Using generalized modes for time domain seakeeping calculations

(1)

Dath Author Address

April2007

Tuitman, Johan and Hansvan Aanhold Delft University of '1 echnology

Ship Hydrornechanics Laboratory Mekelweg 2, 26282 CD Delft

Using generällzed;rnodes for time domain seakeeping calculations

by

ohan Tultman and Hans van Aaflhold

Report No. 1518-P ₂₀₀₇ Proceedings of the22MdZnternatlonal Workshopon Water WavasandrFloatlfl g Bodies, PlitvIce, Croatia 15-18Aprll 2007

IU

Defift

DeiftUniverslty of TechnolOgy

(2)

Li

(3)

22 _{International Workshop}

on Water Waves

and Floating Bodies

Proceedings

Editors:

(4)

ISBN: 978-953-95746-0-2

Published by: \TIDICI d.o.o., Velika Rakovica, Samobor, Croatia

April 2007

(5)

Foreword

The international Workshop on Water Waves and Flbatmg Bodies is an annual meeting of engineers and scientists with special interests _{m water waves and the effects of waves on}

floating or submerged bodies. The workshop was initiated over twenty years ago by Professor Nick Newman from MIT and Professor David Evans from Bristol University. Since its

inception, the workshop has grown from strength to strength and annually brings together marine hydrodynamicists, naval architects, offshore and arctic engineers and other scientists

and mathematicians, from both industry and academia, to discuss current research and

practical problems in a focused week of activity. Attendance is restricted to the authors of submitted extended abstracts that are reviewed for acceptance by a small committee. These proceedings include the extended' abstract for every presentation made at the 22 workshop.

The proceedings of previous workshops_{are available online at www.rina.org.uk thanks to the} cooperation of the Royal Institution of Naval Architects. The list of the previous Workshops

is shown in the table below.

The22nd _{International Workshop on Water Waves and Floating Bodies was jointly organized}

by Bureau Veritas - Research Department and Faculty of Mechanical Engineering and Naval Architecture of Zagreb University. The workshop took place in Hotel Jezero at Plitvice Lakes.

in Croatia.

time Malenica & Ivo Senjanovié

111

[ist

L3rd 116/02/1986 19/02/1986M1T(MA) USA

14I1/p3/219/03/1987IBrIstol

--- UK jUSA Norway U 10/04/1988 _13/04/1988 _{I T(MA)} tOystese Manctiesr j4th J 07/05/1989 10/05/1989 128/03/1990 15th[25/03/1990

6th 14/04/1991 _{17/04/1991 Woods Hole (MA)}

4vai deReu!l

l6//1993ohn'sNndIand

USA 17th 24/05/1992 27/05/1992

_France:

Canada 8th 123/05/1993 19th 117/04/1994 20/04/199 Kuju )apan

I91P2/0495 05/04/1995

ord _UK 11th I 17/03/1996 20/03/1996 Hamburg Germany Li 113th 11th1

1 16/03/1997 19/03/199? Carry IeRouet _{- ---}France

29/03/1998 01/04/1998 iphen aan den Rijn Netherlandj

11/04/1999 _{14/04/1999 Port Huron (MI)} _USA

116th

11h27/02/2009 O1IO3/2000Caesarea

25/04/2001 jHiroshima --

japanIsraeI

(6)

Makoto Ohkusu

The 22' IWWWFB is dedicated to Professor Makoto Ohkusu who left us suddenly last year.

Professor Obkusu was a regular contributor to the Workshop, indeed he hosted the 9th

IWWWFB in Kyushu. He travelled extensively, often with his family, lecturing and

collaborating with colleagues around the world.

After studying with Takao Inuj at the University of.Tokyo, Makoto began his prolificcareer

at Kyushu University, working initially in association with the late Professor Fukuzo Tasai.

Ohkusu performed seminal research on the hydrodynamic interactions among multiple floating bodies, which greatly contributed to the development of multi-hull ships and offshore platforms. Later he developed the unsteady wave-pattern analysis method, which provided a

new technique for studying ships running with forward speed in waves. He also published many other noteworthy papers, concerning such topics as the nonlinear behaviour of a long flexible cable; a new evaluation method for the oscillating and translating Green function; and

its application to the boundary-value problem for the flow around ships. He performed

extensive studies of the hydroelastic problems associated with very large floating structures

such as floating airports.

