Time domain simulations of the behaviour of fast ships in oblique seas

Date Author Address

March 2008

Pepijn de Jong and Frans van Wairee Deift University of Technology Ship Hydromechanics Laboratory

Mekelweg 2, 26282 CD Deift

TUDeift

Deift University of Technology

Time Domain Simulations of the Behaviour of Fast

Ships in Oblique Seas

by

Pepijn de Jong and Frans van Wairee

Report No. 1602-p

2008

Published in: Proceedings of the6th Osaka Colloquium on Seakeeping and Stability of Ships, 29 March 2008, Osaka, )apan

THE 6TH OSAXACOLLOQUILPM ON

SEAKEEPING AND STABILITY OF SHIPS

2008

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ABSTRACT

The fundauiieiitals of a tinie (loniajn seakeepiiig cotte are

presented. Although the foriiiulaiioiis enable a non-linear

treatment of t lie submerge(l h uil form, pari ¡a t I iiicari,ation ¡s

required for coniputatioiial efficiency. Current and future code developments are described. The seakeeping code

PANSIJIP is applied for two fast vessels operating in oblique seas and results are compared svitii experinieiital data,

KEY WORDS: Time domain panel code, seakeeping, course keeping, ride control systems, high speed RoPax

ferry, high speed trimaran, dynamic (in)stability. INTRODUCTION

The continuous demand for high speed operation while

fulfilling existing and extended operational and mission

requirements has become a constant challenge for the naval architect. There is a perpetual competition in the industry to

develop innovative methods of reducing resistance and

expanding maximum speeds in a seaway.

Evaluation of advanced and/or high speed concepts requires advanced numerical tools that can deal with the

hydrodynamic issues involved on a first principles basis. Investigations are not limited to issues like linear motion

induced accelerations in the vertical plane, but need to

address slamming, whipping, fatigue damage, course

keeping and dynamic stability as well.

The present paper discusses a numerical method that can

be applied to high speed hull forms. The method is at present limited to non-linear motions including course

keeping and dynamic stability. Simulation results are shown for a high speed RoPax ferry and a trimaran and illustrate tise application and validity of the method.

NUMERICAL FORMULATION

The numerical method presented in tisis paper is an

extension of tise work presented by Lin and Yue (1990),

Pinkster (1998) and Van Walree (2002). Tise PANSHTP code

TIME DOMAIN SIMULATIONS OF THE

BEHAVIOUR OF FAST SHIPS IN OBLIQUE SEAS

Frans van WALREE

Maritime Research Institute Netherlands, THE NETHERLANDS

Pepijn de JUNG

Ship Hydroniechanics Laboratory, Dcl ft University of Technology, TI-lE NETHERLANDS

contains the numerical method.

Time domain Green function method

Potential flow is assumed based on the following

simplilications of the fluid. It is assumed to be:

homogeneous, incompressible,

without surface tension,

inviscid and irrotational.

Tise medium of interest is water, while there

is an

interface with air. The ambient pressure is assumed to equal zero. The water depth is infinite and waves from arbitrary directions are present. Under tlsese assumptions it cais be

shown tisat the Laplace equation, resulting from

conservation of mass, is valid in the interior of the fluid:

(1)

lise following definitions are

used to

describe the domain:

V(t) is the fluid volume, bounded by:

SF(t) the free surface of the fluid,

S11(t) tise submerged part of the hull of the ship, SL(t) lifting surfaces,

Sw(t) wake slsects and

S(t) tise surface bounding the fluid infinitely far from

the body.

