The development and validation of a time-domain panel method for the seakeeping of high speed ships

Date October 2009

Author Jong, Pepijn de and Frans van Wairee

Address Deift University of Technology Ship Hydromechanics Laboratory

Mekelweg 2, 2628 CD Deift

TU Deift

DeIft University of Technology

Page /of 1/1

The development and validation of a time-domain

panel method for the seakeeping of high speed

sh i PS

By

Pepijn de Jong and Frans van Walree

Report No. 1649-P 2009

Proceedings of the 10th International Conference on Fast Sea Transportation, FAST2009, Athens, Greece, October '09, Edited by G. Grigoropoulos, M. Samuelides and N. Tsouvalis, ISBN: 978-960-254-686-4

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fast sea

transportation

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'5-8QCTOBER 2009

DIVAN I PALACE ACROPOLIS HOTEL, ATHENS, GREECE

Edited by

G. Grigoropoulos, M. Samuelides, N. Tsouvalis

PROCEEDINGS

Proceedings of FAST 2009, lO International Conference on Fast Sea Transportation

The Organizing Committee of FAST 2009 is not responsible for statements or opinions

expressed in the papers printed in these two volumes.

The papers have been prepared for final reproduction and printing as received by the authors, without any modification, correction, etc. Therefore, the authors are fully responsible for all information contained in their papers.

Although all care is taken to ensure integrity and the quality of this publication and the information herein, no responsibility is assumed by the editors and the authors for any

damage to the property or persons as a result of operation or use of this publication and/or the information contained herein.

ISBN 978-960-254-686-4 (set)

ISBN 978-960-254-687-1 (Vol. 1)

Copyright © 2009

Organizing Committee of FAST 2009 All rights reserved

PREFACE

Started in Trondheim, Norway, in 1991, FAST conferences take place every two years and are the world's leading conferences addressing fast sea transportation issues. FAST 2009, the 1 0th International Conference on Fast Sea Transportation is _{held in Athens, Greece, from} October 5 to 8, 2009. The 10th anniversary of FAST coincides with a difficult period for the shipbuilding industry and shipping suffering tinder the impact of a worldwide recession. The

latter is apparent through a common slowdown in the growth of the national economies, though the demand for energy, raw materials and finished goods is continuously raising,

while banks are anxious for the

flow towards the shipping industry. At the same time environmental issues emerged to major parameters of all production and operation activities.

Under these circumstances FAST 2009 briiigs together specialists from all over the world in

all

fields of naval architecture and marine engineering. namely from

structures, ship design. propulsion and safety to present and discuss the current state of the art, the most recent research results and technologies, trends and future needs and opportunities that relate to fast ships.

This year in Athens, FAST conference incitides two keynote speeches. One presents the

future for commercial fast crafts and discusses the experience and lessons learned from eveiits since the first FAST conference in 1991. The other addresses environmental issues that are of paramount importance and a matter of high concern for societies during the last decade.

In order to ensure the high quality of FAST 2009, all papers that are presented in the

Conference and are included in the Conference Proceedings went a thorough two-stage

review process of both abstracts and full manuscripts. The organizing committee wishes to express its thanks to all prominent members of the academia and the industry that participated in the process of review. Furthermore, we would like to express our thanks to the sponsors who supported the organization of the event. The experience and the advice that was provided to us by the international committee are also acknowledged.

Last but iiot least we would like to thank all of you who contributed either with papers or with your active participation in the audience of the conference for a successful eveiit.

We wish you a fruitful and enjoyable stay in Athens,

The Organizing Committee

Prof. G. Grigoropoulos Assoc. Prof. M.S. Samuelides Assoc. Prof. N. Tsouvahis

id" International Conference on Fast Sea Transportation FAST 2009, Athens, Greece, October 2009

10th

International Conference on Fast Sea Transportation FAST 2009, Athens, Greece, October 2009

FAST 2009 COMMITTEES

Organizing Committee

GRIGOROPOULOS G., Professor, National Technical University of Athens, Greece SAMUELIDES M., Associate Professor, National Technical University of Athens, Greece TSOUVALIS N., Associate Professor, National Technical University of Athens, Greece

