Non-linear Motions of Surface Effect Ships (SES)

NON-LINEAR MOTIONS OF

SURFACE EFFECT SifiPS

J. Moulijn

Report 1Ï26-P

December 1997

Published in: International Conference on Air

Cushion Vehicles (ACVs), Royal Institution of

Naval Architects, London, December 3, 1997.

TU Deift

Faculty of Mechanical Engineering and Marine Technology Ship Hydromechanics Laboratory

INTERNATIONAL CONFERENCE

on

AIR CUSHION VEHICLES

(ACVs)

3 DECEMBER 1997 LONDON

PROCEEDINGS

THE ROYAL INSTITUTION OF NAVAL

_ARCHITECTS

RINA

in association with the

ROYAL AERONAUTICAL SOCIETY & THE HOVERCRAFT SOCIETY

RAPID MARINE TRANSPORT GROUP & SMALL CRAFT GROUP

INTERNATIONAL CONFERENCE

AIR CUSHION VEHICLES

(ACVs)

at the

Weir Lecture Hall, RINA, London SWI

3 December 1997

© 1997 The Royal Instjtútion of Naval Architects

The Institution is not, as a body, responsible for the opinions expressed by the individual authors or speakers.

THE ROYAL INSTITUTION OF NAVAL ARCHITECTS

10 Upper BelgraveStreet,

London, SW1X 8BQ

Telephone: 0171-235-4622 Fax: 0171-245-6959 ISBN No: 0 903055 35 X

CONTENTS

SESSION i - ACV TECHNOLOGY - THE STATE OF THE ART

1. ADVANCED HOVERCRAFr - SKIRT TECHNOLOGY

by D R Lavis, B G Forstell, and C Jiang, Band, Lavis & Associates1 Inc. (USA)

2.* _{AEROEISTIC AND HYDROELASTIC DYNAMIC DESIGN PRINCIPLES}

OF HO VERCRAFTRESPONSI VE SKIRT

by M Tao, Marine Design & Research Institute of China and P A Sullivan,

University of Toronto (China & Canada)

3. FANS AND PROPELLERS FOR AIR CUSHION: VEHICLES - PAST, PRESENT

AND FUTURE

by M J Ccx, Hovercraft Consultants Ltd, and C B Eden, Air Vehicles Ltd (UK)

SESSION II- DESIGN

4. AIR CUSHION PASSENGERNEHICLE FERRIES FOR WEST BALTIC ROUTES - A PROPOSAL

by T Jastrzebski, R Michalski and WChadzynski, Technical University of Szczecin (Poland)

5. NON-LINEAR MOTIONS OF SURFACE EFFECT SHIPS

by J MoUlijn, DeIft University of Technolögy (Netherlands)

6. AERODYNAMICAL LIFT-FAN SYSTEM PROBLEMS AND DYNAMIC STABILITY OF ACVs

by A A Dolgopolov, L A Maslov, V V Mitrofovich and S A Isakovich, Central

SESSION III

_{- MILITARY ACVs}

NAVAL HOVERCRAFT - WHAT NAVAL HOVERCRAFT?

by B J Russell, Hovercraft Society

(UK)

THIRD GENERATION, MEDIUM-LIFT_{HOVERCRAFT FOR MODERN} AMPHIBIOUS OPERATIONS

by S E Southby-Tailyour, Ewen SouthbyTaiIyour_{Associates - Amphibious Consultants}

(UK)

9. _{MCM SYSTEM DEVELOPMENT FOR THE SWEDISH NAVY BASED ON}

AIR CUSHION TECHNOLOGY

by M Örnfelt, Swedish Defence Materiel Administration

11. _{EFFECT OF ECONOMICAL ASPECTS}

ON FAST SPEED CRAFT

DESIGN PARAMETERS

by V A Abrarnovsky, Central Marine Design Bureau 'Almaz', Saint-Petersburg and A V Abrarnovsky1 Saint-Petersburg State Marine Technical University

(Sweden)

10. _{THE SRN4 HOVERCRAFT SO FAR - TECHNICAL & OPERATIONAL ASPECTS}

by L Heatley- Hoverspeed Ltd

(UK)

(Russia)

12. _{SUMMARY REPORT OF DISCUSSIONS}

by E C Tupper

PAPER NO.5

NON-LINEAR MOTIONS OF SURFACE EFFECT SHIPS

by J Moulijn, Deift University of Technology, The Netherlands

Paper presented at the

International Conference

AIR CUSHION VEHICLES

(ACVs)

Joøst Moulijnstudied!Naval Architecture at Deift University

of Technology. He obtained his MSc degree in 1994 on

a theses about the trailing vortex wake of marine

propellers. He is currently a PhD student at the Ship

Hydromechanics Laboratory in Deift.

