The Behaviour of Different Types of Aircushion Supported Structures

Date Author Address

September 2006

J.L.F. van Kessel & J.A.Plnkster Deift University of Technology Ship Hydromechanics Laboratory

Mekelweg: 2, 26282 CD Deift

TU Deifi

Deift University of Technology

The BehaviOur of Different Types of Aircushion Supported Structures

by

JL.F. van Kessel & J.A. Pinkster

Report NO. 1496P 2006

Publication: 4"'Internatlonal Conference on Hydroelasticity m'Marine Technology Wuxi, Chlna1September 2006, ISBN:7-11804728-7 November 2006, Launceston, Austrálla

Proceedings of the fourth International Conference

_on

Hydroelasticity in Marine lechnology

Wuxi, China, 10- 14 September 2006

Hydroelasticity in Marine

Te clin ol ogy

Edited by

You-Sheng Wu

Wei-Cheng Cui

China Ship Scien«fic Research 2enter

IILNational Defense industry Press

CIP Data

Hydroelasticity in Marine Technology!

Y. S. Wu, W. C. Cui edited.

Beijing: National Defense Industry Press,

_{2006. 9}

ISBN 7-118-04728-7

I .

4th...

II _.

.©...

III. Hydroelasticity.

iV. TV131.2-53©P75-53

ChinaLibrary CIP (2006) 095647

Hydroelasticity In Marine Technology, 2006, WuxI, _China

Published by

National Defense Industry Press, Beijing, China

23 Zizhuyuan Southern Road

Haidian District 100044

Hydroelaslicily in Marine Technology, 2006, Wuxi, China

Contents

Preface

_ix

Wave Loads and Responses

i Use of Hydroelasticity Analysis in Design

_I

R. D. Harding, S. E. Hirdaris, S. H. Miao, M. Pittilo and P. Temarel

2 The Non-Linear Hydroelastic Responses of a Ship Traveling in Waves

13

C. Tian andY. S.Wu

3 The Influence of Structural Modeling on the Dynamic Behaviour of a

₂₅

Bulker in Waves

S. E. Hirdaris, S. H. Miao, W. G. Price and P. Temarel

4 The Effects of Water Depth

_{on Wave-induced Loads of a Very Large}

₃₅

FPSO By 3D Hydroelastic Theory

Y. H. Xie and R. P. Li

5 Numerical and Experimental Study of the Dynamic Characteristics of a

41

Simplified Compliant Buoyant Tower

J. Z. Xia and J. Dryne

6 The Behaviour of Different Types of Aircushion

_{Supported Structures}

₅₁

J. L. F. van Kessel and J. A. Pinkster

Full Scale Measurements

7 Full Scale Wave and Whipping Induced Hull Girder

_Loads

₆₅

P. J. Aalberts and M.W. Nieuwenhuijs

Whipping, Springing and Slamming

8 Experimental Investigation of The Ship Response to Bow and Stern

79

Slamming Loads

D. Dessi and R. Mariani

9 Springing/Whipping Response of

a Large Ocean-going

₈₉

Vessel-Investigated by an Experimental Method

10 Longitudinal Loads on a Container Ship in Extreme Regular Sea and

103

Freak Wave

T. Kinoshita, S. Nakasumi, K. Suzuki, K. Tanizawa J. S. Shi, H. Kameoka, T. Waseda, and T. Yuhara

11 New Criteria forthe Detection of Slamming

_{Events and Comparison}

₁₁₁

with Theoretical Models

E. Ciappi and D. Dessi

Impact

12 Hydroelastic Impacts in the Tanks of LNG Carriers

Malenica, A. A. Korobkin, Y. M. Scolan, R. Gueret, V. Delafosse, Gazzola, Z. Mravak, X. B. Chen and M. Zalar

