The Effect of a Dual Draft Hull on the Motion Behaviour of a Pipelay/Heavy-Lift Vessel

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Date Author Address

June 2008 J.L.F. van Kessel

Deift University of Technology Ship Hydromechanics Laboratory

Mekelweg 2, 26282 CD Delft

TUDeift

Deift University of Technology

The Effect of a Dual Draft Hull on the Motion

Behaviour of a Pipelay/Heavy-Lift Vessel

by ).L.F. van Kessel

Report No. 1573-P ₂₀₀₈

Published in: Proceedings of the ASME 27tF, International Conference on Offshore Mechanics and Arctic Engineering

O MAE 2008

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TABLE OF CONTENTS

Welcome Letters

4

Important Information

7

Conference Sponsors

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Conference Exhibitors

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Sessions at a Glance

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Final Programme

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Outreach for Engineers Forum

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Maps of Estoril 62

Estoril, Portugal 63

Cascais, Portugal

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Session Index 68

Author Index

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30 www.omae2O08.com

Session Co-Chaff: _{Michael Bernitsas, University of} Michigan, USA

Seismic Analysis of a Double-Hinged Articulated Offshore Tower (OMAE200B-57672)

Syed Hasan, A4garh Muslim Unipe,:ciíy. India, Nazrul Islam, Khalid Mom, Jarnia Mil/ja ls/amia, India

Fluctuating Wind Induced Response of Double Hinged

Articulated Loading Platform (OMAE2008-57723) Mohd Zaheer, Nazrul Islam, Jamia Mi//ia ls/amia, India Hydrodynamic Analysis of Multi-Body Floating Piers (OItAE2008-57849)

Zahra Tajali, Mehdi Shafieefar, Tarbiat Modan's_{Universi!y, Iran,}

Mahmood Akhyani, Science and Reasen'hofIslamic Açad Universi'y -Tehran, Iran

Multiobjective Optimisation of a Floating LNG Terminal

OI'vLE2O08-58003)

Evangelos Boulougouris, Apostolos Papanikolaou, National

Technica/ Univer.ciy ofAthens, Gn'ece

OFFSHORE TECHNOLOGY SYMPOSIUM

OFT-8 Floating Systems V

Tuesday, 17 june, 2008 14h00-15h30 Rootn: 1)1 Session Chair: Celso Morooka, UNICAMP, Brazil

Session Co-Chair: _{Knsh Ihiagarajan, University of} Tcstcrji Australia, Australia

Second-Order Low-Frequency Wave Forces On A Spm Offloading Tanker In Shallow Water (OMAE2008-58048)

Shan Ma, Shari Ski, Hathi,i Engineering Universi'y, China, Moo-Hyun

Kirn, Texas A&M Univet:ciy, USA

Computing Large Amplitude Motions of a Floating

Offshore Structure in the Time Domain (O?L\E20O8-57922) Wei Qiu, Hongxuan (Heather) Peng, Memotial University of

1\JewJòund/and, Canada

Hydroelastic Response of a Subsea Production Platform

(OMAE2008-5701 4)

\Tincent Olunloyo, Charles A. Osheku, Universi ofLa,gos, Ni,ge,ia

The Effect of a Dual Draft Hull on the Motion Behaviour of

a Pipelay/Heavy-Lift Vessel (Or\LAE2008-57357)

Jan Van Kessel, Gu.rtoMSC / Dei/i UnivofTechny, The 1\Tether/ands,

Wj. Van der Velde, Seaway Heavy Lifting, The Netherlands

OFT-7 Spars and TLPs

Tuesday, 17 June, 2008 i 6h00-1 8h0() Rcx,in: 1)1 Session Chair: Knsh Thiagaraian, University of

Western Australia, Australia Session Co-Chair: Celso Morooka, UNICAMP, Brazil

Dynamic Response Analysis of a Spar Platform Subjected to Wind and Wave Forces (0MAE2008-57227)

BerntJ. Lnira, Dag iriyrhaug,jarle Voll, Nonvegiaiz (]niierszyof

Science and Technology, Nonv'rji

FINAL

Effect of Moonpool Hydrodynamics on Spar Heave

(OMAE2008- 57264)

Hinianshu Gupta, BP, USA, Rober-t Blevins, consultant. USA,

Hugh B anon, BP America, USA

Coupled Dynamic and Static Analysis of Typhoon TLP

Accident During Extreme Environmental Conditions

(OMAE2008-57676)

Gabriela Joelsas Timerman, Marcio Araújo de Campos, Kazuo Nishimoto, Oscar Brito Augusto, UniversityofSào Paulo, Brai/ Development of a New Self-Stable Dry-Tree GoM TLP with Full Drilling Capabilities (OMAE2008-57772)

