Project Thesis Larsen

8/12/2019 Project Thesis Larsen

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NTNU

Norwegian University of Science and Technology

Department of Marine Hydrodynamics PROJECT THESIS

Address:

NTNU

Department of Marine Hydrodynamics

N-7!" Trondheim

#ocation

Marinte$nis$ Senter

%& Nielsens vei "'

Tel& (7 7) *!**)*

+a, (7 7) *!**.

Title:

Modelling of wave induced motions of a SPAR buoy in MOSES

Student: Truls Jarand Larsen

elivered: !"#"$#!""!

%umber of &ages:

94

Availability:

MOSES

Wave induced motions

SPAR BuoyOdd M. Faltinsen

Advisor:'eywords:

Abstract:

This wo! is "ased on the use o# MOSES $MultiO%eational Stuctual En&ineein& Simulato'( which is an analysis

tool #o almost anythin& that can "e %laced in the wate. A )uite com%ehensive %o&ammin& lan&ua&e that allowsyou to do cou%led analysis o# S%a %lat#oms in which dam%in& e##ects #om mooin& lines and ises ae included.

The divesity o# the %o&am is #uthe e*%essed tou&h the handlin& o# a newly e*%lained %henomenon( the

Mathieu insta"ility.

Altenative hull sha%es with im%oved heave motion chaacteistics ae investi&ated( showin& inceased heave

dam%in& when di##e #om the classical hull sha%e.

The e##ect o# mooin& system on the linea motion es%onse is investi&ated. +t is seen that even a vey sti## mooin&

system has small in#luence on the linea wave #e)uency es%onse.

The esults #om the cou%led analysis show the im%otance o# includin& mooin& line dynamics and ise #iction

when %edictin& the S%a es%onse. The es%onse was si&ni#icantly educed and the Mathieu insta"ility

%henomenon was su%%essed. E*istin& S%as have dee% da#ts to educe the wave loads and conse)uently the

heave motion. Taditionally( the mooin& line dynamics and ise #iction wee i&noed in estimatin& the heave

es%onse. Since this e##ect is im%otant( the da#t o# the S%a can "e educed while maintainin& an acce%ta"le

heave es%onse. Reduction in S%a hull da#t can educe #a"ication costs su"stantially and as a esult the S%a

solution will "e moe cost e##ective.


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Ac(nowledgement

This %o,ect thesis has "een witten unde the su%evision o# two %eo%le that + would li!e to

than!( Odd M. Faltinsen( su%eviso #om the institute and -on Ei! Bo&en( su%eviso #om the

com%any $+nocean as'.

+n addition + would li!e to than! the de%atment o# +nocean in which + have s%ent most o# these

twenty wee!s.

This wo! concludes my education

OS/O ( 0.. 1 2332

Tuls -aand /asen

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)ntroduction

As a temination o# my Maste o# Science de&ee in Maine Technolo&y at the T5

$owe&ian 5nivesity o# Science and Technolo&y' in Tondheim( + am witin& a thesis at the

de%atment o# Maine 6ydodynamics in co1o%eation with +nocean as. This thesis is a

conclusion o# a 23 wee!s wo!( statin& the 27 tho# -anuay with a hand1in date the 23 tho# -une.

The assi&nment has the title8 Modelling of wave induced motions of a SPAR buoy

in MOSES:( and the e*act wodin& is8

The candidate has to "e #amilia with MOSES $Multio%eational Stuctual En&ineein&

Simulato' and #ind out its limitations in elation to wave #e)uency motions( slowly vayin&

motions in ; de&ee o# #eedom and dynamic sta"ility $Mathieu insta"ility' in oll and %itch. 6ow

MOSES handles cuents( wind and viscous dam%in& ae details that have to "e discussed.

Futhe on it will "e clai#ied how cuents in the moon%ool and the e##ect o# ises and mooin&

ae handled. The candidate will citically indicate any %ossi"le de#iciency.

As a %at o# the thesis a calculation o# the linea wave induced motions o# a s%a "uoy

has to "e caied out. These esults ae com%aed with the calculations done "y 6aslum in his

. At the end the candidate will investi&ate the in#luence o# some

chan&es in the hullsha%e.

As #a as the time allows it the candidate will im%lement the lon& wavelen&th model #o

linea wave induced motions o# a S%a( as in =6aslum 2333>( whee cuents in the moon%ool

ae consideed. Futhe on the model o# 6aslum #o dynamical insta"ility in oll and %itch will "e

im%lemented.:

This assi&nment is "ased on the use o# MOSES( which is an analysis tool #o almost

anythin& that can "e %laced in the wate. +t is a )uite com%ehensive %o&ammin& lan&ua&e

that + #ist &ot to !now duin& a simila assi&nment in Stolt O##shoe in Pais. + have considea"ly

im%oved my ?MOSES1!nowled&e@ "y wo!in& on this thesis.

All the linea esults will "e com%aed to =6aslum 2333>. +n addition a non1linea time

domain analysis has "een caied out. The esults have "een used to %oint out the insta"ility

%henomenon as well as othe as%ects that may "e o# inteest in elation to the time domain(

such as the e*teme es%onse duin& a lon& lastin& $2 hous' huicane.

One o# the moe inteestin& as%ects o# the assi&nment is to see how MOSES handles

the Mathieu insta"ility. This %at has thee#oe "een em%hasised in my wo!.

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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as

As said( + will com%ae most o# my esults with the one %oduced in the


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E*ecutive summary

A#te ceatin& the hull the linea motion es%onse wee calculated. They ae e*%essed as

RAO@s and have "een com%aed to the linea esults %oduced "y 6aslum. The a&eement

"etween the esults is &ood and act as vei#ication #o the MOSES model. The e##ect o# mooin&

system on the linea motion es%onse is investi&ated. To incease the e##ect #om the mooin&

system( the mooin& lines wee modelled )uite sti##. Even vey sti## lines had small in#luence on

the linea wave #e)uency es%onse.

e*t %at o# the thesis is "ased on the time domain. To &et the wanted level o# con#idence #om

the esults a ty%ical thee hous huicane analysis has "een caied out( showin& the heave

and %itch es%onse #o a mooed "uoy. While the de#lections in %itch ae )uite la&e( the heave

es%onse eveals the advanta&es o# a S%a "uoy. The huicane used is a COM huicane with

6sD2.2m and TD4sec( which %oduces a heave es%onse at ma*imum one and a hal# mete.

