Numerical and Experimental Study on Aircushion Supported Srtuctures

Date June 2008 Author J,L.F. van Kessel

Address Deift University of Technology Ship Hydromechanics Laboratory

Mekelweg 2, 26282 CD Deift

TUDeift

Deift University of Technology

Numerical and Experimental Study on Aircushion

Supported Structures

by

.J.L.F. van Kessel

Report No. 1572-P

₂₀₀₈

Published in: Proceedings of the ASME 27th International Conference on Offshore Mechanics _{and Arctic Engineering} OMAE2008

THE

:. ANNUAL INTERNATIONAL CONFERENCE

un Uilsiiore Y3ecnamcs & Arctic nwii

1ì-19 June 20UU Esloi

ess Centre. Esturil, PwlugaI

OMAE ,o»

f

ESTORIL PORTUGAL

4IÒPILØI

rom

oncept to Commissioning

mce the i 920s, J. Ray McDermott has built a

trong reputation as a leader in engineering,

abrication, transportation, installation and

roject management of shallow water,

eepwater and subsea developments.

ith fabrication facilities, engineering offices

nd marine bases in the Americas, Asia Pacific,

aspian, Middle East and India, we integrate

ur worldwide resources to complete

rojects safely, efficiently and effectively.

I

TABLE OF CONTENTS

Welcome Letters

Important Information

7

Conference Sponsors

9

Conference Exhibitors

10

Special Symposia & Workshops

12

Invited Plenary Lectures

13

Sessions at a Glance

14

Final Programme

18

Outreach for Engineers Forum

61

Maps of Estoril

62

Estoril, Portugal

63

Cascais, Portugal

64

Technical & Cultural Visits

65

Conference Committees

67

Session Index

68

Author Index

70

www.omae2008.com I 7

IMPORTANT

CONFERENCE LOCATION

The OMAE 2008 Conference will be held at the Estoril Conference Centre (CCE), in Estoril, located about 25kms from Lisbon. There is a large selection of hotels within walking distance.

CONFERENCE SCHEDULE

Sunday, 15th June 2008 16h00 -19h00 Registration

18h00 - 21h00 Welcome Reception at "Tamariz" Bar on the Sea Front

Monday, 16th June 2008 Tuesday, 17th June 2008 Wednesday, 18th June 2008 Thursday, 19th June 2008 Friday, 20th June 2008 09h30- 10h00 Opening Ceremony

10h00 - 12h30 Plenary Session of Keynote Lectures (Interval at 10h30) 14h00 - 18h00 Technical Sessions 09h00 - 18h00 Technical Sessions (Intervals at 10h30, 12h30 and 15h30) 12h30 - 14h00 Awards Lunch 09h00 - 18h00 Technical Sessions (Intervals at 10h30, 12h30 and 15h30)

20h00 onwards Conference Dinner at Casino Estoril", 09h00- 18h00 Technical Sessions

(Intervals at 10h30, 12h30 and 15h30) 12h30 - 14h00 Session Organisers Lunch

Whole day Technical and Cultural Tours

REGISTRATION PROCEtMJRF

The OMAE 2008 Secretariat will be located on the ground floor (Level 0) of the CCE, and will be open on Sunday, June 15 from16h00 to 19h00. On all the other Conference days, the secretariat will be open from 08h00 through to 18h30.

REGISTRATION CATEGORIES ARE AS FOLLOWS:

Category (A) and (B) registration fees include technical programme attendance, one copy of the proceedings, welcome reception, lunches, coffee-breaks and conference dinner.

Category (C) registration fee includes technical programme attendance, one copy of the proceedings, lunch and coffee-breaks on day of attendance.

Category (D) registration fee, for which student documented proof is required, includes technical programme attendance, one copy of the proceedings, lunches and coffee-breaks.

Category (E-1) registration fee includes welcome reception, conference dinner, and two tourist half-day tours of Lisbon (16 June) and Sintra (18 Jun e).

Category (E-2) registration fee includes the same as (E-1) plus a full day tour of Obidos/Nazaré/Fátima and Batalha (17 June) and a full day tour of Evora (19 June).

PROCEEDINGS

To continue a tradition that was started 10 years ago at OMAE 1998 in Lisbon, the OMAE 2008 Conference Proceedings will be pu-blished on CD-ROM.

NAME BADGES

FiNAR

Fluid-Structure listeraction Simulation Using An Incompressible SPH Method ((M\LE2008-575 10)

Ashkan Raflee, Krish Thiagarajan, UniversityofWeslitw Australia,

Australia

Experimental Results of Tsunami Bore Forces on Structures

(OMAE2008-57525)

Ian Robertson, Ron Riggs, Abdulla Mohamed, Uníversi of Haniaii

at Manoa, USA

Wave and Current Induced Cumulative Fatigue Damage

Assessment for Offshore Pipeline on Free-Span (O\LE2008-573 17)

Ali Valipour C.C., Mehrdad Zoroufi, Abbas Yeganch Bakhtiary,

Reza Valipour, Iran University of Science and Technology, Iraii

Hydrodynamic Interaction and Drift Forces on a

Rectangular Barge and Modified Wigley Hull Arranged

Side-by-Side (OMAE2008-57943)