13 SPH Analysis of Hydrodynamic impact, Including

_Hydrodynam

Fluid-Structure Coupling

J-B Deuff, G Oger, M. Doring, B. Alessandrini and P. Ferrant

14 Breaking Wave Impact onto Elastic Wall

A. lafrati and A. A. Korobkin

15 The Fluid-structure Interaction during the Water Impact

of a

Cylindrical Shell

H. Sun and O. M. Faltinsen

16 Compressible Jet Impact onto Elastic Panels

A. A. Korobkin, T. I. Khabakhpasheva and G X. Wu

Sloshing and Fluid Tank

17 Hydroelastic Sloshing Induced Impact with Entrapped Air

₁₆₉

O Rognebakke and O. M. Faltinsen

18 A Numerical Investigation of Natural Characteristics of

a Partially

181

Filled Tànk Using a Substructure Method

M. Tan, Y. P. Xiong, J. T. Xing and M. Toyoda

19 An Experimental Study on Vibration Characteristics of A Thin Spherical

₁₉₁

Tank-Water Interaction System

M. Toyoda, J. T. Xing, Y. P. Xiong and M. Y. Tan

Shock

Very Large Floating Structures

21 Hydroelastic Response of the ISSC VLFS Benchmark

H. R. Riggs, H. Suzuki, Y. Yasuzawa, J. W. Kim and R. C. Ertekin

22 Hydroelastic Behavior and Drift Force of a Very Large Mobile Offshore

215

Structure in Waves

K. Takagi and J. Noguchi

23 Local and Global Hydroelastic Analysis of a VLFS

₂₂₅

M. Greco, G Colicchio and O. M. Faltinsen

24 Hydroelastic Analysis of Flexible Floating

_{Structures with}

₂₃₅

RigidHinge-Mode

S. X. Fu, T. Moan, X. J. Chen and W. C. Cui

25 Hydroelastic Response of VLFS Coupled with

_{OWC-Type Breakwater}

₂₄₅

S. Y. Hong and J. H. Kyoung

26 Experimental and Numerical Study of the Wave Response of a Flexible

255

Barge

F. Remy, B. Mohn and A. Ledoux

27 Hydroelastic Response of Very Large Floating

_{Structures under the}

₂₆₅

Combined Action of Waves and Currents

G. Y. Cheng and B.S. Wang

28 Time Domain Analysis on Hydroelastic Response of VLFS Using Finite

273

Element Method

J H. Kyoung, S.Y. Hong and B. W. Kim

29 Fundamental Study on the Collapse Analysis of VLFS in Waves

283

T. Y. Xiao, Y. Zhao and M. Fujikubo

30 Unsteady Motion of a Two-Dimensional Elastic Plate Floating on the

293

Surface of Deep Water

I. V. Sturova

Flow Induced Vibration

31 Vortex Induced Vibrations of Deepwater Rises and PipelinesReview of

303

Model Test Results

H. Lie and C. M. Larsen

32 Issues Important to VIV Suppression Design for Marine Applications

323

L. Lee andD W.Allen

33 WV and Hydrodynamic Forces of Circular Cylinders Attached under a

331

Flat Spring with Forced Oscillation Tests in Still Water

H. Maeda, K. Masuda, T. Ikea and N. Kondo

34 Insight into Data from Forced Oscillation Tests in Prediction of VIV of

341

Flexible Risers

Z.Y. Pan, W. C. Cui and Y. Z. Liu

35 Effect of Strakes on Fatigure Damage due to Cross Flow VIV

₃₄₉

G S. Baarholm, C. M. Larsen and H. Lie

Devices f1'r Energy Extraction

36 Extreme Motion Predictions for Deepwater. TLP Floaters for Offshore

361

Wind Turbines

J. J. Jensen and A. E. Mansour

37 Wave Drifting Free Model Experiments with Flexible Fin

369

Y. Terao, K. Watanabe and H. Katuura

Risers, Cables and Pipelines

38 Transverse Motion of Towed Cables

₃₇₇

S. Ersdal and O. M. Faltinsen

39 Linear Dynamics of Catenary Risers

₃₈₇

I. K. Chatjigeorgiou

40 An Experimental Investigation of Interaction between

_{Adjacent Spans in}

₃₉₇

Pipelines

P. K. Soni and C. M. Larsen

Fishing Nets and Cages

41 Fatigue Design of Floating Fish Farms Based on Load and Response

405

Interaction

P. E. Thomassen and B. J. Leira

42 Dynamic Behaviour of a Complete Trawl Gear (Manoeuvrability and

413

Security)