In 1981 Ohkusu was promoted as a Full Professor at Kyushu University. He served from 1997

to 1999 as the Director of the University's Research Institute of Applied Mechanics. Many students benefited from his tutelage and support. When he retired in 2001, an International Conference on 'Hydrodynamics in Ship and Ocean Engineering' was held in his honor. From 2004 to 2006 he served as the Director of the Marine Technology Center at the Japan Agency

for Marine-Earth Science and Technology.

We all remember Makoto Ohkusu, both for his kindness and the high quality of his work. His

research and generous spirit have inspired us, and his absence is mourned by our community.

(7)

22' _{International Workshop on Water Waves and Floating Bodies}

GrueJ.

' 105

Nonlinear wave-body interaction by a formulation in spectral space

Harter R., Abrahams I.D. and Simon MJ. 109

(9)

L

22m1_{IWV44IFB Plltvice, Croatia 2007}

lafrati A. and Korobkin A.A 113

Numerical analysis of initial stage of plate impact on water surface

Kashiwagi M. 117

Reciprocity relations of waves generated by an antisymmetric floating body

Khabakhpasheva TI. and Wu G.X. 121

Coupled compressible and incompressible approach for jet impact onto elastic plate

Klopman G., Dingemans M. W.. and van Groesen B. 125

Propagation of wave groups over bathymetty using a variational Boussinesq model

Korobkin A. and Malenica 129

Steep wave impac.t onto elastic wall

Malenica ., Senjanovié L, Tomaevié S. and Stumpf E. 133

Some aspects of hydroelastic issues in the design of ultra large container ships

Malleron N.,.Scolan Y.-M. and Korobkin A.A. 137

Some aspects of a generalized Wagner model

Miloh T 141

Structural acoustics ofa floating circular elastic plate

Molin B., Kimmoun 0. and Remy F. 145

Nonlinear standing wave effects on the weather side of a wall with a narrow gap

Nabergoj. R. and Prpié-0rié J. 149

A comparison of different methods for added resistance prediction

Nam B-W. and Kim Y. 153

Effects of slosbing on the mtion response of LNG-FPSO in wayes

Newman J.N. 157

Trapping structures with linear mooring forces

Noblesse F., Yang C. and EspinosaR. 161

Nearfield and farfield bounday-integral representations of free-surface flows

PiDkster J.A. and Hermans A.J. 165

A rotating wing fOr the generation of energy from waves

Pistani F. and Thiagarajan K 169

Experimental campaign on a moored FPSO in complex bi-directional sea states

Qiu W. and Peng H. 173

Numerical solution of body-exact problem in the Time Domain with a panel-free method

(10)

x

22' I44t7FB 2O7

181

Scolan Y.M., Kimmoun 0., Branger H. and Remy_F. ₁₇₇ Nonlinear free surface motions close to a vertical wall

Influence of a local varying bathymetry

Sturova I.V.

Tme-dependent hydroelastic response of an elastic plate floating, on shallow

water of variable depth

Sun H. and Faltinsen O.M. ₁₈₅

Hydrodynarnic forces on a planing hull in forced heave orpitch motions in calm water

Taylor P.H., Zang J., Walker A.G. and Eatock Taylor R. ₁₈₉ Second order near-trapping for multi-column structures and near-flat QTFS

Thompson I., Linton. C. M. and Porter R. ₁₉₃

A new approximation method for scattering by large arrays

Tuitman J. and van Aanhold H. ₁₉₇

Using generalized modes for time domain sakeeping calculations

Vanden-Broeck J.-M., Parau E. and Cooker M. ₂₀₁ Three-dimensional capillary-gravity waves generated by moving disturbances

Zang J., Ning D., Liang Q., Taylor P.H., Borthwick A.G.L. and Eatock Taylor R. 203

(11)

Figure 1: Barge

The response is calculated using two approaches. For the first approach the barges are two bodies coupled with springs. In this case the first six DoFs are the rigid body displacements

of the first barge and the second six DoFs are the rigid body displacements of the second barge. For the second approach the two barges are considered to be one flexible body. The first six DoFs are the rigid body motions of the two barges together and the other six are

flexural modes between the barges. The heave and pitch motions of the two approaches are shown in figure 2.