J oão Pessoa, Nuno Fonseca, C. Guedes Soares, Instituto Stipenor

Técnico, Portugal

OFFSHORE TECHNOLOGY SYMPOSIUM

oFT-i 3

Offshore Developments

Wednesday. 18_June, 2008 16h01)- 18h00

Room: 1)2 Session Chair: Halvur Lie. MARINTEK, Norway

Session CoChair:

loanrus Chatjigeorgiou, National Technical University uf \thens, Greece

Risk Based Fuzzy Modeling of Cost Estimating Relationships for Floating Structures (OMAE2008-57116)

Erebi Cocodia, University of Western Australia, Australia

Vessel Adapted for Multiple Installation and Salvage

(OI\LE2008-57776)

Jean Marc Cholley, Nicolas Tcherniguin, TE(HNIP, Fmni

Simulation of Vibration Control of Offshore Platforms Under Earthquake Loadings (()MAE2008-57553)

Rujian Ma, University off/nan, China, Jungang Wang, Tar/rn University, c'hina, Dong Zhao, University o/Jinan, China

YOSHIDA AND MAEDA SPECIAL SYMPOSIUM

ON OCEAN SPACE UTILIZATION

Y&M-1

Wave Responses of Platform I

Wednesday, 18 J une, 2008 09h()0- 10h30

Room: 1)3 Session Chan: Tumiiki Ikuma, Nihon University, Japan

Hydrodynamic Forces and Motion Responses of Feeding

Platform and Sea Cages (OMAE2008-57 170)

Daisuke Kitazawa, Takeshi Kinoshira, Sho Ito, Tomoyuki Tsunoda, \Veiguang Bao, Hiroshi Itakura, Masatoshi Fujino,

University of To,yo. Japan

Concept of an Offshore Aquaculture System With an

Automated Feeding Platform (OLE2008-577 19)

Tomoyuki Tsunoda, Daisuke Kitazawa, Takeshi Kinoshita, Sho Ito, Weiguang Bao, Hirosbi Itakura, Masatoshi Fujino, University

of Tokjo, Japan

On the Research and Development of Floating Offshore

Platform (OMAE2008-57958)

www.omae20O8.com 45

Shigesuke Ishida, Yutaka Obkawa, Tosino Niwa, Shigehiro

Ohkoshi, Kentaroh Kokubun, National Maritime Res Institute, Japan

KEYNOTE LECTURE

Foundations of Marine Structural Mechanics for the Education (O\L\E2008-58069)

Kuichiro Yoshida, National Maritime Research Institnte, Japan

YOSHIDA AND MAEDA SPECIAL SYMPOSIUM

ON OCEAN SPACE UTILIZATION

Y&M-4

Wave Responses of Platform II

Wednesday, 18 June, 2008 1 lhou-12h30

Room: D3 Session Chair: Shigesuke Ishida, National Maritime

Research Institute, Japan

A Prediction Method of Hydroelastic Motion of Aircushion Type Floating Structures Considering With Draft Effect

Into Hydrodynamic Forces (OM.AE2008-57 189)

Tomoki Ikoma, Masato Kobayashi, CST, Ni/ion University, Japan, Koichi Masuda, Ni/ion University, Japan, Chang-Kyu Rheem, JIS, The University of Tokj'o. Japan, Hisaaki Maeda, CST, Ni/ion University, Japan

Numerical and Experimental Study on Aircushion Supported Structures (OI'vLE2008-57884)

J an Van Kessel, GustoMSC / Delfi University of Technology, The

Netherlands

Wave Fields Diffracted by an Array of Truncated Circular

Cylinders (OMÀE2008-57 167)

Fenfang Zhao, Takeshi Kinoshita, Weiguang Bao, University of

Tok)o, Japan

KEYNOTE LECTURE

Bessho's Reverse Time Potential And Wave Free Potential

(OM.AE2008-58070)

Hisaaki Macda, CST, Ni/ion University, Japan

YOSHIDA AND MAEDA SPECIAL SYMPOSIUM

ON OCEAN SPACE UTIUZATION

Y&M-S Wave Responses of Platform 111

\Vednesday, 18_June, 2008 14h00-1 5h31)

Room: D3 Session Chair: Takashi Tsuhcigo, ( )saka Prefecture

University. .lapaii

Numerical Simulation on Motion Responses of the

Tsunami-Induced Grounding on a Wharf of Floating

Structures Using the MPS Method (OM.AE2008-57 190)

Koichi Masuda, Ni/ion University, Japan, Tomoki Ikoma, Mitsuhiro Masuda, Yuta Suzuki, CST, Ni/in,, University, Japan

A Study on Predictions of Fully Nonlinear Motion Aircushion Type Floating Structures Using 2D MPS

Method (OMAE2008-57387)

I\Iitsuhiro Masuda, Tomoki Ikoma, CST, Ni/ion University, Japan, Knichi Masuda, Ni/ion University, Japan, Hisaaki Maeda, CST, Ni/ion University, Japan

Validation Study of MPS (Moving Particle Semi-Implicit Method) for Sloshing and Damage Stability Analysis

Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering 0MAE2008 June 15-20, 2008, Estoril, Portugal

OMAE2008-57884

NUMERICAL AND EXPERIMENTAL STUDY ON AIRCUSHION SUPPORTED STRUCTURES

).L.F. van Kessel

Offshore Engineering Department, De/ft University of Technology,

Deift, The Netherlands

ABSTRACT

The use of aircushions for very large floating structures has been investigated in recent years at Delft University of Technology. Model tests were performed to validate the results of numerical calculations based on a linear three-dimensional potential

method. A linear adiabatic law was used in

the numerical approach to describe the air pressures inside the cushions. It is assumed that air cannot escape from the cavity underneath the structure. The water surface within the aircushions and the mean wetted

surface are modelled by panel

distributions representing oscillating sources.