D. Mancha! and B. Vincent

43 Model Investigation of Dynamic Behaviour and Wave Loads on a Fish

421

Farm Cage

R. Kishev, V. Rakitin and Y. Yovev

Author Index

₄₂₈

Hydroelasticity In Marine Technology, 2006, WuxI, China

The Behaviour of Different Types

_{of Aircushion Supported Structures}

J.L.F. van Kessela, J.A. Pinksterb

a

Offshore Engineering Department, Deift University of Technology, The Netherlands bship

Hydromechanics Laboratoiy, DeIft University of Technology, The Netherlands

ABSTRACT

The behaviour of different types of aircushion supported structures is described aíid compared

with a rectangular barge having the

_{same dimensions. All structures are free-floating and}

subjected to regular waves of different directions. Calculations are based on a linear three-dimensional potential method using

_{a linear adiabatic law for the air pressures inside the}

cushions. The water surface within the aircushions and the mean wetted surface are modelled by panel distributions representiñg oscillating sources. The description of the behaviour includes the

motion characteristics, mean second order drift forces, surrounding wave field

as well as

enclosed waves inside the cushions, bending moments and vertical shear forces. In this paper, the merits of aircushion supported structures in waves are discussed and as such can be of interest for large floating structures

KEYWORDS

Floating Structures; Aircushion; Compressibility; Motion Behaviour; Wave Forces; Drift Forces; Wave Field; Shear Forces; Bending Moments; VLFS

i INTRODUCTION

The use of aircushions to support floating structures has been known for a long time in the

offshore industry. In most cases the draft of the structure was decreased by pumping compressed air underneath the construction to allow franspoiation over a shallòw water area.

At DeIft University of Technology, the behaviour of large _{aircushion supported structures in}

waves has been studied using three-dimensional computations and model tests.26 The existing linear three dimensional diffraction code DELFRAC was modified to take into account the effect of one or more aircushions under a structure at zero forward speed in waves.

In the present paper a short review is given of the main elements underlying the computational

method. Successively a brief description is included of the behaviour of different types of

aircushion supported structures with respect to motion characteristics, mean second order drift forces, surrounding wave fields, bending moments and vertical shear forces..

2 AIRCUSHION THEORY

PVK =constant

_(I)

The pressure in the aircushion due to wavesand oscillations of the structure can be expressed by:

P(t)

1O[)j

₍₂₎

in which:

= Initial volume of the aircushion

V(t) = Volume of the aircushion (V + Lt V)

P,, _{= Initial cushion Pressure (F, + Pi.)}

P(t)

= Pressure inside the aircushion

X = gas law index (1.4 for air)

In the above, P is the atmospheric pressure, P is the pressure due to the support of the

structure and _{V is the volume variation of the cushion.}

The given non-linear expression for the _{pressure was rewritten in a linear form as the general} calculations are also based on linear methods Eq.(2) can be made linear by a Taylor expansion

of ((V0 +

_{around point (v =0),, assuming that the volume}

variations are small

compared to the total volume of the cushion, this results in1:

P(t)=P_KPØ!I

₍₃₎

The spring stiffness of all (NAC) aircushions together is equal to the sum of the individúal

cushions. The total spring coefficient as given below is derived from the previous equation. with

use of V = h 4, in which h is the cushion height and A the cushion_area:

NAC _A

C33=KPo

(4)

It should be noted that the spring coefficient in Eq.(4) is for aircushions only, i;e. the spring stiffness of the buoyant part of the structure is not taken into account in this expressiow The

contribution of structure will be discussed in the next sectiOn.

2.1 Aircusliion supported structure

The previous section described the heave stiffness of

_{aircushions only. Henceforward the}

buoyant part of the floating body is also taken intoaccount.

