Catamaran Seakeeping Predictions

Catamaran Seakeeping

Predictions

Riaan van 't Veer

Report 1086-P March 1997

The 12th International Workshop on Water Waves and FIoatng Bodies,

Carry le Rouet, France, 16 - 19 March 1997

TU Deift

Faculty ofMechanicaI Engineering and Marine Technology Ship Hydromechanica Laboratory

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CCI Marseille Provence

Groupe ESIM

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Proceedings of the Twelfth International

WORKSHOP ON WATER WAVES

AND FLOATING BODIES

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Proceedings of the

TWELFTH INTERNATIONAL WORKSHOP

ON WATER WAVE.S AND FLOATING BODIES

Carry-le-Rouet, 16-19 March, 1997

Edited by

B. MOLIN

Ecole Supérieure d'Ingénieurs de Marseille

Also including written abstracts to the 'GeoÈg Weirniblurn Special

Meetings held at Carry-le-Rouet on 19-20 March,, 1997

Cover photograph: the Geo:rg Weiniblurn Special Meeting lecturers (courtesy

DH. Peregrine).

Back, from left to right: H Maruo, M. Tu/in, T. Wu, L Breslin, J. Wehawsen,

F. Ursell

Front, from left to right: T.

Mi/oh, L. _Larsson, N. Nèwrnan, E. Tuck,

O. Faltinsen, S. Sharma

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ABSTRACT

The Workshop. was held at 'Vaçanciel la Calanque' in Carry-le-Rouet,, near

Marseille,, from 16th to 19th March., It was followed by a Special Meeting

dedicated to the memory of Georg Weinbium, in celebration of the 100th

anniversary of his birth.

The Workshop was attended by over 100 participants..

This publication contains extended abstracts of the presentations, and summaries

of the discussions. Appended are written abstracts of the Georg Weinbium

lectures.

SPONSORS (in alphabetic ordér

Association Universitaire de Mécanique (AUM)

Conseil Général des Bouches du' Rhône .

Direction de 'la Recherche et de la Technologie ('DREI)

Groupement de Recherches en Genie Oceanique et Côtier (GReGOC) Ministère des Affaires Etrangères

Ministère de 1'EducationGénérale, de l'Enseignement Supérieur et de la

Recherche

Office of Naval Research Europe Single Buoy Moorings Inc. (S.B.M.)

This. work relates to Department of the Navy Grant N00014-97-1-0517 issued by

the Office of Naval Research European Office The United States has a royalty-free license throughout the world in all copynghtable material contained herein

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TABLE OF CONTENTS

Workshop Information iv

List of Presentations V

Abstracts i

Georg Weinbium Special Meeting

279

List of participants 327

WORKSHOp INFORMATION

Ordering information for recent Workshop Proceedings.

1 i.th _{V. BERTRAM} ('1996) Institut für Schiffbau Lämmersieth 9G 22305 Hamburg GERMANY e-mail: bertrarn@schiffbatì.uni-hamburg.d4Ode' 12th

B MOLIN

(1997) _{EccIe Supérieure d'Ingénieurs de Marseille}

Technopôle de Château-Gombert 13451 Marseille Cedex 20

FRANCE

e-mail: molin@esim.imt-mrs.fr

Contacts for future Workshops

13m PrOf. Ai. HERMANS.

(1998) Deift University of Technology

Department of Applied Mathematics

Mekelweg 4

2628 CD Delft

'flffi NETHERLANDS

e-mail: a.j.hermans@ math.tudelft.nl

14th Prof. R.F. BECK and W.W. SCHULTZ.

(1999) University of Michigan

Dept. of Naval. Architecture & Marine Eng 2600 Draper Rd

48109 Ann Arbor, Michigan

USA e-mail: rbeck@enginumich'.edu e-mail.: schultz@engin.uniich.edu 15th Prof. T. N'ffl OH

(2000)

University of Tel-Aviv School of Eng. Ramat-Aviv .69978 Tel-Aviv ISRAEL e-mail: rnilúh@eng.tau.ac.il iv

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1- ARANHA J. + MARTINS M.: 'Slender body approximation for yaw

velocity terms in the wavedrift damping matrix'