International Standing Committee

HOLDEN K., Marintek AIS, Norway ARMSTRONG T., Austal Ships, Australia

CU! W., China Ship Scientific Research Center, China

DOCTORS L.J., Professor, The University of New South Wales, Australia

FALTINSEN 0., Professor, Norwegian University of Science and Technology, Norway GEE N., BMT Nigel Gee & Associates, United Kingdom

MOAN T., Professor, Norwegian University of Science and Technology, Norway

ROZHDESTVENSKY K., Professor, St-Petersburg State Marine Technical Univ., Russia

National Scientific Committee GALANIS K., Naval Officer, Hellenic Navy

GEORGIOU I., Associate Professor, National Technical University of Athens GIANNOULIS P., Ocean King Ltd

KAKALIS N., DetNorske Veritas, Manager of Piraeus R&D Hub KAVOURAS D.t, KAPPA Marine Consultants Ltd

KOKARAKIS J., Bureau Veritas

KYRTATOS N., Professor, National Technical University of Athens MITSOTAKIS K., Chief Naval Architect, Elefsis Shipyards S.A.

PAPANIKOLAOU A., Professor, National Technical University of Athens PSARAFTIS H., Professor, National Technical University of Athens SPYROU K., Professor, National Technical University of Athens YFANTIS E., Professor, Hellenic Naval Academy

THE DEVELOPMENT AND VALIDATION OF A TIME-DOMAIN

PANEL METHOD FOR THE SEAKEEPING OF H1GH SPEED SHIPS

Pepijn de Jong1 and Frans van Walree2

Ship Hydromechanics and Structures, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands

2

Ship Manoeuvring and Seakeeping, Maritime Research Institute, Haagsteeg 2, 6708 PM, Wageningen, The Netherlands

ABSTRACT

A time domain boundary element method is presented for the seakeeping of fast vessels. The method uses a

free surface Greeti function with combined source-doublet panels on the body surface, while satisfying two

boundaty conditions explicitly. Firstly, a zero normal tiow on the body condition and secondly a condition at the transom stern based on the unsteady Bernoulli equation to model transom stern flow. Although the formulations

enable a non-linear treatment of the submerged hull form, partial linearization is employed for computational efficiency. The fundamentals are elaborated and subsequently a comparison of experimental and simulation

results of two advanced fast nionohull concepts, the Enlarged Ship Concept and the Axe Bow Concept, in calm water and in irregular head seas are presented as a validation of the seakeeping method at a number of different

forward speeds. The simulation results show good agreement with the measured results when observing the

standard deviations of the time traces, nevertheless the prediction of extreme motions is hot yet satisfactoiy. The latter can partly be attributed to the applied linearizations.

1. INTRODUCTION

There is a continuous demand for ships capable of high speed operations providing crew

and passengers a comfortable and safe environment while fulfilling existing and extended operational requirements. Typically these craft are used for patrol and navy duties, fast

offshore crew and supply services, and SAR operations. Where previously most attention was

focused on minimizing resistance, more recently the focus has shifted towards seakeeping

behaviour, added resistance in waves, dynamic stability, course keeping, operability, extreme acceleration levels, slamming, and fatigue life.

iam international Conference on Fast Sea Transportation

FAST 2009, Athens, Greece, October 2009

Fig. 1. Right: 'Zeearend' a DAMEN Stan Patrol 4207 of the Dutch Coast Guard, an example of the Enlarged Ship Concept, left: 'Silni' a DAMEN Fast Crew Supplier 3507, an example of the Axe Bow Concept

To assess the hydrodynamic performance of fast vessels advanced computational tools are required that can deal with the hydrodynamic issues involved based on first principles. The investigations that cati be done with these tools should not be limited to the vertical motions

but should also include the previously mentioned areas as dynamic stability and course

keeping.

The present paper reports on the development of a numerical model for the seakeeping of fast ships based on a 3D time domain Green function method. Fast in this context is defined

as the range of Froude numbers over length from 0.5 to 1.2. Although ships are not fully

planing in this speed regime, hydrodynamic lift becomes of importance and

significant dynamic trim and rise of the centre of' gravity. This change in running attitude can result in essentially different motion behaviour in a seaway.