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OF'l- 12 _{Riser I'echnology Forum I}

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Hybrid Catenary Riser for Spar Application (0MAE2008-57064)

Mark Chang, Yongming Cheng, ILa1coIm Vass, Vincent Ledoux,

Technib, USA

SCR Application for Turret Moored FPSOs in West Africa (OMAE2008-57454)

Howard Wang, Wan Kan, Juan Orphee, Mark Crawford, Jim

Sutherland, ExxonMobi/ Development companj', USA, Paulo Gioielli, John Miller, ExxonMobil Ups/ream Research, USA

Risers Clashing Induced by the Wake Interference

(OMAE2008-57639)

Antonio Fernandes, cOPPE/UFRJ, Bra7l, Stefania Rocha, PETROBRAS, Braj/ Fabio Cnelho, COPPE/UFRJ, Brai/, Breno Jacob, Fed Uni,'ofRio de Janeiro, Braii,Joseane Quciroz, Brucia Capanema, Jorge Merino, COPPE / (JFRJ, Bra a/I

OFFSHORE TECI-INOLOGY SYMPOSIUM

OFF-27 Riser i'cchnology Forum II

Tuesday, 17 June, 2008 11h00-12h30

Room: D2

Session Chair _{Celso Pesce, Universidade de So} Paulo, Brazil

Session Co-Chair: Mark Chang, Technip, USA

Numerical and Experimental Investigation on the Dynamics of Catenary Risers and the

Risers-Induced-Damping Phenomenon (OMAE2008-57616)

bannis Chatjigeorgiou, Nationa/ Technical UniversityofAthens,

Greece, Marc Le Boulluec, Gilbert Damy, IFREMER, France Coupled Analysis of DP-Tugboat and Onshore Pre-Assembled SCR (Steel Catenary Riser) Transportation System (OMAE2008-5757l)

Fabiano P. Rampazzo, Marcio M. Tsukanioro, Kazuo Nishimoto,

Luis Quadrante, University of São Paulo, Bra a/I, Ricardo Franciss, PETROBRAS, Braa//, Marcos Siqucira, Fed Univ of Rio De Janeiro, Bras/I, Felipe R. Pereira, University of São Pau/o, Bras/I

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Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE2008 June 15-20, 2008, [stonI, Portugal

OMAE2008- 57357

THE EFFECT OF A DUAL DRAFT HULL ON THE MOTION BEHAVIOUR OF A PIPELAY f HEAVY-LIFT

VESSEL

J.L.F. van Kessel W.). van der Velde

GustoMSC, Seaway Heavy Lifting

Schiedam, The Netherlands Zoetermeer, The Netherlands

ABSTRACT

The motion

behaviour of a

Dual Draft vessel was calculated and experimentally validated by means of

model tests. Both the tests and computations showed that the roll behaviour of a Dual Draft vessel in pipelay ¡transit

mode does not correspond to the usual observed response amplitude operator (RAG), where the roll RAO decreases with increasing wave height due to non-linear

damping. When the wider top section of the Dual Draft

vessel enters the water due to a roll motion, the buoyancy

increases at that side and results in an increase of the

excitation moment and roll RAG.

Non-linear damping is of significant importance on the

ship motions and is particularly noticeable in roll motions. This paper describes the effect of a Dual Draft hull on the motion behaviour of a pipelay I heavy-lift vessel in beam seas. The non-linear damping of a Dual Draft vessel will be discussed and calculations of the motion behaviour will be presented and compared with results of model tests.

KEYWORDS

Dual Draft vessel, pipelay vessel, heavy-lift vessel, motion behaviour, roll damping, roll statistics, model tests.

INTRODUCTION

The need for new and improved offshore

pipelaying equipment is growing, since oil and gas discoveries are

being made in deeper and rougher waters. In addition,

many pipelay and heavy-lift vessels operating today were built

during the seventies and eighties and

will be replaced in the near future.

In recent years, pipelay functionality was added to several crane vessels. Besides, many contractors considering

buying a new heavy-lift vessel are also interested in (future) pipelaying possibilities with the same vessel. In that case the vessel can be used for pipelay operations in periods with no (or few) heavy-lift assignments.

Design requirements with respect to stability and motion behaviour of a heavy-lift and a pipelay vessel are often conflicting. In general, metacentric heights (GM) of heavy-lift vessels are relatively high to provide sufficient stability

for lifting operations, which are normally performed in calm weather conditions. On the other hand, pipelay

operations will also be performed in more severe weather conditions.

