be pointed out the researches carried out by Wichers withSPM* and turret moored tanked, MARINTEK* for a turret FPSO, Bernitsas*for SMS, and Nishimoto et al for SPM* and turret moored tanker .

The main problem found in the analysis of the moored ship dynamics is theevaluation of the damping forces. In fact, the determination of appropriatedamping terms may be observed in all the works listed above. Even with theutilization of more precise mathematical models, there have been alwayssome discrepancy between the calculated and the experimental results.

There are different sources of damping forces which should be taken intoaccount: the ship hull, the mooring lines and also the interaction betweenwaves and current. In a previous paper^ the authors investigated twodifferent models to represent the hull damping forces. In the present paperthe main concern is related to the analysis of the wave drift and mooring linesdamping. This analysis is presented in the next section which gives a briefdescription of the mathematical models. Afterwards the mathematical modelsare used to simulate the behavior of a spread moored tanker in the DICASconfiguration. The simulation results are compared with model test data inorder to validate the models proposed to represent the damping terms

Finally the main conclusions of the study are presented.

MATHEMATICAL MODELS

The mathematical models required to represent the motion of a mooredtanker are presented in this section. Firstly it is shown the equations ofmotion for the horizontal plane slow ship dynamics. Afterwards we describethe formulation for the wave forces and mooring lines.

Equations of Motions for the Slow Ship Dynamics

Figure 1 depicts two coordinate systems used to represent the motion of amoored ship:


Offshore Engineering 13

Figure 1 - Coordinate systems

- the OXYZ axis system fixed on the earth (inertia! system);- the Gxyz axis fixed on the ship with origin at the ship center of gravity.

Applying Newton's law of motion, the following differential equationsdescribing the relationship between the motion variables, referred to theGxyz system, and the external forces may be obtained:

where M is the ship mass, 1% is the moment of inertia about the Gz axis, u andv are, respectively, the surge and sway velocities, r is the yaw angularvelocity, z/, v and r are the time derivatives of u, v and r, respectively; F,\ «u

Fy ext and FN ext are the excitations forces in x and y directions, and momentabout the z axis.

The external forces and moment for each ship may be expressed in terms ofthe different factors that affect the ship dynamics, as for instance for FX ext :

Fxe*t=Fx, + Fxh ~ Fx» + Fxc + Fx™ + Fxm+ FMD +FWD (2)

where Fx, and FXH, are the hull inertia and damping forces, respectively, />»,FXC and FX™ are the wind, current and wave forces, respectively, Fxm is themooring force, FMD and FWDD are the mooring line damping forces and wavedrift damping forces respectively, in which will be discussed with detail inthis paper. All this forces are represented in the ship coordinate system.

Hydrodynamic Models

In a previous paper* the authors compared two different formulations tomodel the ship hull hydrodynamic forces (inertia and damping) which act onthe ship hull: the first one is a classical model used by several authors likeWichers\ Obokata^ ; the other one is based on a maneuvering model



proposed by Takashina , specially developed to represent low speed shipmotion. Considering that the second model gives a better representation forthe hull damping forces, it has been used in the later studies.

A brief description of the maneuvering model may be found in Nishimoto^;the modifications introduced in Takashina's model to deal with the dynamicsof mooring systems are also specified there. In this formulation the currentforces are taken into account by substituting the absolute ship velocities bythe corresponding relative ones.

Mooring Line Restoring Forces

The mooring line forces that act on the ship are computed using a simplerestoring curve obtained from catenary formulation. For each mooring line,the restoring characteristics are calculated and this force-elongation curve(stiffness characteristic) is used as a input data.

Wave forces

The wave forces on the ship hull are evaluated considering separately themean wave drift forces, the slow varying (second order) wave drift forcesand the high frequency (first order) forces. For the scope of the presentpaper, the first order component will not be considered.

Mean wave drift force The mean wave drift force acting on the ship hull isevaluated considering the procedure described below:

-the quadratic transfer functions of wave drift forces for a regular wave areevaluated for different angles of incidence, %, and different frequencies, co,within a specified sea spectrum (ITTC). Considering only the terms thatinfluence ship motion in the horizontal plane, situated on the diagonal ofthe matrix of quadratic transfer functions, we obtain the following terms:Xdm(x,(o), Yom(x,co) and NDmOc,a>)- A 3D source distribution method isused to compute the quadratic transfer functions.