Experimental results and numerical calculations of two configurations of aircushion supported structures at zero speed are presented in this paper. The results show that model tests of different aircushion supported structures can be well predicted

by means of 3D diffraction calculations.

KEYWORDS

Aircushion supported structure; motion behaviour; model tests; wave forces; air pressure; wave elevation; VLFS.

INTRODUCTION

The Khazzan Dubai oil storage tanks installed in the early 70's are probably the first large floating structures passively supported by air [1]. Air was needed to decrease the draft of the structure while being towed to the installation site, At the final location,

air was released from the cavity underneath the

structure in order to install the tank on the seabed.

Aircushions can also be used to reduce the wave loads on very large floating structures, Normally a breakwater is used to reduce these loads. However, from a practical and economical

point of view breakwaters are not feasible when water depths are large.

On the other hand, a wave absorbing device consisting of an air chamber connected to a very large floating structure can also effectively reduce the wave loads and (elastic) responses of the structure, as described by Maeda et. al. [2, 3].

The behaviour of large aircushion supported structures in waves has been studied by Van Kessel [9 11] and Pinkster et. al. [5 -7] at DeIft University of Technology. The existing linear three dimensional diffraction code DELFR.AC was modified to take into account the effect of one or more aircushions under a structure at zero forward speed in waves.

This paper discusses the results of computations by making use of the model experiments performed by Tabeta [8]. First the numerical approach will be discussed in this paper. Next the model tests will be described and a comparison between numerical and experimental results will be given. Finally conclusions will be drawn from the computational method and

model experiments.

NUMERICAL APPROACH

When considering a conventional rigid body, it is customary to determine the wave forces on the captive structure based on the

undisturbed wave potential , the solution of the diffraction

potential Ø,, and the added mass and damping coefficients of the structure oscillating in any one of the six modes of motion in still water based on the motion potentials çb,. The motions of the structure are then determined by solving a 6 d.o.f. equation of motion taking into account the wave forces, added mass and damping and restoring terms.

With a construction partially supported by one or more aircushions, different approaches may be followed in order to

determine the motions of the structure, pressure in the cushions and other relative quantities such as the structural loads,

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 of individual cushions may be substantially different from 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 material 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 of panel n within cushion c. It will be clear that properties such as added mass coupling and damping coupling exist between all free surface panels and the rigid part of the construction. The total number of degrees of freedom (D,O,F.) therefore amounts to:

D.O.F. = C) + (1)

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 for an aircushion supported structure can be written as:

in which: Al,,, = = b, = c,1i = xi = xfl =

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 , -mode

In the above equation j=i,6 and n=J,Ó represent motions and force modes respectively of the rigid part of the structure. The case of 1>6 and n>ó represents the coupling between the panels of the free surfaces of the aircushions. The case of j=I,ó and n>6 represents the coupling between the rigid

part of the

construction and the vertical forces of the free surface panels in the cushions. j>6 and n=6 represents the coupling between vertical motions of the free surface panels in the aircushions and the six force modes on the rigid part of the structure.

The wave force X, , the added mass and damping coupling coefficients a and b1 are determined in the same way as is customary for a multi-body system. The mean underwater part of the structure is discretised into a number of panels

representing pulsating sources as is the case with each free surface panel within an aircushion.

The contribution of the total

potential due to the discrete pulsating source distributions over the structure and the free surface of the aircushions can be expressed as:

01 ()=

o,, (A)G(A, Ä)As

(3)

in which: N. X A

G(Ä)

AS,

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

= X1,X2,X,= a field point

= A1, A2, A. = location of a source

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

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

= strength of a source on surface element s due to motion mode j

= potential in

point X 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 the panels:

The right hand side of the above equation depends on the case to be solved. If the source strengths for determination of the diffraction potential are required the normal velocity vector

becomes:

dOd (5)

dn,,,

It should be remembered that in this case the wave loads due to the incoming waves and diffraction effects are defined as being the loads on the structure and the individual free surface panels in the cushions, all being fixed. The added mass and damping coupling coefficients are found by applying normal velocity requirements. For the six rigid body motions (/= 1,6) of the structure:

2 Copyright © 2008 by ASME

L'O. I-.

{a(M,1 +a,1) iwb,1, +c,jx, =X,,,

,,=I,2...D.O.E. (2)

=, m=1,2....

(4)

n = nfl,1

j

= 1,6

in which the panel index ,n covers only the panels on the

structure. n,, are the general directional cosines for the panels on the structure given by:

COS(flm ') COS(flm , x2) cos(n,,,,x3) (7) x,,,2 _m3 x,,,3 n,,,2 X,,,3 n,,,1 X,,,1 n,,,3 X,,, n,,,2 - X,,,2 f,,,1 in which:

X,,, = co-ordinates of the centre of a panel relative to the body axes.

For this case the normal velocity components on all cushions panels are equal to zero.