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LIST 0F PRESENTATIONS

BA M. + FARCY A.+GUILBAUD M.: 'A time domain method to

compute transient non linear hydrodynamic flows' 9

BRATLAND A. KORSMEYER T.+ NEWMAN J.N.: 'Time domain

calculations in finite water depth' 13

BUNNIK T. +_{HERMANS A.: 'A time-domaiñ algorithm for motions}

of high speed' vessels using a new free surface condition' 19

CELEBI S. + KIM M.H.: 'Nonlinear wave-body interactions in a

numerical wave tank' 25

CHEN X.+_{NOBLESSE F.: 'Dispersion relation and far-field waves'} 31

CLEMENT A.: 'A shortcut for computing time-domain free-surface

potentials avoiding Green function evaluations' 37

DI MASCIO A. +PENNA R. + LANDRINI M. +CAMPANA E.:

'Viscous free surface flow pasta ship in steady drift motion' 45

DIAS F.: 'Solitary waves with algebraic decay' 49

DOUTRELEAU Y. + CLARISSEJ.M.: 'Recent progress in dealing

with the singular behavior of the Neumann-Kelvin Green function' 53

FARSTAD T.: 'Impulsive diffraction by an array of three

cylinders' ₅₉

FERRANT P.: 'Nonlinear wavecurrent interactions fl the vicinity

of a vertical cylinder' ₆₅

FINNE S: 'Higher-order wave drift forces on bodies with a small

forward speed' based on a long wave approximation' 71

FONTAINE E. + _{FALTINSEN O.: 'Steady flow near a wedge shaped}

bow' ₇₅

FRANK A.: 'On new mode of wave generation by moving pressure

disturbance' '

' 81

GENTAZ L. + ALESSANDRINI B. +_{DEL'HØMMEA:U G.: 'Motion}

simulation of a two-dimensional 'body at the surface of a viscous

fluid by a fully coupled solver' 85

GREAVES D. + BORTHW'ICK A. +_{WU G.X.: 'An investigation of}

standing waves using a fully non-linear boundary adaptive finite

element method' ₉₁

'V

GRILLI S. + HORRILLO J.: 'Fully nonlinear properties of shoaling

periodic waves, calculated in a numerical wave tank' 97

GRUE J. + PALM E.: 'Modelling of fully nonlinear internal waves

and their generation in transcritical flow at a geometry' 101

HERMANS A.: 'The excitation of waves in a very large floating

flexible platform by short free-surface water waves' 107

HUANG j. + EATOCK TAYLOR R. + RAINEY R.: 'Free surface

integrals in non-linear wave-diffraction analysis' 111

HUANG Y. + SCLAVOUNOS P.: 'Nonlinear ship wave simulations

by a Rankine panel method' 115

IWASHITA H. + BERTRAM V.: 'Numerical study on the influence

of the steady flow field in seakeeping' 119

JANSON C.E.: 'A companson of two Rankine-source panel methods

for the prediction of free-surface waves' 125

J1ANG. L. + SCHULTZ W. + PERLIN M.: 'Capillary ripples on

standing water waves' 129

KHABÄKHPASHEVA T. + KOROBKIN A.: 'Wave impact on elastic

plates' 135

KIM Y. + SCLAVOUNOS P.: 'The computation of the second-order

hydrodynamic forces on a slender ship in waves' 139

LAGET + de JOUETTE C + Le GOUEZ J.M. + RIGAUD S. 'Wave

breaking simulation around a lens-shaped mast by a V.O.F: method' .. 143

LANDR1NI 'M. + RANUCCI M. + CASCIOLA C.M. + GRAZIANI G.:

'Viscous effects in wave-body interaction' 147

LINTON C.: 'Numerical investigations into non-uniqueness in the

two-dimensional water-wave problem' 151

MA Q.W. + WUG.X. + EATOCK TAYLORR.: 'Finite element analysis

of non-linear transient waves in a three dimensional long tank' 157

MAGEE A: 'Applications using a seakeeping simulation code' 163

MALENICA S.: 'Higher-order wave diffraction of Water Waves by

an array of vertical circular'cylinders' 167

MAYER S. + GARAPON A. + SORENSEN L.: 'Wave tank simulations

using a fractional-step method in a cell-centered finite volume

implementation' 171

Mc IVER M.: 'Resonance in the tinbounded water wave problem' 177

vi

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36 Mc IVER P. +KUZNETSØV N: 'On uniqueness and trapped modes

in the water-wave, problem for a surface-piercing axisymmetric

body' . 183

37- MOTYGIN O. + KUZNETSØV N.: 'On the non-uniqueness in the 2D Neumann-Kelvin problem for a tandem of surface-piercing