To incease the dam%in& in heave altenative hull sha%es have "een tied out. When altein&

the lowe %at o# the "uoy( eithe "y addin& a cicula disc sli&htly "i&&e than the est o# the

S%a o "y inceasin& the diamete at the "ottom section o# the S%a( the heave dam%in&

inceases.

An inteestin& as%ect o# the assi&nment was to see how MOSES handles the Mathieu

insta"ility. This insta"ility is a )uite newly e*%lained %henomenon that is testi#ied "y

com%licated theoy. By showin& this Mathieu insta"ility in a time domain analysis( the %o&am

eveals its divesity.

The esults #om the cou%led analysis show the im%otance o# includin& mooin& line dynamics

and ise #iction when %edictin& the S%a es%onse. The es%onse was si&ni#icantly educed

and the Mathieu insta"ility %henomenon was su%%essed. E*istin& S%as have dee% da#ts to

educe the wave loads and conse)uently the heave motion. Taditionally( the additional

dam%in& #om mooin& lines and ises wee i&noed in estimatin& the heave es%onse. Since

this e##ect is im%otant( the da#t o# the S%a can "e educed while maintainin& an acce%ta"le

heave es%onse. Reduction in S%a hull da#t can educe #a"ication costs su"stantially and as

a esult the S%a solution will "e moe cost e##ective.

MOSES does not allow you to alte the %aametes in the di##action calculations. onse)uently

to im%lement the lon& wavelen&th model #o linea wave induced motions o# 6aslum $as

%o%osed in the intoduction' is had to accom%lish.

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Table of contents

ACKNOWLEDGEMENT.............................................................................................................2

INTRODUCTION.........................................................................................................................3

EXECUTIVE SUMMARY.............................................................................................................5

TABLE OF CONTENTS...............................................................................................................6

1.0 INOCEAN AS A BRIEF PRESENTATION OF TE COMPANY.......................................!

2.0 MOSES CALCULATION PROCEDURES AND GENERAL ISSUES..............................."

3.0 TE SPAR BUOY................................................................................................................1#

3.1 MOVEMENTOFTHESPAR ..........................................................................................................16

#.0 TE PROCESSES...............................................................................................................1"

4.1 RAO- FREQUENCYDOMAIN........................................................................................................ ..18

4.2 TIMEDOMAIN................................................................................................................................20

4.2.1 Low frequency behaviour .....................................................................................................20

4.2.2 The damping problem ..........................................................................................................22

4.2.3 Hurricane analysis................................................................................................................23

5.0 TE MATIEU INSTABILITY.............................................................................................26

6.0 COUPLING EFFECTS.........................................................................................................30

!.0 ALTERNATIVE ULL SAPES.........................................................................................32

".0 RECOMMENDATIONS FOR FURTER WORK................................................................35

$.0 REFERENCES.....................................................................................................................3!

LIST OF FIGURES.....................................................................................................................3"

SYMBOLS AND NOMENCLATURE.........................................................................................3"

APPENDIX.................................................................................................................................3$

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7/39

+,a&ter - -#" )nocean as . a brief &resentation of t,e com&any

+nocean as was esta"lished in 99; in Oslo( and also has o##ices in Stavan&e and 6ouston.

+nocean is a technolo&y com%any within naval achitectual desi&n( en&ineein& and maine

o%eations( sevin& ma,o o##shoe com%anies and shi% ownes at home and a"oad. +nocean is

set to ta!e %at in the #utue develo%ment o# #loatin& stuctues and maine o%eations.

Engineering

+nocean deals with evey %hase o# maine en&ineein&( such as &lo"al and local stuctual

desi&n and calculations( hydodynamic and hydostatic calculations( ise and mooin&

calculations( technical dawin& and documentation and the desi&n o# s%ecial tools.

Marine operations

+nocean analyses( %lans( e*ecutes and leads maine o%eations and mo"ilises vessels #o

o##shoe constuction wo!. The com%any@s aim is to educe o##shoe weathe1elated delays to

a minimum thou&h usin& s%ecial tools and advanced simulations. +nocean also %ovides the

%esonnel needed to %e#om the actual o##shoe o%eations.

In-house design and products

+nocean o##es a an&e o# %oducts( such as8

/o%hius semi1su"mesi"le

Fle*istin&e

Ancho handlin& and stand1"y desi&n Steel %oduction /1ise desi&n

1O


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+,a&ter ! !#" MOSES . calculation &rocedures and general issues

As a %at o# this assi&nment it will "e e*%lained a #ew thin&s a"out the MOSES@ calculation

%ocedue and the handlin& o# some &eneal issues in elation to analysis o# the SPAR "uoy.

This is im%otant #o the evaluation o# the elia"ility in the esults and in addition "ein& a"le to

ma!e a com%aison with the esults o# the


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JDefines the co-ordinates for points

-33 3.3 3.3 3.3

-3 3. 3.3 3.3

-32 23. 3.3 3.3

- 3 3. 3.3 N.3

J

JSupplementary loads

Gdesci"e loadK&ou%

M-TS -3 .N

J

Ginstate loc s%a 3 3 1232.N 3 3 3

These ae ,ust a #ew e*am%les #om a Moses #ile. +n addition to these commands( the s%eci#ic

commands #o %e#omin& the analysis and e&ulatin& the out%ut $whee and how' ae many

and have to "e ada%ted to each case.

Fo moe details a"out the Moses #iles( see A%%endi* 2 and .

Ste%wise and "ie#ly e*%lained( this is how MOSES #unction8

. Statin& out "y ceatin& a model o# a SPAR with s%eci#ied de&ee o# accuacy. This

is done "y de#inin& %oints at the end #ace o# the cylinde #ollowed "y ceatin&

%anels "etween these %oints. The model is now a cylinde consistin& o# %anels(

which has to "e im%ated with %hysical )ualities that coes%onds to the "uoy( i.e.

mass disti"ution $cente o# &avity( %atial loads etc.' and some mateial

%o%eties. Futhe on you can model mooin& and ises to include thei sti##ness.

The model is then ?%laced@ in e)uili"ium with s%eci#ied da#t( and all the hydostatic

%o%eties ae then calculated.