The total potential can be split into Iwo the wave

potential and tise disturbance potential:

(2) The wave potential is giveis by:

tI)' =

-'-e

sin (k(x0 cosy' + s' siiT)

oIt) (3)

The subscript '0' refers to earth fixed coordinates. At the free surface two conditions are imposed. First, a kitsernatic condition assuriisg that the velocity of a particle at the free surface is equal to the velocity of the free surface itself:

2J[l

-

cos(I(t -

_{t))1e0*)Jo (kr)dk}

for

pq,tr

where R=

-

Ç)1 + (y0 - q)2 + (z0 -Ç)2 R0 = Jtv0 -Ç)2 + (y0 -1)2+(z11+ Ç)2 1- = - Ç)2 + (y0 1)2 In equation (IO):

the G°-term is the source and doublet plus biplane image part (or Rankine part), while

the d-terin is the free surface memory part of the Green's function, and

J0 is the Bessel function of order zero, r is time while t

is the past time.

lt has been shown, by fur example Pinkster (1998), that the Green function satisfies both the Laplace equation and the boundary conditions, making it a valid solution for the

boundary value problem stated above.

Using the above, it is possible to derive a boundary integral formulation. The first step is to apply Green's

second identity to:

'(') and

aG/ar(.0,,r_r)

(Il)

Next, the free surface integral is eliminated by virtue of the Green function. Finally, a general formulation of the nonlinear integral equation is obtained for any field point:

4,rTt1) (p,r)

J(1G

- G°(D)dS+

fdrf

((DGr - GrI )ds+ (12)

!fd

(OY'G G,(D)VNdS

g1

(r)

VN is the projection of the normal velocity at the curve

C in

the plane of the free surface, for example

G = ¿3G Ian etc., and Tis defined as:

E

v(r)

T(p)=

1/2 PESJ,(t) (13)

O otherwise

A source distribution will be present on the body surface and a combined source-doublet distribution on lifting surfaces. The source strength is set equal to the jump in the nornial derivative of the potential between the inner and

outer sides of the surface, while the doublet strength is set equal to the jump of the potential across the inner and outer

surfaces.

Using such source and doublet distributions finally results in the principal equation to be solved for the unknown

singularity strengths:

(

¿3D 4,'rlV

---i=2,rci +

r _¿3n0) J

cr(q,f)dS+

_anp (10) L,.

(,(P(t)fl,,fl0 dS

.0 Ô2G' oir L,,1(r) atan,, ¿33G' ctS-atafIpauug

-

_L

rdr

a(q,t).2J_VrÇdL

(r) _atan0

In this equation a subscript p of n indicates a normal derivative at the field point p and subscript q at singularity point q. r';, is the normal velocity at the collocation point.

A wake model is necessary for an unique solution of (14). The wake model relates the dipole strength at the trailing edge of lifting surfaces to the location and shape of a wake sheet, in order to both satisf' the Kutta condition and Kelvin's circulation.

(14)

¿3f at

V S,. (4)

Second, a dynamic condition assuring that the pressure at the free surface is equal to the ambient pressure. For this condition use is made of the unsteady Bernoulli equation in

a translating coordinate system:

1 2

----+gq+(Va) =0 V x0eS

(5)

Both can be combined and linearized around the still water free surface, yielding:

¿3j

ôz,

+g=0 at

z11 =0 (6) at

On the instantaneous body surface a zero normal flow condition is imposed by setting the instantaneous normal velocity of the body equal to:

r';, =-+- V

x9 CS/IL(I) ¿3d

¿3

¿3n ¿3n

(7)

At a large distance from the body the influence of the

disturbance is required to vanish:

(I), *0 --*0 when r*S

(8)

at

At the start of the process, apart from the incoming waves, the fluid is at rest, as is reflected in the initial condition.

(Du1=0

=±

0

¿3

(9)

In this tinie-c oniain potential code the Green function given in (IO) will he used. This Green function specifies the influence of a singularity with impulsive strength (submerged source or doublet) located at singularity point

q (Ç, q, Ç) on the potential at field point p (x11, vo, z0).

These requirements are satisfied by transferring the net circulation at the trailing edge into the adjacent wake sheet elements. For the wake sheets the doublet elements are

replaced by equivalent vortex ring elements as a discretization of the continuous vortex sheet. The sum of the circulation strengths along each individual vortex ring segment is always zero, as detailed in Katz and Plotkin

(2001).