- the mean wave drift forces and moment acting on the ship for each angle ofincidence, Xom(li), YomOCi) and ND™(XI), can be computed through:

(3)

where S(co) is the considered sea spectrum.



Slow varying wave drift forces In a random sea, besides the mean wavedrift forces, a body is subjected to low frequency oscillating wave driftforces. These forces, that have frequencies equal the sum and difference oftwo regular wave frequencies, are usually of low amplitude but they mayhave significant effect when their frequencies are near the system naturalfrequencies. In this condition a moored ship may exhibit large amplitudeoscillating motions.

The slow wave drift forces spectra, SXL, SYL, SNL, may be computed from thecross-correlation of the sea spectrum and the quadratic transfer function, asshown below:

C/CO(4)

where |i = ml -co 2 is the frequency difference.

In equations (4) we used, as proposed by Aranha and Fernandas™, jj. equalzero.

Once the slow wave drift spectra has been obtained, we may evaluate thecorrespondent time varying forces, FDux, FDLY, FDtN, using the inverseFourier transform.

The mean wave drift forces and the slow varying drift forces are introducedin equation (1) in order to compute the second order ship motion in thehorizontal plane.

Wind forces

Wind forces acting on the ship hull are modelled using traditionalaerodynamic drag formulation whose coefficients are based on model tests.We adopted in our study the OCIMF™ experimental curves.

Wave Drift Damping

It had been shown that there is an influence of drift velocity of an oceanvehicle on the exciting forces that cause it. This effect is called wave driftdamping and may be the dominant damping mechanism. Description of the



phenomenon and derivation of computing methods were presented bydifferent authors - Wichers**, Grue^ and Aranha^.

In the present paper we use the procedure proposed by Aranha^ to computethe wave drift damping matrix and the interaction between wave and current.

The wave drift damping matrix (for a motion in the horizontal plane) B^is

given by:

0

sinab cosab 0 (5)

where :

do is the wave direction relatively to ship longitudinal axis

b = 4.D,,(<y,a,,) + codco

b = -2.-

I = identity matrix

in which DO(W, do) is the vector of slow drift forces:

D/w,eJ = D,/w,ajr + D r ,«jy + D,/w,eJ

The matrix of wave drift damping for a random sea is given by:

B ia> (6)

The oscillatory force on the vehicle due to the wave drift damping and theinteraction between wave and current is given by:

cos a,

0

(7)

The first term in equation (7) corresponds to a variation of the mean wavedrift force which may be positive or negative, depending on the wave and



current directions. The second term represents a damping force caused bythe horizontal motion of the vehicle.

In order to check the results given by this formulation, it was performed acomparison between the calculated forces in the frequency domain withthose given by Wichers based on experimental results. Figure 2 shows thatthe calculated mean wave drift force and wave drift damping are very closeto those obtained by Wichers* V

it*5 80

II.

w(rad/sec)

a) Proposed Mathematical Model

b)Experimental Results (Wichers)

Figure 2 - Mean wave drift force and wave drift dampingfor a fully loaded 200kDWT tanker



The increase of the mean wave drift force of surge is significant with theintroduction of current as can be verified in the Figure 2. As a consequence,it will increase the ship mean offset causing high mean tension and a smalleroscillation amplitude due to the wave drift damping.

Mooring Line Damping

There are some procedures proposed to estimate this source of damping, likethose proposed by Huse & Matsumoto^ and recently Le Boullec^. In thispaper, a methodogy proposed by Nishimoto and Aranha^ is used.