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2. By usin& the model and the &eomety "eneath the wate su#ace( the %otential

disti"ution o# the %essue on the %anels is &iven "y the lineaied Benoulli

e)uation

56

g!p

+= $2.'

whee

= #luid density

=g acceleation o# the &avity

=! de%th

= velocity %otential

By inte&atin& the %essue ove the "ody we o"tain the hydodynamic #oces on a

%otion o# the "ody. The %o&am now calculates the added mass( dam%in&

matices and in addition all the hydodynamic %o%eties.

. On "asis o# the hydodynamic #oces the linea motions in si* de&ee o# #eedom

ae estimated as the RAO $Res%onse Am%litude O%eato'. This is stai&ht#owad

done "y usin& the e)uations o# motions #o a #eely #loatin& "ody8

[ ] 56562

"

"#$%& '(

('(('(('('( =+++=

$,D((;'

$2.2'

whee

='(& "ody mass

='(% hydodynamic mass $added mass'

'($ dam%in& coe##icient

='(# estoin& coe##icient

= "ody movement

='" e*citation #oce

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The RAOs ae consideed as tans#e #unctions and ae #uthe #ound "y estimatin&

the coe##icients in the e)uations o# motions #o each %eiod de#ined( and #inally end

u% with the coes%ondin& RAO. These ae de#ined as vectos in si* de&ee o#

#eedom and e*%esses the lineaied wave induced motions in the #e)uency

domain.

Futhe on it is im%lied that the es%onse is linea such that the RAOs can "e

multi%lied with a chosen wave s%ectum( to #inally o"tain the es%onse s%ectum

$e*%essed as RMS values Root Mean S)uae'8

565656 -

") *+%,* = $2.'

whee

=56)* es%onse s%ectum

=56"* wave s%ectum

The ma,o disadvanta&e with s%ectal es%onse is that this es%onse is a%%lica"le

to a sin&le envionment and thus the %ost %ocessin& o%tions ae limited.

4. So #a( all the static %o%eties have "een #ound. e*t one wishes to analyse the

movements in elation to a time seies. That leads us to the sten&th o# MOSES(

the time domain.

As a statin& %oint it utilises the hydodynamic %o%eties calculated in the

#e)uency domain to satis#y the "asic e)uations o# motion. These e)uations ae

inte&o1di##eential. This means that the un!nown is %laced in an inte&al

e*%essed as the deived. +n a linea system a !nown deceleation #unction is

included in the inte&and. This deceleation #unction is estimated #om the added

mass and dam%in& coe##icients( which ae de%endent on the #e)uency. This

e)uies &eat numeical accuacy that in %actice can lead to inaccuacy.

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The %o&am will %esistent calculate and "in& u% to date the %aametes li!e the

cente o# "uoyancy( wate%lane aea etc. as the "uoy moves and the wet su#ace

chan&es. The hydodynamic #oces ae calculated at the dis%laced %osition and the

#inite am%litude e##ect o# the chan&in& wate%lane aea is ta!en into account. The

dynamics o# the system ae in othe wods ta!en cae o# and the non1linea wave

induced motions ae #ound( i.e. the %esence o# one o# the Mathieu insta"ility

%henomena will "e( accodin& to the theoy( detected duin& a time domain

analysis. The dynamic sta"ility can "e vei#ied in all si* de&ee o# #eedom. The

calculations ae "ased on a cuent envionment $wave s%ectum( si&ni#icant wave

hei&ht and %ea! %eiod'.

N. A #unction allows one to scale the wave e*citation #oce in the time domain. This

means that you can $in %ecenta&e' s%eci#y the inteaction #om the wave

e*citation #oce on the model. Fo e*am%le eo( which esults in the diect wave

#oce not "ein& a%%lied to the system. By this you can investi&ate the low

#e)uency "ehaviou( i.e. slowly vayin& motions.

;. uents and wind can easily "e modelled "y s%eci#yin& the chaacteistic aea and

de#inin& the velocity and diection o# the load. As an altenative the wind can "e

s%eci#ied "y a wind s%ectum. E##ects #om wind and cuents ae howeve not

a%%lied in this model.

. The %o&am allows you to model the SPAR with ises and all the &eometical

&ad&ets inside the moon%ool. +t is di##icult to %edict how the %o&am mana&es to

simulate the com%le*ity inside the moon%ool with es%ect to the dam%in& and the

added mass e##ects( "ut it is li!ely to thin! that the %o"lem will not "e handled

satis#actoy. Altenatively the "uoy can "e sealed at the "ottom and e&aded as a

closed cylinde. This is not #a #om the eality( since the actual o%enin& in the

moon%ool( "etween the ises and the "uoyancy tan!s etc.( is )uite small. The

model used hee is thee#o consideed as a closed cylinde.

7. At last in this "ie# MOSES ?intoduction@( a #ew wods a"out the envionment.

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+t is %ossi"le to choose wave s%ectum $+SS o -OSWAP' o any sied e&ula

wave( e%esented "y the diection( the wave hei&ht and %ea! %eiod.

The wave is e%esented "y a cosine wave

D a cos$t Q !* cosQ !y sin' $2.4'

D wave headin&

R D RAOcos$t Q '

D %hase lead

The envionment diections ae as #ollows8

- ") -

Fi&. 2.. MOSES Re#eence =/asen 3>

270

225

180

135

0

45

0

315

!

"

O


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+,a&ter / /#" T,e S&ar buoy

A s%a %lat#om is a la&e vetical cicula cylinde with a la&e da#t that educes the heave

es%onse si&ni#icantly and %emits i&id ises and su#ace tees( i.e. the motion es%onse ae

cucial #o the S%a "uoy. on#i&ued with oil stoa&e and su#ace com%leted well( a s%a may

"e a"le to com"ine the "est chaacteistics o# the T/P $Tension /e& Plat#om' and FPSO

$Floatin& Poduction Stoa&e and O##loadin&' #o #ields whee the esevoi can "e eached #om

one dillin& cente =MPT 997>.