This development is part of the second phase of the FAST project, that was initiated following the development of two fast monohull collcepts aimed at improved seakeeping

behaviour, the Enlarged Ship Concept in 1995 and the subsequent Axe Bow Concept in 2001

(Fig. 1) at the Ship Hydrodynamics Laboratory of the Delft University of Technology ii

cooperation with Damen Shipyards (Kenning 2006). The need to develop limiting criteria and to systematically assess the merit of both concepts led to the first phase of the FAST project

carried out as joint effort of' the Royal Netherlands Navy, the United States Coast Guard, Damen Shipyards, Damen Schelde Naval Shipbuilding, Mann, and Deift University of

Technology.

142

Fig. 2. Enlarged Ship Concept (left) and Axe Bow Concept (right) during tank testing

The first phase of FAST consisted of a full scale study for developing limiting criteria for the motions and acceleration levels of fast ships operating in waves aiid a study comparing the

results of towing tank experiments of three design concepts in head, stern-quartering and

following waves. The results of this study are reported by Keuning and Van Walree (2006).

Fig. 2 shows the Enlarged Ship Concept and the Axe Bow Concept during seakeeping

experiments in the towing tank of the Ship Hydromechanics Laboratory. Clearly visible in the right picture is the characteristic Axe Bow.

FAST phase 2 was setup to develop practical numerical models for the assessment of the seakeeping behaviour of high speed vessels in terms of motions, acceleration levels, loads and

dynamic behaviour. For this a two-track development was foreseen. The first track was to further develop the code FASTSHIP, a 2D time-domain nonlinear code based on

semi-empirical impact of 2D wedges for the seakeeping of high speed ships developed at the Ship

1-lydromechanics Laboratoiy. The second track was to adapt a 3D time-domain potential

Green function boundaiy element method PAN SHIP developed by Mann to cope with high forward speeds and is the topic of the present paper.

The formulation of the numerical model behind PANS1-IIP is based on the work of Lin and

Yue (1990) and further developed by Van Walree (1999, 2002). The numerical model is capable of dealing with significant forward speeds and arbitrary three-dimensional (large amplitude) motions due to the use of a transient Green function, as shown by for example

King et al. (1988). The free surface boundary conditions are linearized to the undisturbed free

surface, while it is possible to retain the body boundary condition on the actual submerged

143

reduce the computational burden of the method, enabling the seakeeping analysis to run on a normal desktop computer.

Modules to include the forces due to propulsion systems and due to motion control

appendages such as rudders, trim flaps, interceptors and lifting surfaces into simulations have

been iniplemented. Previous developments of PANSHIP for high speed applications have

been presented by De Jong et al. (2007) and Dc Jong and Van Walree (2008) and include the implementation of pressure stretching based on the calculation the free surface deformation and the modelling of transom flow by using an appropriate wake model.

The current paper is intended to provide an overview of the development of the seakeeping code PANSHIP and to show validation results in calm water and in head waves. Although the

method is setup to be able to deal with arbitrary wave directions and motions in all six degrees of freedom, for the purposes of the current paper the application of the method is limited to head waves. Section 2 presents the potential flow model and solution method of

PAN SI-LIP. In section 3 the results of the Enlarged Ship Concept and the Axe Bow Concept

advancing with constant forward speed in calm water trim and sinkage predicted by

PANSHIP are compared to the measured trim and sinkage during the FAST towing tank

experiments. Seakeeping simulations of both concepts in head waves at a number of different forward speeds are presented in section 4. Section 5 concludes the paper with a summary of the findings and proposed future work.

2. NUMERICAL FORMULATtON

The numerical method presented in this paper is an extension of the work presented by Lin and Yue (1990), Pinkster (1998) and Van Walree (2002).

2.1 Time domain Green function method

The 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. Potential flow is assumed based on the following simplifications of the fluid:

The fluid is homogeneous. The fluid is incompressible.

The fluid is without surface tension. The fluid is inviscid and irrotational.

Under all these assumptions it can be shown that the Laplace equation, resulting from

conservation of mass, is valid in the interior of the fluid. The following definitions are used to define the fluid domain:

V('t,) is the fluid volume, bounded by:

S('t,) the free surface of the fluid,

S,1't,,) the submerged part of the hull of the ship,

S;z('t, wake sheets and,

S('r,) the surface bounding the fluid infinitely far from the body.

Assuming linearity, the total potential can be split into two pa1s, the wave potential and the disturbance potential, with the wave potential given in Eq. 2.

cIJ =cV+D"

(I)

q"

_{sin (k(xo cosf+yosinW)wt)}

The subscript 0 refers to earth fixed coordinates. At the free surface the kinematic and the dynamic boundary conditions are imposed. The kinematic condition enforces that the velocity

144

of a particle at the free surface equals the velocity of the free surface itself. The dynamic

condition sets the pressure at the free surface equal to the ambient pressure. Both conditions can be combined and linearized around the still water free surface, resulting in Eq. 3.