Motions are for a large extent determined

by the

metacentric height of the vessel, which itself is to a large extent influenced by the breadth. A small breadth results in most cases in favourable motion behaviour. When a heavy-lift vessel is in lifting mode, the load in the crane will shift the centre of gravity upwards and decreases the

GM-value. When not engaged in lifting operations but performing other functions, such as pipelaying or in transit, the motion behaviour of heavy-lift vessels is often unfavourable with high accelerations due to an excess in

stability (GM height). In order to improve the motion behaviour

of these types

of vessels during pipelay operations, the metacentric height should be relatively low compared to the lifting mode.

For these reasons a Dual Draft hull was developed that combines a relatively large stability during heavy-lifting operations with good motion behaviour during transit and

pipelay operations.

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In addition the new developed hull shows good motion behaviour in pre-lifting mode when the vessel is at site

and the crew is preparing the heavy-lift operation.

THE DUAL DRAFT VESSEL

The patented hull of a Dual Draft vessel comprises a

narrow lower section from keel level to a widening level,

and a top section with a larger width than the lower

section extending from the widening level upwards toward deck level [7], as shown in Fig. 1.

t

Figure 1: Body plan of the Dual Draft vessel

The vessel is ballasted to a relatively deep draft level in

lifting mode such that the widening level is below water level. For pipelay and transit conditions the vessel is ballasted to a relatively shallow draft, in a way that the

wide top section is above water level.

The sponsons start at the transom and run forward along the hull preferably between 50% and 90% of the length

of the vessel. The sponsons have a simple rectangular

form since they are only submerged during lifting operations. When submerged, they also contribute to a

shift of the centre of buoyancy to the aft of the vessel.

Figure 2 shows the Dual Draft vessel in 3D. The hull

design features a wave piercing bulbous bow and a

slender fore ship which are both beneficial for transit speed. Compared to conventional pipelay

_/

heavy-lift vessels, the resistance of the vessel is further reduced by ballasting to the shallow draft, resulting in a higher speed or more beneficial fuel consumption.

The aft ship was designed with a full form to offer

sufficient buoyancy in lifting mode whilst still allowing for

a good flow pattern to the propulsion thrusters. Due to the full aft ship and slender fore ship, the longitudinal centre of buoyancy (LCB) is located aft of the midship. Since the longitudinal centre of gravity (LCG) is also

located aft of the midship, the amount of ballast water

required for controlling the trim of the vessel is relatively small.

f1

., _-

.-:-4-Figure 2: Dual Draft vessel

NUMERICAL APPROACH

This section briefly describes the main theory underlying the results of the next sections. Numerical calculations are

performed with the linear 3-dimensional

diffraction/radiation program AQWA-LINE. The floating structure is modelled in the usual way by means of panels representing pulsating sources distributed over the mean wetted surface of the vessel. The combinations of source strengths are calculated, which are required to diffract an incoming regular wave of given period, and to allow body oscillation in each degree of freedom.

The calm water wetted surface of the Dual Draft vessel is

modelled by 3172 panels. In addition a lid was used to

suppress the irregular frequencies which otherwise may occur. For non-linear time domain calculations the upper

hull extending above the still water line is modelled by 2716 elements.

The source strengths laying in the centre of the panels are used to calculate the diffraction force, added mass and damping coefficients. Subsequently, the motions of the

structure are determined by solving a six degree of

freedom equation of motion taking into account the wave forces, added mass, damping and restoring terms.

The thus obtained diffraction force, added mass and

damping coefficients are subsequently used by the time

domain program AQWA-NAUT to calculate the wave frequency motions in irregular seas.

AQWA-NAUT calculates the hydrostatic forces and moments directly from the integral of hydrostatic pressure on all the elements which make up the submerged part of the body at each time step. The hydrostatic force on each element is given by:

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Since the added mass/inertia and damping are not

constant over the wave frequency range, these forces are modified to allow for this variation.

The total wave frequency force

(i.e. diffraction plus Froude-Krylov) in each degree of freedom is calculated by the Cummins equation [8]:

f

K(tr)(r)dr+ C(t)C(t) = F1

(t) (3) where:

A(oo) =

the Added mass

coefficient at infinite frequency

B(oo) the damping coefficient at infinite frequency

C(t) = the matrix of hydrostatic restoring force coefficients, recalculated at each time step

The entries in the matrix

K(t - r)

in the convolution integral are retardation functions of time, in which

r

= t - c/i . When the retardation function is based on the

damping only one single added mass entry should be known to obtain the whole added mass curve as described by Van Oortmerssen [8].