'bodies' 189

.38- NGUYEN T. _{YEUNG R.: 'Steady wave systems in a} two-layer

fluid of finite depth' . 195

39-. NYG'AAR'D J. + GRUE J.: 'Wavelet and spline methods for the

so1ûon of wave-body problems" . . 201

OHKUSU M. + _{NANBA Y.: 'Hydroelastic response of a flóating}

thin plate in very short waves' 207

PORTER R. + _{EVANS D.V.: 'Recent results on trapped modes and}

their influence on'finite arrays of vertical cylinders in waves' 211

RAINEY R.: 'Violent surface motion around vertical cylinders in large, steep waves. Is it the result of the step change in relative

acceleration?' 215

SCORPIO S. +BECK R.: 'Two-dimensional inviscid transom stern

flow' . 221

SIEREVOGEL L. +HERMANS A.: 'Stability analysis of the 2D

linearized unsteady free-surface condition' 227

'SKOURUP J. +_{,BÜCHMÁNN B.+BLNGHAM H.: 'A secönd- order 3D}

BEM for wave-structure interaction' . 1233

TANIZAWA K. + NAITO S.: 'A study on wave-drift damping by

fully nonlinear simulation' . 237

TENG B. +KATO S.: 'Third-harmonic diffraction force on

axisyminetric bodies' 243

TUCK E. + SIMAKOV S. +WIRYANTO L: 'Steady splashing

flows' 249

VAN'T VEER R.: 'Catamaran seakeeping predictions' . 255

VOGT M. + KANG K-J.: 'A level set technique for computing 2D

free surface flow' 261

'S'i WOOD D. + PEREGRINE. H.: 'Application of pressure-impulse theory

to water Wäve' impact beneath 'a deck and on a vertical cylinder' 267

52- ZHU Q. + _{LIU Y.} +YUE D.K.P.: 'Resonant interactions of Kelvin ship

waves with ambient ocean waves' 273

Catamaran Seakeeping Predictions

Riaan van 't Veer, Deift University of Technology

i

introduction

To solve the motions of_{a vessel sailing in waves the strip theory is a widely used method. The}

results are in most cases satisfactory. However, the method becomes less. accurate if 3D effects

become more important.

By research work done in the past [6] it became clear that for catamaran vessels at low

and moderate fòrward speed the strip theory over predicts the heave and pitch motions if the

interaction between the two hulls is included in the cä1cu1ations When a catamaran is sailing at high forward speed, the interaction between the two hulls will vanish since thewaves generated by one hull can not reach the other hull of the catamaran. It was found that in that case the strip theory could predict the motions of the vessel with more satisfactory results.

Thus, to take interaction èffects between the two hulls of a catamaran correctly into account

a 3D method is needed.

2

The Boundary conditions

A Rankine panel method has been designed for monohull and catamaran vessels. In this method the hull surface and still water free surface are discretised, using flat quadrilateral panels with a

constant source strength singularity (1/r) in the collocation point of the panel.

The total velocity potential is written

as 'Is(,t) =

where cD is the double body potential, _{is the steady velocity potential and p is the unsteady velocity potential. The} assumption is made that the steady and unsteady potential are independent so that the steady

and unsteady problem can be solved separately.

The exact free surface boundary condition on the unknown free surface is linearised to the stili water free surface, assuming that the _{wave elevation from the double body potential allows} such a linearisation. The free surface boundary condition for the steady and unsteady problem

read, respectively:

g+

V(V. V)

- Vc - U2).( +

q) =0

(1) and,

-

+ 2iWe

Vk +

V.

. V) +

. V(V. V)

-zz(ek

+ V

Vk) -

-

_U2)(gk

+ kt) =

0 k = 1,.., 7 (2)

where k, is the mode of oscillation with k = 7 being the diffraction potentiaL

The hull boundary condition for each potential is that no water an penetrate the hull, thus:

' '

(3)

---iWeTl'k+?flk

_k=1,.,6,

ôn

where n is the normal vector pointing into the fluid domain. _{The incoming wave potential is} given by Cpa. The in-terms in the unsteady hull boundary condition are calculated analytical,

using Newman [3] and de Koning Gans [1]. The in-terms contain second order derivatives and

especially the rotation terms are sensitj, e for errors in these derivatives due to the length factors

with which they are multiplied, in equation (4) the in-terms are written out:

(ini, in2, in3)

_{= -(}

.

== (ni

+ 7l2xy + ii3xz,

il1yx + i12'I'yy + fl3yz,i11zx+ fl2zy + n3)

(in4, in5, in6)

= (i V)( x V) = (yrn3 - Z7fl2 - 2z + fl3y,

Z1fl1 X7TL3 - fl3x + flI,xm2 - yin.! - iii _{+ n24x)}

3

Solving the steady or unsteady potential

The Green's identity is used to solve the steady or unsteady potential. That is for the unsteady

po tent ial:

2lrçok(:p)

-

ff

ff

= 0 (5)

&lq ôflq

FS,H FS,H

and a similar expression for the steady problem.