82i1 ôz

at z0=O

at2

+g

a

On the instantaneous body surface a zero normal flow condition is imposed be setting the

instantaneous normal velocity of the body equal to the sum of induced velocities and the

undisturbed wave velocities.

ad

=+

on On

r

V X0ESj(t)

At a large distance from the body the influence of the disturbance is required to vanish as indicated in Eq. 5.

-+0 0 when

r

at

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

aI

(U =

'1=0 _at

t=0

The Green function given in Eq. 7 specifies the influence of a singularity with impulsive strength (submerged source or doublet) located at singularity point q on the potential at field point p.

G(p,i,q,r)

2 fri _cos(J(t -

r))]ek

(ki)dk

R R0 L

for pq,tv

In Eq. 7 the G°-term is the source and doublet plus biplane image part (or Rankine part), while the G"-terrn is the free surface memoiy part of the Green's function, and Jo is the Bessel

function of order zero. It has been shown, by for 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. After applying

Green's second identity a boundaiy integral equation appears. The free surface integral in this equation can then be eliminated by virtue of the Green function given in Eq. 7. The far field boundaiy and sea bed boundaiy integrals can be eliminated by using the radiation condition,

The final step is the distribution of singularities on the remaining surfaces. In this case the

choice is made to distribute constant strength combined source-doublet singularities on the hull surface and vortex ring elements on a wake sheet extending backward from the (transom)

stern. (3) (4) (5) (7)

=0

Together with the application of the body boundary condition, Eq. 4, this results in an

expression for the normal velocity at field pointp(xO,t) in terms of integrals over time and

source points q(xO,t.

3G°

4,r V

=2irap(p,t)+J

a(q,t)

dS+

p(q,t)

dS- r

a(q.r

IJ

VNVfldLdV-i(q,r)

-

p(q,r)

_8nör

The solution of Eq. 8 constitutes a Neumann exterior problem. Eq. 8 is the principal equation to be solved to obtain the unknown singularity strengths. Using these, the forces

acting on the ship can be obtained.

2.2 Linearization

Especially the evaluation of the free surface memory integrals, the integrals over t in the right hand side of Eq. 8, requires a large amount of computational time. These terms need to be evaluated for each control point for the entire time histoiy at each time step. To decrease this computational burden, the evaluation of the memoiy term has been simplified. For near time history use is made of interpolation of non-dimensional predetermined tabular values for the memory term derivatives, while away in history polynomials and asymptotic expansion are used to approximate the Green function derivatives.

Moreover, the position of the hull relative to the past time panels is not constant due to the unsteady motions, making recalculation of the iniluence of past time panels necessary for the

entire time history at each time step. This recalculation results in a computational burden

requiring the use of a supercomputer. To avoid this burden, the unsteady position of hull is linearized to the average position (moving with the constant forward speed). Now the rnemoiy 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 hull. Again a constant distance exist of each collocation point to the past time wake

panels. Only the iiifluence 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 nmltiplying the influence by their actual circulation.

2.3 Wake model

The formulation originally adopted by Van Wairee employed unsteady impulsive sources

on the hull with combined source-doublet elements to represent submerged lifting control

surfaces. For fast vessels typically fitted with a transom stern the flow is characterized by high

pressure values in the stagnation regions along the waterline in the fore part and smooth

separation from the stern at moderate and high speeds. This flow develops significant

hydrodynamic lift, while the transom typically is left dry. In the original code the high

pressure regions near the bow were well predicted, however the flow leaving at the stem was not modelled very well and an empirical near-transom pressure correction based on the work of Garme (2005) was applied to incorporate this effect.

(8)

De Jong and Van Walree (2008) presented a more rigorous implementation in order to include the effect of transom flow directly into the potential flow solution. A combined

source-doublet distribution on (lie hull already present in section 2.1 is coupled with a trailing

edge condition and wake sheet equivalent to the one used for foils. The condition is

formulated in a way so that the flow separates tangentially at the transom and while setting the dynamic and hydrostatic pressure at the transom edge equal to the atmospheric pressure.