Taking into consideration the geometric and dynamic definitions indicated inFigure 3, the horizontal drag force that the line applies to the system in thevertical plane containing the line Fx, can be obtained from:

Figure 3 - Geometric and dynamic definitions of a

catenary (q=submerged weight)

where,

q J 1 - cos 6* h o cos" 9



RH = 6 FX / 8 Xa , CD is the drag coefficient, D is the line diameter, h is the

water depth, p is the water density, and

f (8) = —. * sin 9 - sin B.sinh* (tan 8) + (l- cos 8).sin 8

Let 8yA be the displacement imposed in the plane perpendicular to the planeof the line. If the friction between the line and the seabed is ignored one mustconsider that the line slips on the ground, pivoted at the anchor placed at s =

- l&. Ignoring also the fluid drag on the part of the line that rests on the

ground but assuming that Z/is relatively smaller than Z/+ k, the displacement

at each point of the line is roughly equal to 8yA, leading to the followingexpression for the drag force applied at A:

(11)

The components Fx and Fy, that each line applies to the vessel, calculated inthe line coordinate system, should be projected in the system of axis fixed onthe ship.

The results of full scale tests performed with a 30 kDWT tanker in 1995^were used to validate the mathematical model proposed for the mooring linedamping. Such tests consisted of a tug pulling the ship with a known force,and then releasing it. The resulting motion was then measured with the helpof a precise GPS device. Several tests covering a range of forces and pullingdirections were performed then. The input used in the simulation was theinitial position of the ship in each test.

Figure 4 shows an example of one of such tests: the solid shaded linerepresents the full scale test results; dotted line represents the calculatedresults without the effect of line damping; and solid thin line represents thecalculated results with the mooring line effect incorporated.



Figure 4 - Comparison between full scale and simulateddecay tests (surge direction)

One can notice that in the initial decay cycles there is a good adherencebetween the tests results and the simulation results obtained with theincorporation of the line damping. The observed difference could be due toweak environmental conditions in the full test area, which were neglected inthe simulations, and/or caused by bottom friction effect .

RESULTS AND DISCUSSION

Ship And Mooring System DataThe mathematical models were used to simulate the dynamic behavior of aselected FPSO system in a DICAS configuration. The particulars of thestudied ship are indicated in Table 1. The mooring system characteristics areshown in Table 2. The data adopted for ship and line characteristicscorrespond to those of the moored tanker investigated by MARINTEKA

DesignationLengthBreadthDraftDepth

DisplacementMass

SymbolLBDHVM

Unit (SI)mmminm*Kg

Magnitude260.0044.5016.2026.801539101.57x10*

Table 1 - Particulars of the ISOkDWT full loaded tanker



Line123456789

S/D*DDSDSDSDD

Initial Tension (kN)27402130101014207801420101021302740

Azimuth (deg)294271268185180175928966

Length (m)191019101910191019101910191019101910

Table 2 - Mooring lines characteristics

*(Single Chain 084mm, Double chain 0119 mm)

Environment

The environmental parameters used in the simulation tests are shown inTable 3, with reference to the number of the model tests carried out atMARINTEK facilities. The water depth is 300m for all tests.

Test

331338342

Vc(

111

n

233

currl/S)

:nt4)c(deg)

135.090.067.5

Vw(m/s)37.230.230.2

wind<t>w(deg)

135.090.067.5

Hs(m)

7.66.36.3

wavesTp(s)

12.912.112.1

4>v(deg)

135.090.0675

Table 3 - Environmental Conditions

Analysis of System Behavior

Several tests were carried out to validate the mathematical models and to geta better understanding of the wave drift damping and the line damping. Thesystem behavior is characterized by the time series of the horizontal planeship motion and the time series of the line tensions.

In order to make the comparison between the simulation and model testresults we adopted the same variables that MARINTEK use to represent themotion of the model: the position of a specific point in the ship bow and theship heading (angle), referred in the next tables as Res. Bow and Yaw,respectively.

There was a large difference between the simulation and the model testresults for the three tests defined in Table 3, as it may be seen in Tables 4 to6. Since that difference was not expected, an investigation was carried out todetermine its cause. It was found out that the discrepancy in the results is



mainly due to differences between the values of wind and current dragcoefficients used in the simulation and those which should be used torepresent MARINTEK test conditions. The aero and hydrodynamiccoefficients in the sway direction obtained by MARINTEK from the testmeasurements are almost twice as large as OCIMF coefficients.