1. INTRODUCTION

In recent years, the interest in large Surface Effect Ships (SES) sailing in open sea has raised. Therefore an

adequate computational method for seakeeping of SES must be developed and validated. This paper describesa

computational method for motions of a SES in waves. The method is validated using experimental results of

MARIN. When the motions of a SES can be calculated accurately, important aspects such as added resistance due to ambient waves and wave loads on the structure can be calculated. These aspects are subject to further

research.

A Surfäce Effect Ship is a hybrid of a catamaran and a hovercraft. An air cushion is enclosed by the side hulls,

the deck, the water surface and flexible seals forward and aft (Fig. 1). Most of the vessels weight is carried by the air cushion. The rest is carried by the hulls. The air cushion is pressurised by a system of fans, as air leaks from the cushion under the seals.

Compared to catamaran SES have a low resistance.

Advantages of SES with respect to hovercraft are water

born propulsion, a smaller amount of air leakage and

bettor manoeuvring characteristics Astheside hullsof a SES provide stability, there is no need to have several compartments in the air cushion. A major disadvantage of SES with respect to hovercraft is of course the loss of the amphibious capabilities.

When studying seakeeping of Surface Effect Ships two

frequency ranges of interest occur: the "normal frequency

range up to a frequency of about 1 Hz, and the high

frequency range. In the normal frequency range the

motions of a SES are small compared to a catamaran In

the high frequencyrangethed isplacement amplitudes are only small, but the acceleration level can be quite high

resulting in a poor ride quality. _{These high frequent}

oscillations are caused by acoustic resonances of the air in cushion as was pointed out by Nakos et aI [1 1 This

NON-LINEAR MOTIONS OF SURFACE EFFECT SHIPS

Joost Moulijn

Deltt University of Technology

SUMMARY

Results of a currently running four year research project on seakeeping of Surface Effect Ships (SES) ara presented. A nonlinear computationalmethod for the motions of a Surface Effect Ship in waves isdescribed. The resuitsof the method are compared wh experimental data of MARIN The agreement is good The effect of simplifications of the methodon

the results is investigated.

AUTHOR'S BIOGRAPHY

1

phenomenon is usually referred to as cobblestone effect.

The cobblestone effect was studied extensively by Søresen[2], Steen[3] and Ulstein[4].

The present method deals with the normal frequency

range. The excess pressure in the air cushion is always assumed to be constant in space so acoustic resonance cannot be resolved. Air compressibility is taken into

account, so the spatially constant pressure resonance of

the air cushion (Helmholtz resonance) is resolved. Motions of SES werefirst studied by Kaplan and Davis[5].

In Kaplan et aI[6] a non-linear six degree of freedom

motion program is presented. An extensive overview of the hydrodynamics of ACV's and SES' was presented by

Doctors(7].

By many authors air leakage is considered important and

highly non-linear ([1], [8], [9]). Nevertheless air leakage is often linearised or even neglected ([1], [81). Steon[3]

shows the importance of air leakage for cobblestone

effect. Wlstein[4] carried out extensive air leakage

computations using a non-linear panel method. He found that a simple one dimensional approach also yields good results as long as the contraction of the escape air jet is taken into account.

The bag-type seal common!y usedto closethe air cushion

at the aft end is also considered to have an important

effect on the motions of SES. The bag is pressurised at a slightly higher pressure than the air cushion. Lee[1O]

developed a two dimensional model. He neglects

gravitational and inertial forces and the dynamic pressure

distribution under the seal due to air leakage.

Steen[3] presented a two dimensional model. He also

neglects gravitational and inertial forces on the flexible bag membrane, but he does take the dynamic pressure

distribution due to air leakage into account. Steen

showed the. importance of the seal model with respect to

cobblestone effects.

Masset and Morel[9],[11] developed and validated a

similar model. Ulstein(4] developed a model that includes

the inertia of the bag membrane. The finger type seal

commonly used to close the air cushion at the fore side is

considered less important for motions of SES. The seal

does not need to be pressurised, and the forces acting on

Some confusion appears to exjst about the importance of the interaction of the air cushion and the wave surface in the cushion. Kaplan etaI[5].[6] only consider undisturbed incident waves in the air cushion; Kaplan[12] claims that the waves induced by the vessel are small and only have

a minor effect on the overall motions; According to

Doctors[13] and Kim and Tsakonas[14] this

is an

oversimplified procedure.

McHenry et aI [8] report only a small effect of cushion

induced waves but Nakos at al [1] show

that the inclusionj of cushion induced waves damps the Helmholtz resonance and also shifts the Helmhottz

resonance to a higher frequency. Moran[15],

Kapsenberg[1'6] and Masset et al [9] found from model

tests that the amplitude of the free surface waves is

affected by the air cushion.

Another important aspect of SES is the air supply system.

In all existing methods for SES motions, including the present method, steady fan characteristics are used.

Durkin and Luehr[1 7], Sullivan at aI [18], Masset et al [9] and Witt[1 9] show that the fans respond in a dynamical way to the oscillating pressure in the air cushion. Sullivan et al [18] also show that the dynamic behaviour of the lift fan has a large damping effect on the heave motions of a

hovering box.