A further requirement is that the wake sheet should be force free. It is not a solid surface, so no pressure difference can be present between the upper and lower sides of the sheet. The force on a vortex sheet is given by the Kutta-Joukowsky law:

Ê=pJxy

(15) From this law can be determined that for zero force the vorticity vector should be directed parallel to the velocity vector. This can be accomplished by displacing the vortex element corner points with the local fluid velocity. However, a reduction of the computational effort is achieved by prescribing the wake sheet position and form. This prescription is simply, that a wake element remains stationary once shed. This eliminates the effort needed to calculate the exact position of each wake element at each time step. This violates the requirement of a force free wake sheet. However, for practical purposes this does not have significant influence as shown by Van Walree (1999) and Katz and Plotkin (2001).

The equation is discretized in ternis of a source element distribution on the hull, a doublet element discretization on the litling surfaces and equivalent vortex ring elements ori the wake surface. In the current method constant strength

quadrilateral source and doublet panels are used. This leads

to the discretized form of (14).

At the start of the simulation the body is impulsively set into motion. At each subsequent time step the body is advanced to a new position with an instantaneous velocity. Both position and velocity are known from the solution of the equation of motion. The discretized form of (14) is

solved to obtain the singularity strength at each time step.

Linearization

Especially the evaluation of the free surface niernoty terni of the Green's function requires a large amount of computational time. These ternis need to be evaluated for each control point for the entire time history at each time step. To decrease this computational burden, the evaluation of the memory term has been simplified. For near time history use is made of interpolation of predetermined tabular values for the memory terni derivatives, while for larger values further away in history polynomials and asymptotic expansion are used to approximate the Green function derivatives.

Moreover, the position of the hull and lifting surfaces relative to the past time panels is not constant due to the unsteady motions, making recalculation of the influence of past time panels necessary for the entire time history. This recalculation results in a computational burden requiring the use of a supercomputer. To avoid this burden, the unsteady position of Indi and litling surfaces is linearized to the average position (moving with the constant forward speed).

Now the memory integral can be calculated a priori for use

at each time step during the simulation.

The prescription of the wake sheets in this linear approach

leads to a flat wake sheet behind the lifting surface. Again a constant distance exist to the past time wake panels. Only the influence coefficients of the first row of wake elements need to be calculated at each time step, until the maximum

wake sheet length is reached. For all other rows the induced

velocity can be obtained by multiplying the influence by their actual circulation.

Force evaluation

Forces can be obtained from integration of the pressure at

each collocation point over the body. The pressures can be obtained by using the unsteady Bernoulli equation (in a body fixed axis system):

- - V V + gz

at

In (16) ¡7 is the total velocity vector at the collocation point of the rigid body, including rotations.

The spatial derivatives of the potential in (16) follow straight from the solution. The only difficulty remaining is to obtain the time derivative. For the contribution of the

wake and the Rankine part of the doublet panels this can be

done by utilizing a straightforward backward difference

scheme. However, this gives unstable results when used for the contribution of the source panels and the memory part of

the doublet panels to the time derivative. This instability is

solved by calculating the time derivative of these

contributions analytically from the Green function

derivatives.

This means that additional Green function derivatives have to be obtained, besides the derivatives needed for the solution itself. Furthermore, the time derivative of the source strength is needed. One solution is to derive this derivative directly from the solution itselft

(17)

to this equation A is the solution matrix relating the singularity strengths via the Rankine influences to the Ri-IS. The vector

i,

is the RHS vector of the solution, containing all intluences due to incident wave, free surtuice memory effects and rigid body motions in terms of normal velocity in the collocation points. To obtain the time

derivative of the free surface memnoty part of this vector, again extra Green function derivatives need to be obtained. The time derivative of the wave contributions can be obtained analytically. The time derivative of the rigid body velocity is the rigid body acceleration. This acceleration is multiplied by the inverse of the Rankmne influence matrix that equals the added mass. This contribution can be transferred to the mass times acceleration part of the equation of motion.

p -p

I (a2

II +1I

(2

2 (ôx)

,t')

(2

-i-II

_(..az) -t-(16) = p

Ventilated transon sterns

Methods using a transient Green function are not able to deal with ventilated transom sterns. To compensate for this

two measures can be taken:

Add a dummy section at the transom that ensures flow alignment. Do not take into account the forces acting on such a segment on the body. This dummy segment avoids the occurrence of unrealistically high velocities

around the transom.