Reed et al. (1991) proposed a similar condition making use of the steady linearized Bernoulli

equation applied just fore and aft of the transom stern. To allow for dynamic effects the

unsteady Bernoulli equation as shown in Eq. 9 is adopted in the current implementation.

(aid

+ +

ax

3x1

Eq. 9 will be approximately satisfied at the transom edge. in fact, it will not be satisfied exactly at the transom edge due to numerical problems arising when evaluating influence

functions on panel edges. instead, the condition will be satisfied at the collocation points of

the last hull panel row in front of the transom edge. The wave potential derivatives can be

obtained from Eq. 2 in a straightforward manner. The derivatives of the induced potential can

be obtained by careful differentiation of the corresponding terms.

One particular important term that appears is the x-derivative of the doublet strength at the transom edge. Due to the use of constant strength panels it is not possible to obtain this term

directly. The solution is to estimate this derivative at the transom edge panel by using the

value of ji at the panel just in front of this panel and at the panel just behind the transom edge panel, the first wake sheet panel and dividing over the length as shown in Eq. 10. i+1 refers to

the panel directly upstream and i-I refers to first wake panel downstream of the transom

panel.

a,i(w,t)

3X _2Lpan

The wake model introduces for

hull panels adjacent to the transom edge n extra

unknowns, namely the wake elements shed at the trailing edge of each the n hull panels. Eq. 9 provides one extra condition for each of the n hull panels adjacent to the transom edge. 2.4 Solution

Eqs. 8 and 9 are discretized in terms of a combined source-doublet element distributionon

the hull and equivalent vortex ring elements on the wake surface. In the current method

constant strength quadrilateral source and doublet panels are used. As detailed by De Jong et

al. (2008) the solution is setup in two steps. The first is to solve for the source strength

without wake influences and without the current time step influences of the doublet panels, but including the full memory integrals. This is a NxN system for N hull panels.

The second step consists of a solution for the N unknown doublet strengths and first n wake row strengths including the current time influences of the source strengths determined in the

first step and the remaining wake strengths in the right hand side. This results in a

(N+n) x(N+n) system.

2.5 Force evaluation

Forces can be obtained from integration of the pressure at each collocation point over the

body. The pressures can be obtaiiied by using the unsteady Bernoulli equation (in a body

fixed axis system):

PaP

p

(a2 (

- +1 + -

+ - - V . \71 + gz

147

In Eq. 11 V is the total velocity vector at the collocation point of the rigid body, including

rotations.

The spatial derivatives of the potential in Eq. 11 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 o the doublet panels this can be done by utilizing a straightforward backward

difference scheme in time. 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. In fact a similar procedure is used in the time derivatives

needed in the wake model.

The hydrostatic pressures and the undisturbed wave pressures are calculated on the actual

submerged body below the calm water surface. The pressure in between the calm water

surface and the undisturbed wave profile is assumed to vary linearly with the distance to the

calm water surface in wave crests and set to zero between the calm water surface and the

wave profile in wave troughs. 2.6 Inclusion of viscous flow effects

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, when

forces that arise due to separation in the bilge region due to vertical motions can cause

significant damping of the motions. The magnitude of these forces depends on the oscillation

frequency, Froude number and section shape. In 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. The following formulation is used in a strip wise

manner:

=

P'.SCD

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 GD has values in-between 0.25 and 1.33.

3. APPLICATION AND VALIDATION

Simulations performed with the PANSHIP code were compared with the results of towing tank measurements of the Enlarged Ship Concept (designated Parent Hull Form, or PHF) and

the Axe Bow Concept (designated AXE), obtained during phase 1 of the FAST project.

Models constructed at a scale of 1:20 were tested in calm water, in irregular head waves,

stern-quartering,

and following waves in

140 m towing tank

of the

Hydromechanics Laboratory of the Delft University of Technology and in Mann's SMB basin. The present paper focuses on the comparison of experimental data and simulation

results obtained in calm water and in head waves at three forward speeds: 25 kls, 35 kis and

50 k/s.

The full scale main particulars of the P1-IF and the AXE are presented in Table I. Both

designs have identical aft bodies, while the lore body shape is markedly different. The P1-IF has a regular, though slender, bow with moderate flare, while the AXE has the 'axe'-bow with

a vertical bow contour protruding downwards past the mean draft line and highly slender,

nearly wall-sided section shapes.