For the determination of the added mass and damping coupling arising from the normal motions of individual cushion panels the normal velocity boundary condition is zero except for one cushion panel at a time for which the following value holds:

n,,,

lino = f,,,6 =

where the -1 follows from the fact that the free surface normal is pointing in the negative X3-direction.

From the solutions of the source strengths for all these cases the wave force vector X?? and the added mass a,, and damping coupling coefficients b,.,,

can be obtained. The wave force

follows from: X,, = - p O2 _{(0k + ødk )} i n,k k-I (8) (9) b,,1 = Im (10) D.O.F.

-i+}.3

X,,, ,i"7,D.O.F. 3 _{Copyright © 2008 by ASME}

In this equation, the added mass and damping coefficients and

in which: _{the wave forces are the same as applied in Eq. (2). From the}

0,1,6 = diffraction potential at k -panel obtained from Eq. solution of the equations of motions of the cushion panels the

(3) total wave forces on the captive structure can be determined as

X,,

= wave force

in the n -mode, n = 1,6

for the

well as the pressure variations within the cushions. structure

N,, = number of panels involved in the force in the n - _{So far, added mass and damping data are only derived for the} mode. For the force on a cushion panel N,, = I For structure and the individual cushion panels. In order to obtained the force on the structure N,, = N,

these data for the oscillating

structure, including the free n,,6 = generalised directional cosine of k -panel related to surfaces in the aircushions, the following approach is taken:

n-mode - Firstly, it is necessary to determine the solution of the source

area of k -panel related to the force in the n -mode strengths and fluid pressures for the case that the structure is oscillated while the cushions remain fixed. This is

The added mass and damping coefficients follow from: _{accomplished by solving Eq. (4) for the case that the normal} velocities on the panels of the structure are in accordance a,,

=_Re[PØJk

fl,,.k

6=l

p ú) 0.1,6 fl,,,k15fl.k] k-I

in which:

01.6 = motion potential value on k -panel obtained from Eq. (3)

The restoring coefficients c,,1 in general consist

of two

contributions i.e. an aerostatic spring term and a hydrostatic spring term as described in [6]. The hydrostatic restoring term is equal to the product of the waterline area, specific mass water and acceleration of gravity. This applies to both the structure and the free surface panels. The aerostatic restoring terms are related to the change in air pressure in an aircushion due to, for instance, unit vertical displacement of a free surface panel and the corresponding forces applied to the particular panel, all other panels belonging to the same cushion and the force on the structure. Conversely, displacing the structure in any of the three vertical modes of heave, roll or pitch will change the volume of an aircushion thus inducing pressure changes and as a

consequence forces on all free surface panels and on the structure itself.

For the determination of the aerostatic part of the restoring terms, use is made of a linearized adiabatic law as described in [6].

with Eq. (6) while the normal velocities on the cushion panels are equal to zero.

For each of the six modes of motion of the structure, this results in hydrodynamic loads on the structure and on the cushion panels. To these loads we also need to add the aerostatic forces since the oscillations of the structure change the pressure in the cushions.

- Based on the total forces on the cushion panels, the added mass and damping coupling coefficients and the aera- and hydrostatic spring coefficients the equations of motion of the cushion panels can again be solved:

1).O.F

-a/a, -ie'b,7 +c,,jx1

=X,,

n=7, D.O.F. (12)

- In this equation, the coefficients and wave forces are again in accordance with Eq. (2). From the solution of the motions of the cushion panels, the additional hydrodynamic and aerodynamic contributions to the forces on the structure can easily be obtained thus yielding the added mass and damping including cushion effects.

VALIDATION OF COMPUTATIONAL M ETHOD

Results and model tests are given for the actual model and are not extrapolated to any full scale concept. Extrapolation to full scale entails discussion with respect to the influence of the model and stiffness of the aircushion at full scale. This aspect was already described by Moulijn [4] and will not be addressed in this contribution.

MODEL TESTS

Model tests were carried out by Tabeta [8] in towing tank No.1 of the Ship Hydrodynamics Laboratory of Deift University of Technology. This facility measures 140 m x 4.25 m x 2.5 m. It is equipped with a hydraulically operated, flap-type wave maker, by means of which regular or irregular waves can be generated. The test program contained both captive model tests and oscillating tests

A simple rectangular barge model measuring 2.50 m x 0.70 m

was constructed out of wood. The model consisted of a

horizontal deck surrounded by vertical side walls. The depth of the model (wall depth) amounted to 0.50 m. The draft of the barge measured to the lower edge of the side walls was equal to 0.30 m. A vertical wall was added amidship to support the structure by two aircushioris instead of one. The thickness of the walls surrounding the aircushion(s) and the deck plate was 2.0 cm. Prior to all tests, the static (air) pressure in the cushion(s) was increased relative to the ambient pressure to bring the mean water level inside the aircushions 0.15 m below the mean waterline of the barge. The main particulars of the model are presented in table 1. The single cushion configuration is for 87% supported by air, in case of the two cushion configuration this is 85%.

Table 1: Main narticulars of the aircushion model

The test program contained both captive and oscillating tests. Captive tests were carried out in regular head waves, while the model was attached to the vertical legs of a vertical motion oscillator fixed to the carriage of the basin. During these tests the heave forces, pitch moments, cushion pressures and the water elevation inside the cushion (at .v = 0.10 m, y = 0.0 m) were measured.