The matrix of hydrostatic restoring force coefficients and the wave force are re-calculated at every time step. The restoring coefficients significantly change when the wider top section enters the water. For this reason the stiffness matrix is non-linear and should be recalculated at every time step.

The total wave force in Eq. (3) is calculated and added to

the sum of other forces to form the equation of wave frequency motions:

+flid} x(t) = F.

(t)+F.

(t)+F (r)+i, (t)+F,1 (t) (4)

where:

X = the acceleration vector

M = the structural mass

= the added mass and inertia at drift frequency

[j;;] _{= the current forces}

[EJ

= the wind forces

[I;;' = the mooring forces [Eh] = the hydrostatic forces [Fd] =the damping force

The total motion of the structure consists of a slow drift

motion and a fast wave frequency position. The final

position of the floating body in time-domain calculations is calculated

by superposition of the

'slow' and 'wave frequency' positions.

-j:

(1)

where:

p(x,y,z) = -pgz

for zO

, i.e. the hydrostatic

pressure

n = the outward normal vector to the element

A = the area of the element

p = the density of water

g = the acceleration due to gravity

The cut waterplane area together with the locations of the centre of buoyancy and the centre of gravity of the body determine the hydrostatic stiffness matrix. At each time step of the simulation the hydrostatic forces and moments are re-calculated based on the new submerged volume. The Froude-Krylov wave forces are calculated at each

time step by integrating the dynamic pressure acting on all submerged plate elements of the structure. The force

on each element is calculated again by eq. (1), though

this time p is the dynamic non-linear wave pressure for deep water [1]:

p(x,y,

z)

= pg

cos(k x

wt) -

k

Ce2)

(2)

At each time step in the simulation, the position and

velocity are known since they are calculated in the

previous time step. From these, all position and velocity dependent forces, i.e. damping, mooring force, total wave force,

drift force etc. are calculated. These are then

summed to find the six total forces and moments for the structure. Next, the total force is equated to the product

of the total mass (structural and added) and the rigid body accelerations.

The acceleration at the next time step can thus be

determined. Forces are recomputed with the new position

and velocity and the process is repeated to create the time history of motion. 20,000 time steps of 0.1 second are used to simulate the vessel motions in this contribution.

The model is kept in place by four soft-spring mooring lines in time domain calculation. Due to the large mass

and soft-mooring system, the natural periods of oscillation

in the horizontal degrees of freedom is in the order of

minutes. At these periods there are no first order spectral

energy so the system is not appreciably excited by first

order forces in these degrees of freedom.

Though, AQWA-NAUT does not calculate low order drift

forces, the structure can be excited by these forces as well.

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MODEL TESTING

Model tests were performed to verify

the numerical calculations and to establish the general seakeeping behaviour of the vessel.

Model tests were carried out in the Seakeeping and Manoeuvring basin at MARIN. The length, width and

water depth of the basin are 170 x 40 x 5 m respectively.

The basin is equipped with a flap type wave generator with 331 individual flaps of 0.4 m, each driven by an independent servo motor. This system facilitates the generation of regular waves and long crested or

short-crested irregular waves in more or less arbitrary directions

through the basin. A beach at the opposite side of the basin absorbs the incoming waves.

For the seakeeping tests a wooden model was built with a geometric scale of 1 to 36. The model was equipped with

bilge keels and two azimuthing thrusters. Tests were performed for (pre-) hoisting and transit condition. The

main particulars in full scale and for the model are given in Table 1.

Prior to the tests the longitudinal weight distribution of the

model was determined on a low mass pendulum. The required longitudinal radius of inertia was obtained by

fitting ballast at pre-calculated locations. The transverse

weight distribution was adjusted in such a way that the natural period of roll matched the calculated natural

period. The metacentric height was checked by means of a heeling test in calm water.

Table 1: Main oarticulars of the Dual Draft Vessel in DiDelav a

4

nd heavy-lift mode

C

Figure 3: Scale model of the Dual Draft vessel being tested at deep (heavy-lift) draught

The program consisted of various tests in both the (pre-) hoisting condition and transit condition. In hoisting condition it was needed to bring ballast weights outside

the model to meet the k, GM and T0, requirements, as shown in Fig. 3.

In the transit condition the test program consisted of

decay tests, tests at zero speed, tests for determining the current coefficients, and free sailing tests.

The model was moored fore and aft in an arrangement of soft springs during all zero speed tests and tests performed to determine the current coefficients. The

natural frequency of the soft spring

arrangement was selected such that first-order resonant response was avoided. The mooring lines are connected close to the free-water surface at an angle of 45 deg in the

xy-plane at the bow and stern of the vessel.