Scale effects play an important role in model testing of

ACV and SES (see for instance Lavis et aI [20]). For

Froude scaling of the air compressibility the ambient pressure also should be multiplied by the scale factor, otherwise the stiffness of the air cushion is much too

large. Kapsenberg[2 1] performed oscillation experiments in a depressurised towing tank. He found an important effect of the ambient pressure on the added mass and

damping coefficients. Kapsenberg and Blume[22]

performed modeltests atdifferent scaleratios with models

equipped with a flexible membrane on top of the air

cushion; This membrane (usually referred

to as

diaphragm) also reduces the cushion stiffness as ft

supplies some extra volume when the cushionpressure

increases. They found good agreement and concluded

that the diaphragm technique is a valid way of scaling cushion dynamics.

In the present method the cushion dynamicsare retained

in full non-linear form; Non-linear air leakage is included. The motions 'and cushion excess pressure are solved in

a time simulation procedure. A two-dimensional non-linear model for the bag-type stern seal is implemented.

This model is similar to the models of Steen[3) and

Masset and Morel[1 1].

A linear three-dimensional Rankine source panel method is used to compute the hydrodynamic forces on the side hulls and the wave height in the cushion. _{Interaction of}

the air cushion and the wave surface is taken into

account. _{Results of the method are presented ànd}

comparedto experimental data of MARIN. The effects of cushion-surfaceinteraction, the sternseal, air leakage and

the

fan system on the

computational results are

investigated. _{The importance of scale effects during}

experimènts is demonstrated.

2

DEFINITION OF COORDINATE SYSTEMS,

DISPLACEMENTS AND EXCESS PRESSURES

Two right-handed coordinate systems will be used. One

system is fixed to the vessel, that sails at a mean velocity

U. This system is called the body fixed system; O-XYZ The X-axis points in the direction of the bow,.the Y-axis points to the port side, the Z-axis points upwards. The origin Odoes not necessarily coincide with the centre of gravity of the vessel. This system is used to define the geometry of the vessel. The other system advances with a constant velocity Um positive x-direction. This system is called the directionally fixed system; o-xyz. The x- and

y-axis are located in the undisturbed free surface, and the z=axis points vertically upwards; The displacement of the

body fixed system with respect to the directionally fixed system is only small; The displacement is described by

three translations: and_,' in x-, y- and z-direction respectively, and three rotations: _114, 15and 116 around the

x-, y- and z-axis respectively.

The six small displacements i ...i1 are the actual

unknowns of the problem. Two additional unknowns will occur: the excess pressure in the air cushion plenum

and the excess pressure in the bag stern seal plenum p3.

Up to now heave (ib) and pitch

(115) are the only

displacements that are considered iñ the actual program,

so it is only suitable for head and following seas.

EQUATIONS OF MOTION

The equationsof motion followfrom Newton second law:

6

d2'rlk

= F1

j = i...6,

(1)

k-1 dt2

where MJk is the generalised mass matrix, t denotes time

and F...,F6 are the total force acting on the vessel in x-,

y- and z-direction and the total moment acting on the vessel around the x-, y- and z-axis respectively. For conveniencethe moments around the x-, y-and z-axis will

be designated force in 4, 5" and 6th direction. The total force in

f

direction acting on the vessel can be divided into several components:

F1 = F°+ F?»+ F4'+

a) (2)

where the affix denotes gravitational force (g), propulsive force (p), hydromechanic force (h), air cushion force (a) and seal force (s) respectively. The propulsive force is assumed to be balanced by the resistance of the vessel. The hydromechanic force, the air cushion force and the seal force Will be treated in following Sections.

CUSHION AND SEAL DYNAMICS

In this' section two additiönal equations for the two

equations follow from the equations of continuity for the

air cuhion and stern seal plena.

_{The equation of}

continuity for a plenum reads:

p(Q(fl) Q(OUI))

= _.(pV),

(3)

where d" is the air volume flux into the plenum, d"u is the air leakage volume flux from the plenum, p is the density of air, and V is the volume of the plenum. The

equation of state for the air in the plenum isgiven by the 'isentropic gas law:

Pa + P

______ = constant,

piC

where Pa S the ambient pressure, p is the (spatially

constant) excess pressure in the plenum, and = 1.4 is

the ratio of specific heats for

air. The equation of

continuity and the equation of statecan be combined and rearranged to:

V dp _{(Q(ifl) - 0(01)1)) -}

f.

'«PPa) dt

dt

(4)

(5)

The air volume flux through a fan into

a plenum d is

appoxirnated by the stationary fan characteristic

linearised in the design operation point:

0(in)

=

5

₊ (6)

where S is the design flux through the fan, and _{¡s the} design excess pressure in the plenum. Sullivan et_a([1'81 showed the importance of a dynamic model for the fan of

air cushions. They determined the 'linear dynamic response of a fan from experiments. The dynamic characteristics of full scale fans is not known however. The author is not aware of any theoretical dynamic fan

model.