Forced heave oscillations were carried out with the longitudinal axis of the model at right-angles to the axis of the basin. During these oscillations, the

heave added mass and damping

coefficients were measured, as well as the cushion pressure variations and the water elevation inside the cushion.

Figure 1 shows the test set-up and location of the measuring devices, _h is the location where the water elevation inside the cushion is measured, the cushion pressure variations are measured at locations I and P.

c _&

0.70 m

-f

0.50 m

0.1 ro

Figure 1: Set-up of the model tests

NUMERICAL MODEL

Two Different panel models for both the single cushion and the double cushion configuration

are constructed to show the

influence

of the

panel

size on the

results. The structure supported by one single aircushion is modelled by 364 panels,

2.5 m

- --t

1a0,5rn I If=O.Srn

F2

-0.15 m (att cushion) -(fore cush,on)_V

.1iG -A(0) '7 4 _{Copyright © 2008 by ASME}

i Cushion

case 2 Cushions case Length m 2.50 2.50 Breadth m 0.70 0.70 Draught (structure) m 0.30 0.30 Draught (cushion) m 0.15 0.15

Area of Water Line m2 1.75 1.75

Displacement m3 0.2815 0.2834

while the free surface ¡nside the cushion is modelled by 120 panels, this can be seen in Fig. 2. In the second computation, the cushion ¡s modelled by 480 panels, while the number of panels on the structure remains unchanged.

For the two cushion configuration, the rigid structure is modelled by 400 panels. In case of the first model, the cushions are modelled by 120 panels as shown in Fig. 3. In the second model the aircushions are described by 480 panels.

fi'ure 2: Panel model of the structure with i aircush/on (upside down)

Figure 3: Panel model of the structure with 2 aircush/ons

(upside down)

DISCUSSION OF RESULTS

First the results of the captive model experiments will

be

discussed and compared with those of numerical computations. Subsequently, the results of two different aircushion supported structures oscillating in still water will be analyzed.

CAPTIVE TESTS

Figures 4 - 6 and 10 - 13 show experimental and computational results for two different configurations of aircushion supported structures captive in head seas. The first set of figures describes different quantities

of a structure supported by a

single aircushion. The second set of figures concerns a structure with two aircushions.

First the results of the structure with one

aircushion will be treated, followed an analysis of the body with two cushions.

Figure 4 shows that the heave force on a floating body with one large aircushion is particularly small when the wave length is equal to the length of the structure. In this case the pressure variations in the cushion are nearly zero, as can be seen in Fig. 5, and the only wave forces acting on the structure results from the rigid skirts surrounding the aircushion. The same consideration

holds when the cushion length is equal to a multiple of the wave length. Air pressure variations are largest when L,. /2 = 1.50 and consequently the heave forces will be large as well. The peaks in the heave forces and air pressures variations are not exactly located at L/2=1.50 since the cushion length (L,) is not exactly equal to the structure length (L) . Figure 9 shows that irregular frequencies occur

around L12= 1.50

and

LIA = 2.35. These effects are also noticeable in other figures and can not easily be suppressed in the normal way by applying a lid on top of the structure, since each cushion panel is treated as an individual moving body as described in the second section. The effect of irregular frequencies increases for smaller cushion panels at higher frequencies, besides these numerical errors occur at higher frequencies for smaller cushion panels as can be seen in Figures 4 - 17.

Figure 6 shows the wave elevations at the centreline underneath the structure at x = 0. I m, i.e. approximately amidship. Results of the computations show good agreement with experimental results for low frequencies up to LIA = 1.50. The peaks in the computations appear to be larger than experimental values, particularly at higher frequencies.

Figures 4 - 6 show that the accuracy of the calculations is better when the cushion is described by 120 instead of 480 panels, due to the existence of irregular frequencies.

The effect of the irregular frequencies is larger when the structure is supported by two cushions instead of one as can be

seen in Figures

10 - 13.

Despite these numerical errors, occurring around LIA = 1.50 and LIA = 2.35 , the computations show again good agreement with experimental results.

Figure 10 shows the heave forces in head seas mainly due to air pressure variations in the front and aft cushion as presented in Fig. 11 - 13. Heave forces of a structure supported by two aircushions are approximately equal to those of a floating body supported by one cushion.

The air pressures in the aft cushion are slightly smaller than those in the front cushion since the skirt in middle diffracts the waves. As a consequence less waves will be transmitted underneath the structure to the aft cushion, which is particular noticeable when LIA >2.50. Figures 11 and 12 also show that the air pressure between both cushions is 180 deg out of phase when LIA = ,i/2, with n = 2,4,6...Conversely, air pressure variations of the two cushions are approximately equal but opposite of sign when LIA = n/2, with n = 1,2,3,....

Figure

13 shows the maximum difference of the cushion

pressure variations between the forward and aft cushion. The values are largest when LIA = 0.50 and subsequently decrease with wave length. A peak occurs at LIA = 2.35 due to a large phase difference in aircushion pressure.

Wave elevation in the cushion of an oscillating structure can be well predicted by means of calculations as shown in Fig. 14. Both the maximum values and phases show good agreement and the accuracy would further increase when irregular frequencies were filtered out.