All wave conditions were

represented by JONSWAP spectra, which describe the wave energy

distribution over the frequencies of young (growing) wind seas. A peak enhancement factor of 3.3 was used.

For sake of brevity, only results of

the transit I

pipelay condition in beam seas will be discussed in the

remainder of this paper, as this

condition clearly shows the effect of the unconventional hull on the motions of the vessel.

Quantity Symbol Unit Pipelay Heavy-lift

Length between perpendiculars [ml 170.00 170.00

Breadth max B [m] 47.00 47.00

Breadth on waterline BWL [m] 36.40 47.00

Draught T [ml 7.51 13.50

Draught on AP TA [m] 7.51 13.51

Draught on FP TF [m] 7.51 13.49

Displacement volume moulded y [m3] 33,358 70,977

Displacement mass in seawater A [t] 34,192 72,752

LCG position from APP LCG 1ml 74.99 72.31

Transverse metacentric height GMT [mJ 4.20 11.70

Vertical position centre of gravity KG [m] 15.95 12.10

Mass radius of gyration around X-axis Kxx _[ml 17.64 19.29 Mass radius of gyration around Y-axis Kv _[m] 55.40 46.44 Mass radius of gyration around Z-axis Kzz _[ml 52.60 46.72

Natural period of roll [s] 19.30 12.06

Block coefficient CB - 0.72 0.66

Length-Breadth ratio Lp/B - 4.67 3.62

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VISCOUS DAMPING

The influence of viscous damping on the roll motions of a

vessel can be relatively large. An obvious _{source for}

viscous damping is the presence of appendages _{like bilge} keels. _{Flow separation can also occur} _in _{absence of} appendages, which ¡s referred to as hull _{circulatory effects} and adds viscous damping to the _{motion equation as well.} Tanaka [6] determined these effects by means of model

tests, while Ikeda et. al. [2-4] presented much _research

on roll damping in general.

Difficulties in predicting the roll damping of _{ships arise}

from its non-linear characteristics due to the effect of fluid

viscosity. Besides, the forward speed of ships will also result in non-linear contributions.

Without viscous damping the motion equationsare linear, i.e. the motion per unit wave amplitude (RAU) in each of the six degrees of freedom can be used to calculate the response in irregular seas. Consequently, the response in an irregular sea is the summation of the _{responses in}

regular waves, which define the spectrum.

The roll damping coefficient was derived from the decay test. Figure 4 shows the viscous part of the roll damping estimated as a function of the significant roll angle _(dotted line). The viscous roll damping to be added is a function

of the actual roll angle and depends _{on the actual} sea-state.

The RAU's are

calculated in AQWA using different

percentages of added roll damping. With _{use of these} RAU's the highest significant roll angle of _{a JONSWAP}

spectrum (Hs = 4.5 m, T

_{= 8.5 sec, 2' = 3.3)}

is calculated. The resulting significant roll angle as a function of added roll damping is shown in Fig. 4 (solid

line). The intersection of the two lines gives the actual significant roll angle and the corresponding maximum

viscous roll damping to be added.

In this case the added viscous damping is _{approximately} l.8% of the critical damping (br), whichcan be expressed as:

b,.r =2..J(M + A).0

The thus obtained added damping is only valid for the maximum roll angles around the natural roll frequency. For smaller roll angles, at other frequencies, _{the viscous} roll damping will be less than 1.8%.

I

25 2 15 05

MdU "viscots" dng

5iiIÑcit roHarjIe ¿s a lurdion of ackhJ dil rig UrIza1 vicoi danjilrig ¿s a Íur1iion of roH arigk? nstit1ng from caiiy T&

O

05% 05% 15% 15% 25% 25% 35%

Mded VIscous rtlI dan*Anq (% of ultical) Figure 4: Added viscous damping

The wave energy spectrum and the heave RAU are presented in Fig. 5. This figure shows that maximum wave energy is located around the natural heave frequency. Figure 6 shows the roll RAU in combination with thesame wave energy spectrum. It can be seen that there is little

energy in the waves around the natural roll frequency.

Nevertheless this sea state with 1,, = 8.5 sec. is chosen as it also clearly shows the effect of the dual draft hull _on the roll motions of the vessel, this will be discussed in the next section.

Heave RAO & Wave Spectrum

t

e 3.6

i

t

E 24 s

r

i \_I 2.4 I I i 1.2 _{_J.-}

'

12 04 08 12 16 Frequency Erad/sl

Figure 5: Heave responses in regular beam waves and energy density spectra for waves (Hs = 4.5 m,

= 8.5 sec. and = 3.3)

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Figure 6 shows the RAO in which 1.8% of the critical

damping is added to the potential damping according to Fig 4.