The air leakage volüme flux from a plenum dohlt) ¡s

calculated from the orifice flow formula:

= (7)

where c is the orifice coefficient, A1 is the leakage area

and tip is the pressure Jump across the orifice. The

orifice coefficient depends on the local geometry of the

orifice. _{For a sharply edged orifice like the leakage gap}

3

under the front seal it can be set to 0.61, while for a

smoothly rounded orifice like the leakage gap under the stern seal it may be set to 1.0. A derivation of equation

(7) and an elaborate discussion on the choice ofc1 can be

found in Ulstein[4]. Theleakage areas under the fore and

aft seals follows from the seal modéls. Thisarea is highly

non-linear in the relative motions.

The system of plenaof a SES and the volume fluxes 'into

and out of these plena are presented in Fig. 1. The equations for the cushion excess pressure p and the seal

excess pressure p5 are now written as:

V dp (Q(lfl) Q(OU1)) dV

+ Pa) dt

V dp5 _{(Qfl) Q(OU1))} dV5

+ Pa) dt

(in) (in) (in)

where Q = ₊ which is the sum of the flux through the cushion fan and the leakage flux frOm the

(ouf) (out) (ouf)

stern seal, and = Qe,, , which is the sum

of the leakage flux under the foré seal and the leakage flux under the stern seal, (see Fig. 1). The air cushion volume V5is expressed (up to linearorder:jn i 1,...,r6) as:

VC = C - V5 +

ff(13 +

14 + Xii5) dS + dS,,

deck FS

(9)

where V is the design cushion volume, V5is the part of

the cushion volume that is taken up by the stern seal, Ç is

the wave height in the air cushion and FS is the part of the free surface that is covered by the air cushion. The volume of the stern seal plenum V and the volume of the air cushion that is taken up by the stern seal V5 follow

from the stern seal model, which is treated in the next

section. The wave height in the air cushion Ç is calculated

by means of a three-dimensional panel method.

The air cushion force follows from integration of the air cushion excesspressure pover the deck and the side

'hulls.

The equations of motion ('1)

and the equations of

continuity for the cushion and stern seal (8) plena are

solved simultaneously in a time simulation procedure. A Runge-Kutta scheme is used. The simulations result in time traces'Ofthedisplacements, velocities, aelerations, excess pressures and air leakage areas.

5. SEAL MODELS

A two-dimensional model ('x-z-plane) for the flexible

bag-type stern seals of' SES' hasbeendeveloped. Usually

a stern seal has two or three lobes. Each lobe consists of a loop of thin flexible, material. These loops are open to the sides, where the bag is closed by the hulls of the SES. The bag is pressurised by a fan at a slightly higher pressure than the air cushion pressure. The wave height

and wave slope are assumed to be constant over the width of the ir cushion. The gravitational and inertial forces on the bag are neglected. The following variables determine the bag geometry: heave and pitch

displacement, excess pressures in the cushion and the seal plena, and wave height and wave slope at the seal. The bag geometry is calculated in a static way. However,

the complete seal: model is not static through the cushion

and seal dynamics.

The three-dimensional bag membrane is analysed as a two-dimensional cable.

The cable has no bending

stiffness and only transmits tension. Force equilibrium for a cable segment yields the following relation:

where T is the tension in the cable, p is the pressure differenc6 across the seal and Ris the radius of'curvature of the cable.

When the seal does not touch the water surface, air will

leak from the cUshion will. This air flow results in a

pressure distribution under the seal. This air leakage flow has been studied elaborately by Ulstein[4]. He 'foundthat a simple one-dimensional analysis gives good results.

This one-dimensional analysis leads to the following

pressure distribution:

where p(x) is the spatially varying excess pressure under the seal, p is the excess pressure in the air cushion, h, is

the height of the air leakage area, and h(x) is the local

height of the seal above the wave surface (see Fig 2).

The derivation of the set of non-linear eqUations that

govern the bag geometry is quite lengthy, and is therefore

omitted in this paper. The equations can be found in

Moulijn[23]. Newton-Raphson's method is used for

solving the non-linear system.

V24 = O

g_ +

-

2U.!

+ U2.! + !(.

-

U.E) = O

àz 7

axat _ax2

_{p at}

àx

Vil,= Un1

6 °'Ik + (._._ + k.1 4

When the geometry of the bag and the tension in the bag membrane, which is also a part of the stern seal solution, are known, the seal force F!5' , the volumeof the seal V5,

the volume of the cushion t(iat is taken up by the seal V

and the air leakage area can easily e calculated. A

typical solution of the bag geometry is presented by Fig.

2.

In the equations (8) the time derivatives of V5 and V5

occurred. Direct evaluation of dV5/dt and dV5/dt is

difficult. Lee[1O] uses a finite difference scheme using previous time steps. He needs a filtering technique to preventamplification.ofthetruncation errori Thereforethe following expression for dV/dt will be used:

dV

av.

av.

av.