In frequency domain both approaches result in exactly the same response. In the time

domain the one flexible body approach will be incorrect when the relative angles between the barges are large. When for the two bodies the (Euler) rotations are correctly taken into account

the shape of the bodies will still be correct with large rotations. The flexural approach will

result in a distorted shape if the angles are large. The difference between the two approaches is shown in figure 3. This difference shows also the need to account for the rigid body dynamics of all bodies.

22d IWWWFB, PIiMce, Croatia 2007

Using generalized modes for time domain seakeeping calculations

Johan Tuitman', Hans van Aanhold2

(1) DeIft University of Technology, Ship Hydromechanics and Structures (2) TNO, Centre for Mechanical and Maritime Structures

Introduction

For calculation of whipçing, springing and multi-body interaction more than the standard six degrees of freedom are needed. By generalizing all degrees of freedom to flexural modes it is possible to create a code which can be used for whipping, springing, single and multi body problems.This approach is described in [1] and [2] for frequency domain calculations.

Usually the hydrodynamic coefficients are calculated using pre-defined displacements of every panel for the six degrees of freedom. Using the general modes approach, the

displace-ments of the panels is an additional input for the hydrodyna.rnic calculation. For example: a heave mode is created by a shape vector with (0,0, 1) for all panels. The shape vector as

calculated by e.g. a beam or 3D FEM is used for modes for whipping or springing calculations. In the frequency domain, rigid bodies and the bending modes can be treated exactly equal. After the hydrodynanilc coefficients are calculated the system of unknowns displacements can be solved and the response of all modes is known. Due to the non-linear terms in the time

domain calculation, it is not possible to solve rigid body and bending modes in a similar way.

It is necessary to account for the rigid (multi) body dynamics.

Example

The response of two coupled barges, see figure 1, is calculated to illustrate the use of gener-alized modes in time domain. Springs in all directions are used to couple the barges.

'0

(12)

198

Figure 4: Coordinate systems

Modal description

The mode shapes are described by the mdai shape vector hj. This vector is created for all

points: panels and masses. The same vector is also used for the frequency domain calculation. For the non-linear time domain calculation an additional matrix S is introduced which trans-fers the modes to the six rigid 'body DoFs of the individual bodies. Matrix S has a 'number of

columns which is equal to the number of modes and the number of rows is equal the number

of bodies-tirnes-six--Fora--normal-single-body--caJ'cu1at'ion-this-matrix will bth idéiitity

matrix. For two body calculation with only heave and pitch modes, matrix S will bea 12 by 4 matrix.

Figure 3: Shape of 30 degree pitch for single body (dotted) and double body

Time domain

The response Of the modes are calculated using the procedure proposed by Cummings [3]:

pt

(m+m0).+j

_{K:(tr).dr+k.='(t)}

0

Vectors },

and 1 are the actual acceleration, velocity and displacements of all modes.

The 4th order Runge Kutta method is used to integrate this equation of motion.

Figure 4 shows the differént coordinate systems that aie used. Every body has his own

ship-fixed system.

Zsj

(1)

(a) Multi body

(b) Single body

(13)

The rows of the S-matrix for bending modes for whipping and springirig are filled with zeros because these are not rigid body motions. It is assumed that all modes are either rigid or pure biending without a rigid component.

Dynamics

The accelerations for all DoFs are solved in the ship-fixed frames. The motions are integrated

in a earth-fixed frame. Before the acceleration can be integrated, all accelerations of rigid body modes have to be transfered to the earth-fiied frame using the Euler transformation

matrix.