Fi&. .. +sometic view with mooin& Fi&. .2. Font view with mooin&

When ceatin& the hull( di##eent levels o# accuacy wee tied out. Fist a hull was ceated in a

%o&am called Fem&en. The model was made "y hoiontal %anels evey 3 thmete and

%anels vetically( "e#oe it was conveted into a MOSES model. This &ave a la&e num"e o#

%anels( which was un%actical to wo! with. To co%e with this %o"lem( MOSES has a #unction

that allows you to e#ine you model at a s%eci#ied level o# accuacy. All the hoiontal %anels

wee then deleted and le#t a model consistin& o# seventeen vetical %anels. This made the wo!

easie and not so time demandin&. As e*%lained ealie( the e%oduction o# the hydodynamic

data"ase e)uied a lot o# time. By usin& a )uite ou&h mesh this was no lon&e a %o"lem.

When the analysis e)uied seveal di##eent data"ases $di##eent an&e o# %eiods'( the mesh

was chosen )uite ou&h and a #ine mesh was chosen when the data"ase was used #o the non1

linea analyses.


15/39


The main %aticulas o# the s%a used in this assi&nment ae the same as used in =6aslum

2333>( e*ce%t some small ad,ustments in the diamete to o"tain the hydostatic %o%eties as

coect as %ossi"le. A#te the im%atment o# the &eomety( MOSES calculated a cente o#

"uoyancy too low( com%aed to the s%a in =6aslum 2333>. This lead to ne&ative CM. By addin&

moe "uoyancy in the u%%e section( the cente o# "uoyancy ascended and the CM value

"ecame close to the actual one.

A lot o# wo! has "een %ut down to vei#y the MOSES model and conse)uently "e a"le to

com%ae it to the model o# =6aslum 2333>. Many o# the static %o%eties not &iven in the


16/39


%etension in each #ailead is set to 433 !. A discussion o# the mooin& lines and thei

in#luence on the linea wave #e)uency motions will #ollow late.

+n the e##ot o# modellin& the i&ht mooin& system( di##eent %aametes have "een evaluated

and tied in the model. The %etension( the wei&ht and the e1modulus o# the lines ae

%aametes that ae continuously chan&ed and ada%ted. The whole %ocess culminated in

modellin& an e)uivalent mooin& line at each #ailead.

6oweve( to detect the Mathieu insta"ility in section N.3 the mooin& lines ae deactivated.

/#- Movement of t,e SPAR

A i&ht hand co1odinate system is a%%lied as illustated in #i& ...

Fi& ...The si* de&ees o# #eedom

E*istin& s%a %lat#oms have dee% da#ts to educe the wave loads and conse)uently the heave

motions. Taditionally( the dam%in& #om mooin& lines and ises was i&noed in heave

es%onse analyses. By simultaneously %edict the dynamic es%onse o# the s%a( mooin& lines

and ises one has evealed that mooin& lines dynamics and ise #iction can have si&ni#icant

e##ect on the s%a heave es%onse. As a conse)uence the da#t o# the s%a can "e educed and

still maintain an acce%ta"le heave es%onse. Reduction in s%a hull da#t can educe the

- "2 -

yaw

pitch

roll

Sway 6y5

S/rge 6,5

Heave 65


17/39


#a"ication and tans%otation costs( which will esult in ma!in& s%a solutions moe cost

e##ective. =OT 2372>

+m%otant ?ty%es@ o# motions ae the slow di#t motions. They ae caused "y non1linea e##ects

#om waves( wind and cuents. These motions aise #om esonance oscillations and a%%ea in

su&e( sway and yaw #o a mooed "uoy. /ow #e)uency "ehaviou is consideed in section

4.2..

+n addition to the slow di#t motion $low #e)uency' a #loatin& stuctue can e*%eience wave1

#e)uency motion( hi&h1#e)uency motion and mean di#t. /inea e*citation #oces mainly cause

the wave1#e)uency motion( while the hi&h1#e)uency motion and mean di#t ae caused "y

esonance oscillations =Faltinsen 93>.


18/39

SPAR

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 10 20 30 40 50

T [sec]

Pitch[deg/m]

Moored

Free floating

SPAR

0

5

10

15

20

88 90 92 94 96 98 100 102

T [sec]

Pitch[deg/m]

+,a&ter 0 0#" T,e Processes

Both the time domain and the #e)uency domain %ocess &ive ade)uate solutions in most

cases. The time domain %ocess does %o%ely account #o all as%ects o# a %o"lem "ut is

com%utationally e*%ensive. A solution in the #e)uency domain is in many cases a &ood

altenative solution( which is much less time demandin&.

The theoy "ehind the time and #e)uency domain is e*%lained in section 2.3.

0#- RAO1 fre2uency domain

The movements o# the SPAR ae e*%essed statically "y the RAO $Res%onse Am%litude

O%eato' as a #unction o# the si* de&ees o# #eedom $Su&e( sway( heave( oll( %itch and yaw'.

+n the #ollowin& #i&ues( a %esentation o# the lineaied motions in heave( %itch and su&e ae

&iven. The calculations ae done with and without mooin& and the esults ae shown in the

same dia&am.

6ow MOSES calculates the tans#e #unctions( ae e*%lained ealie in section 2.3.Fi&. 4... Pitch RAO Two #e)uency intevals( to illustate the natual %eiod in %itch.

- ". -


19/39

SPAR

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

3 N E3 EN 23 2N B3 BN 43 4N

T [sec]

Surge

3m4m5

Moored

6ree floating

SPAR

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30 35 40 45

T [sec]

Heave

[m/m]

Moored

Free floating


Fi&. 4..2. 6eave RAO Fi&. 4... Su&e RAO

The s%a is #loatin& with a da#t dD232.Nm. The main %aticulas o# the s%a ae &iven ealie in

section .3.

6oweve( the tans#e #unctions $RAO Res%onse am%litude o%eatos' ae de#ined as the

#e)uency de%endent steady state motion es%onse am%litude divided "y the wave elevation

am%litude =6aslum 2333>8

RAOi$T' Da

i

=m0m> $4.'

i D =(2((4(N(;> D de&ees o# #eedom

+n the is &ood( as well as the a&eement "etween 6aslum and the MOSES1esults

%esented hee.

As ealie e*%lained( the mooin& system used is vey sti## to incease its e##ect.


20/39

Free floating SPAR

-200

-150

-100

-50

0

50

100

150

200

0 10 20 30 40 50

T [sec]

Phase[deg]

Heave

Pitch!"rge


Fi&. 4..4 show that %itch and su&e motions ae in %hase with each othe( and they ae 93

de&ees out o# %hase com%aed to the

wave. This means that they ae

conti"utin& to dis%lacements o# the

dec! simultaneously. +t is shown that

the heave "etween TDsec and

TD

Fi& 4..4.