=___3

+_75+_

+

dt & ai15 _ap

av

av.

(10) Ps + - +

(12)

where Vis either V5 or V5, Ç and Ç are the mean wave

height and wave slope at the seal and a dot denotes

differentiation with respect to time. The partial derivatives

of V5 and V5 can be found from finite differences, as _113,

115' p6, Ç and Ç are 'input variables of the seal model.

The fore seal of SES is usually of the finger type. The

fingers consist of vertical loops of thin flexible material. The loops are open lo 'the cushion side When the local

deck height is smaller than the height of the seal, the

lower part of the fingers' is simply bent backwards at the water'surface, and no air will leak under the seals. When the local deck height is larger than the height of the seal, the seal will leave a gap above the free surface, and air

will leak from the cushion. The frictional forces of the

water on the fore seal are neglected.

6. HYDRODYNAMICS

The hydrodynamic problem is solved by means of a

3-dimensional Rankine' source panel method. The flow is

assumed to be incompressible and nonrotatiönal, so

potential flow theory can be used

The boundary

conditions on the hulls añd the free surface are linearised around the undisturbed flow (Neumann-Kelvin

linearisation) This leads to the following boundary value

problem:

field equation

on the free suilace

on the hulls

whereg is thegravitational acceleration constant, is the perturbation velocity potential, p is the excess pressure at the free surface (equals zero outside the air cushion) and

F is the normal vector pointing into the fluid domain.

Further, T (n1,n2,n3)

= n

(n41,n5,n6).T

_Ø

(mi,m2.m3.)T (m4,,m5,m6)T

_{= (O,Un,Un2)T,}

where X is the vector to some point ori the hulls. A

radiàtion condition is 'imposed ensuring, that no other waves than the prescribed incident waves propagate

towards the vessel.

Application of Green's second identity to the unknown

potential and the Rankine source potential G(.f)ioads to a Fredholm integral equation of the second 'kind

=

_J

_f5

_{G(Z )}

dS' +

2it _an"

Lff) .L

G(Z)

2lts

where S is the boundary of the fluid domain, and aia n denotes differentiation in the direction of the normal

vector.

fle normal derivative of

follows from the appropriate boundary condition (13). The hulls and ¿ part of the free surface are panelled using flat quadrilateral panels having a constant source and dipole distribution.

In the middle of each. panel. a collocation point is defined

where the integral equation is satisfied. This leads tothe following, linear system of equations:

Òi=-._

ff.i')dS'

' paneli (14) (15)

+j_.jf _G(')dS'

panoli an

where j = i...N and N is the number of panels. The

tangential derivatives of the potential, that occur in the freesurface boundarycondition, followfrom differentiation of a bi-quadratic splirie approximation, of . Nakos[24J

also uses this spline scheme, but 'he uses a quadratic

singularity distribution on the panels.

When the boundary valúe problem for is solved, the pressure pand the wave height follow from:

p-= -p(.. -

u.P_ + gz)

(.16)

ç =

- U.)

gat

ax

5

The hydrodynamic forces follow from integration of the pressure overthe hulls. Details of the panel method can be found in Moulijn(25].

The hydrodynamic problem is solved in the frequency domain, thus avoiding a complicated time stepping

algorithm and saving muchcomputational time. However,

as non-linear cushion dynamics will. be implemented, the motions have to be solved in a time simulation procedure.

Therefore the theory of Cummins(26] and Ogilvie[27] is used to transform the frequency domain results of the panel method to the time domain.

7 RESULTS

In this section the results of the computational method will

be presented and compared to experimental data. All

results concern the target vessel of the HYDROSES project (see Kapsenberg and Blúme[22]). The main dimensions of this vessel are can be found in Table 1..

TABLE i Main dimensions

The Rit to weight ratio of the vessel is about 0.85. The vessel sails in head waves at a speed of' 45 Kn. In the

experiments a diaphragm was used to obtain a proper

scaling of the air cushion dynamics (Kapsenberg and

Blume[22fl. In the computations' the full scale ship was

modelled. The hydromechanics 'are linearised around the mean sinkage and trim of the higher frequency

experiments. This position corresponds to = 0.0 m and 115 = -0.0115 rad.

Figure 3' presents the time traces of a simulation in

regular 'head waves The figure presents the following traces incident wave height at station 10 (Ç, in m) heave displacement (1 in m) pitch displacement ( in rad),

cushion and stern seal excess pressure (p and _PS ri

kPa) air leakage gap height at the front and at the stern seal (hI,and h!5 in rn) and vertical acceleration at station

O (A0 in m/s2), station 10 (A10 in m/s2) and station 20 (A20

in mis2). No higher harmonics can be observed in the

displacements signals. In the pressure and acceleration signals higher harmonics, caused by non-linearities, are clearly present. The signals of the escape height under the fore and stern seal illustrate the non-linear nature of air leakage. Note that the cushion excesspressure signal

is strongly' correlated to the vertical acceleration at station

10. The air cushion gives the 'largest contribution to the

vertical force, which is proportional' to the vertical acceleration of. the vesseL

L0

.1 530Om L 144.0Cm

B 35.00m

26.00m

Figures 4 and 5 present the Response Amplitude

Operators (RAO's) for heave and pitch displacement of the vessel. These RAO's give the amplitude of the

displacement divided by the wave amplitude. Theyare

based on the first harmonic component of the, time

signals. _{Results for several levels of wave steepness}

(kA)are shown.