Equation (5) is discretised using N number of flat quadrilateral panels. The unknown vari-ables are discretised using a spline representation, as was presented by Nakos [2]. The spline function is a C-2 function, thus upto the second derivative can be discretised.

4

Some details of the Rankine panel method

A typical free surface ¡)a1el discretisation for a catamaran problem is presented in Figure (i). The free surface grid is divided into three different grid area's, called FS1, FS2 and TR. The

transom grid is omiiy pressent if the hull ha_s a transom stern.

Most catamaran vessels have a transom stern. to install the waterjet units for propulsion.

However, the flow around a transom is typical nonlinear if the transom ends below the still water free surface. Due to the linearisations carried out before the depth of the transom below

z = O must be. limited.

in solving the problem the different grid area's must bç connected with each other using 1)hysical values at the connection lines. The extra conditions are introduced by assuming ami extra set of unknowns, virtually positioned near each border panel of a grid area.

The disturbance due to the vessel are assumed to vanish upstream of the vessel. Practily this means that in the unsteady problem the reduced frequency r must be greater timan 0.25. Thus for time steady and time unsteady problem the conditions ( = O and (/ôx = O are discretised at time instream side of time grid.

At time outer-border of the grid the second derivative of the potential in y irection is set to vanish.

Since the problem is symmetric around the x-axis no flow is going through the xOz plane. This means that at y = O the velocity V must be zero.

Time continuity of the flow must be satisfied going from one grid to the other grid. This is carried out by discretising the potential itself and the normal vector of the velocity in the direction and using these two conditions at the intersection. The same conditions are applied

between the hull surface amid the free surface grid.

1f a transom stern is present it is assumed that the flow is leaving the hull surface smoothly,

thus the condition ac/Ox = a where a is the transom edge angle, is prescribed in time extra

collocation point of the transom sheet. The wave elevation itself is also fixed by the transom edge depth. Using the transom edge angle time wave elevation in the first collocation point aft of time transom becomes ( = tan a where h is the first transom sheet panel length in the x

direction. (4) 256 o. o. o.

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5

Results

in Figure (2') the steady seascape is given for a Wigley catamaran at Fn = 0.30. The stern and bow wave system are clearly spotted Where the two bow waves meet each other a high peak

in the wave system is found.

In Figure (3) the heave and pitch motions of a wigley catamaran vessel are compared with data from experiments [5] The 3D calculations are refered to as SEASCAPE The strip theory calculations are perforìned with the program ASAP, in which ASAP O indicates that the inter-action between the two hulls is not inclúded in the calculations and ASAP 2 indicates that the 2D interaction between the hulls is taken into account.

The added mass and fluid damping results are presented in Figure (3) as well. A reasonable

comparison is found over almost the whole frequency range.

To obtain an indication for the transom stern wave profile calculations, a comparison is presented, Fig. (4), between a non-linear calculation by Raven [4] and the linear calculation

from SEASCAPE.

References

H. .1. de Koning Gans. Numerical Time Dependent Sheet Cavitation Simulations using a Higher Order Panel Method. PhD' thesis, 'Delft University of echnology, .Janua.ry 1994.

Delft University Press.

D. E. Nakos. Ship Wave Patterns and Motions by a Three Dimensionat Rankine Panel

Metlios. PhD thesis, Massachusetts Institute ofTechnology, .June 1990.

.J. N. Newman. Distributions of sources and normal dipoles over a quadrilateral panel.

Joui nal of Engzneerzng Mathematics, 20(1) 113-126, 1986

H. C. Raven. A Solution Method for the Nonlinear Ship Wave Resistance Problem. PhD thesis, Delft University of Technology, .June 1[996

F. R. T. Siregar. Experimental results of the wigley hull formm with advancing forward speed in head waves. Technical Report 1024, Delft University of Technology, Ships Hydrodynamics Laboratory, February 1995.

A. P. Van 't Veer. Catamaran seakeeping prediction. Technical Report 980-S, Delft University of Technology, October 1993.