21/39


Fo mooed la&e stuctues as the S%a( the natual %eiods in the hoiontal de&ees o#

#eedom ae much la&e than the wave %eiods with considea"le ene&y. The hoiontal low

#e)uency e*citation is in &eneal la&e than the linea wave #e)uency motions( des%ite the

#act that second ode di##eence #e)uency #oces $'ae &eneally an ode o# ma&nitude

smalle than linea wave #e)uency #oces. This e##ect is thee#oe im%otant in elation to the

desi&n o# the mooin& system =6aslum 2333.>

As e*%lained ealie( the desi&n %hiloso%hy "ehind a dee% da#t S%a( im%lies that the da#t is

ade)uately la&e to educe the heave es%onse. The natual %eiods in heave( %itch and oll is

si&ni#icant la&e than wave %eiods containin& im%otant ene&y. onse)uently the second

ode e*citation #oces may conti"ute to the total motion es%onse in vetical de&ees o#

#eedom. This motion is a limitin& #acto #o S%a %oduction %lat#oms( with e&ad to the desi&n

o# i&id ises and #o the dillin& o%eations =6aslum 2333>.

+n #i&. 4.2.. the low #e)uency su&e motion is illustated as well as the ai &a% in #i&. 4.2..2.

The envionment used is an +SS s%ecte with 6sDm and TD2sec.

Fi&. 4.2... /ow #e)uency su&e motion #o the 232.Nm da#t s%a.

Fi&. 4.2..2. Ai &a%( simultaneously ecoded as #i&. 4.2..

- " -

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0 500 1000 1500

T [sec]

Surg

e

10

15

20

25

30

35

0 500 1000 1500 2000

T [sec]

Airgap


22/39


$'Second ode di##eence #e)uency #oces occu due to "i1s%ectal inteaction in "icomatic waves. Such secondode #oces may "e e%esented "y )uadatic tans#e #unctions( which ae de%endent on the wave #e)uencies o#the two inteactin& waves and inde%endent the wave am%litudes =6aslum 2333>.

To simulate the low #e)uency motions in MOSES the diect wave #oce has not "een a%%lied.

This sim%li#ies the calculations "y allowin& investi&atin& this e##ect without havin& to use small

time ste%s to co%e with the hi&h #e)uency "ehaviou.

The es%onse o# the S%a is )uite com%le* es%ecially "ecause o# the inteaction "etween wave

#e)uency and low #e)uency motions in su&e %itch and heave.

4.. 'he damping pro%lem

As a statin& %oint MOSES uses the e)uations o# motion. By su%%osin& that we !now the

solution at time twe can estimate the solution at time t2. A#te a #ew ste%s the e)uations o#

motion can "e witten8

S=2$t2' 2$t'> Ds $4.2'

whee

SD c)Q #+Q ' and

s D s =a)Q d+> 56 "q 1=")Q e+> 56 "q

a3 " - "8

"3 - 6"85

c3 "8

d3 6" 9 85

e3 6" 9 /5

#3 /

6ow the %o"lem is #uthe solved is e*%lained in =MOSES manual>. The customised

%aametes #o the dam%in& %o"lem ae the ewma! %aametes and . To detect the

insta"ility %henomenon in section N.3( the de#ault values .2N and .N wee used. Thee is almost

no numeical dam%in& with these values. +n #act( #o some %o"lems( the scheme esults in

- -


23/39


small ne&ative dam%in&. This is o# no concen hee. +# these values ae chan&ed #om the

de#ault to . and .;;( then a small "it o# numeical dam%in& is induced. Fo %o"lems such as

decay %o"lems in calm seas( the de#aults do not wo! vey well. The #ollowin& #i&ue illustates

this e##ect #o the heave decay o# the S%a.

Fi&. 4.2.2.. E##ect o# ewma! %aametes

These esults ae #ound #o the S%a at da#t D 232.N metes and no mooin&. A e&ula wave

with 6DNm and TD3 seconds was used.

4..( )urricane analysis

The len&th o# the simulation should "e chosen such that it will &ive a s%eci#ied level o#

con#idence. To avoid the tansient #om the stat o# the simulation and to ensue that the

es%onse has eached a steady state the #ollowin& esults ae "ased on a thee hous ty%ical

COM $Cul# O# Me*ico' huicane condition with 6sD2.2m and TD4seconds. An +SS s%ecte

is used.

- ) -

-97.32

-97.3

-97.28

-97.26

-97.24

-97.22

-97.2

-97.18

-97.16

-97.14

0 200 400 600 800 1000

T [sec]

Heave[

= .33 = .66

= .25 =.5


24/39


Fi&. 4.2... 6eave es%onse #o a thee hous huicane

+t is )uite ema!a"le that des%ite the ou&h envionment( the heave es%onse is no moe than

one and a hal# mete at most. As e*%lained ealie this is due to the la&e da#t and %o"a"ly the

taut mooin& system. As o%%osed to the linea motions( the second ode motions %oduced

duin& a time domain ae clealy a##ected "y the estoin& #oces #om the mooin& lines. +n

addition one should ta!e the dam%in& e##ect o# the ises in account. These would have had an

additional dam%in& e##ect on the heave motions( as will "e shown late in section ;.3( whee a

#ully cou%led analysis will "e caied out.


25/39


The evaluation o# #oces in the #ou mooin& lines is as well investi&ated.


26/39

+,a&ter 7 7#" T,e Mat,ieu instability

5nde cetain conditions( s%a %lat#oms can "e e*%osed to la&e une*%ected motions. This is

e*%lained "y the Mathieu insta"ility %henomenon( and occus "ecause o# two s%eci#ied

situations. The #ist and sim%lest case is ti&&ed due to an a"u%t chan&e in wate%lane aea

and thee#o a chan&e in the heave estoin& #oce. This is the case when the hull coss section

aea chan&es alon& the hei&ht $Fi&. N.' =6aslum 2333>.