1.2

Roll RAO & Wave Spectrum

-RoiIRA0withB,,,, 18%b

Figure 6: Roll responses in regular beam waves and energy density spectra for waves (Hs = 4.5 m,

T = 8.5 sec. and y = 3.3)

RAO(a))

B44 added (a)) =B.added (°,

RA O (w,)

Table 2 shows the viscous damping coefficients based on

Eq. (7) at different wave frequencies for the sea state

with a significant wave height of 4.5 m.

Table 2: Viscous damping at different frequencies in irreciular seas (Hs = 4.5 m. T = 8.5 sec).

1.2

Since Ç(w) and Ç(w,,) are equal in the linear frequency domain, Eq. (6) can be written as:

(7)

The use of different viscous damping coefficients results in different roll RAUs as illustrated in Fig. 7. These RAUs

(H) are obtained from the wave spectrum (S:) and

response spectrum (S.) and can be calculated as follows:

S(a))=H2s(w)

(8)

Figure 7 shows the results of experiments and non-linear calculations for roll motions in irregular seas in which Hs = 4.5 m, T = 8.5 sec. and y = 3.3.

The use of Eq. (6) in estimating the viscous part of the roll damping shows good agreement with model tests at low and high frequencies. When the added damping is equal

to O.18% of the

critical damping the measurements correspond well

with the experiments at 0.50 rad/s.

However, the computations tend to underestimate the

results of model tests at frequencies between 0.75 and 1.05 rad/s. At higher frequencies the results of the computations are again close to those of model experiments, though roll responses are small.

Figure 7 shows the responses in the range from 0.5 to 1.1 rad/s since the wave energy is small outside this region.

84 05

Roll responses, Heading = 90 deg JONSWAP: Hs 4.5 m, Tp = 8.55, = 3.3

Exp H4.5 y=3.3

----.CaIcB4O

-Caic 018%

- Caic B.M.d,.d= 180% b,

Figure 7: The effect of viscous roll damping on the roll RAUs

DISCUSSION OF MOTION BEHAVIOUR

Compared to existing pipelay / heavy-lift vessels, the unconventional hull shape and relatively low GM-value of

a Dual Draft vessel will result in a different motion behaviour, especially at transit / pipelay mode.

First the motion behaviour of the Dual Draft vessel will be discussed based on responses in different sea states. The responses are normalized by dividing them by the wave amplitudes, which gives an 'average' impression of the motions in the frequency range.

Next, the motion behaviour will be discussed statistically and finally a short conclusion will be given.

(i) _{Viscous damping}

[radis) [t.m2is] [% of bcr]

0.35 1 .55E+05 1 .80%

0.5 1 .54E+04 0.18%

0.95 2.80E+03 0.03%

The roll RAO in regular beam waves can be used to 2

estimate the viscous damping at smaller roll motions. The

1.8-viscous roll damping at different frequencies can be

estimated by: 1.6 B,,ddvd (a) = B.a1ded (a z,(W) 1 4-z, (a),,) o -(6) OE8 0.8 = B,dd,d (a) 0.4 z, (ak,) / (ai,) 0.2 04 08 12 1.6 Frequency [radis) 48 l' E s 36 (I) 24 0.6 0.1 08 0.9 11 12

Wave Frequency (radis]

48

(13)

Figure 8 shows the sway motions of the vessel in beam seas for different sea states in transit mode. An important variable in the sway motions of the vessel is the stiffness of the mooring system. A stiffness of 35 kN/m was used in the computations, resulting in a natural frequency of the

mooring system (with vessel) which is approximately five

times as small as the smallest natural frequency of the

vessel. In this way the natural frequency of the mooring

system will not influence the first order motions of the vessel.

Sway RAO's of the vessel should be approximately equal at different sea states since non-linear effects are small. Figure 8 confirms this and shows that the responses can be best predicted by linear diffraction calculations. Non-linear calculations tend to overestimate the experimental values at low and high frequencies.

Figure 9 shows that heave responses increase when the wider top section of the Dual Draft vessel enters the water. This effect is largest around the natural heave frequency of the vessel and is only visible in the results of the model tests. Non-linear calculations do not show a difference in

heave response between different sea states.

At higher frequencies, results of experiments and computations are approximately equal and do not change with sea state. Results of linear calculations are slightly higher than those of non-linear computations around the

natural frequency. lust like the sway motions, heave

motions of the Dual Draft vessel can be well predicted by a linear approach.

Contrary, Fig. 10 clearly shows the non-linear behaviour of roll responses. In general, viscous roll damping increases when roll motions increase. The increase of viscous damping at large roll angles normally results in a decrease of roll RAO5.