Another measure that can be taken is to set the pressure

to atmospheric at the transom by applying a smooth function over a certain length from the transom that

rcduces the pressure accordingly.

Inclusion of viscous flow eJ/ècts

With respect to the viscous resistance R, empirical forniulations are applied to each part separately (hull, outriggers, liliing surfaces). The formulations used can be

generalised as follows:

R, =

IpU2S(l+

k)C,.

0.075

(Iog,0(R,)- 2)

where U is the ship speed, S is the wetted surface arca, k is a suitable form factor, and R,, is the Reynolds number of

the body part considered.

Viscousdarn¡ing

Especially for high speed vessels, having only slight potential damping, viscous damping can play an important role. This is especially true around the peak of vertical

motions. Then forces that arise duc to separation in the bilge

region due to vertical motions can be of significance. The magnitude of these forces depends on oscillation frequency, Froude number and section shape. En the current model a cross flow analogy is used to account for these forces. The viscous damping coefficient only depends on section shape, other influences are neglected. l'lie following formulation is

used in a strip wise manner:

F=PIVrIV,SCD

(19)

Vr is the vertical velocity of the section relative to the local flow velocity, while S is the horizontal projection of the section area. The cross-flow drag coefficient C0 has

values in-between 0.25 and 0.80.

An additional term is incorporated for the hull roll

damping K,,:

K,,

_(bp+bIpIp)

(20)

where p is the roll velocity and b,, and b,,,, are linear and quadratic roll damping coefficients respectively, determined by means of MARIN's FDS method, see Blok and Aalbers (1991).

Ride control system

A ride control algorithm is included in the code actuating

control surface settings. The basic equation is:

Ô= P(i-

,)+ D(- i)+ A(- ç)

(21)

where is the control surface deflection; P, D, and A are proportional, damping and acceleration coefficients

respectively; and and i, are the required and actual motion vectors respectively; and an overdot denotes

differentiation with respect to time. Equation (21) is used for both the ride control and the auto pilot systems. Furthermore, a time delay between the instant of motion

sensing and flap actuation can be specified.

Control systems consisting of' one or more lifting surfaces (T-foil, stabilizer fin) are modeled as such in the code. Stern trim flaps are modeled as an extension of the hull bottom with a time-varying orientation. Interceptors can not be modeled in a potential flow method, in Panship an empirical formulation based on systematic model tests is used as

specified in Equation (22). Herein force and moment coefficient vectors are used, F andë51 respectively, in

(18) combination with tlìe interceptor pitch z. The interceptor width is gïven byb.

l

!pub:

(22) içí=

Propulsion and steering

A propulsion and steering system for water jets is

included. The formulations are based on captive model tests

on several types of high speed craft and read as follows for

the side force and yaw moment, Y, and N,,. respectively:

N, = p(7;1,,n2 + T,,Un) smii(F)x

= P('"2 + T,,Un) sin(Fb)

(23)

where T is a thrust coefficient, U is forward speed, n is the RPM and F5 is an empirical coefficient.

ONGOING WORK

Free surface evaluation and mod(fication of the pressure

distribution

En order to coiTect the pressure distributioii for the change

in submerged geometry due to the rigid body motions and

the free surface deformation caused by the incident,

ditfracted and radiated waves, De Jong et al. (2007) proposed an extension of the code. In this extension the free surface deformation is calculated using the potential

solution together with influence functions which relate the solution to a free siirtice grid. By applying the free surface

boundaiy condition at the free surface grid points the free surface elevation follows.

Together with the rigid body position this gives an

instantaneous wetted surface. The pressure on the linearized

wetted surface is modified such that it extends over this

instantaneous wetted surface. This new pressure distribution is used in the evaluation of the forces and the equation of

motion.

This method forms a partial

correction of both the

linearization of the free surface boundary condition and the

linearization

of the

body boundary condition, while

retaining the computational advantages of the linearized

potential code.