Due to the fact that the air underneath the structure is enclosed by water instead of a rigid construction, the heave stiffness of the cushions will be less than described in Eq.(4) The cushion height influences the compressibility of the enclosed air, the polytropic process as

presented in Eq.(l) can therefore be writtenas:

f

\I/K

h

IJ)

The air pressure P is equal to the atmospheric pressure P0 in case the structure is

fi.illy

supported by its floaters The cushion pressure can be described as follows:

P(t) = P + pg T

in which 1

is the vertical distance of the free surface in the cushion

_{below the mean sea}

level.When e is defined as a small dimensionless number representing the compressibility of the

aircushion, the aircushion itself is

_{compressed by eAT in case the structure}

_{moves down.}

Substitution of Eq.(6) in Eq.(5) finallyresults in:

hr I/K

[iJ .h=(1+Ei(T+(l_e)LT)J

.(heAT)

The right hand side of the express 'on can be rewritten with use of a Taylor expansion around AT =0, resulting in the compressibility factor of the aircushion:

6

pg

(8)

KP+p'gh

where P is P(t) as defined in Eq.(6).

2.2 Stiffness coefficients and stability

The aircushion supported structure can be modelled as a mass spring system shown in Fig.!. The structure is supported by water and air. Air underneath the Construction is in its turn supported by the surrounding water. Displacing the structure in any of the three vertical modes heave, roll or

pitch will change the volume of

_{an aircushion thus inducing pressure changes. In order to}

determine the heave spring stiffliess of the structure, both air and water can be modelled _as springs with stifThess C and C,1 respectively, resulting in a general expression of the heave

stiffliess:

c3 = pg

_{(k -}

A) + c33 C33,C

(9)

c33 +pgA

in which

k

_{is the total waterline area of the structure. The first term represents the hydrostatic} restoring force of the buoyant part of the structure, the second and third part are contributions of the aircushion.

In order to determine the stability of the floating body with multiple cushions, the displacement

of the centre of buoyancy (B) has to be determined, _{see Fig.2. In case of small heeling angles} (ç$) the vertical displacement of B can be neglected. Both the structure and the cushionsare

subjected to a buoyancy force, the distance B B0 ofthe structure is:

j1 f,2 y tanØdy, dx

BB0 = 2 ₍₁₀₎

The distance BB0 of the cushion can be calculated in a similar way:

B

'3l

- e)dydx

in which:

-

_{z = mean increase of the cushion height}

(-

y

+y.

2

c.mln

tanqi

= centre of the cushion in y-direction

resulting in an expression of the BM-value for aircushion supported structures:

J

Jy2dy, dx3 +

{1

e)

Ymax ± Ymm.)2

J fdy th }

BM =

₍₁₂₎

In general the transverse stability (G MT)

_{can be found by adding the distance BG to the}

previous expression.

The rotatibnal stiffness coefficients are expressed as follows:

(X, +Xmin'

2

3 NUMERICAL APPROACH

The interaction between the aircushions, the structure and the surrounding water are based on a three dimensional potential theory. The rigid part of the structure is modelled in the usual way by

means of panels representing pulsating sources distributed over the mean wetted surface of the construction.

The free surface within each aircushion is modelled _{by panels representing oscillating source} distributions laying in the mean free surface of each cushion. The mean surface level ofan

individual cushion may be substantially different from _{the other cushions and the mean water} level outside the structure.

All panels of the free surface within an aircushion are assumed to represent a body without niaterial mass but having added _{mass, damping, hydrostatic restoring and aerostatic restoring}

characteristics. Each free surface panel has one degree of freedom being the vertical motion. The total number of degrees of freedom (D.O.F.) therefore amounts to:

D.O.F.=6+N

₍₁₉₎

in which:

N = number of panels in cushion c

The number 6 represents the six degrees of freedom

_{of the rigid part of the structure. The}

equations of motion can in this case be writtenas: 110F. -

{_w(M. +aq)_iwbj ±c,}x

=X

n=1,2,...,D.O.F.