Vector Ya,sf are the ship-fixed accelerations of all modes. The ship-fixed accelerations of rigid body modes are obtained by:

Ya,r,8f = S Ya,3f (2)

The same transformation is applied to obtain the rigidbody motions:

Yd,r S (3)

For every individual body, n, the ship-fixed accelerations are transfered to earth-fixed accelerations:

Ya,r,e,(6n-5:6n) = Tse (d,r,(6n-2:6n)) Ya,r,.f, (6n-5:6n) (4)

Where Tae is the Euler transformation matrix from ship-fixed to earth-fixed. The earth-fixed acceleration vector Ya is obtained by: 1

=ST

.Va,r,e (5)

For the non-rigid body modes there are no differences between the earth and ship fixed

coordinate systems:

Ya,r,e,(i), where S(n,:) 0 (6)

The earth-fixed acceleration vector } is used for integration of the motions

Forces

ndof

i= 1

22 fl,1N/1#/FB P1/tv/ce, Croatia 2007

The pre-calculated hydrodynamic coefficients are used to calculate the diffraction and radiated forces. These coefficients are obtained using the mode shape vectors, therefore the coefficients will give the correct excitation for all the modes.

The radiation force is calculated using retardation functions The hydrodynarmc coeffi-cients are considered to be earth-fixed, therefore the radiation force can be obtained by the

history f the I vector.

The diffraction force is calculated using the frequency domain RAOs. The actual location of the different bodies is used to calculate the diffraction force for all modes of the bodies.

The same, kind of transformation as used in equations (2)' to (6) are used to transfer the earth-fixed force to ship-thed.

The pressure of the incoming wave and the hydrostatic pressure are calculated for every

panel. This pressure is dependent, on the earth-fixed location of the panel. The earth-fixed

location is the earth-fixed' displacement of the COG of the 'body to which the panel belongs plus the earth-fixed distance between the pahel and the CoG. The non-rigid modes displace in the ship-fixed frame. The total ship-fixed distance between the CoG and the' panel is:

199

(14)

200

'tiJt-b iI,tt//CE. :JtJ1

Where is x the ship-fixed coordinate of the panel and h the mode shape vector, i3 is the

number of the body to which the panel is attached. The earth-fixed location of the panel, Xe is equal to:

Xe _{Yd,r,(6i5-5:6i-3) + Tes(Yd,r,(6i8_2:6is))} (8)

The force by the pressure at the panel, f will give an excitation force at the modes, F of:

After all forces are known the accelerations are calculated and the next time step is

calculated.

Results

The motion of the coupled barges are calculated for an irregular head sea with a significant wave height of 8 meter. Figure 5 shows the relative pitch angle between the barges using both approaches in the time domain calculation. The results are almost identical. This shows both

approaches are valid in time domain. In the case the springs between the barges are much

weaker or when there is no coupling between the barges only the multi body approach will be correct because the flexural modes can not describe large rotation correct.

2.5 1-4 bO Q - 1 0.5 0 -0.5 '1) c' -1.5 -2 0 'Single iody Multi body I 10 20 30 40 50 time [s]

Figure 5: Relative pitch motion between barges

By introducing generalized modes for the hydrodynamic calculation it is possible to cal-culate whipping, springing and multi body interaction. The (multi) body dynamics should be accounted for if generalized modes are used in time domain.

References

. Malenica, F. Remy and I. Senjanovi, Hydroelastic response of a barge to impulsive

and non-impulsive wave loads, 3td mt. Conf. on Hydroelasticy in Marine Technology,

2003

J.N. Newman, Wave effects on deforrnable bodies, Applied Ocean Research, Vol 16, pp

47-59, 1994

W. E. Cumrnins, The Impulse Response Function and Ship Motions, Schiffstechnik, Vol.

9, 1962

Using generalized modes for time domain seakeeping calculations

IU

Defift

22

International Workshop

on Water Waves

and Floating Bodies

Proceedings

Editors:

Foreword

[ist

14I1/p3/219/03/1987IBrIstol

l6//1993ohn'sNndIand

France:

I91P2/0495 05/04/1995

25/04/2001 jHiroshima --

Makoto Ohkusu

IWWWFB in Kyushu. He travelled extensively, often with his family, lecturing and

CONTENTS

GrueJ.

Using generalized modes for time domain seakeeping calculations

Johan Tuitman', Hans van Aanhold2

Introduction

Example

Modal description

Time domain

(m+m0).+j

K:(tr).dr+k.='(t)

Vectors },

(a) Multi body

Dynamics

Forces

Results

References

_{International Workshop}

_France:

_{K:(tr).dr+k.='(t)}