For those waves having a larger

steepness than kA = 0.01 it was impossible to findproper

solutions for the stern seal in a range around the pitch resonant frequency, because ofthe large relative motions

at the stern seal. The effect of wave steepnesson the RAO's appears to be very limited. The computed heave displacement agrees very well with the experiflental_data. The computed pitch displacement agrees well with the

experiments in the intermediate and high frequency range.

In the low frequency range the computational results_are much larger. At first, when no stern seal model was

implemented, the stern seal was expected to dampthe

pitch resonance. This prcved to be wrong; the stern_seal

only shifts the pitch resonance frequency to a slightly higher frequency. Now this discrepancy is attributed to

the hydrodynamics. Probably the poor modelling of the flow around the transomsof the side hulls_{causes the lack} of damping. Viscous effects also might play sorne role.

On the other hand the experimental results might _be

affected by the connections between the model and the

carriage (cables and flexible hoses of the air supply

system).

Figures 6 and 7 present the RAOs for the first harmonic

component of the cushion and the seal excess _pressure.

The computational and experimental results for the

cushion excess pressure agreequite well. The correlation

for the seal excess pressure is rather poor. In the experiments the seal pressure appears to follow the

cushion pressure. This might be attributed to a difference

in the air supply system of the stern seal.

In the

experimental model the air from the aft fan is fed into an

air supply box, which distributes the air _{over the seal and} the cushion. Air also flows from the seal via.special ducts

to thecushion. In the computational model allair from the aft fan is fed into the seal. Again air flows from the seal

to the cushion, but not via special ducts.

Figure 8 presents the RAO for the vertical acceleration_at station 10. However, this RAO is not based on the first harmonic component of the acceleration signal. _{Il gives} the peak accelerationjevel divide&by thewave amplitude.

The RAO based on the first harmoniccomponent would have shown only a small dependence on wave height, just

like the RAO for the cushion excess pressure (Fig. 6). The RAO based on the peak level shows considerable

dependence on wave height. _{As the first harmonic}

component is not very sensitive to wave, height, this has to be caused by higher harmonic components.

Figure 9 presents the sinkage of the vessel. Waveheight

has an important effect on the amount of air leakageand

hence on cushion excess pressure. A decrease in cushion pressure. causes the draught

_{of the SES to}

increase. _{The experimental data in this figure are}

selected from the total set of'

_{data, to have a wave}

steepness (kA) that differs not too much from 0.05. The

6

experimental and computational data differ considerai

but the Irend is the same. The difference might caused by a poor prediction of the steady hydrodynar lift force on the side hulls. Another likely explanation ¡

somewhat :10w cushion excess pressure during I

experiments.

Figures 10 and 11 present the _{effect of} sev

simplifications and scaling on the computed h02

displacement and cushion excess pressure. The effect

pitch motion is generally very small.

The first simplification was the linearisation of the st seal around a mean posftion When the air leakage ai under the stern seal gets negative it is set equal to ze

so air leakage is retained in non-linear form. The effect

this simplification appears to be very small, afthoug

should be mentioned that the effect on sinkage and higi

harmonics is much larger. This simplification is vi

attractive; the computational burden is reduced a lot, a

the method gets more robust, as no difficult stern si

solutions have to be found for every time step.

The second curve is

the result of a simple 11m

frequency domain:calculation. In this calculation the st

seal and air leakage where neglected. The results

poor, and the method of course gives no informati

about sinkage. and higher harmonics.

The third curve is a result of a non-linear simulation, I the interaction of the air .cushion and thewave surf 2

was neglected. This implies that the waves generated the oscillating cushion pressure are neglected and ti

theincident waves are assumed toipropagateund isturb

through the air cushion. The effect of this simplificati

appears to be limited. _{However, when the resoni}

frequency of the air cushion is not damped as much the fan system and air leakage under the stern seal, ti effect becomes much more important. Inprevious studi neglecting cushion surface interaction appeared to sI

the resonant frequency of the air cushion downwar

(Moulijn[25]). _{The hypotheses of Kaplan[12J that t}

vessel induced waves only have a minor effect on t motions cannot be confirmed

The fourth simplification implies neglecting the fan slot

i.e. _{assuming that the volume flux through the fans}

constant. The effect appears to be very large. The f system appears to have a large damping effecton the

cushion resonance. This shows that the fan system h an important effect on the motions of SES Perhap5

more sophisticated fan model should be implement

Finally the effect of scaling is shown.

