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8/12/2019 Project Thesis Larsen
1/39
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.
8/12/2019 Project Thesis Larsen
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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
- -
8/12/2019 Project Thesis Larsen
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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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8/12/2019 Project Thesis Larsen
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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
8/12/2019 Project Thesis Larsen
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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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8/12/2019 Project Thesis Larsen
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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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8/12/2019 Project Thesis Larsen
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+,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
8/12/2019 Project Thesis Larsen
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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
8/12/2019 Project Thesis Larsen
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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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.
- ! -
8/12/2019 Project Thesis Larsen
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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
2. By usin& the model and the &eomety "eneath the wate su#ace( the %otential
disti"ution o# the %essue on the %anels is &iven "y the lineaied Benoulli
e)uation
56
g!p
+= $2.'
whee
= #luid density
=g acceleation o# the &avity
=! de%th
= velocity %otential
By inte&atin& the %essue ove the "ody we o"tain the hydodynamic #oces on a
%otion o# the "ody. The %o&am now calculates the added mass( dam%in&
matices and in addition all the hydodynamic %o%eties.
. On "asis o# the hydodynamic #oces the linea motions in si* de&ee o# #eedom
ae estimated as the RAO $Res%onse Am%litude O%eato'. This is stai&ht#owad
done "y usin& the e)uations o# motions #o a #eely #loatin& "ody8
[ ] 56562
"
"#$%& '(
('(('(('('( =+++=
$,D((;'
$2.2'
whee
='(& "ody mass
='(% hydodynamic mass $added mass'
'($ dam%in& coe##icient
='(# estoin& coe##icient
= "ody movement
='" e*citation #oce
- "' -
8/12/2019 Project Thesis Larsen
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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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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8/12/2019 Project Thesis Larsen
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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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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8/12/2019 Project Thesis Larsen
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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
+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
8/12/2019 Project Thesis Larsen
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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.
8/12/2019 Project Thesis Larsen
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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
The main %aticulas o# the s%a used in this assi&nment ae the same as used in =6aslum
2333>( e*ce%t some small ad,ustments in the diamete to o"tain the hydostatic %o%eties as
coect as %ossi"le. A#te the im%atment o# the &eomety( MOSES calculated a cente o#
"uoyancy too low( com%aed to the s%a in =6aslum 2333>. This lead to ne&ative CM. By addin&
moe "uoyancy in the u%%e section( the cente o# "uoyancy ascended and the CM value
"ecame close to the actual one.
A lot o# wo! has "een %ut down to vei#y the MOSES model and conse)uently "e a"le to
com%ae it to the model o# =6aslum 2333>. Many o# the static %o%eties not &iven in the
8/12/2019 Project Thesis Larsen
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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
%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
8/12/2019 Project Thesis Larsen
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Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
#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>.
8/12/2019 Project Thesis Larsen
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.
- ". -
8/12/2019 Project Thesis Larsen
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
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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.
8/12/2019 Project Thesis Larsen
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
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
Fi&. 4..4 show that %itch and su&e motions ae in %hase with each othe( and they ae 93
de&ees out o# %hase com%aed to the
wave. This means that they ae
conti"utin& to dis%lacements o# the
dec! simultaneously. +t is shown that
the heave "etween TDsec and
TD
Fi& 4..4.
8/12/2019 Project Thesis Larsen
21/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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
8/12/2019 Project Thesis Larsen
22/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
$'Second ode di##eence #e)uency #oces occu due to "i1s%ectal inteaction in "icomatic waves. Such secondode #oces may "e e%esented "y )uadatic tans#e #unctions( which ae de%endent on the wave #e)uencies o#the two inteactin& waves and inde%endent the wave am%litudes =6aslum 2333>.
To simulate the low #e)uency motions in MOSES the diect wave #oce has not "een a%%lied.
This sim%li#ies the calculations "y allowin& investi&atin& this e##ect without havin& to use small
time ste%s to co%e with the hi&h #e)uency "ehaviou.