I'able I.Full scale main particulars of the Enlarged Ship Concept (PFIF) and the Axe Bow Concept (AXE)

The wave spectrum for the seakeeping simulations was a JONSWAP spectrum with a

gamma of 3.3, a peak period of 7.8 seconds and a significant wave height of 3.5 meters. The typical run length of the seakeeping experiments was equivalent to 30 minutes full scale wave

exposure and was obtained by performing a series of towing tank runs in the same wave

condition, in different parts of the actual wave realization.

148

Fig. 3. Typical panel arrangements for PHF (left) arid AXE (right)

Representative panel arrangements used for the simulations are presented iii Fig. 3, on the left hand side the PHF, on the right hand side the AXE. Typically around 800 elements were

used on the submerged part of the hull; it was found that the calculations were sufficiently

converged at this panel size. The wake sheet and the memory effects were broken off at 100 time steps back into histoty. Typical seakeeping simulation lengths were between 10000 and 20000 time steps at a time step of 0.05 seconds, chosen such that the distance traveled by the body in one time step roughly equaled the characteristic panel length.

Fig. 4 shows a comparison between the calm water trim and rise obtained from the

measurements and from calculations at 25, 35 and 50 kis. The calculated trim and rise were determined in an iterative fashion where simulations were performed in calm water while the

hull was free to trim and rise. When the trim and rise became constant at the end of each

simulation, they were used to update the panel geometry and the simulation was restarted. As

soon as the trim and rise at the end of the calculation equaled the trim and rise of the panel

geometry within a small margin the iteration process was stopped and the trim and rise at the corresponding speed were found.

The left hand side figures show the results for the PHF, the right hand side figures the

results for the AXE. Although there are differences the trends obtained are reasonable. The main difference between calculated and measured data for both designs is apparent in the rise

Entity Symbol Unit PHF AXE

Length waterline L,.1 [m] 55.00 55.00

Beam waterline B,., [m] 8.46 8.46

Volume of displacement V [m3] 516.00 517.40

Maximum draft [in] 2.66 4.38

Wetted area S [m2] 480.58 512.84

Longitudinal center of gravity LCB rn] 22.41 24.36

Metacenter height GM [m] 1.52 1.52

at 25 kts and at 50 kts. The calculated trim shows a favorable comparison with the measured data. -0.2 -0.3 -0.4 -0.5

I

U

a1in ward nrc olCoG PIlE coirn woler rIse of CoG AXE

0.4 0.3 0.2 (LI 540 -0.1 -0.2 -0.3 -0.4

I

Fig. 4. Comparison calm water trim and rise (PHF left, AXE right) at 25, 35 and 50/as (negative trim: bow up, positive rise: upwards)

Fig. 5 shows a comparison of the motion responses obtained with the measurements and the seakeeping calculations of the PHF in terms of the standard deviation of the motion time traces (heave, pitch, vertical acceleration at the center of gravity and the vertical acceleration

at the bow) divided over the standard deviation of the wave elevation time trace. The

agreement is very good for the heave and pitch motions and reasonably good for the vertical accelerations at the center of gravity. The vertical acceleration levels at the bow on the other hand are 10 to 15% underpredicted. The increasing damping of the heave and pitch motions

with increasing forward speeds

clearly visible in both the measurements and the

calculations.

Fig. 6 shows the same comparison for the AXE design. Not only are the motionsresponses

and the trends with increasing forward speed captured very well for the AXE, but also the

vertical acceleration levels at the bow and at the centre of gravity are correctly predicted. The only exception Inay be the acceleration levels at the highest forward speed of 50 k/s.

The superior prediction of the motions of the AXE could be caused by the fact that the waterline intersection at the bow remains constant over a large range of vertical motions of

the bow. This constant waterline shape yields a highly linear motion response, whereas the P1-IF has much more pronounced bow flare, causing a much more nonlinear motion response

that is much more difficult to capture in the body-linearized seakeeping simulation. In fact part of the reasoning behind the 'axe'-bow shape was to generate much smoother linear motion responses, the other part being the avoidance of bottom and bow-flare slamming