Res. BowYaw

Line -1Line -2Line -3Line -4Line -5Line -6Line -7Line -8Line -9

Units

mdeg.kNkNkNkNkNkNkNkNkN

Model Test

MeanValue27.8-20.74196283612571541814126984517642606

Stand.Dev3.771.9177444727216911414785163278

Simulation (OCIMFcoeficients)

MeanValue17.7-16.23789263812411465764131585718712569

Stand.Dev6.361.14265128637143652873158

Simulation(corrected windcoeficients)

MeanValue17.6-20.43896279213461620842141483218022387

Stand.Dev6.021.02260138759847643074154

Table 4 - Comparison between simulation andexperimental results (Test 331)

Res. BowYaw

Line -1Line -2Line -3Line -4Line -5Line -6Line -7Line -8Line -9

Units


Model Test

MeanValue34.5-26.644913767179927511341196776515291878

Stand.Dev5.221.78102198656960234437550100137


MeanValue25.2-23.442973126145922901176178082116731996

Stand.Dev8.371.273172541132961471653693194


MeanValue36.3-27.4142863781188928301415199572915601779

Stand.Dev6.351.043053521943631741704698187




Res. BowYaw

Line-1Line -2Line -3Line -4Line -5Line -6Line -7Line -8Line -9

Units


Model Test

MeanValue42.2-27.842643903188833511673242972514641730

Stand.Dev4.131.049469846125903123234588116


MeanValue24.7-23.742833221150025901319193281516541927

Stand.Dev8.431.613102661153171571583690180


MeanValue40.15-28.543113932198732131579215071715391711

Stand.Dev4.540.8331238221142418818048100180


The simulation tests were then repeated with the proper coefficients and theobtained results, as it is shown in the right hand column of Tables 4 to 6,indicate a relatively good agreement with the experimental data.

The simulation results shown in the following figures were obtained with thecorrected wind and current drag coefficients, as explained above.

A most illustrative comparison between the simulation and the model testresults for the horizontal ship motion is given in Figure 5, corresponding toTest 342. This figure represents the simulated trajectories of twocharacteristic points on the ship hull - the ship center of gravity and theaforementioned point on the ship bow. Two straight lines drawn in thefigure, which connect the mean position of the above mentioned points,represent the mean value of the ship heading in the steady state condition forsimulation and model test. It may be seen that there is a good agreementbetween the calculated and measured motion.



I

Model Test-Simulation with Complete Model

Figure 5 - Comparison between simulation and model test

Wave Drift Damping under the Influence of Current

The effect of wave drift damping as well as the effect of wave and currentinteraction may be visualized in Figures 6 and 7. Figure 6 is a modification ofFigure 5, where another straight line, representing the mean value of the shipheading in steady state was included. This line was obtained by simulatingthe ship behavior in the absence of the wave drift damping effect, that meansneglecting the matrix of wave drift damping. It is quite clear from this figurethe effect of interaction between wave and current in determining the shipposition and heading at steady state.

X(m)

Figure 6 - Comparison between simulation and model test - Effect of wavedrift damping



Figure 7 presents the time series of a ship motion in surge. It may be seen inthis figure the effect of interaction between wave and current leading the shipto a greater mean offset while, due to the wave drift damping, there is adecrease in the motion amplitude. In terms of line tension, there is anincrease of the mean value as well as the tension amplitude.

Effect of Mooring Line Damping

The effect of mooring line damping is illustrated in Figure 8 which presentsthe time series of the ship motion in surge. It may be seen that there is not asignificant change in the amplitude of ship motion, which indicates that theline damping is of second order when compared to the other damping terms.

/ ",%/" ," ";\'" f' " ,^)

Without InteractionWith Interaction

ME(s)

Figure 7 - Effect of wave drift damping on the ship motion in surgeMARINTEK Test 342

.

~ No Una Damping EffectLine Damping Effect

i 1 I I I i 1 I I 1 | I I

Figure 8 - Effect of mooring line damping on the ship motion in surge -MARINTEK Test 342



However, the mooring line damping may have a greater effect for deepwaters, when the total line length is larger, or for smaller ships. It was alsoobserved that the amplitude of the line tensions present a slight decrease withthe introduction of the line damping.