(20) ifl which: Ymax + Ymin C44 =

pg [

fJ3,2 ds + 1(1

-2

j

ffds

4,

4

_(Yrnax +)/ 2 54

(

C32 = c54 =

pg (k A ) x1

_{y. + j}

c33

-

C A I

x1 .y

(17)

c33 +pg

where x _{and y1 are coordinates of the centre of the water plane relative to the origin of the}

axis system. The subscripts 'c' and 's'_{are for the cushion and structure respectively. In case both}

structure and cushions are rectangular shaped then x and can be expressed as:

(18)

C55=

Pg[

jjx2_{ds5 + {(.i} )(Xm + Xmin)2

_{fJds}_}

v

(14)

The non-zero coupled restoring coefficients_are:

= _{mass coupling coefficient for the force in the n -mode due to}

acceleration in the j-mode. Zero for cushion panels. added mass coupling coefficient

damping coupling coefficient spring coupling coefficient mode of motion

wave force in the n-mode

)Ç, the added mass and damping coupling

_{coefficients a, and b, are}

determined in the same way as is customary for a multi-body system.

The contribution of the total potential due to the discrete pulsating source distributions over the structure and the free surface oftheaircushions can be expressed as:

qs,

()G(,

_)As5 a,, = b,!, = cfi = xi = xn =

The wave forces

(21) in which: N =

X

= A =

G(Ï,)

=

total number of panels of the structure and free surfaces of all cushions

X1,X2,X3=afieldpoint

A1, 4, 4 = location of asource

Green's function of a source in relative to a field point

= _{surface element of the body or the mean free surfaces in the aircushions}

o.si = strength of a source on surface element _{s due to motion mode j}

= _{potential in point Ï due to j -mode of motion}

The unknown source strengths o _{are determined based on boundary conditions placed on the}

normal velocity of the fluid at the centres of thepanels:

-()+

4it51

ôn A)LSÇ

=:._L _{m=1,2,...,N1 (22)}

4 BEHAVIOUR OF DIFFERENT TYPES OF FLOATING STRUCTURES

The behaviour of different types of aircushion supported structures was calculated and compared

with that of a conventional rectangular barge. Both the barge and aircushion variants had the

following main particulars:

Length

150.0 m

KG

5.Om

Breadth

50.0 m

15.0 m

Draught

5.0 m

42O m

Displacement 38437.5 t k

42.0 m

The height of all cushions is 5 m and the ambient

_{air pressure was taken equal to100kPa}

Different configurations of the structure resulted in _{different natural frequencies and stability}

Table 1: Main particulars of the structures, natural frequencies and stabili

A graphical representation ofthe lAC _{and l2AC cushion variants is given in Fig.9.. The whole}

waterline area ofthe structures I AC to 75AC is covered by aircushions. The negative GM-values result from the fact that a single cushion covers the whole waterline in longitudinal or transverse direction. The. wall thickness of the skirts _{was equal to zero. Due to small heeling angles the} centre of buoyancy will not shift in these cases. Accordingly the buoyancy force acts through_a

fixed point at halfdraught ofthe_{structure and the GM-value corresponds to the distance}

between

the centre of buoyancy and the centre ofgravity.

The structures with a negative GM-value are unstable, but nevertheless have been included to show the effect of different aircushion configurations on the behaviour ofthe structure. In these cases additional stability can be gained by giving the skirts _{a thickness, this is the case for the} structure referred to as "Combi 1". Therigid skirts surrounding "Combi 1" havea thickness of 5 m resulting in an aircushion of 140X 40 m.