The heave es%onse o# this hull sha%e has "een calculated in the linea #e)uency domain(

shown as the RAO( and "y the non1linea time domain method.

alculatin& the hydodynamic e*citin& #oces at the mean %osition%oduces the RAO( accodin& to the linea theoy e*%lained ealie. +n

time domain( the hydodynamic #oces ae calculated at the dis%laced

%osition and the e##ect o# the chan&in& wate%lane aea is ta!en into

account.

The unsta"le wave %eiod is e*%ected in the vicinity o#

Fi& N. =T( T(02T(>( whee Tis the natual %eiod in heave. This is

o"viously de%endent on the system dam%in&. Accodin& to the theoy %esented in =6aslum

2333> thee should "e a citical wave %eiod at T D ;.N sec. By calculatin& the heave

es%onse in #e)uency and time domain( one should e*%ect a disa&eement "etween the

methods at wave %eiods aound ;.N sec. The model used in MOSES did not show this

di##eence. This !ind o# insta"ility is )uite sensitive when it comes to viscous dam%in&( and the

esults o"tained ae %o"a"ly a conse)uence o# the dam%in& a%%lied to the model.

The othe situation that %ovo!es the Mathieu insta"ility is a heave0 %itch am%li#yin& inteaction.

+t may occu even i# the hull has a constant coss section. One should e*%ect this insta"ility at a

cetain wave %eiod that is a #unction o# the natual %eiod in heave and %itch8

):*:

""

"

--

.ave

TT

T

+

=

$N.'

whee

):-T

natual %eiod in heave

- 2 -


27/39


*:-T natual %eiod in %itch

When a wave at this #e)uency occus( the heave motion will oscillate with "oth the natual

heave #e)uency and the wave #e)uency. This %oduces an envelo%e %ocess. Fo a cetainwave %eiod( this envelo%e %eiod coincides with the natual %eiod in %itch( and you &et the

e)uation e*%lained a"ove.

Fo the s%a used hee $see #i& N.' with a natual %eiod in %itch T (ND3;(3 sec( and a natual

%eiod in heave T(D(3 sec( this citical wave %eiod is8

))

"

"'2

"

"

+

=.aveT D 2N(2 sec

By calculatin& the heave and %itch es%onse in "oth #e)uency and time domain( this citical

wave %eiod is #ound when the two methods disa&ee. As #i&. N.2 and #i&. N. show( the

a&eement "etween the two methods is &ood( e*ce%t #o TwaveD 2N(N sec.

Fi& N.2. +llustation o# the Mathieu insta"ility %henomenon in %itch( shown "y a disa&eement "etween the

#e)uency and time domain.

- 7 -

Pitch motions, H=!m

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40

T [sec]

Pitch[deg]

Fre#"enc$ do%ain

&i%e do%ain


28/39


Fi& N.. 6eave motions. The Mathieu insta"ility %henomenon is shown "y the disa&eement "etween the

#e)uency and time domain.

To %oduce the time domain esults( a e&ula wave with 6D3m was used and the steady state

am%litude was measued. +n ode to com%ae the two methods the RAO@s wee multi%lied "y

the wave hei&ht.

A &eat e##ot has "een made in %oducin& the time domain esults. Since MOSES only allows

de#inin& one %eiod at the time( the simulation has "een caied out #o each %eiod. This is a

)uite time demandin& tas!. +n addition each simulation has "een un with di##eent levels o#

dam%in&( di##eent hull sha%es and di##eent ty%es o# envionment. The alteation o# the

ewma! %aametes $dam%in&' is thoou&hly e*%lained in section 4.2.2.

MOSES does not calculate the e*act natual %eiods #o a system( "ut allows you to investi&ate

them "y loo!in& at the RAO@s #o di##eent de&ees o# #eedom. This means that the natual

%eiods &iven hee ae manually #ound at the %ea! o# the RAO cuves. This is %o"a"ly the

e*%lanation why MOSES &ives the hi&hest heave am%litude at TwaveD2N(N sec. Anyway( it is in

the vicinity o# the %eiod TD2N.2 sec calculated #om the #omula $N.'.

The envelo%e %ocess o# the heave motion is then illustated "y the #ist 433 seconds( "e#oe

the insta"ility accues at a%%o*imately 33 seconds. The +llustation in #i&. N.4 shows that the

envelo%e #o the heave motion has the same %eiod as the natual %eiod in %itch $TD3; sec'(

i.e. the heave envelo%e ti&s the %itch insta"ility.

- . -

Heave motions, H=!m

0

10

20

30

40

50

0 5 10 15 20 25 30 35

T [sec]

He

ave[

&i%e do%ain

Fre#"enc$ do%ain


29/39


Fi& N.4. The envelo%e %ocess o# the heave motions.

TD2N.N sec. 6D3m

Ceneally( this e##ect is caused "y two #e)uencies in the si&nal. When these #e)uencies ae

close( the envelo%e %eiod is la&e and the e##ect is clealy %onounced. 6ence the envelo%e

e##ect is educed i# the #e)uencies ae moved a%at. This e##ect is caused "y the am%li#yin&

%itch0 heave inteaction.

The non1linea heave e*citation causin& the insta"ility can also "e e*%lained i# considein& the

dis%laced %osition instead o# the mean %osition. The vetical com%onent o# the hoiontal st

ode total #oce when the S%a has a %itch inclination e*%lains this e##ect =6aslum 2333>. See

#i&ue N.N.

Fi&. N.N. Second ode heave #oce conti"ution due to su&e and %itch inteaction.

- ! -


30/39

+,a&ter $ $#" +ou&ling effects

When %edictin& the S%a es%onse the e##ect #om mooin& line dynamics and ise #iction is

im%otant. Thei conti"ution to the total dam%in& can constitute seveal metes in the S%a

es%onse. Results o# this cou%led analysis eveal that mooin& and ises have si&ni#icant e##ect

on the S%a heave es%onse. A chaacteistic #eatue o# a S%a %lat#om is the slow oscillatoy

motion that occus at esonant #e)uencies. The dam%in& is low at esonant %eiods and coect

estimation o# the dam%in& is thee#oe im%otant to &et elia"le esults =OT 2372>.

oncens a"out e*cessive heave and %itch es%onse o# S%a aisin& #om the Mathieu

insta"ility have "een aised #o lon& %eiod waves $See section N.3'. This insta"ility occued #o

the S%a shown in #i&. N. without mooin& lines and ise e##ects included. A new analysis was

caied out includin& these e##ects showin& the Mathieu insta"ility "ein& su%%essed. The heave

es%onse is shown in #i&. ;..