The amu

pressure was raised a factor ten in order to simulate t motions of a t:10 scale model Without a device to sci the air cushion dynamics. The scale of models is usu2

much smaller than 1:10, so much care must be taken the proper scaling of cushion dynamics.

8. CONCLUSIÓN

The results of the computational method _{are generally}

although some discrepancies occur. The linearisalion of.

the stern seal model only has a small effect on the results. Air leakage appears tobe an important effect_that cannot be. neglected. The effect of the interaction of. the

air cushion and the wave surface. is limited, but _this

interaction cannot be neglected.. The fan system appears

to have an important effect on the results; Scale effects that occur during experiments are important.

ACKNOWLEDGEMENT

The author would like to thank the Royal Netherlands

Navy and the Matime Research Institute Netherlands _for their financial support of this research project.

REFERENCES

NAKOS, D E,. NESTEGAARD A, IJLSTEIN, T, and

SCLAVOUNOS, P D: _{'Seakeeping Analyses of} Surface Effect Ships', Proc. First International

Conference on Fast Sea Transportation (FAST'91), Trondheim, Norway, 1991.

SØRENSEN, A J: 'Modelling and Control of SES in the Vertical Plane', PhD thesis, Norwegian Instituteof Technology, 1993.

STEEN, S: 'Cobblestone.Effect onSES', PhD thesis, Norwegian Institute of Technology, 1:993.

ULSTEIN, T: 'Nonlinear Effects of a Flexible Stern Seal Bag on Cobblestone Oscillations of an SES',

PhD thesis, Norwegian lnstitute.of. Technology, 1995. KAPLAN, P and DAVIS, S: 'A Simplified

Representation of the Vertical Plane Dynamics of

SES Craft', AIAAJSNAME Advanced Marine Vehicles

Conference AIAA Paper No.74-314, 1974.

KAPLAN, P, BENTSON, J andDAVIS, S: 'Dynamics

and Hydrodynamics of Surface Effect Ships',

Transactions of SNAME, Vol. 89, pp.211 -247, l;981.

7 DOCTORS, L J: The Use ofPressure Distribution to Model the Hydrodynamics of Air-Cushion Vehiclés

and Surface Effect Ships, Intersociety High

PerformanceMarina VehiclesConferenceand Exhibit (HPMV92), Arlington, VA, 1992.

MCHENRY, G, KAPLAN,. P, KORBIJN, F and

NESTEGARD, A: 'Hydrodynamic Analyses of Surface Effect Ships: Experiences with a.

Quasi-Linear Model', Proc. First International Conference on Fast Sea Transportation (FAST9I), lTrontheim, Norway, 1991.

MASSET, J F, MOREL, J P and KAPSENBERG, G

K: _{'Large Surface Effect Ship (SES) Air Cushion}

Dynamics: An Innovative Methodologyfor Theoretical Modelling Validation!, Proc. Third International

Conference on Fast Sea Transportation (FAST91:),

Lübeck-Travem ünde,. Germany, 1995.

7

1.0. LEE, G J: 'On the Motions of High Speed

Surface-Effect-Ships in waves', Journal of Hydrospace

Technology, vol.1, No.2, 1995.

il. MASSET, J F and MOREL, J P: 'A Test Rig for the Analyses of a Large Surface Effect Ship Seals

Dynamics: Design, Manufacturingand Results', Proc.

NAV'94, Vol. 1, 1994.

KAPLAN, P: 'The Effect of Motion-Induced Surf ace Wave Generation on SES Vertical Plane Motions in

Incident Wàves',. Intersociety Advanced Marine

Vehicles Conference, Washington, 1989.

Doctors, L J: 'The Effect of Air Compressibility on

the Nonlinear Motion of an Air-Cushion Vehicle, Eleventh Symposium on Naval Hydrodynamics,

pp.373-388, 1976.

KIM, C H and TSAKONAS, S: 'An Analysas of

Heave Added Mass and Damping of

Surface

Effect Ship' Journal of Ship Research, Vol.25, No.1,

198.1..

MORAN, D D: 'The Wave Height Under a High

Length-to-Beam Ratio Surface Effect Ship in Waves',

Technical Report SPD-587-0i, NSRDC, 1975. KAPSENBERG, G K: 'Seakeeping Behaviour of a SES in Different Wave Directions!, Proc. Second International Conference on Fast Sea Transportation

(FAST93), Yokohama, Japan, 1993.

DURKIN, J M and LUEHR L: 'Dynamic Response

of Litt

Fans Subject to Varying

Backpressure', AIAA/SNAME Advanced Marine Vehicles Conference,

AIAA Paper NO.78756r 1978.

SULLIVAN, P A, GOSSELIN, F and HINCHEY, M J:

'Dynamic Response of an Air Cushion Lift Fan',

Intersociety High Performance Marine Vehicles

Conference and Exhibit (HPMV'92), Arlington, VA,

1.992.