Results of the pitch moment are not presented in this paper since there is serious doubt whether the experimental results are correct. In case of the one cushion arrangement, the measurements of Tabeta [8] show a peak value at LIA. = 1.00 while a minimum is to be expected since air pressure variations inside the cushion are nearly zero. For the two cushion

arrangement, the measurements are approximately zero when

L/A. = 1.00, while in this case the air pressure variations in both cushion are high and 180 degrees out of phase.

OSCILLA TING TESTS

Figures 7 - 9 and 14 - 17 show experimental and computational results of two different aircushion supported structures oscillating in still water. The first set of figures shows the results of the single aircushion supported structure and the second set describes the floating body with two cushions.

Wave elevations were measured during the oscillation tests and are presented in Fig. 7. The figure shows good agreement

between the calculations and experimental values for low frequencies up to the first peak at LIA. = 1.50 , this peak is overestimated due to numerical errors occurring at this wave

length. From LIA = 1.50 to 2.50 ,

computational results are 180 deg out of phase with experimental values. Experiments showed that the wave heights underneath the oscillating body are small when LIA.> 2.50, though values of the computations

remain relatively high.

The heave added mass is well predicted by computational results as can be seen in Fig. 8. The use of smaller panels describing the free-water surface in the aircushion shows little difference in the results of the added mass.

However, results with respect to the heave damping show better results when more panels are used, this is particularly noticeable at higher frequencies. If LIA >2.20, the results of the heave damping are negative in case the free-water surface is described by 120 panels. When the aircushion s modelled by 480 panels, the heave damping is approximately zero for high frequencies. The experimental results are underestimated by the computations when L/A.>1.50 . Results of the calculations show a reasonable good average of the fluctuating experimental

values in case LIA 1.50.

The computations of the cushion pressure variations due to heave oscillations correspond well with the experimental results as illustrated n Fig. 9.

When comparing Fig. 15 with Fig. 7, it can be seen that the wave elevation (at x = 0.1 ni,y

= 00m )

underneath an oscillating structure with two aircushions is approximately the same as for a structure with one cushion.

Figure 16 shows the heave added mass and damping for a structure supported by two cushions. The experimental values are approximately the same as for a structure supported by a single aircushion. The heave added mass is again well predicted by the numerical approach. The analysis of the heave damping is

the same as

for a single aircushion supported structure discussed before.

Figure 17 shows the pressure variations in the forward cushion due to heave oscillations. Unfortunately no data is available for the aft cushion or the pressure difference between both cushions. Nevertheless, Fig. 17 shows good agreement between experimental and computational results.

CONCLUSIONS

The heave force, heave added mass and cushion pressure variations can be well predicted by means of 3D diffraction calculations.

The calculated wave elevations underneath the structure inside the aircushion correspond well with experimental values, though the peaks are over-predicted mainly due to the effect of irregular

frequencies.

These numerical errors cannot be suppressed in the usual way by applying a lid on top of the structure since the free-water surface inside each cushion is modelled by panels which are free to oscillate individually in vertical direction.

In addition, cushion panels should be small in order to minimize the difference between experimental and computational results in heave damping at high frequencies.

In general it can be concluded that the results of model tests of different aircushion supported structures can be well predicted

by means of 3D diffraction calculations. REFERENCES

Burns, G.E. and Holtze, G.C., Dynamic submergence analysis of the Khazzzan Dubal subsea oil tanks. Offshore

Technology Conference, 1972, paper no. OTC 1667.

Maeda, H., and Washio, Y., Osawa, H., Rheem, C-K., Ikoma, T., Onishi, Y. and Anta, M., Hydro-elastic Response

Reduction System of A Very Large Floating Structure with

Wave Energy Absorption Devices, Proceedings of OCEANS

00, 2000, pp.527-531

Maeda, H., Rheem, C-K., Washio, Y., Osawa, H., Nagata, Y., Ikoma, T., Fujita, N. and Anita, M., Reduction Effects of Hydroelastic Responses on a Very Large Floating Structure With Wave Energy Absorption Devices Using OWC System, Proceedings of the 20th International Conference on Offshore Mechanics and Arctic Engineering (OMAE'Ol), 2001, pp. 49-58

Moulijn, J., Scaling of air cushions dynamics. Report 1151, Laboratory of Ship Hydrodynamics, Deift University of Technology, DeIft, 1998

Pinkster, JA., The effect of air cushions under floating

offshore structures. Proceedings of Boss'97, 1997, 143-158.

Pinkster, JA., Fauzi, A., Inoue, Y. and Tabeta, S., The behaviour of large air cushion supported structures ¡n waves.

Hydroelasticity in Marine Technology, 1998, 497-506.

Pinkster, JA. and Meevers Scholte, E.J.A., The behaviour of a large air-supported MOB at Sea. Journal of Marine

Structures, 2001, 14, 163-179.

Tabeta, S., Model experiments on barge type floating

structures supported by air cushions. Report 1125,

Laboratory of Sh,o Hydromechanics, DeIft University of Technology, DeIft, 1998.

9. Van Kessel, J.L.F. and Pinkster, JA. The effect of aircushion division on the motions of large floating structures.

Proceedings of the 26th International Conference on

Offshore Mechanics and Arctic Engineering (OMAE'07), ASME, 2007, No. OMAE2007-29512.