MLved source-doublet formulation on the hull sumface

In order to simulate lift forces generated by the ship hull itself the code is currently being adapted to apply a mixed source-doublet distribution to the hull surface together with a wake sheet extending from the stern. This is done to study the effects of lift forces in the horizontal plane and also to provide a better estimation of the vertical hydrodynainic lift acting on high speed vessels.

When applying a combined source-doublet distribution to a surface piercing body, a new waterline integral arises for

the doublet distribution. This integral suffers even more

than its source equivalent from numerical instabilities,

necessitating careful numerical treatment. Work is

undei'ay to compute the Green function contributions with high accuracy, yet with high computational efficiency.

The application of a mixed source-doublet formulation enables a better description of ventilated transom sterns by applying a local pressure condition.

APPLICATION AND VAlIDATION

Two cases will be discussed here. Both concern high

speed ships operating in mainly oblique seas. The first ship is a high speed RoPax ferry with a low directional stability. In order to reduce roll induced yaw motions (broaching), it was required to keep roll within limits by means of a ride control system. The general characteristics of the vessel are shown in Table I.

Table I. General characteristics of RoPax feny

l'he ride control system comprised:

3 steerable waterjets (yaw)

bow T-foil with incidence control (pitch) one pair of stabilizer fins (roll)

one pair of movable transom interceptors (roll and

yaw)

one pair of movable transom trim flaps (pitch) A I to 24 scale model was tested in MARIN's SMB, with

all control surfaces present and active. Figure I shows a

stern view of the model while Figure 2 shows the model

during testing.

Figure 2 RoPax ferry model during testing

Table 2 Test conditions

Appendages on RoPax ferry model

Comparisons between experimental and calculated results for irregular waves are given in Figures 3 through 14. The PANSHIP simulations have been performed in the

linearized mode, i.e. the Green function contributions G°and dare determined for the initially submerged hull forni. The wave excitation and hydrostatic pressures are evaluated in a non-linear manner, i.e. the actual submerged hull forni is taken into account. Also, the disturbed wave elevation is accounted for on basis of the disturbance pressure at water

line body panels.

All results shown denote motion standard deviations

divided by the wave height standard deviation.

Accelerations are provided for the bow passenger area. The duration of the tests and simulations was such that at least 200 wave encounters were recorded. The test conditions are

given in Table 2. Length Lpp 123.70 ni Beam 22.00 Dm-tI 2.45 Displacement 3000 toils Design speed 45 kt (iM 3.75 ni Speed [kt] Wave direction [deg Significant wave height [m} Peak period {sec) 25 180-90-45 5.0 11.20 40 180-90-45 2.5 SSO

1 00 080 060 34 0.40 020 000 3.5° 300 250 E 200 1.50 loo 050 000 2.50 2.00

I

90 Headtrtg (deg]

E

45

I

DEap Partahip OEop UPeeshlp DE.xp Panshgl 000 065 0,40 -E 300 250 Ol50 1.00 050 000 E 1 20

-

020-000 500 450 400 350

I

180 90 Headtng (dog]

Figure 6 Comparison roll 4Okt Figure 10 Comparison yaw at 40 kt

45 DEep POnshp DEep UPanShip DECO UP000lep 00 11X1 CO .00 itgo

-I

L__

Figure 1.00 090 080 3 Comparison heave at 25 kt Heave al 4081 Figure 100 0.10) 080 7 Comparison pitch at 25 kt Pttch 0140 kt o io 0.70 0.00 0.60 OEOp DEep 2 050

e PannO p lIOSO e Panes p

040 0.40 0,00 0.20 O 10 060 100 90 too 90 45

Heodtng (degj HeadIng (dog]

Roll at 2561 Yaw at 25k)

Roll at 4Okt VOW 414061

180 90 45 100 90 40

180 90 45 100 90 40

IteelOng (dog] 000tSflg (dog] IteelOng (dog] 000tSflg (dog]