Fi&. ;.. 6eave es%onse. Two cases8 ' #ee #loatin& and 2' cou%lin& e##ects included. Re&ula wave( 6D3m and

TD2N.Nsec

Two cases ae %esented in the #i&ue. The heave es%onse #o a #ee #loatin& S%a( i.e. no

additional dam%in& and cou%lin& e##ects #om mooin& and ises included. The mooin& lines

used ae desci"ed ealie in section .3( and the ise system consists o# ; ises each with a

diameteD 4;mm and a %etensionD 33 !. As tied with the mooin& system( the ises wee

modelled as one e)uivalent ise with %etension e)ual the sum o# the ; ises. The %o"lem

aisin& with the intoduction o# an e)uivalent ise( was the ada%tation o# the sti##ness and

- )' -

-120

-115

-110

-105

-100

-95

-90

-85

-80

500 1000 1500 2000 2500 3000

T [sec]

Heave

%oored 'ith ri(er(

free floating


31/39

-10

-5

0

5

10

500 700 900 1100 1300 1500 1700 1900

T [sec]

c

eg

%oored) 'ith ri(er(

free floating

Fi&. ;.2. Pitch es%onse. ou%led and uncou%led withmooin& and ises.


wei&ht and attachment to the sea"ed. With ; se%aate ises( the se%aation o# the

attachment %oints at sea"ed &ives a cetain e##ect( which is %o"a"ly not ta!en cae o# "y one

e)uivalent ise.

The esults show the im%otance o# includin& all the dam%in& e##ects in %edictin& the es%onse

unde esonance conditions. This ty%e o#

analysis is consevatively done "y

e*cludin& the dam%in& #om mooin& and

ises and does o#ten lead to S%as with

hull da#t &eate than necessay. A

eduction in the da#t will educe the costs

si&ni#icantly =OT 2372>.

As well as the heave motions( the esonant %itch es%onse is su"stantially educed "y includin&

the e##ects #om mooin& and ises. Fi&. ;.2 shows the

%itch es%onse #om the same analysis as in #i&. ;.. The uncou%led %itch es%onse shown is

the Mathieu insta"ility es%onse. Accodin& to analysis done =OT 2372> the cou%led e##ect

&ets even moe im%otant when o%eatin& in dee% sea.

The es%onse chaacteistics #o a S%a ae #aily com%le* due to the inteaction o# wave

#e)uency and low #e)uency motions. When cou%lin& the e##ects #om mooin& and ises with

the vessel es%onse( la&e eductions in e*temes ae o"tained. As e*%lained( these eductions

ae im%otant to ta!e into the desi&n o# the mooin& lines and ises in an ealy sta&e.

Finally( thee is a ole #o cou%led analysis in the validation o# the desi&n( in %aticula when

desi&nin& dee% wate S%as whee lac! o# e*%eience is a %o"lem. The limitations o# model

"asins to access the #ull vessel0 ise0 mooin& system in vey dee% wate ma!es the a"ility to

accuately simulate cou%led e##ects %actically a e)uiement #o new systems =OT 237>.

ot many com%ute %o&ams can handle these e##ects. ou%led esults #om MOSES in

elation to a S%a "uoy( as %esented hee( ae thee#oe use#ul and have a cetain commecial

value.

- )" -


32/39

+,a&ter 8 8#" Alternative ,ull s,a&es

+t is "ecause o# its elatively low dam%in& in esonant motions and low natual %eiod in heave

the classical s%a $hull +( Fi&. .' may e*%eience the la&e heave motion e*%lained. Accodin&

to =6aslum 2333> some measues ae %ossi"le to educe the heave es%onse8

. +ncease the dam%in& in heave

2. +ncease the natual heave %eiod out o# the wave ene&y e&ion

. Reduce the linea heave e*citation #oce

Fi&. . shows altenative hull sha%es to co%e with these thee %oints. The #ist %oint is in

theoy dealt with "y addin& a cicula dis! at the

"ottom o# the s%a $hull ++'. The heave es%onse

#o hull sha%e ++ #om a time domain analysis is

illustated in Fi&. .2. The time domain shows

small deviations #om the classical s%a $hull +'.

The RAO@s wee also calculated without

Fi&. .. Altenative hull sha%es

showin& any ma,o di##eences "etween the two hulls. +t is howeve uncetain whethe o not

the esults ae com%aa"le. The %hysical %o%eties ae chan&ed as a conse)uence o# the

&eometical di##eences and the esults com%aed hee ae the actual heave motion #o each

s%a.

Fi&. .2. 6eave es%onse #om an +SS s%ectum with 6sD3 m and TD4 sec. Two di##eent hull sha%es ae

consideed.

- ) -

-98.5

-98

-97.5

-97

-96.5

-96

500 700 900 1100 1300 1500

T [sec]

heave[m

]

h"ll (ha*e +

h"ll (ha*e ++


33/39


Es%ecially hull sha%e +++ has ma,o di##eences in cente o# &avity( metacentic hei&ht etc. To

deal with this %o"lem in a di##eent mano( the dam%in& coe##icients in heave #o the thee hull

sha%es have "een com%aed. They ae shown in #i&. ..

The second %oint( inceasin& the natual heave %eiod( is done "y addin& a %ontoon at the !eel(

i.e. hull sha%e +++ has a natual %eiod in heave hi&he than the classical s%a.

An incease in the added mass inceases the di##action tem and thus educes the heave

e*citation #oce. Fo e*am%le addin& a dis! at the !eel will in theoy incease the added mass(

"ut %actical tests shows that the dis! has to "e vey la&e to have an im%otant e##ect on the

heave e*citation #oce. +t is %actical tou"lesome to constuct s%as with la&e dis!s =6aslum

2333>. 6ull sha%e +++ howeve( shows la&e added mass coe##icients in heave #o a &iven

inteval o# %eiods com%aed to hull + and ++.

Fi&. .. 6eave dam%in& coe##icients #o thee di##eent hull sha%es

The dam%in& coe##icients ae nomalied "y the mass o# the "uoy and e*%ess the linea heave

dam%in& $e*clusive o# added mass e##ects'.