Heave Force in Head Seas

E z 0) o o LL. o 0.00 Figure 5: 12 4 12 10 8 6 4 2 e 2 o O exp:= 0.01 [m] X exp. = 0.02 [ml -CaIc: 364+120 panels - CaIc: 364+480 panels O eap: = 0.01 1ml X exp:=002m) -CaIc: 364+120 panels - CaIc: 364+480 panels 0.50 1.00

Wave Elevation Underneath a Captive SES at(x = 0.1, y = 0.0)

O exp: = 0.01 [ml X exp:=0.02[m[

-CaIc: 364+1 20 panels - CaIc: 364+480 panels

Cushion Pressure Variations of a Captive SES in Head Seas

1.50 L/A 2.00 2.50 3 00 180 a û. 60 120 a a

r

360 300

Van Kessel, J.L.F. and Pinkster, JA. "The effect of aircushion division on the structural loads of large floating offshore structures," Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering (OMAE'07), ASME, No. 0MAE2007-29513

Van Kessel, J.L.F. and Pinkster, JA. "Wave-induced structural loads on different types of aircushion supported structures," Proceedings of ISOPE'07, 2007.

Phase of Heave Force in Head Seas

240 o 360 300 240 a 60 150 a -a

r

0-150 o 0.00 210 90 30

-3o

O exp: = 0.01 [mi X exp:=0.02lmj -CaIc: 364*120 panels - CaIc: 364+480 panels O exp:= 0.01 [m[ X exp:=0.02[m[ -CaIc: 364*120 panel - CaIc: 364+480 .anel o o 0.50 o 1.00 o exp: = 0.01 Im] X exp:,=0.02(m] -CaIc: 364+120 panels - CaIc: 364+480 panels 0.50 1.00 o o

Phase of Cushion Pressure Variations of a Captive SES in Head Seas

o

1.50

L/A

2.00

Cushion pressure variations in head seas of a captive structure supported by one aircushion

Phase of Wave Elevation Underneath a Captive SES at (x = 0.1, y = 0.0)

o

o

0.00 0.50 1.00 1.50 2,00 2.50 3.00 -210

L/A L/A

Figure 6: Wave elevations in head seas underneath a captive structure supported by one aircushion

2.50 O O 3.00 00 7 Copyright © 2008 by ASME 0.00 0.50 1.00 150 2.00 2.50 3.00 0.00 0.50 1.00 1.50 2.00 2.50 3.00 LIA LIA

Figure 4: Heave forces in head seas on a captive structure supported by one aircushion

E E C o o E 1'3 o s) > 16

Figure 7: Wave elevations underneath an oscillating aircushion supported structure with one cushion 14 12 lo 6 4 2 o 0.00 2.0 -1.8 16 1.4 - 12-(I, ,O8 O6-w

-04

<0.2 0.0 0.00 o exp:0.01 [m) X exp: = 0.02 [m] CaIc: 364+120 panelS - CaIc: 364+480 panels o exp:=O.01 [m] X exp:=0.O2[m] -CaIc: 364+120 panels - Calc: 364+480 panelS o

'ø°o0

o 050 1.00 1.50 2.00 2.50 3.00 120 -L/A 0.50 1.00 L w2) g ) 2.00 2 50 300 -10

Figure 8: Heave added mass and damping of an aircushion supported structure with one cushion

Cushion Pressure Variations Phase of Cushion Pressure Variations due to Heave Oscillations in still water due to Heave Oscillations n still water 45 40 30-25 s) 20 s) Cn 15 10 5 0 0.00 o exp: = 0.01 Im) X exp=002[m] -CaIc: 364+120 panels - Calc: 364-i-480 panels

0.50 1.00 1.50 2.00 Lw2! (2g ir) o w u) Cs -c Q-300 240 180 120 C) 5) -60 0) -90 -120 Cs -c Q. -150 2.50 3.00 -180 60 o o-00 -60

00 e e

o o exp:=0.O1Im] X exp:=0.02[m) -Calc: 364+120 panels - Calc: 364-i-480 panels

0

cP..

0.50 1.00

Figure 9: Cushion pressure variations of an oscillating structure with one aircushion

0 0 LIA Lw2! (2g ir) o o

oI'I.

2,00 2.50 o 000 Lw2! (2g ir) 0 0.50 1.00 1.50 2.00 2.50 3.00 o exp: = 0.01 fmJ X exp: = 002 [m)

-CaIc: 364+1 20 panels - CaIc: 364+480 panels

O exp: = 0.01 [m) X exp:=0.02)m)

-CaIc: 364+120 panels - CaIc: 364+480 panels

8 _{Copyright © 2008 by ASME}

Wave Elevation Underneath an Oscillating SES Phase of Wave Elevation Underneath at(x = 0.1, y = 0.0) an Oscillating SES at (x = 0.1, y 0.0)

2.0 1.5 1.0 E 6 0.5 o

z

0)0.0 C

Heave Added Mass Heave Damping

I4 8 E

z

o LC..2 o 0.00 Figure 10: 12 2 o 12 10 E

Q-aS

e 5,4 w Q-2 o O Exp:0.01 [mJ X Exp: = 0.02 [m] ale: 400+120 panels

-

- C: 400+480 panels

Heave Force in Head Seas

0.50 1 .00

Heave forces in head seas on a captive structure supported by two aircushions

O Exp:= 0.01 [m] X Exp; = 0.02 [m] -Calo: 400+120 panels - Calo; 400+480 panels O Exp: = 0.01 [mJ X Exp; 0.02 [m[ -Cale: 400+120 panels - Cale: 400+480 panels o Exp: = 0.01 [ml X Exp:=0.02[m] -Calc: 400+120 panels - Cale: 400+480 .aneisr 1 .50 LIA 2.00 2.50