However, roll RAOs of the Dual Draft vessel increase when the sea state increases due to an unconventional hull. The

excitation moment on the body significantly increases

when the wider top section of the hull enters the water at

one side. This moment is highly non-linear in case of a Dual Draft hull resulting in large roll RAO's at high sea states.

Results of non-linear computations show good agreement for

the two highest sea

states at low frequencies. However, the computations tend to underestimate the

results of model tests at frequencies between 0.75 and 1.05 rad/s as discussed in the previous section. In addition, roll responses are small at low sea states and

high frequencies, by which it is difficult to predict them accurately.

Since the influence of non-linear effects is small at the lowest sea state, the results of linear and non-linear

computations are approximately equal for this condition.

1.4 E 1.2 o

<1

io: 0.8 Q, 0.8 04 02

Figure 8: Sway RAOs at different sea states

Heave responses 2 I.e 08-O 6-04 Sway responses Exp l-101 5,1.5,7=3.3

a Exp H =30, IO8 S, y=33

Exp Hn4 5, T 8.5, yn3 3

Non-linear caic HI 5, T8 5, p3.3 - -. - Non-linear caic H 03.0, 1=8 5. y3.3 - - - - Non-linear cain H4 5 T=8 5,7=3.3

hrrearcalc. H =1.5. T =8.5.1=33 hnear caic H,3.0. T,=8 5. 3 3

hnear cdc H 4,5, T =8.5, yo3.3

4 08 06 07 08 09 II 12

Wave frequency (red/sl

Figure 9: Heave RAGs at different sea states

Roll responses

05 06 07 0.8 0.9

Wave frequency Erad/sl

E. U=1 .5, Tt 5, 3.3

Exp H'o3O 'T85 .=33

Exp. Ha=4 5. l=8 5 r=3 3 Non-In ceic H=1 5, T9=8.8, y3.3 -. Non-In Cain H3 0, T=e.S. y=3.3

- -Non-In nain H=4.5, 1,-8 Inne coin HI 5. T,-0.5 y=3 3

Inner cain Ha-3 0. T5,5 yo3.3 Inner c.9v No.4 5. 1,005 r3.3

e 0

Exp Hoi .5, 18 s 7=33 Exp H3.0. T,=8 5. =3.3

- Exp H 4.5. I=S 5, y=3 3

Non-linear caic H=1 5, T 8.5, 5=3 3 -- NonIixear caic H=3 0, T =8.5, r3 3 - - - - Non-linear caic H4 5, T =8.5,7=33 linear cdc HOi 5, T =8.5, 7=3.3 linear nIç H-3 0, T =8.5, 7=3.3 mear cdc H4 5, 7n5.5, yn3.3 0000000 0

Fìgure 10: Roll RAOs at different sea states

'1.

'n.

o

<1

84 05 06 07 08 09 l'i 12

Wave frequency frad/si

18-1.8 14

t

o O 2-8

(14)

The amount of added damping in Fig. 8-10 is 0.18% of

the critical damping as discussed in the previous section. Consequently, the results of the linear computations in Fig.

10 are (approximately) equal to those of the linear

frequency domain in Fig. 6.

Hitherto, the discussion of the motion behaviour of the

Dual Draft vessel was based on responses in different sea states. Responses were normalized by dividing them by the wave amplitudes, which gives an 'average' impression of the motions in the frequency range.

In addition, motions of the Dual Draft vessel are also analyzed statistically. Such an approach will provide a

better understanding of the distribution

of the wave

amplitudes over time.

In this case the extremes of the complete time-domain simulations are analyzed. For this reason it is necessary to add 1.8% of the critical damping to the linear (potential) damping coefficients as discussed in the previous section. Since the wave spectrum is narrow banded and wave

amplitudes satisfy a Gaussian distribution around zero,

wave statistics can be approximated by a Rayleigh distribution as described by Journee [5]:

f(xIa)=--exp

o- 2o

x

(x2

(9)

¡n which x is the wave amplitude and a its standard

deviation.

250

3 hours Roll Probability Density Function JONSWAP: Hs = 4.5 m, Tp = 8.5 s, y = 3.3

Data

- Rayleigh eatmate (a = 1.09)

Figure 11: Rayleigh Probability Density Function of

number of roll amplitudes in irregular beam sea

As the roll spectrum is also narrow banded, Eq. (9) holds for the roll motions as well. Figure 11 shows the Rayleigh

probability density function

of the

roll amplitudes in

irregular beam seas of 4.5 m significant wave height. When the results of time domain calculations are compared with the Rayleigh estimate, it is clear that the Rayleigh approach underestimates the number of low and high roll amplitudes, see Fig. 11, This figure shows the maximum roll amplitudes occurring in time-domain simulations of 3 hours.