The motions ofthe various structuresare given in Fig.3,, for sake ofbrevity only results forheave,

roll and pitch are shown since these motions _{are most affected by the aircush ions. The heave}

motions for all structures are approximately equaL Roll motions are nearly zero in case a single

cushion covers the total breadth of the

_{structure, this is due to the fact that no natural roll}

frequency is present for these bodies. When the waterline beam is divided by multiple cushions the roll motions decrease with cushion width. In case of small cushions like the 75AC, the roll motions approach those of the pontoon. The same conclusions can be drawn for pitch motions,

though in this case the length of the cushions has to be considered. Additionally, the figure

clearly shows that the natural pitch frequency increases when the skirts :are given a thickness. The mean drift forces in Fig.4 show that the effect of the cushion configuration is largest in head seas. For cushion lengths smaller than 25 m, drift forces are almost equal to those of the pontoon while other multiple cushion variants with larger cushions show higher peaks at 0.65 -0.70 rad/s.

In addition, at higher frequencies the drift force for structures with less than 12 cushions is small compared to those of the pontoon.

Moreover, the drift force reaches a minimüm when the wavelength is equal to the cushion length, this is the case for the single cushion variant at 0.65 radis and for the 2AC and 4AC at 90 radis. The figure also shows that the drift force in head seas is equal for the I AC, 2AC and 4AC for

waves smaller than 75 m (0.90 rad/s), the wavelength corresponds in this case to the cushion length of the two and four cushion variants. In _{general: it can :be concluded' that for different}

structures, the mean drift force in a considered direction is approximately equal for wavelengths smaller than the 'length of the smallest cushion, providing that all bodies have similar dimensions and are totally' supported by air.

56

Structure'type / name Cushión size _{w5 GM1 GML}

Length Breadth

[m] _[ml [radis] [radis] [radis] [m] [mf

Heave forces in head and beam _{seas are presented in Fig.5. The values are approximately the}

same with the exception of the high frequencies. The small heave forces at low frequencies are

.

due to compressibility effects ofthe aircushions.

Roll moments in beam seas

_{are smallest in case the cushion covers the total width of the}

structure. The moments are almost similar for structures having cushions of equal breadth, but they are significantly higher when the waterline beam is divided by multiple cushions.

Pitch moments in head seas are generally lower for the aircushion variants, though they

significantly increase with decreasing cushionlength.

Figs. 7 and 8 show the surrounding wave field as well as the height of the waves inside the cushions. The wave heights

_{are given for different types of structures in terms of}

non-dimensional respoiie amplitude operators RAOs).

For beam waves with a wavelengthequal to the width ofthe structure (1.10 radIs) the waves are transmitted underneath the structure. The aircushion does not absorb energy from thewaves, i.e.

the waves can travel freely underneath the structure resulting in a small wake behindthe floating body. The reflected waves at the front are also small as could be expected from the drift forces given in Fig.4.

The difference in the surrounding wave field between the pontoon and the aircushion variants is even more evidént in head seas. For all wave frequencies, the incident waves are more distorted

by the pontoon than by the single aircushion variant. The wave field surrounding the four

cushion variànt is similar to the oneof the single and tWo.cushion variants, parenthetically this is thecase for all wavelengths smaller thän the cushion length of 75 m.

Less waves are transmitted into the cushion when the skirts are given a thickness, moreover the front skirt attenuates the waves resulting in lower values underneath 'Combi 1' compared'. to the single cushion variant.

In addition, the wave field and drift forces in oblique seas are presented in figures lOa and' lOb, the wave frequency is 095 radis corresponding to a wavelength of 68 m approximately equal. to the diagonal distance between the side skirts of the structure. Again, the surrounding wave field

is less disturbed 'in case the length of the _{cushions in. the. considered direction is equal to the}

wavelength.

The vertical shear forces and midship bending moments around the y-axis are given in Fig.6. In both cases the values of the rigid pontoon are highest and show a significant difference with'the single cushion' variant.

The large vertical shear forces of the 2AC'and4AC in comparison with the three cushion variant are due to the relatively high .pitch motions. The thickness of.the rigid skirt also has a significant effecton the vertical shear force of the structure as can' be seen in the same figure.

The bending moments increase with decreasing cushion size and approach those of'the pontoon

in case of the 75AC. In general it

_{can be concluded that the midship bending moment is}

significantly reduced by an aircushion. In comparison' with the pontoon the maximum midship bending moment of a single aircushion in head seas decreases by 44% in case the skirts have a

thickness of 5 m, when the bottom of the structure' is totally covered by an aircushion the

reduction ¡s, 96%.