FREE SURFACE I

I RANSOM FREE SU'RFAC

Figure 1: Caiçulàtion grid for a catamaran with transOm

257

E W > w

I

o o -S C, 4.0 3-5 3.0 2.5 2.0 1.5 1.0 0.5 0,0 0.6 0.8 180.0 ui 90.0 U) 0.0 w -180.0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 300.0 250.0 E g' 200.0 150.0 I-. Q. o 100.0 50.0 0.0 1.0 1.2 1.4 1.6 1.8 2.0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 '; 180.0 ÊXPÊRtN'TS SEASCAPE -ASAPO ---A$AP2 90.0 co

I

Q. -90.0 I-. 0. -180.0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 < 0.2 0.1 O 2 D) 4 3-5

.3

2.5 o z 1.5

<1

o 0 0.5 D -J U- ₂ 4 6 8 10 12 14 X/SHIP LEN6TH

Figure 4: Transom stern wave, Fn 0.40, RAPID results from Raven [4]

258 p.-L. SA-L.

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0.8 o _I 0.7

'ea.

0.6 0.5 80.4 803

Figure 2: Steady Seascape, Wigley Cat L/B = 7, Fn 0.30 r

WAVE LENGTH / SHIP LENGTh WAVE LENGTH I SHIP LENGTH FREQUENCY (rad/sec]

Figure 3: Heave, Pitch, and Added mass and fluid damping results Wigley Catamaran, L/B = 7, Fn = 0.45

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DISCUSSI ON

Newman J.N.: The highlytuned heave

resonance at U

O is not really due to

wave interactions between the hulls, but to a Helmholtz "pumping" mode in 2D or

a longitudinal standing wave in 3D. Do you have any ideas about how this

resonant mode is affected by forward velocity?

Van't Veer R.:

Thank you for your interesting question about interaction

phenomena.

At zero forward speed the added

mass and damping coefficients are measured for

several heaving twin cylinder configurations by Lee et. al (1971). In most of the

measurements the heave added mass drops to negative values where at the same

time the fluid damping value goes to zero. This 2D resonance frequency is indeed

telated to the Helmholtz pumping mode,

or can be seen as the behaviour of a

moonpool. The resonance frequency can be approximated using the horizontal

watercolumn between the two hulls extended with half

a circular cylinder

underneath Which yields

oJ=Jpgh/(phT+ith2/8)

_{where h}

is

the distance

between the two hulls and T is the draft of the hull.

With increasing forward' speed the moonpool effect will decrease since the

watercolumn is nöt bounded at the fore and aft 'side. In experiments lately carried

out w:ith a catamaran vessel, added mass values close to zero were measured at

Fn =0.30

_{at 'low frequencies. This indicates in my opinion that a weakened}

moonpool effect can exist in 3D, if forward speed is not to high. At higher Froude

numbers the 'added mass values became

more or less constant over the tested

frequency range, indicating no profound interaction effects.

Lee, C.M., Jones, H.. and Bedel, J.W.: 1971, Added mass and damping coefficients of heaving twin cylinders' in a free súrface, Technical 'Report 3695, Departement of

the Navy Naval Ship' Research 'and Development Center, Bethesda.

Rainey R.C.T.: Standing on the extreme aft deck of the

_{high-speed catamaran}

"Ho'verspeed France", during her sea 'trials in Hobart (a harbour discovered

_by

your countryman and my ancestor Abel Tasman, incidentally), I was much struck

by the beautiful transom-shaped "groove" cut in' the

_{water behind the ship. Its}

effects appeared w dominate the Wave pattern left 'behind. You mention

_{this in'}

connection with, Figures 1 and 4. Can you teIlt me how the wave resistance of a

catamaran compares with the simplest effects of this "groove", i.e. with the

259

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horizontal hydrostatic force that would be felt on the transom at zero speed in still

water (and thus is felt, in the opposite sense, by the rest ofthe hull)? Catamaran

designers always appear to minimise the draught of the transóm, at the expense of

its breadth, which is consistent with minimisingthis hydrostatic force (since it is

proportional to breadth X draught2).

Van't Veer R.: Thank you for your question in relation to the Wave resistance.

The flow around a transom stern is an interesting topic and rather challenging

since viscous effects can play an important role This is especially the case at low

Froude number where the transom flow does not leave the transom edge smoothly

and a 'dead water' region behind the stern exists Minimising the transom stern

draught (or area) is expected to decrease the resistance since the flow separation

will decrease and less energy is lost in the wake pattern.

At hig:her forward speed or when the transom stern draught is decreased the flow

is likèly to detach smoothly at the transom edge leaving a nicely shaped 'groove'

cut in the water behind. Since the transom stern remains dry there is no horizontal

hydrostatic pressure present at the transom. I expect that to obtain a smooth flow

detachment it is not always necessary to minimize the transom edge draught, but

that it is more important to obtain a smooth hull curvature with a small buttock

curvature.

y-260 L. a..

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