WITT, K C:

'Lift Fan Stability for SES', Proc;

Second International Conference on Fast Sea

Transportation (FAST'93), Yokohama, Japan1 1993. ....

LAVIS, D R, BARTHOLOMEW, R J and JONES, J C:

'Response of Air Cushion Vehicles to Random

Seaways and the

Inherent Distortion in Scale

Models', Journal of Hydronautics, Vol.8, No.3, 1974. KAPSENBERG1 G K: 'Added Mass and Damping

Coefficients for a Large SES Including an

Appreciation of Scale Effects!, Proc. NAV'94, Vol. 1,

1994.

KÁPSENBERG, G K and BLUME, P: 'Model Tests

for a Large SUrface Effect Ship at Different Scale

Ratios', Proc. Third International Conference onFast Sea Transportation (FAST91), Lübeck-Travemünde, Germany, 1995.

23 MOULIJN, J C:

'A Model for Flexible Bag Stern

Seals', Technical Report 1082-O, Delft University of

Technology, Ship Hydromechanics Laboratory, 1996.

24. NAKOS, D E: 'Ship Wave Patterns and Motions by a Three Dimensional Rankine Panel Method', PhD thesis, MIT, 1990.

-7

Transverse Section

Q(OUl)

Q(l)

Longitudinal Section

Fig. i Transverse and longitudinal section of a Surface Effect Ship

deck

wave surface

MOULIJN, J C: 'Motions of Surface Effect Ships',

Technical Report 1051-O, Detft University of

Technology, Ship HydromechanicsLaboratory, 1996.

CUMMINS, W E: 'The Impulse-Response Function

and Ship Motions!, Technical Report 1661, David

Taylor Model Basin, Washington D.C., 1962.

27 OGILVIE, T F:

'Recent Progress Toward the

Understanding and Prediction of Ship Motions', Fifth Symposium on Naval Hydrodynamics, 1964.

8

Fig. 2 Typical solution for a 3-lobe flexible stern seal

JcJ

cushion plenum

('s'

i

% I I I I

'

l

I _I % I ,1

\

j

I I

\

hi1!

\

,I I

J

9 5 1:0 _{15 20} t [s]

173

RAO'

[rn/rn]

1.2

1-

0.8-

0.6-

0.4-

0.2-o 0

0.03

0.025

0.02

-1/5

0.015

-Erad/ml

0.0'l

-Pc

[kPa/rn]

6

5-

4-9 1 o

+

simulation kA = 0.01

simulation kA = 0.05

simulation kA

0.10

simulation kA = 0.15

MARIN experiments

+

I I

simulation kA = 0.01

simulation kA = 0.05

--simulation kA = 0.10

simulation kA = 0.15

MARIN experiments

₊

simulation kA = 0.01

simulation kA = 0.05

simulation kA = 0.10

simulation kA = 0.15

MARIN experiments

₊

+

2 3

[rad/s]

lo

4

Fig. 5 Response amplitude operator for pitch

5

O 1 3 4 5

We

[rad/sJ

Fig. 6 Response amplitude operator for cushion excess pressure

0.005-(J

O

i

i 2 3 4

We

[rad/s]

Fig. 4 Response amplitude operator for heave

PS

kPà/rn]

A}0

RAO

sinkage

[m]

0.4

0.2

o-

-0.2-

-0.4-

-0.6-

-0.8-

-1--5

+

simulation kA = 0.01

simulation kA = 0.05

simulation kA = 0.10

simulation kA = 0.15

+

1+ I 11 1 2 3 4 5

w [radis]

Fig. 9 Sinkage (positive üpwards)

simulation kA

simulation kA =

simulation kA

simulation kA =

experiments kA

I

001

0.05

0.10

---0.15 0.05

+

i

2 3 4 We

[rad/s]

Fig. 7 Response amplitude operator for seal excess pressure

1 2 3

4

5

We

[rad/s]

Fig. 8 Response amplitude operator for acceleration at station 10

+

I I

simulation kA = 0.01

simuiation kA = 0.05

simulatión kA = 0.10

simulation kA = 0.15

= =

MARTh experiments

+

13

RAO'

{m/m]

Pc

RAO'

[kPa/ m]

1.2

1

0.8-

0.6-

0.4-

0.2-0 12

10-

8-

6-I I

linearised stern seal

linear frequency domain ----

-no cushion-surface interaction

no fan slope

scale effect (1:10. model)

MARIN experiments

₊

+

I I

linearised stern seal

linear frequency domain

no cushion-surface interaction

no fan slope

scale effect (1:10 model)

MARIN experiments

₊

.5.

-

5.S

/

+

o O 12 o 1 2 3 4 5

w [rad/s]

Fig. lo

Effect of several simplifications on heave RAO, kA = 0.05

'S * 't

'SI

2

t'

4 5 1

2'

₃

w [rad/s]