5 CONCLUSIONS

The results shown in this paper indicate that the behaviour of large floating, structures partly or wholly suppoiled by aircushions can be predicted by means of three dimensional linear potential theory. Computations have shown that aircushions' can significantly influence the behaviour of floating structures

distorted resulting in low second order mean drift forces, and the wave frequency forces and

moments decrease. Moreover, the midship bending _{moments are significantly reduced by the}

aircushion, in a theoretical

_{case the reduction can amount to 96% in comparison with}

_a

rectangular barge, in practice a reduction of 44% will be more realistic.

The results have shown that an aircushion supported structure can be a good alternative for large floating structures. In addition, the computational method proved to be a suitable tool to optimize cushion configurations for a particular application.

REFERENCES

Ikoma, T., Masuda, K., Maeda, H. and Rheem, C.K., Hydroelastic behavior of air-supported

flexible floating structures. Proceedings

_{of the 2l}

_{International Conference of Offshore}

Mechanics and Artic Engineering (OMAE '02,), 2002, _1-8.

Pinkster, J.A., The effect of air cushions under floating offshore structures. Proceedings of

Boss '97, 1997, 143-158.

Pinkster, LA., Fauzi, A., moue, Y. and Tabeta, S., The behaviour of large air cushion

supported structures in waves. Hydroelasticity in Marine Technology, 1998, 497-506.

Pinkster, J.A. and Meevers Scholte, E.J.A., The behaviour of a large air-supported MOB at Sea. Journalof Marine Structures, 2001., 14, 163-179

Peters, O.A.J., Effect of Aircushións applied

_{to Floating Storage Units. Report 1069,}

Laboratory of Ship Hydromechanics, DeIft University of Technology, DeIft, 1996.

Tabeta, S., Model experiments on barge type floating _{structures supported by air cushions.}

Report 1125, Laboratory of Ship Hydromechanics, DeIft University of Technology, DeIft, 1998.

Figure 1: Mass spring system ofan

aircushion supported structure

-Pontoon -1AC -o-2AC 3AC

4AC -12AC ---24AC -75AC

_{: Combi i}

iba Motions in an Sens

o 0.1 0.2 03 04 0.5 0.6 07 0.8 0.9 1 1.1

frequency (radis]

0 0.1 0.2 03 0.4 0.5 0.6 07 0.8 0.9 1 1.1

Vbe frequency (radisj

Yc,min\ Yc. max

pgV

Figure 2: _{Stability of a structure with two}

aircushions

I'b Motions in ibad Sons

2 1.8 1.6 1.4 1.2 0.8 0.6 04 02 o 0 0.1 02 0.3 04 05 06 0.7 0.8 09 1 1.1

Vibvo frequency (radis)

0 0.1 02 0.3 04 0.5 06 0.7 0.8 09 1 1.1

P,bye frequency (radis]

Figure 3: Motions of a pontoon and aircushion supported structures

--Pontoon

_{-IAC -ó-2AC ---3AC}

_{4AC --I2AC -$--24AC} 75AC Cambi i 8E*04

7.'04

6.E'04 aoco4

2'O4

l.O4

0.cxE.00

i:

I

aoeE« 200E. 1 5aE.o4

OE.

0 Ql 02 0.3 0.4 05 0.6 0.7 0.8 0.9 1 1.1

Vve frequency (radis]

Figure 4: Mean drift forces on a pontoon and aircush ion supported structures

Iba%u Forces In Sean Seas

0 0.1 02 0.3 0.4 05 06 0.7 0.8 0.9 1 1.1

Ve frequency (radfsj

II Monienta In Sean Seas

0 Ql 0.2 0.3 04 05 06 0.7 0.8 09 1 1.1 frequency [radfsj 60 E z l50 u o u-50 8.WE'04 7.E.04 6.+O4 5.c04 4.00E.04

3+04

2sO4 l.WE.04

a+

aocE. l.5cE.