Figure 4 Comparison heave 40 kt Figure 8 Comparison pitch at 40 kt

loo 90 45 180 00 45

loo 90 45 180 00 45

HoadWg (dog] Hoot8rtg dog] HoadWg (dog] Hoot8rtg dog]

Figure 9 Comparison yaw at 25 kt

Figure 5 Comparison ¡oIl 25 kt Figure 9 Comparison yaw at 25 kt

Figure 5 Comparison ¡oIl 25 kt

050

n-

₁₈₀

2.00 1 00 1 60 . 1.40 120 1.00 0.00 060 040 020 000 2.50 200 E 31.50 E il 1.00 IP 0.50 0.00 Transverso acceleration al 25 Et

i

P.

leo go Heeding deg]

Figure 12 Comparison transverse acceleration at 40 kt

Verbat acceleration et 25 El

Figure 13 Comparison vertical acceleration at 25 kt

Vertical acceleration at 40 Et 45

100 90 45 Heading ]degJ

Figure 14 Comparison vertical acceleration at 4Okt

OEvp UPenship DEep Parbolt6, dEep Paos DEep Parcohip

Motions jis the vertical plane are quite well predicted, considering the complex ride control arrangement. The transverse and vertical acceleration at the bow are well

predicted too. Roll and yaw are reasonably well predicted, but might improve when additional lifting tenus for both

horizontal and vertical plane motions are included in the

code in the future. Such lifting terms are of importance for yaw moments, roll-yaw coupling effects and vertical plane

lift damping.

The second case concerns a high speed Trimaran. The

main particulars of the vessel are shown in Table 2 while

Figure 15 shows the model in the Seakeeping and Manoeuvring Basin of MARIN during a run in 5.5 m stern quartering seas.

Table 2. General characteristics of the Trimaran Length Ljip II 0.00 n Beam 26.40 ni Draft 4.60 ni Displacement 2310 tolls Design speed 45 kt GM 170m too 50 45 Heading dog]

Figure 11 Comparison transverse acceleration at 25 kt

Transverse acceleration at 40 Et

Figure 15 Trimaran model in the SMB

An interesting feature of the vessel is that it suffers from a

dynamic instability in heel, especially at higher speeds.

Figure 16 shows the calculated pressure distribution on the submerged outrigger hull portion for a speed of 45 kt and a heel angle of 10 deg. The low pressures result in a suction force which tends to reduce the restoring moment to about zero. lise GZ curves at rest and at a 45 kt speed are shown

in Figure 17.

Both curves are based on calm water

PANSHIP simulations whereby the vessel was fixed in all nsodes of motion. Similar results have been obtained for a

range of speeds and have been stored in tise linear mode

code as a hydrodynamic correction on the restoring moment. At heel angles above 20 degrees the deck connecting tise outriggers to tise hull is submerged and greatly increases the static stability which makes the vessel virtually impossible

to capsize.

Figure 16 Pressure distribution on outrigger at 10 deg heel and 45 kt speed

tao 90 Heeding dog] 45 0.70 060 ? 050 to 040 t 030 3 , 0.20 0 tO 000 000 060 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

09 08 0.1 00 -0 GZ curves Heel (dug] -GZ-U=0 a'GZ45

Figure 17 GZ curves at zero speed and at 45 kt. Figures 18 through 21 show parts of the experimental and simulated time traces for roll at a 45 kt speed in an irregular

wave with a 2.5 ni significant wave height, for wave

directions of 135 (bow quartering) and 45 (stern quallering) degrees respectively. For bow quartering seas the signals show isolated large roll excursions, for stern quartering seas

alternating large mean heel angles occur. Although the

actual wave trains in the simulations are different 0om these in the experiments, the general behavior is welt captured by the simulations.

Figure 18 Experimental ioll time trace at 45 kt and 135 deg heading.

Figure 19 Calculated roll time trace at 45 kt and 135 cleg heading.

n

n

n

i,,

n

8LCOMIS

Figure 20 Experimental roll time trace at 45 kt and 45 (leg

heading.

Figure 21 Calculated roll time trace at 45 kt and 45 deg

heading.