Figure 12: Aft cushion pressure variations in head seas of a captive structure supported by two aircushions Difference in Cushion Pressure Variations

Between Forward and Aft Cushion in Head Seas

3.00 360 300 240 w 120 a Cs

r

û. 60 360 300 240 '180 w V l20 a CS

r 60

Q. O o 200 150 100

0-0.00 0.50 0.10 -60 50 o) V w 0.00 0,50 (S Cs

r

Q. 100

-Phase of Heave Force in Head Seas

O Esp: = 0.01 (m] X Exp: = 0.02 [m) -Calo: 400+120 panels - Cale: 400+480 panels. O Exp: = 0.01 [mi X Exp; = 0.02 [m[ -CaIc; 400*120 panels - CaIc: 400+480 panels o 1.00 I_00 o Exp: = 0.01 (m] X Exp: = 0.02 [m] -Cale: 400+120 panels - Cale: 400+480 panels o Exp:=0.01 [m] X Exp: = 0.02 [mJ -Calo: 400+120 panels - Cale: 400+480 panals 1 .50 LIA X o o 2.00 "C _3.00 o o

Phase Difference in Cushion Pressure Variations Between Forward and Aft Cushion in Head Seas

o

o o

Figure 13: _{Difference in air pressure variations between the forward and aft cushion of a captive structure supported by} two aircushions in head seas

g Copyright © 2008 by ASME

0.00 0.50 1.00 1.50 2.00 2.50 3.00 0.00 0.50 1 .00 1.50 2.00 2.50 3.00

LIA LIA

Figure 11: Forward cushion pressure variations in head seas of a captive structure supported by two aircushions Aft Cushion Pressure Variations Phase of Aft Cushion Pressure Variations

of a Captive SES in Head Seas of a Captive SES in Head Seas

j4

w û. o 2 12 10 2.00 2.50 3.00

Forward Cushion Pressure Variations Phase of Forward Cushion Pressure Variations

of a Captive SES in Head Seas of a Captive SES in Head Seas

.8 7 C o4 o E

ti -

_w

>0_

2.0 1.8 1.6 1.4 1.2 cs 0.8 -0.6 G) o 0.4 0 0.2 -00 45 40 30 25 G). 20 15 w & lo 5 o O Exp:=0.01fm] X Exp: = 0.02 [m[ -CaIc: 400+120 panels - CaIc: 400480 panels

Figure 14: Wave elevations ¡n head seas underneath a captive structure supported by two aircushions Wave Elevation Underneath an Oscillating SES Phase of Wave Elevation Underneath

at (x = 0.1, y = 0.0) an Oscillating SES at (x = 0.1, y = 0.0) 16 14 1 o Exp:= 0.01 [m] X Exp: = 0.02 [ml 12 -Calc: 400*120 panels 10 - CaIc: 400+480 panels, - 8 o E 6 4

t

ø 2 > o O Exp:..0.01[mJ X Exp: 0.02 [m] -CaIc: 400120 panels - CaIc: 400+480 panels o Exp:=0.01[m] X Exp. = 0.02 [m) -Calc: 400+120 panels - CaIc: 400+480 panels V (i 3.00 -300 L/A 210 150 90 30 -9° ca -C 0- -150

Figure 15: Wave elevations underneath an oscillating structure supported by two aircushions

Heave Added Mass Heave Damping

E z 2.0 -1.5 1.0 -0.5 0) 0.0 0.00 a 0.00 050 1 00 1.50 2.00 2.50 3.00 -1.0 L.i2/ (2g ir)

Figure 16: Heave added mass and damping of an Forward Cushion Pressure Variations due to Heave Oscillations in still water

-60 C) Q) _-90 ( -120-Cs -C Q--150-30 o 0. 0 -30 O Exp: 0.01 [m] X Exp: = 0.02 [m] -CaIc: 400+120 panels - CaIc: 400+480 panels o 0 o

OX

_o O

Os

- o i. Lw2/ (2g ir) aircushion supported structure with two cushions

Phase of Forward Cushion Pressure Variations due to Heave Oscillations in still water

Figure 17: Forward cushion pressure variations of an oscillating structure with two aircushions o O Jo.o o L 0 50 1.00 1.50 2.00 250 3.00 O 2.50 3.00 O Exp: 0.01 Em] X Exp:=0.02[m[ -CaIc: 400+120 panels - Calc: 400+480 panels O Exp: = 0.01 [m] X Exp:=0.02[rn[ -CaIc: 400+120 pan s - CaIc: 400+480 -ne 10 Copyright © 2008 by ASME

Wave Elevation Underneath a Captive SES Phase of Wave Elevation Underneath

at(x = 0.1, y = 0.0) _{a Captive SES at (x = 0.1, y = 0.0)}

0,00 0.50 1.00 1.50 2.00 2.50 300 -180

Lc..i21 (2g ir) _{Lw2/ (2g ir)}