l.O4

50.O5 0.crE. 0 0.1 _{0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 11.1}

Vtvo frequency (ra1J

Ibavo Forces In I-bad Seas

0 0.1 02 0.3 0.4 0.5 06 0.7 0.8 0.9 1 1.1

Vibve frequency [radis]

Pitch Monients In I-bad Seas

0 01 02 0.3 04 0.5 0.6 07 0.8 09 1 1.1

Vibve frequency (radis]

Figure 5: Wave frequency forces and moments on a pontoon and aircushion supported structures

Qift Forces In Sean Seas Dift Forcos In Fbad Seas

0.ocE.00

..

-

'-O Ql 0.2 0.3 0.4 0.5 0.6 0.7 8 0.9 1 _{0 0.1 0.2 0.3 0.4 0.5 06 0.7 0.8 0.9 1 1.1}

Vve frequen, Ir&i _{Vitsu frequency (ra1}

Figure 6: Vertical shear forces and bending moments around the y-axis for a pontoon and aircushion supported structures

loo 200 ₂₀₀ 150 ₁₅₀ 100 ₁₀₀ 50 ₅₀

j

Midship Verticd 'iear Forces In Fbad Sme

a5cE.cX3 z5«x3 ZE.U3

i.5c

1 5.cXE.

og

-100 0 100 o

I

I

I

5.00E.04

Midship V _{ndIng Moments In IbI Se}

-100 0 100

RAO[ni/mJ:LlØracI/s:

0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.7 0.8 0.9 1.0 1.0 1.1 1.2 1.3 1.3 1.4 1.5 1.6 1.6 1.7 1.8 1.9 1.9 2.0

Figure 7: Wave fields surrounding

_{a pontoon and different types of aircushion supported}

structures in case of beam waves with wave frequencies of 1.10 rad/s (2 =50 m).

Respectively the following cases are presented: lAC, 3AC, 4AC, I2AC, 75AC and a

62 o -50 -100 -150 -200 -100 0 100 o -50 -100 -150 -200 -100 0 100 o -50 -100 -150 -200 -100 0 100 200 150 100 50 200 150 100 50 200 150 100 50 200 200 200 150 ₁₅₀ 150 100 ₁₀₀ 100 50 ₅₀ 50 -50 _-50 -50 -100 -100 _-100 -150 -150 _-150 -200 -200 _-200 -100 0 100 -100 100 -100 0 100

1

RAO[mJmJ:0.9ørad/s: 0.1_{0.2 0.3 0.4 0.5 0.6 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.8 1.9 2.0 2.1 2.2}

Figure 8: Wave fields surrounding

_{a pontoon and different types of aircushion supported}

structures in case of head waves with wave frequencies of 0.90 radIs (2 = 75 m).

Respectively the following cases are presented: lAC, 3AC, 4AC, 75AC, a pontoon and "Combi 1"

Figure 9: Graphical representation of the single (lAC) and twelve (I2AC) cushion variants

200 150 100 -50 o 50 o -150 200 -100 200 150 100 50 150 100 50 o RAO[mImJ:Ø.95racJ/s: 0.10.2 0.3 0.4 0.5 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.1 1.2 1.3 1.4 1.5 1.6 1.6 1.7_{1.8 1.9 2.0 2.1 2.1}

Dift Forces In allque Se

200

o

Figure 1 O(a): Wave fields surrounding a

pontoon and different types

of aire ush ion supported

structures in case of oblique waves with frequencies of

0.95 rad/s(..%=68m).

Respectively the following cases are presented: lAC, 3AC, 4AC, 75AC, a barge

and "Combi 1 ". q -100 0 100 -150 200 200 150 100 50 o Figure 1O(b):Meandriftforcesona

o 0.1 0.2 0.3 0.4 0.5 0.8 0.7 GB 0.9 1 1.1 rectangular barge with and Vke frequency IFadJ _{without aircushions}

-Pontoon --1AC -&-2AC --3AC -4l-4AC

_{12AC -'--24AC -75AC Combi i}