CONCLUSIONS

The paper presented an analysis of moored ship dynamics with the discussionof two terms which were incorporated in the mathematical model used tosimulate the moored ship behavior.

It was shown that the wave drift damping and the interaction between waveand current plays an important role in the ship motion in surge.

It was also shown that the effect of mooring line damping may be importantin determining the ship response. However, for large ships, at least in smallwater depth, its effect is of second order.The comparison between simulated and experimental results showed a largediscrepancy. However, when wind and current drag coefficients based onMAEJNTEK model tests are used instead of OCIMF coefficients, there is afairly good agreement between simulation and experimental results.

REFERENCES

[1] Wichers, J.E.W., "The prediction of the behaviour of single pointmoored tankers", Developments in marine technology, 4, Floatingstructures and offshore operations, nov 1987

[2] Wichers, JEW, "On the low frequency surge motions of vesselsmoored in high seas", 14th Annual OTC in Houston, Texas, USA, 1982

[3] MARINTEK, "DICAS Development", Report, Trondheim, June 1996[4] Bernitsas, MM, Garza-Rios L. O, "Effect of Mooring Line

Arrangement on the Dynamics of Spread Mooring Systems"; OffshoreMechanics and Arctic Engineering OMAE - 1995; Volume 1 - Part B,1995

[5] Nishimoto, K., Brinati, L.H., Fucatu, H.C., "Analysis of Single PointMoored Tanker Using Maneuvering Hydrodynamic Model",Proceedings of the ASME 14™ International Conference on OffshoreMechanics and Arctic Engineering ( OMAE'95), Vol, , Denmark ,1995

[6] Nishimoto, K., Brinati, L.H., Fucatu, H.C., "Dynamics of MooredTankers - SPM and turret", ISOPE 1996, 1995



[7] Obokata, 1, "On the basic design of single point mooring systems (1streport)", Journal of the Society of Naval architects of Japan, vol!61,June 1987.

[8] Takashina, J., "Ship Maneuvering Motion due to Tug boats and itsMathematical Model", Journal of the Society of Naval Architects ofJapan, vol. 160, Dec 1986.

[9] Takashina, J., Hirano, M, "Ship Maneuvering Motion by Tugs in Deepand Shallow Water", MARIN&ICSM90, June 1990.

[10] Aranha, J.A.P. , Fernandes, AC , "On the second order low frequencyforce spectrum", Applied Ocean Research, 1994

[11] Oil Companies International Marine Forum, "Prediction of Wind andCurrent Loads on VLCCs"-(first version), OCIMF, 1977

[12] Wichers, J.E.W., "A Simulation Model For A Single Point MooredTanker", Publication No. 797, Maritime Research Institute, Netherlands

[13] Grue,J. , Palm, E , "The mean drift forces and yaw moment on marinestructure in waves and current", J. Fluid Mech. 150, pp. 121-142, 1993

[14] Aranha, J.A.P, "A formula for "wave damping" in the drift of a floatingbody", J. Fluid Mech. 275, pp. 147-155; 1994

[15] Aranha, J.A.P. "Damping and Environmental Forces", PROS AM 1 -Research Project, PETROBRAS/USP, Report 1, Sao Paulo, 1995

[16] Huse, E. & Matsumoto, K, "Mooring line damping due to first andsecond order vessel motion", OTC 6137, 21th Annual OTC inHouston, Texas, USA,May 1-4, 1989

[17] Le Boulluec, M. , Le Buhan, Ph. , Chen, X-B. , Deleuil, G. , Foulhoux,L., Molin, B. and Villeger, F., "Recent Advances on the Slow-DriftDamping of the Slow-Drift Damping of Offshore Structure", Behaviourof Offshore Structures (BOSS), Vol.1, 1994

[18] Nishimoto, K. , Aranha, J.A.P., Kaster, F, PETROBRAS/USP,"Monitoring Report and Numerical Simulation(in Portuguese)", FinalReport, February 1996


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