This #i&ue con#ims the theoy e*%lained. 6ull sha%e +++ %oduces at the most #i#teen times the

dam%in& o# hull + and ++ $TD23sec'( and hull sha%e ++ has a #ew %ecent moe dam%in& than hull

+. This di##eence is sli&htly e*%essed in the heave es%onse duin& a time domain analysis(

shown in #i&. .2. +n addition to these stuctual chan&es( inceasin& the da#t can educe the

heave es%onse. This is an e*%ensive measue and is seldom the solution used #o a s%a

"uoy.

The thee hulls shown in #i&. . ae the same as used in =6aslum 2333>. 6ull sha%e + is the

classical s%a sha%ed as a cylinde. 6ull sha%e ++ is the same cylinde with a cylindical dis! at

"ottom. The dis! diamete is .2


34/39


The last hull sha%e consists o# two cylindes. The u%%e is the same as hull + and the "ottom

cylinde has a diameteD2.N9;< and hei&htD3m.

The idea "ehind the inceased heave dam%in&( to&ethe with the use o# this enomous hull is

that due to the counteactin& di##action #oce and the la&e da#t( the motion es%onse o# the

%lat#om should "e ade)uately low to %emit installation o# i&id ises with dy wellheads.

Thee#oe( the motion es%onse $in %aticula heave and %itch' is cucial #o the conce%t.

- ) -


35/39

+,a&ter 9 9#" Recommendations for furt,er wor(

Wave induced motions on a S%a "uoy ae %esented. Motions in #e)uency and time domain

ae calculated and illustated. An analysis includin& mooin& line dynamics and ise #iction is

also %esented. +n addition( thee ae some issues in elation to wave induced motions on a

S%a that ae not teated in this thesis. These issues ae use#ul to conside in an oveall

evaluation.

E##ects %oduced "y wind #oces and cuents ae not a%%lied to the MOSES model. They will in

some cases a##ect the S%a motions. Es%ecially low #e)uency motions can "e caused "y wind

&usts with si&ni#icant ene&y at %eiods at the ode o# ma&nitude o# a minute. This is due to thehi&h natual %eiods o# the S%a =Faltinsen 93>.

A well !nown %henomenon in many #ields o# en&ineein& is esonance oscillations caused "y

vote* sheddin&( ty%ical #o cylindical sha%ed stuctues as the S%a. To avoid these vote*1

induced oscillations( helical sta!es ae o#ten used $see the illustation in A%%endi* '. To

contol the insta"ility in %itch that is discussed( moe %itch dam%in& is e)uied. 6elical sta!es

conti"ute to this !ind o# dam%in& and will conse)uently %lay a %at in su%%essin& this

insta"ility =Faltinsen 93>. An analysis with helical sta!e should "e caied out.

+n section .3 altenative hull sha%es have "een tied out( in the e##ot to incease the dam%in&

in heave. By #uthe investi&atin& the e##ect o# di##eent hull sha%es( one should "e a"le to #ind

an o%timisation o# the S%a hull with es%ect to the heave motion. By o%timisin& the hull with

es%ect to one de&ee o# #eedom( it will %o"a"ly a##ect the motion chaacteistic o# the "uoy in

the othe modes. To which e*tend this &eometical chan&e will a##ect the motions o# the "uoy(

should "e investi&ated(

The #looded centewell o# the S%a called moon%ool( may have some e##ects on the motion

chaacteistics. Fo the classical S%a the natual %eiod o# the vetical #luid motion is close to

the natual %eiod o# the %lat#om in heave. This ma!es it sometimes di##icult to simulate. +n

cases whee the moon%ool is constucted #o la&e e)ui%ment to "e loweed thou&h it( the

%assa&e "etween the ises is )uite la&e. The sim%li#ied method o# considein& the S%a as

closed at the !eel( is in such cases %o"a"ly too sim%le. The esonance es%onse o# the wate

column could "e im%otant =6aslum 2333>.

- )* -


36/39


The Mathieu insta"ility %henomenon could as well "e studied moe cae#ully. The e##ect o#

altein& the wave am%litudes and the wave %eiods on the insta"ility( could "e e*amined. This

%o"lem is teated in =6aslum 2333>( whee the esults ae %esented as a 1< chat( to

illustate the in#luence #om the wave am%litude at the an&e o# %eiods whee the insta"ility

occus.

+n addition to the mentioned means( thee ae a lot o# %ossi"ilities in the use o# MOSES. Once

the time domain simulation has "een tuned success#ully( seveal esults have "een %oduced

and stoed in a data"ase. +t is then %ossi"le to s%eci#y the esult wanted( eveythin& #om

evaluation o# the #oces in the ises to sta"ility vei#ications o# the "uoy.

- )2 -


37/39

+,a&ter #" References

. The ente #o Maine and Petoleum Technolo&y $MPT' $997'. Floatin& Stuctues8

a &uide #o desi&n and analysis( Uolume One.

2. The ente #o Maine and Petoleum Technolo&y $MPT' $997'. Floatin& Stuctues8

a &uide #o desi&n and analysis( Uolume Two.

. Faltinsen( Odd M. $993'. Sea loads on shi%s and o##shoe stuctues. am"id&e

5nivesity Pess.

4. 6aslum( 6e",Hn A. $2333'.


38/39

List of figures

Fi&ue 2. MOSES e#eenceFi&ue . +sometic view with mooin&Fi&ue .2 Font view with mooin&Fi&ue .. The si* de&ees o# #eedomFi&ue 4.. Pitch RAO. Two #e)uency intevals( to illustate the natual %eiod in

%itchFi&ue 4..2 6eave RAOFi&ue 4.. Su&e RAOFi&ue 4..4


39/39

A&&endi*

A&&endi* - )llustration of a moored SPAR wit, ,elical stra(e and risers

A&&endi* ! MOSES files

A%%endi* 2a ommand #ile8 S%a;.ci# $'

A%%endi* 2" Ceomety #ile8 S%a;.dat $6ull sha%e +'

A&&endi* / MOSES files; alternative ,ull s,a&es

A%%endi* a 6ull sha%e( #i&. N. $S%a7.dat'

A%%endi* " 6ull sha%e ++ $S%a.dat'

A%%endi* c 6ull sha%e +++ $S%a9.dat'

A&&endi* 0 MOSES file; out&ut

Documents

Project Thesis Larsen