Further statistical comparisons for heave, roll, pitch and

yaw motions are given

n Figures 22 through 25 for

conditions as specified in Table 4.

Table 4 Test conditions

Heave

2 3

Tesi no.

Figure 22 Comparison heave response

Roll

F,ich

2 3 4 5

Tesi no

Figure 24 Comparison pitch response

OEep Ponuhip Eup UpanOSip DEep Panship Test Speed {kt] Wave direction [deg] Significant wave height [mj Peak period [sed I 45 135 2.5 7.0 2 45 90 2.5 7.0 3 45 45 2.5 7.0 4 27 6t) 5.5 9.5 5 35 60 3.5 8.0 2 3 5 Tesi no

Figure 23 Comparison roll response

dis _{y' u}

0c9

1.40 1 20 1.00 080 0.60 -0 0.40 0.20 0.00 30,00 25,00 2000 ' 1500 1000 5.00 000 1.40 120 1 00 080 060 - 040 020 000

400 350 300 250 :: I_00

-::ÏT,

Yew Test no

Figure 25 Comparison yaw response

The comparisons show that heave and pitch are quite well predicted, considering the strong noii-linear etiects due to the large roll motions. The roll prediction is quite acceptable

fur tests I through 3, but starts

to deviate from the

experimental value for test 4 and is not so well predicted for test 5. Yaw is well predicted lòr the first tests, but deviates

again for test 5. No apparent reason is available for the

mismatch of results for test 5. It should be noted that for test

5 the mean wave encounter frequency is quite low (0.13

rad/sec). The experimental number of wave encounters does

not satisfy the usual criterion of 200, in fact the actual number of wave encounters for test 5 was only 70. Due to the highly non-linear behavior in roll, and thereby iii yaw, it is difficult to compare standard deviations for roll and yaw on basis of such a low number of wave encounters.

CONCLUSIONS

A time domain panel method for prediction of the

dynamic behavior of (high speed) unconventional hull

lòrms in waves is presented.

Simulation results are presented and compared to

experimental results for two high speed ships: a RoPax feriy with a complex ride control system and a Trimaran with a

dynamic stability problem. Predictions for vertical plane motions are generally quite good. Despite the use of a

relatively simple method for viscous flow damping,

predictions for horizontal plane motions are deemed

acceptable.

lt is anticipated that through the treatirient of the hiil I forni

as a lifting surface even better predictions for both vertical and horizontal plane motions can be obtained in the future, and the use of empirical "viscous flow coefficients" can be

reduced.

ACKNOWLEDGEMENTS

The pennission from Naval Sea Systems Command USA

to

publish the experimental data on

the Trimaran is

gratefully acknowledged.

LiEop

Penship

REFERENCES

Blok J.J. and Aalbers A.B. (1991). "Roll Damping Due to

LIft Effects on High Speed Monohulls", Proceedings

FAST'91 Conft'rence, Vol 2, pp 1331.

Jong, P. de, Walree, F. vari, Keuning, JA., Huijsmans,

R.H.M. (2007). "Evaluation of the free surface elevation

in a time-domain panel method for the seakeeping of

high speed ships". In Proceedings of the Seventeenth liii. Of/shore and Polar Engineering Conference, Lisboa Katz J. and Piotkin, A. (2001). Low-speed aerodt'nwnics.

Cambridge University Press, second edition.

Lin, W. M. and Yue, D. (1990). "Numerical solutions for

large-amplitude ship motions in the time domain". In

Proceedings

of

the 18th Symposium on Naval Hydroineclianics, Ann Arbor, pp. 41-65

Pinkster, H. J. M. (1998). Three dimensional ti,ne-domain analysis offin stabilised ships in waves. Master's thesis, DeIft University of Technology, Department of Applied

Mathematics

Walree, F. van (1999). oInpu1ationa/ methods for hydrofoil

craft in steady and unsteady flow. PhD thesis, Deift

University of Technology

Walree, F. van (2002). "Development, validation amid

application of a time domain seakeeping method for high speed craft with a ride control system". In Proceedings of

the 24th Symposiuni on Naval Hydrodynamics, pp.