(Keuning 2006). 149

I

cabs warer lam P1W _{roim water rim AXE}

F

150 E 3 15 '.5 0.5

I

heave niotion pitch niotiun

3.5

I

kLsI

- calculated

ineastttvtd

vcfllcid acceleration at how

35 50 V IkIni cakulntcd meauwed

j

I

I

Fig. 5. Comparison heave (top left) and pitch (top right) motions and vertical accelerations at CoG (bottom left) and at bow (bottom right) for the PHF

heave motion pitch nwiton

4 3.5

3%

I

Vh. Ikt,.I

vettical ji..cki&iliiiii at CoO vcflical uccekroi,i,n at bow

25 3% 50 2% 3%

V4lktvI Vhtktvl

Fig. 6. Comparison heave (top left) and pitch (top right) motions and vertical accelerations at CoG (bottom left) and at bow (bottom right) for the AXE

Based oii the above comparisons it is not evident that the vertical acceleration levels at the

bow are significantly lower for the AXE relative to those of the PHF, as is clear when

comparing the measurements of both designs. This becomes even more apparent when

studying the peak accelerations in the following figures.

I

I

I

vezttcaI accclemtion at CoO

The motions of high speed and planning vessels are characterized by significant impact

accelerations especially when operating in head waves. Several authors have commented on this and have performed measurements, devised methods and proposed alternative designs to better cope with these high acceleration peaks (see for example Garme (2005) and Keuning

(2006)). It is interesting to investigate how the present method deals with these impact

occurrences.

Fig. 7 shows a comparison of the distribution of the peaks for the wave elevation at the

centre of gravity for the PHF at35 kis in head waves of3.5 in significant wave height. Fig. 8 shows a comparison of the distributions of the peak values for the vertical accelerations at the centre of gravity and at the bow for the PHF at 35 kis in head waves of3.5ni; Fig. 9 shows

the same comparison for the AXE under the same conditions. On the left hand side are the

calculated peak distributions shown and on the right hand side the measured peak

distributions. The straight lines mark Rayleigh distributed data with the same standard

deviation as the calculated and measured data. When the peaks would be Rayleigh distributed (and thus straight lines) this would essentially mean that the response would be linear.

I.)

wabe eic dub fl cog ciskulateul

5 -.-- 5

I

4

ubIVC eICa)IOI, all cog IlleiLSulled

Fig. 7. Comparison of the distribution of the peaks of the wave elevation, calculated results are on the left hand side, measured results on the right hand side

The comparison in Fig. 7 indicates that the peaks in the normal distributed wave elevation signal are indeed Rayleigh distributed, as theoiy suggests for normal distributed signals. Nevertheless, the measured wave elevation shows a slight deviation from the Rayleigh

distribution. This can possibly be attributed to the fact that the waves are measured with wire-type wave probes attached to the towing carriage that are known to perform less than optimal when measuring waves at high forward speeds.

From the measured data in Fig. 8 and Fig. 9 (right hand side) it can be seen that the peak values encountered by the AXE are much lower than those encountered by the PHF for the vertical accelerations both at the centre of gravity and at the bow. This significant reduction was already reported by Keuning (2006) and Keuning and Van Walree (2006).

Nevertheless, when comparing the calculated data with the measured data for both the PHF and the AXE clearly the magnitude of vertical acceleration peaks at the center of gravity and

at the bow encountered during the measurements is not found in the calculated data. For

instance for the P1-IF bow accelerations up to 50 in/v2 are found during the measurements, while calculations estimate the maximum bow acceleration at around 15 in/s2. For the AXE, a

ship designed to behave 'linear' the comparison is still quite favorable, for the P1-IF on the

other hand, the significant acceleration peaks occurring at the bow are absent in the calculated data. Apparently the variation in submerged geometty due to the bow shape of the PHF, only

partly taken into account in the body-linear code, is not captured sufficiently by the

calculations.

It should be noted that the deviations between the peak distributions of the calculated and measured bow acceleration levels of the AXE show roughly the same trend as the deviations

151 0.5 50 2)) Ii) 5 2 PcwcnuageorIt.uccuLiicc '4I 115 50 2)) II) 5 2 l'encntuge .1 Iicccdancv '41

between the peak distributions of the calculated and measured wave elevations and are possibly related. 152 Crusts Troughs - Raylcigh

scilicul accvlcuiitioii at how cusk'ulalcd

Fig. 8. Comparison of the distribution of the peaks of the vertical accelerations for the PHF at35 kts,

calculated results are on the left hand side, measured results on the right hand side

uttlucul ucceicraluon a, how calculitcul

2 05

6 0

ucftical accckcuuuouu at bow mcnsurcd

50 20 40 5 1

Icrcciilagc of Eucccdj,wc 1%

vcflical iccelerauion a) cog muasuird I2

'4)'