The es%onse o# the S%a is )uite com%le* es%ecially "ecause o# the inteaction "etween wave
#e)uency and low #e)uency motions in su&e %itch and heave.
4.. 'he damping pro%lem
As a statin& %oint MOSES uses the e)uations o# motion. By su%%osin& that we !now the
solution at time twe can estimate the solution at time t2. A#te a #ew ste%s the e)uations o#
motion can "e witten8
S=2$t2' 2$t'> Ds $4.2'
whee
SD c)Q #+Q ' and
s D s =a)Q d+> 56 "q 1=")Q e+> 56 "q
a3 " - "8
"3 - 6"85
c3 "8
d3 6" 9 85
e3 6" 9 /5
#3 /
6ow the %o"lem is #uthe solved is e*%lained in =MOSES manual>. The customised
%aametes #o the dam%in& %o"lem ae the ewma! %aametes and . To detect the
insta"ility %henomenon in section N.3( the de#ault values .2N and .N wee used. Thee is almost
no numeical dam%in& with these values. +n #act( #o some %o"lems( the scheme esults in
- -
8/12/2019 Project Thesis Larsen
23/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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
8/12/2019 Project Thesis Larsen
24/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
Fi&. 4.2... 6eave es%onse #o a thee hous huicane
+t is )uite ema!a"le that des%ite the ou&h envionment( the heave es%onse is no moe than
one and a hal# mete at most. As e*%lained ealie this is due to the la&e da#t and %o"a"ly the
taut mooin& system. As o%%osed to the linea motions( the second ode motions %oduced
duin& a time domain ae clealy a##ected "y the estoin& #oces #om the mooin& lines. +n
addition one should ta!e the dam%in& e##ect o# the ises in account. These would have had an
additional dam%in& e##ect on the heave motions( as will "e shown late in section ;.3( whee a
#ully cou%led analysis will "e caied out.
8/12/2019 Project Thesis Larsen
25/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
The evaluation o# #oces in the #ou mooin& lines is as well investi&ated.
8/12/2019 Project Thesis Larsen
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 -
8/12/2019 Project Thesis Larsen
27/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
*:-T natual %eiod in %itch
When a wave at this #e)uency occus( the heave motion will oscillate with "oth the natual
heave #e)uency and the wave #e)uency. This %oduces an envelo%e %ocess. Fo a cetainwave %eiod( this envelo%e %eiod coincides with the natual %eiod in %itch( and you &et the
e)uation e*%lained a"ove.
Fo the s%a used hee $see #i& N.' with a natual %eiod in %itch T (ND3;(3 sec( and a natual
%eiod in heave T(D(3 sec( this citical wave %eiod is8
))
"
"'2
"
"
+
=.aveT D 2N(2 sec
By calculatin& the heave and %itch es%onse in "oth #e)uency and time domain( this citical
wave %eiod is #ound when the two methods disa&ee. As #i&. N.2 and #i&. N. show( the
a&eement "etween the two methods is &ood( e*ce%t #o TwaveD 2N(N sec.
Fi& N.2. +llustation o# the Mathieu insta"ility %henomenon in %itch( shown "y a disa&eement "etween the
#e)uency and time domain.
- 7 -
Pitch motions, H=!m
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35 40
T [sec]
Pitch[deg]
Fre#"enc$ do%ain
&i%e do%ain
8/12/2019 Project Thesis Larsen
28/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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
8/12/2019 Project Thesis Larsen
29/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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.
- ! -
8/12/2019 Project Thesis Larsen
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
8/12/2019 Project Thesis Larsen
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.
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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.
- )" -
8/12/2019 Project Thesis Larsen
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 ++
8/12/2019 Project Thesis Larsen
33/39
Diplomoppgave NTNU Tr/ls 0arand #arsen1nstit/tt for hydrodynami$$ 1nocean as
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
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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&( toðe 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.
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+,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>.
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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.
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+,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'.
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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
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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