A Rayleigh probability density function can be derived from the Eq. (9). The probability that the roll amplitude (X4,) exceeds a chosen threshold value (a) can be expressed as:

P(X4, >a)= ff(xla)dx

(_a2 (10)

=exp

i-Figure 12 shows the probability of exceedance in beam

seas of 4.5 m significant wave height. Both results of

time-domain calculations and the Rayleigh estimate are plotted in the same figure. A conventional hull, with constant beam from keel to deck level, would follow the Rayleigh estimate as plotted in Fig. 12.

The figure clearly shows the effect of the wider top

section of the Dual Draft vessel on the roll amplitudes;

Rayleigh overestimates the probability of exceedance at

small wave amplitudes and underestimates it at large wave amplitudes. 01 Q

t

t) t) Q t) o o

û-3 hours Roll Probability Of Exceedance JONSWAP: Hs = 4.5 m Tp = 8.5 s, y = 3.3

- Ral,i.lgh estimate (a 1.09) Data

Figure 12: Probability of exceeding of roll amplitudes in irregular beam seas

In less severe seas when waves do not hit the wider top section

of the

Dual Draft vessel and the restoring coefficients are constant over time, roll amplitudes correspond to those of the Rayleigh estimate, i.e. the

wider top section has no effect on the roll motion and the

o 3 4 5 0 7 0

(15)

motion behaviour is

similar to that of a conventional

vessel.

Figure 13 shows the probability of exceedance of the roll

motions in beam seas with a significant wave height of 1.5 m.

3 hours Roll Probability Of Exceedance JONSWAP: Hs = 1.5 m, Tp = 8.5 s, y = 3.3

REFERENCES

AQWA-NAUT manual, Century Dynamics Limited, 2006.

Ikeda, Y., Himeno, Y. and Tanaka, N. On roll damping force of ship - effect of htAl surface pressure created by bilge keels. Journal of Society of Naval Architects of Japan, 1979 No. 165, pp.41-49.

Ikeda, Y., Himeno, Y. and Tanaka,

N., On eddy

making component of roll damping force on naked

hull. Journal of Society of Naval Architects of Japan, 1977, No.142, pp. pp.59-69.

Ikeda, Y., Ishikawa, M. and Tanaka, N. Viscous effect on damping forces of ship in sway and roll coupling motion. Journal

of the Kansai

Society of Naval Architects, Japan, 1981, No.180, pp.69-75.

Journee, J.M.J. and Massie, W.M., Offshore hydrodynamics. DeIft University of Technology, 2001. Tanaka, N., Himeno, Y. and Ikeda, Y. Comparison of roll damping between prediction and measurement. Osaka University, Department of Naval Architecture, Presented at the ITTC Seakeeping Committee, March 1980.

Van Der Velde,

Wi.,

Wassink, W.J.A. and Commandeur, J.A. Dual draft vessel, Tnt. Patent,

publication number: WO/2007/069897, 2007.

Van Oortmerssen, G. The motions of a moored shio in waves. PhD thesis, DeIft Univ. of Technology, Delft, The Netherlands, 1976. 9 Copyright © 2008 by ASME loo 50 _{- Rayleigh eatimate (o} _0.04) 20 Data lo i o

i al

o o o a-o 005 01 0.15 0.2 0.25

Roll ampftude [deg]

Figure 13: Probability of exceeding of roll amplitudes in irregular beam sea

Finally it should be

noted that the

relatively small waterline beam of the Dual Draft vessel at pipelay I transit mode significantly lowers the GM-value as discussed in

the first section of this paper. As a result the overall

motion behaviour of a heavy-lift I

pipelay vessel will improve compared to a conventional hull.

CONCLUSIONS

The motion behaviour of a Dual Draft vessel was calculated and experimentally validated

by means of

model tests. Both tests and computations showed that the

roll behaviour of a Dual Draft vessel in pipelay I transit mode does not correspond to the usual observed response amplitude operator (RAU), where the roll RAO decreases with increasing wave height due to non-linear

damping. When the wider top section of the Dual Draft

vessel enters the water due to a roll motion, the buoyancy

increases at that side and results in an increase of the

excitation moment and roll RAU.

On the other hand, the excess in stability typically for

these types of vessels is significantly reduced due to the relatively small water line area in pipelay I transit mode. The reduced GM-value results in an improved motion

behaviour of pipelay I heavy-lift vessels in general.

Finally, the overall motion behaviour of a heavy-lift I

pipelay vessel will improve when the vessel is designed with a dual draft hull.