6

50 24) It) 5 2

I'crccutlugc if Escccdance r4j scOicalaucckruut,nii mw iuicasurcd

Fig. 9. Comparison of the distribution of the peaks of the vertical accelerations for the AXE at35 kts,

calculated results are on the left hand side, measured results on the right hand side

05

vudlual aeccicration a) cog CaIcuIakd vct*icaI accckrauion a) cog nicauuucd

50 20

40321

5 21

PrvenIageofEscccdanccI*4 Pcrvcnlage of Euccudance ('hJ

46

cenical accelccauion a cog cakulatcil

i 'a Crush tt II Troughs Kay kugh II, .II

'

_L

Pets enlilge of Eutccuslrncc 1*1

2 05 0.5 5(4 20 10 5 2 t'crcclirigu of l tutuc %t 5 5)) 20 ID

Prcctutugc of t4icccduncc I'kt

5 2 0.5 50 2)) Ia

Perecuuluge of I(sccedauicc thI

2

- to

e

4. CONCLUSIONS AND FUTURE WORK

A time domain panel method for the seakeeping of fast ships is presented. Simulation results are presented for the calm water trim and sinkage and the motions in an irregular

seaway for two comparable designs -an enlarged ship concept and an axe bow concept- for three different forward speeds.

The simulations show vety favorable agreement with experimental data when comparing the standard deviations of the calculated and measured lime series. When studying the peak

distributions on the other hand, in particular the vertical accelerations, the method still

underpredicts the occurrence of peak levels. Taking into consideration that for high speeds operating in a seaway the peak acceleration is the limiting factor -not the 'average' motion

levels- this needs to be addressed in the method.

Future work includes the usage of the free surface elevation combined with adapting the

pressure distribution as described in Dc Jong et al. (2007) in order to partly correct the applied linearizations and the application of the method for motions in the horizontal plane.

ACKNOWLEDGEMENT

The authors ackiowledge their gratitude to the participants of the FAST project, the Royal

Netherlands Navy, the United States Coast Guard, Damen Shipyards at Gorinchem, and Damen Schelde Naval Shipbuilding at Vlissingen, for their support and cooperation in

cartying out this project and their willingness to allow the publication of the results.

References

Garme, K. (2005). Improved time domain simulation of planing hulls in waves by correction of the near transom liii. International Shipbuilding Progress, Vol. 52, No. 3, Pp. 201-230

Jong, P. de, Wairee, F. van, Keuning, iA., l-Iuijsmans, R.l-l.M. (2007). 'Evaluation of the free surface elevation

in a time-domain panel method for the seakecping of high speed ships'. Proceedings of the Seventeenth tnt.

Offshore and Polar Engineering Conference, Lisbon

Jong, P. de, Walree, F. van (2008). 'Hydrodynarnic lift in a time-domain panel method for tile seakeeping of fast ships'. Proceedings of tile Sixth international Conference on High-Performance Marine Vehicles, September

l6t

-

Katz J. and Plotkin, A. (2001). Low-speed aerodynamics. Cambridge University Press, second edition.

Keuning, J.A. (2006) '"Grinding the bow" or 'i-low to improve the operability of fast monohulls". International Shipbuilding Progress, Vol. 53, No. 3, pp. 281-310

Keuning, J.A. and Van Walree, F. (2006) 'The comparison of the hydrodynamic behaviour of three fast patrol

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King, B.K., Beck, R.F. and Magee, AR. (1988). Seakeeping calculations with forward speed using time-domain analysis. Proceedings 17th Symposium on Naval Hydrodynamics, pp. 577-596

Lin, W. M. and Yue, D. (1990). 'Numerical solutions for large-amplitude ship motions in the time domain'.

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Reed, A., Telste, J. and Scragg, C. (1991). 'Analysis of transom stern flows'. Proceedings of tile Eighteenth

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Walree, F. van (1999). Computational methods for hydrofoil craft ill steady and unsteady flow. PhD thesis, Delft University of Technology

Walree, F. van (2002). 'Development, validation and application of a time domain seakeeping method for high

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475-490